Distance Learning Programmes Division (DLPD)
KVPY
Kishore Vaigyanik Protsahan Yojana (KVPY)
Question Paper Booklet (Year 2007 to 2014)
Stream-SB+2 for Class-XII
INDEX CLASS-XII
S. NO.
PAGE NO. KVPY TEST PAPER FOR STREAM-SB+2
1.
Year-2007
1-16
2.
Year-2008
17-31
3.
Year-2009
32-46
4.
Year-2010
47-67
5.
Year-2011
68-84
6.
Year-2012
85-100
7.
Year-2013
101-116
8.
Year-2014
117-130 HINTS & SOLUTIONS
1.
Year-2007
131-151
2.
Year-2008
152-171
3.
Year-2009
172-195
4.
Year-2010
196-218
5.
Year-2011
219-236
6.
Year-2012
237-253
7.
Year-2013
254-272
8.
Year-2014
273-283
15RDLP
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GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2007 Time : 3Hr.
1.
Max. Marks : 160
In Year 2007, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90),Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2008 Time : 3Hr.
1.
Max. Marks : 160
In Year 2008, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2009 Time : 3Hr.
1.
Max. Marks : 160
In Year 2009, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2010 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2011 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2012 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
YEAR-2007 (KVPY-STREAM-SB+2) PART-I (1 Mark) MATHEMATICS 1.
The coefficient of x4 in the expansion of (x1/2 – x2/3) is : (A) 0 (B) – 7 (C) 35
z 2.
The number of complex number z such that (A) 2
3.
(B) 4
z z = 1 and | z | = 1 is : (C) 6
(D) 8
35 37 Let A be an invertible 2 × 2 real matrix. If A–1 = then det (12A) equals : 41 43
(A) –1728
4.
z
(D) – 35
Given
(B) –1
1
n
2
n 1
3
n 1
(D) –1/2
2 (C) 4 6 – 1
(D) 2/6
2 : the value of 6
1 3 5 ... ( 2n – 1)
1
(C) –12
23 3 3 ..... n3
(A) 22/3
is :
(B) 42 /3
5.
If the slope of one of the lines represented by 4ax2 + xy + 4y2 = 0 is the square of the other then a equals: (A) 1/8 (B) 1/4 (C) –1/4 (D) –1/8
6.
Let A and B be two points on the parabola y = 2x2 + x – 2 such that the origin is the midpoint of the line segment joining A to B. The length of AB is : (A) 2
(B) 3
(C) 2 3
(D) 2 2
7.
The triangle formed by x-axis, y - axis and the line 3x + 4y + c = 0 has inradius 1. Then the value of |c| is : (A) 12 (B) 7 (C) 5 (D) 1
8.
Let p, q and r denote the lengths of the sides QR, PR and PQ of a triangle PQR respectively. Then pcos2(R/2) + rcos2(P/2) (A) equals q
(C) equals 9.
pqr 4
(B) equals
pqr 2
(D) cannot be determined with the given data
The number of solutions of the equation : 3cos2 xsin2 x – sin4 x – cos2 x = 0 in the interval [0, 2] is : (A) 8 (B) 4 (C) 6 (D) 3 CLASS-XII_STREAM-SB+2_PAGE # 1
1 sin–1 (1/4) then 64sin + 64cos – 8sec – 8cose + tan + cot equals : 2 (A) 8 (B) 4 (C) 0 (D) –1
10.
If =
11.
Let
lim 1 1 1 2 n L = x – 0 x sin x x sin 2 .... x sin n x x Then (A) L does not exist (C) L = 0 12.
(B) L = 1 (D) L = 1
Let f (x) be a function defined on [0, 2] by :
x 3 for x 1 f(x) = 2 ax bx c for x 1 where a, b and c are constants such that f(x) has second derivative at x = 1. Then a equals : (A) – 6 (B) – 3 (C) 6 (D) 3 13.
If the function f(x) = x3 – 3ax2 + b is strictly increasing derivative for x > 0, then which of the following is always true ? (A) a can take any real value (B) a 0 (C) a < 0
(D) a 0 3
14.
The value of the integral :
xcos 2 x xdx where [x] denotes the largest integer not exceeding x is : 1
(A) 6
15.
16.
(B) 1/6
(D) 6/
1 {(2n + 1) (2n + 2) ------- (2n + n)}1/n, then nlim f(n) equals : n (A) 4/e (B) 27/ 4e (C) 27 e/4 If f(n) =
(D) 4e
If V1, V2, V3 are unit vectors such that V1 + V2 + V3 = 0 then V1 – V2 : (A) equals
(B) equals 3/2
3
(C) can be any value in the interval (0,2)
17.
(C) /6
(D) can be any value in the interval (3/2, 3 )
A fair coin is tossed five times. If the out comes are 2 heads and 3 tails (in some order), then what is the probability that the fourth toss is a head ? (A)
1 4
(B)
2 5
(C)
1 2
(D)
3 5
18.
The number of three element subsets of {1, 2 ......10} sum of whose elements is even is : (A) 50 (B) 60 (C) 70 (D) 90
19.
Suppose x, y are positive real numbers such that 2 log (x – 2y) = logx + logy. Then value of (A) 1
(B)
3 2
(C)
2 3
x is : y
(D) 4
CLASS-XII_STREAM-SB+2_PAGE # 2
20.
Let x,y and z be positive integers such that gcd(x, y, z) = 1 : x < y < z and x2 + y2 = z2. Then which of the following is always true ? (A) 2 does not divide x (B) 2 does not divide z(x + y) (C) 4 divides x + y + z (D) 8 does not divide x + y + z
PHYSICS 21.
A block of mass m sliding down an incline at constant speed is initially at a height h above the ground. The coefficient of kinetic friction between the incline is µ. If the mass continues to slide down the incline at a constant speed, the energy dissipated by friction by the time the mass reaches the bottom of the incline is (A) mgh/µ (B) mgh (C) p mgh/sin 0 (D) mgh sin 0
22.
The energy required to remove both electrons from the helium atom in its ground state is 79.0 eV. The energy required to ionize helium (i.e. to remove one electron) is (A) 24/6 eV (B) 39.5 eV (C) 51.8 eV (D) 54.4 eV
23.
A proton moves in the +ve z- direction after being accelerated from rest through a potential difference V. The proton then passes through a region with uniform electric field E in the +x direction and a uniform magnetic field B in the + y-direction, but the proton’s trajectory is not affected. If the experiment is repeated using a potential difference of 2V, the proton will be (A) deflected in the +ve x- direction (B) deflected in the –ve x-direction (C) deflected in the +ve y- direction (D) deflected in the –ve y- direction
24.
The displacement (y) of an electric wave as a function of position (x) and time (l) is given by : y = cosx sint + cos2x sin2t where the units of x and r are metre (m) and of time, second (s). The equation describes. (A) a monochromatic (i.e. of fixed wavelength) wave traveling along the positive x-direction with speed 1 ms–1. (B) a traveling wave along the positive x-direction with speed 1 ms–1, that is a supper position of two harmonic waves. (C) a stationary monochromic wave of wavelength 2 metre and angular frequency 1s–1 (D) a superposition of two stationary waves of wavelengths 2 metre and metre and equal amplitudes.
25.
Two polaroids are placed 90º to each other and the transmitted intensity is zero. One more polaroid is placed between them bisecting the angle between them. Let l be the intensity of light just after the first polaroid. The fraction of l transmitted by the system is (A) 0
(B)
1 4
(C)
1 2
(D)
1 8
26.
A hydrogen gas filled ballon left free in a fast but uniformly moving bus (with closed doors and windows, so not air currents) rises and touches against the ceiling of the bus. If the bus slow down quickly with uniform retardation of magnitude (A) The ballon displace in the direction of motion of the bus. (B) The ballon displaces opposite to the direction of motion of the bus. (C) The ballon remains where it was before. (D) The ballon displaces along to the vertical determined by the ratio /g.
27.
Blamer lines of deuterium atoms, compared to those of hydrogen atom, are observed to be of (A) higher frequency (B) higher wavelength (C) same wavelength but reduced intensity (D) same wavelength and intensity
CLASS-XII_STREAM-SB+2_PAGE # 3
28.
Cv The isothermal bulk modulus of an ideal gas is - ( = C ) v (A) P
29.
(B) P
(D)
2 1 P
Unpolarized light is incident at a plane interface from medium 1 to medium 2. With refractive indies µ1 and µ2 respectively. The angle of incidence ‘l’ for which the reflected ray is totally plane polarized is -
µ2 (A) tan1 µ 1 30.
(C) ( – 1) P
µ2 (B) sin–1 µ 1
µ1 (C) sin1 µ 2
µ1 (D) tan1 µ 2
The velocity v of waves on the surface of a pool of liquid is given by the formula (A) v2 =
g 2 2
(B) v2 =
g 2 2
(C) v2 =
g 2
(D) v2 =
1 g 2
( wavelength : g acceleration due to gravity : surface tension : : density)
31.
A statelite orbits around the earth at a distance r from the centre of the earth. Taking the zero of gravitational potential energy at infinity (K.E. and P.F. mean kinetic energy and potential energy respectively) (A) Etotal = K.E. + P.E. = O (B) Etotal = –K.E. (C) Etotal = –
1 P.E. 2
(D) K.E. = P.E.
32.
When the armature coil in a motor rotates in a magnetic field, a back emf developes opposing the applied potential v, causing a net current I in the coil. If R is the resistance the coil, the mechanical power output of the motor is (A) I2R (B) I (C) VI (D) VI + I2R
33.
A ball rolling on the floor of a uniformly moving train comes to a stop due to friction after traveling a distance d, losing its initial kinetic energy k into heat H. For an outside observer on the ground, suppose the same quantities have values d1, k1 and H1 respectively. Then (A) K = K’ ; H = H’ ; d = d’ (B) K K’ ; H = H’ ; d d’ (C) K = K’ ; H H’ ; d = d’
34.
(D) K K’ ; H H’ ; d d’
A body is projected horizontal on the top of the Mount Everest with speed much greater than
2gr ,
where r is the distance of the projection point from the centre of the earth and g is the acceleration due to gravity there. The trajectory of the body will be a (A) straight line (B) parabola (C) hyperbola (D) ellipse 35.
Consider two stars A and B having equal radii but different surface temperature. The surface temperature of A is 4000 K while that of B is 40000K. Which of the following statement is false ? (A) A is less luminous than B. (B) A emits more light at infrared wavelengths than it does at ultraviolet wavelength. (C) B emits more light at ultraviolet wavelength than it does at infrared wavelength. (D) In a given infrared wavelength bond, A emits more light than B.
CLASS-XII_STREAM-SB+2_PAGE # 4
36.
Four stars A, B, C and and X are moving with velocities as shown with respect to the interstellar medium. An observer on a planet of the star X measures the frequencies v of the same spectral line in stars A, B and C and finds : (Ignore planetary velocity in comparison to stellar velocities)
v
A
2v
x
B
v (A) VA < VB > VC
37.
38.
C 2v (B) VA < VC < VB
(C) VB < VC < VA
(D) VC < VB < VA
1 The pressure P of an ideal gas is related to mean squared speed V 2 by the relation, P = n m V 2 . 3 Where n is the number density and m is the mass of a molecule of the gas. For a mixture of non-reactive ideal gases 1,2, ---------- this equation becomes (A) P =
1 (n + n2 + ----) (m1 + m2 + -----) V 2 3 1
(B) P =
1 (n m + n2m2 + -----) V 2 3 1 1
(C) P =
1 (n m + n2m2 + ------) V12 V22 ..... 3 1 1
(D) P =
1 1 n1 m1 V12 + n m V 2 + ---3 3 2 2 2
Figure shows two graphs (X) and (Y) related to a charged conducting sphere of radius a and charge Q
a
+Q
X
Y
(A) X represents potential versus distance (from the centre) graph while Y represents electric field versus distance graph. (B) Y represents potential versus distance graph while X represents electric field versus distance graph (C) Both graphs show that potential and electric field are continuous throughout. (D) Both graphs show that potential and electric field have continuous first order derivatives.
CLASS-XII_STREAM-SB+2_PAGE # 5
39.
Figure below show a charge disribution of three charge q, –2q and q located along the y-axis with the charge –2q at centre and the other charges symetrically placed about it :
q y x –2q q The electric field along the x axis. for large x compared to the size of the distribution, varies as : (A) 40.
1 x
(B)
1
(C)
x2
1
(D)
x3
1 x4
In a double silt experiment, two identical point sources S1 and S2 are placed on the line perpendicular to the two slits P and Q as shown. (The figure is not to scale). The screen is placed for away compared to the distance between the slits).
S2
S21 Screen
Q
/////////////////////////////
P
When only S1 is switched on, there is an interference pattern with a peak intensity Ii. When only S2 is switched on, there is an interference pattern with peak intensity I2 (2 < I1). When both S1 and S2 are switched on. (A) there will be a uniform intensity on the screen (B) the intensity on the screen will vary from I1< I2 to I1 + I2 (C) the intensity on the screen will vary from 0 to ( 1 2 )2. (D) the intensity on the screen will vary from 0 to (I1 + I2).
CHEMISTRY 41.
The pH of a 0.1M solution of a weak monoprotic acid having a degree of dissociation of 0.1 in water, is(A) 4.4 (B) 4.0 (C) 2.4 (D) 2.0
42.
An ambidentate ligand is (A) NO2 (B) ClO4
43.
(C) NO2–
A molecule with a trigonal pyramidal structure is (A) H3O+ (B) NH4+ (C) BF3
(D) NH3 (D) CO32–
44.
A molecule whose molar specific heat at high temperature assuming ideal behaviour is 9R. is (A) C6H6 (B) NH3 (C) B2H6 (D) CH4
45.
The solubility of the hydroxide of Be, Mg, Ba and Ca in water follows the order (A) Be > Mg > Ca > Ba (B) Mg > Be > Ca > Ba (C) Ca > Ba > Mg > Be (D) Ba > Ca > Mg > Be
CLASS-XII_STREAM-SB+2_PAGE # 6
46.
The energy required to remove an electron from an isolated atom in the gas phase follows the order. (A) C > B > Be > Li (B) C > Be > B > Li (C) B > C > Be > Li (D) Be > Li > B > C
47.
The dipole moment of BeF2 is (A) 1.5 D (B) 1.0 D
(C) 0.0 D
(D) 1.8 D
A non-planar compound is (A) [Ni(CN)4]2– (B) [NiCl4]2–
(C) [PtCl4]2–
(D) BCl3
48.
49.
Mass of a liquid is weighed correct to three decimal place and its volume is measured correct to one decimal place. The density of the liquid calculated from the above data will be correct to (A) three decimal place (B) two decimal place (C) one decimal place (D) four decimal place
50.
According to Bohr’s theory, the angular momentum of the electron in the ground state of the hydrogen atom is (A) 0 (B) 1 (C) 2 (D) 3
51.
Geometrical isomerism is not exhibited by -
(A)
(B)
Cl
Br
H
l
(C)
(D)
CO2H
52.
The acid strength of o-nitrophenol (I), m-nitrophenol (II) and p-nitrophenol (III) follows the order. (A) I < II = III (B) II < I < III (C) III < I < II (D) I < II < III
53.
In the polymerization of alkene by Zieglar-Natta reaction,the catalyst and the co-catalyst, respectively are (A) TiCl4 and AlCl3 (B) Ti (III) and Et3Al (C) Ti(Et)4 and Al(III) (D) TiCl2 and Et3Al
54.
Saponification of oils gives (A) Glycerol and alkali salts of fatty acids (B) Glyceric acid and long chain alcohols
55.
(B) Glyceraldehyde and alkali salts of fatty acids (D) Ethylene glycol and alkali salts of fatty acids
The expected order of boiling points of I - IV would be (I)
(II)
(III)
(IV)
(A) I < II < IV < III (C) IV < III < II < I
(B) III < IV < II < I (D) IV < II < III < I
56.
Azobenzene will be obtained as a major product when nitrobenzene is treated with (A) Sn and HCl (B) Raney Nickel/H2 (C) Zn/NaOH (D) Pb-C/H2
57.
The order of nucleophilicity of halides is : (A) I– > Br– > Cl– > F– (C) Cl– > Br > I– > F–
58.
(B) F– > Br– > Cl– > I– (D) F– > Cl– > Br– > I–
The compound that will give lactide on heating is (A) CH3CH2CH(OH)COOH (B) CH3CH2CH(NH2)COOH (C) CH3CH(OH)CH2COOH (D) CH3CH(NH2)CH2COOH
CLASS-XII_STREAM-SB+2_PAGE # 7
59.
A compound that shows a distinct colour change on treatment with alcoholic ferric chloride is (A) Anisole (B) Aspirin (C) Salicylic acid (D) Methyl benzoate
60.
The order of increasing stability of carbanions in compound I-IV is -
(I)
(II) H3CO
(III) O2N
– CH2
– CH2
– CH2
(IV) H3C
– CH2
(A) III, IV, I, II
(B) IV, II, I, III
(C) III, I, IV, II
(D) II, IV, I, III
BIOLOGY 61.
Exclusion of the thymus, the primary lymphoid organs in mammals, results in severe immunodeficiency. This due to the absence of the following in the peripheral circulation. (A) All nature leucocytes (B) Mature T and B cells (C) Mature T cells (D) Mature B cells
62.
Which of the following organelle of a mammalian cell has the genetic material transferred only from the mother to her offspring ? (A) Nucleus (B) Mitochondria (C) Endoplasmic reticulum (D) Centrosome
63.
Water contaminated with Vibrio cholerae can be made potable (A) By boiling alone (B) By passing through filter (C) By treating with chloride (D) By freezing the water
64.
A patient suffering from splenomegaly undergoes splenectomy. Which of the following processes will be affected ? (A) RBC production will be stopped (B) Removal of old RBC will be impaired (C) Decreases in antibody production (D) Generation of B cells will be stopped
65.
During exercise when body temperature rises, the skin capillaries dilate and receive more blood resulting in increased heat loss. Which of the following is NOT associated with the maintenance of the body temperature in general ? (A) Exocrine and apocrine sweat glands. (B) Release of bradykinin, a potent vasodilating peptide (C) Sebum secretion from sebaceous glands (D) Sub-cutancous fat
66.
In which of the following digestive juice are DNase and RNase found ? (A) Gastric juice (B)Intestinal juice (C) Saliva (D) Pancreatic juice
CLASS-XII_STREAM-SB+2_PAGE # 8
67.
Which of the following is NOT considered as a function of Liver ? (A) Synthesis of vitamins (B) Production of heat (C) Regulation of blood sugar (D) Stimulation of peristalsis
68.
The hypersensitive reaction in response to a type I allergen which produces characteristic symptoms is described as allergic response. Which of the following immunoglobulin is mostly involved in this type of cellular response ? (A) IgA (B) IgM (C) IgD (D) IgE
69.
Which of the following is NOT considered as a cause of lung carcinoma ? (A) Cigarette smoking (B) Atmospheric pollution (C) Vitamin A deficiency (D) Airborne pollens
70.
If the blood group of father is ‘A’ and that of mother is ‘B’ . The blood group of their child could be (A) A or B or AB (B) AB only (C) A or B or AB or O (D) A or B only
71.
Certain gases in the atmosphere known as ‘green house gas’ which absorbs and emits heat and contribute to global warming. Which of the following gases is not considered in the list of gases known to have ‘green house effect’ ? (A) Carbon dioxide (CO2) (B) Chlorofluorocarbons (CFC) (C) Ozone (O3) (D) Nitrous oxide (NO)
72.
Which of the following hormones would supress inflammation caused by injury ? (A) Glucocorticoid (B) Progesterone (C) Thyroxin (D) Insulin
73.
Many aquatic plants float on water during day time but sink during night because (A) During day evaporation of water increases the density of the impure water of the reservoir whereas during night condensation of atmosphere moisture into the reservoir decreases the density of water. (B) Accumulation of gaseous oxygen in plants makes them buoyant during day time. The oxygen is used up during night making them heavier (C) Lipid synthesis increases during dar time making them buoyant and the lipids are used up during the night. (D) Accumulation of starch by the end of the day makes them heavier and they sink into the water during night time.
74.
If the husband is Rh+ and the wife is Rh–. (A) The couple cannot be children (B) The couple’s first child may be born but they are not likely to have their second child without medical intervention. (C) Their first foetus will not survive but the subsequent ones will (D) The couple’s reproductive life will be normal
75.
Maximal level of DNA replication in a mammalian cell occurs during. (A) GI phase (B) M phase (C) S phase
76.
(D) G2 phase
Many blue green algae can be used as bio-fertilizers because . (A) Their photosynthetic ability results in production of hydrocarbons used by the plant (B) They reduce atmospheric nitrogen to nitrogenous compounds (C) They serve as food for the beneficial microorganisms in soil (D) They are toxic to the plant pests
CLASS-XII_STREAM-SB+2_PAGE # 9
77.
Which of the following oxidizes ammonia to nitrogen ? (A) Nitrosomonas during day and night (B) Nitosomonas only during day (C) Rhizobium during day and night (D) Rhizobium only during day
78.
Bioluminescence involves the emission of light from biological systems. The energy source for this light is primarily. (A) Heat (B) Chemical (C) Magnetic (D) Photosynthesis
79.
The volume of blood pumped out by ventricle during each beat is known as stroke volume. If a healthy adult has a pulse rate of 72 and stroke volume of 70 ml, then the cardiac output is. (A) 70 ml/min. (B) 72 ml/min (C) 5040 ml/min (D) 140 ml/min
80.
Fats provide more energy than carbohydrates because (A) Fats contain higher percentage of C and H and lower percentage of O than carbohydrates (B) Fats gets readily oxidized than carbohydrates (C) Fats contain higher percentage of O than C (D) Fats can be absorbed readily by our bodies than carbohydrates
PART-II (2 Mark) MATHEMATICS 81.
If a, b, and c are nonzero real numbers such that ab = 2 (a + b), bc = 3( b + c) and ca = 4 (c + a) then the value of 5a + 7b + c is : (A) 18 (B) 72 (C) 108 (D) 120
82.
Let and be nonzero real roots of the quadratic equation x2 + ax + b = 0 and + , – – + and – – be the roots of the equation x4 + ax3 + cx2 + dx + e = 0. Then which of the following statement is false? (A) a = 0 (B) c = 0 (C) d = 0 (D) e = 0
83.
A point P lies on the line y = 2x in the first quadrant. Another point Q lies on the line y = 3x in the first quandrant. Suppose QP is perpendicular to the line y = 2x and QP = 5. The distance of P from the origin is : (A) 7 5
84.
(B) 1/2
(D) 39
B C cot is : 2 2
(C) 1/3
(D) 3
Let ABCD be a square. E and F be points on AC such that AE = EF = FC = AC/3. Then tan (EBF) equals : (A) 3/4
86.
(C) 35
In a triangle ABC, if b + c = 3a , then the value of cot (A) 2
85.
(B) 25
(B) 1 / 3
(C)1/2
(D) 1/3
An open box is constructed by netting squares of side length x from each the corners and of a square sheet of side length equal to 2007. Then the sides are folded up to form a box. The volume of the resulting box is maximum when x equals : (A) 669 (B) 669/2 (C) 2007/2 (D) 2007/4
CLASS-XII_STREAM-SB+2_PAGE # 10
87.
The coordinates (x0,y0) of the point on the line y = x + 2 which is closed to the parabola y2 = 4x is : (A) (0, 2) (B) (1/2, 5/2) (C) (5/2, 9/2) (D) (1, 3)
88.
A polynomial p(x) = x4 + ax3 + bx2 + cx + d has roots
e
2 , e and and no other roots. Let I =
p( x )dx 2
and J =
p(x)dx . Then : e
(A) I and J must have opposite signs (B) I and J can be both positive but not both negative (C) I and J can be both negative but not both positive (D) we do not have enough information to compare the signs of I and J. 89.
Let z1, z2 and z3 be three complex numbers on the unit circle |z| =1. Then |z1z2 + z2z3 + z3z1| equals : 2 2 2 (A) z1 z 2 z 3
(C)
90.
(B) z1 z 2 z3
1 z z z3 z 2 z 3 z1 z 3 z1 z 2 2 1 2
(D)
1 2 z1 z 22 z 32 z1z 2 z 2 z3 z3 z1 2
All the inner angles of a - 7 gon are obtuse, their sizes in degree being distinct integers divisible by 9. What is the sum (in degree) of the largest two angles ? (A) 300 (B) 315 (C) 330 (D) 335
PHYSICS 91.
A cylinder of mass M and the radius R has a radially dependent density. The cylinder starts from rest and rolls without slipping down an inclined plane of height H. At the bottom of the plane its translational speed is (8gH/7)1/2. The rotational inertia of the cylinder is (A)
1 MR2 2
(B)
3 MR2 4
(C)
7 MR2 8
(D) MR2
92.
If a 66 cm long air column closed at one resonates at a frequency 625 Hz, the number of other possible frequencies for resonance less than 1 kHz will be : (A) 8 (B) 5 (C) 7 (D) 3
93.
A copper pendulum of period T0 on the ground is taken down a mine shaft to a depth d. If the thermal expansion co-efficient of copper is (ºC–1) and the temperature in the mine is ºC higher than on the
T ground, the period changes to T. where the ratio T is given (in te first order by) 0
1 d (A) 1 1 2 R
d (B) (1 + ) 1 – R
d (C) (1 + ) 1 R
1 d (D) 1 1 2 2R
(R is radius of the earth lgnore variation in density of the earth’s crust)
CLASS-XII_STREAM-SB+2_PAGE # 11
94.
A parallel monochromatic beam of yellow light ( = 6 × 107m) Next to be central bright maximum, the angle of the first minimum in the diffraction pattern (with respect to the initial direction of the beam) is approximately. (A) 17º (B) 37º (C) 0º (D) 8.5º
95.
In an oscillating LC circuit with negligible resistance, at a certain instant, energy is fully stored in the capacitor. The least time it takes for the energy to be equally shared between the capacitor and the inductor is (A)
96.
1
LC 4
(B)
(C)
LC 2
(D)
LC 4
A parallel plate capacitor has a plate separation d and plate area A. An u charged metal salb of thickness a is inserted midway between the plates. The capacitance of the device is (A) infinite
97.
LC
(B) zero
(C)
0 A d
(D)
0 A d–a
The vertical motion of a huge piston in a machine is approximately simple harmonic with a frequency f. A block of mass m is placed on the piston. The maximum amplitude Amax of the piston’s simple harmonic motion that is possible, for the block and the piston to remain together, is given by (max : maximum speed) (A)
g
(B)
4 2 f 2
mg f2
(C)
g f2
2max (D) g
98.
In a certain region of space, electric field is along the positive z direction throughout. The field is, however, non-uniform ; its magnitude increases uniformly along the positive z-direction at the rate of 105NC–1m1. The force and torque experienced by a system having a total dipole moment of 10–7 C × m in the negative z-direction are (A) 10–2 N in the negative z-direction ; torque = 0 (B) 10–2 N in the positive z-direction torque = 0 (C) Force = 0 ; torque = 10–2 Nm so as to decreases potential energy. (D) Force = 10–2 N in the negative Z-direction, torque = 10-2 Nm so as to decrease the potential energy
99.
In one model of an atom, a positively charged point nucleus of charge Ze is surrounded by a uniform density of negative charge up to a radius R. The atom as a whole is neutral. In this model the electric field at a distance r from the nuelus is given by Ze r (A) E(r) = 4 3 r R 0 Zer
(B) E(r) =
4 0R 3
rR Ze 1 r (C) E(r) = 4 2 – 3 r < R r R 0 =0 r>R Ze (D) E(r) = 4 r 2 0
r 1 – , for all r R
CLASS-XII_STREAM-SB+2_PAGE # 12
100.
A particular ideal gas is supplied 10.61 J of heat at a constant pressure of 1.01 × 105 Pa. If the volume of the gas increases by 3 × 10–5 m3 , the gas consists of (A) monatomic molecules. (B) diatomic molecules. (C) polyatomic molecules. (D) a mixture of mono and diatomic molecules.
CHEMISTRY 101.
Optically pure 3-bromopent-1-ene upon addition of 1 mole of Br2 produces a tribromo compound. The number of stereoisomers in the product is (A) 2
102.
(B) 4
(C) 6
(D) 3
The plot that is not valid for an ideal gas where P is the pressure and V is the volume of the gas, is -
(A) PV
(B) PV
1/V
P
(C)
V
(D)
P
1/P
103.
V
The volume of 0.1M acetic acid (pKa = 4.76) that should be added to 10ml of 0.2M sodium acetate solution to prepare a buffer solution of pH 4.91 is (A) 14.2 ml
104.
(B) 4.0 ml
(C) 20.0 ml
(D) 70.0 ml
A hydrated salt of a bivalent metal when heated strongly produces a mixture of gases which when bubbled through Ba(OH)2 solution produces a white solid. This solid on treatment with dilute HCl dissolves a part of the solid leaving another part insoluble which is filtered. The filtrate on treatment with Br2 water slowly precipitates another white solid, which is not soluble in HCl. The gas mixtures are (A) CO2 and CO
105.
(B) SO3 and SO2
(C) SO3 and CO2
(D) SO2 and CO
An electron is accelerated from rest through a potential (V) and then diffracted on a Ni crystal to measure its wavelength (). The wavelength is related to V as (A) V
(B) 1/V
(C) V1/2
(D) 1/V1/2
CLASS-XII_STREAM-SB+2_PAGE # 13
106.
A dilute aqueous solution of a polymer of known molecular weight shows an elevation of boiling point of water by 0.052 K. The molar boiling point elevation constant of water is 0.52 K kg mol–1. Using these data(A) it is possible to calculate the relative lowering of vapour pressure of water and the magnitude of freezing point depression, but not the osmotic pressure at 300 K. (B) it is possible to calculate the relative lowering of vapour pressure of water, but neither the magnitude of freezing point depression nor the osmotic pressure at 300K. (C) it is possible to calculate the relative lowering of vapour pressure but neither the magnitude of freezing point depression nor the osomotic pressure at 300 K. (D) it is possible to calculate the relative lowering of vapour pressure and the osmotic pressure at 300K but not the magnitude of freezing point depression.
107.
An organic compound fused with metallic sodium dissolves in water and the solution is divided into two parts. One part is treated with FeSO4, boiled and filtered. In the filtrate addition of FeCl3 does not produce any precipitate. To the other part, addition of sodium nitro prusside produces violet color. The organic compound contains.
108.
(A) only nitrogen
(B) both bromine and nitrogen
(C) only sulphur
(D) both sulphur and nitrogen
The main product III obtained in the following reaction sequence is -
NH2
(CH3CO)2O
Me
+
I
Br2/CH3COOH
II
H2O/H
NH2
NHCOCH3
(A)
(B) Me
Br
Me
Br
NH2
NHCOCH3
(C)
(D) Me Br
109.
III
Br
A water droplet spreads on a clean gold surface. The droplet, however, does not spread onto a gold surface which is pre-treated with a dilute solution of hexanethiol [CH3 – (CH2)5-SH] and washed with excess water. This is because (A) chemisorption of hexanethiol on gold surface renders it hydrophilic (B) chemisorption of hexanethiol onto gold surface renders it hydrophobic (C) physisorption of hexanethiol onto gold surface renders it hydrophobic (D) physisorption of hexanethiol onto gold surface renders it hydrophilic.
110.
Ir (CO)Cl (PPh3) when reacts with O2, the oxidation state and coordination number of Iridium, respectively, become. (A) +1 and 5
(B) + 2 and 5’
(C) + 4 and 6
(D) + 3and 6
CLASS-XII_STREAM-SB+2_PAGE # 14
BIOLOGY 111.
If our body fluid were alcohol instead of water, which of the following would happen to our body temperature if everthing else in the body remains the same (A) Temperature control would be maintained as well as it happens now (B) We will maintain a constant temperature of 37ºC (C) Fluctuations of body temperature will be more since alcohol has a lower specific heat capacity (D) We will feel feverish all the time
112.
A gene has two alleles ‘A’ and ‘a’ with a frequency of p and q respectively the genotypic frequencies would have the proportion : (A) (p + q)2 = 1 (B) p2 – q2 – 1 (C) pq = 1/2 (D) (p – q)2 = 1
113.
At low concentrations sodium ions are good for the heart, but excess of the same results in hypertension or high blood pressure. This is because. (A) The balance between Na and K ions is destroyed (B) Blood becomes thicker with excess of Na+ ions (C) Na+ ions narrow down the artery (D) Water retention in kidneys increases with excess Na ions and heart requires to pump more
114.
When Edward Jenner inoculated Joseph with the cow pox pustules from a milkmaid, the small boy did not get small pox because (A) Pustules contained lgG against small pox which gave passive immunity to Joseph (B) Pustules contained IFN which killed the small pox virus (C) Pustules contained cow pox virus which gave protection against small pox (D) Pustules contained immune cell which gave protection against small pox
115.
‘Camoulflage and Mimicry are adaptations in animals. Which of the following statement is NOT correct ? (A) Camouflaging represents the ability of the animal to blend with surrounding. (B) Mimicry means one specie imitates or resembles another species to gain some benefit. (C) Mimicry helps to escape from predators (D) Camouflaging is only meant for desert animals.
116.
Heparin secreted by the mast cells present in the inner walls of the blood vessels is known to inhibit blood coagulation. Which of the following statement is NOT correct ? (A) It help neutralizing the action of thrombin (B) It prevents conversion of prothrombin to thrombin (C) It prevents conversion of fibronogen to fibrin (D) It was originally isolated from liver cells
117.
During winter, frost often kills plants because. (A) It leads to crystallization of cellular water (B) Low temperature decreases the rates of catabolic pathways to an extent that the energy produced is inadequate to sustain life (C) Low temperatures decreases the rate of anabolism to an extent that the rate of ATP production is far lower than the rate of ATP consumed (D) The water in soil is frozen and the roots are unable to transport it to various parts of the plant
CLASS-XII_STREAM-SB+2_PAGE # 15
118.
If the two genes ‘A’ and ‘B’ on a chromosome are located next to each other (A) Chances of crossing over between them are very low (B) Chances of crossing over between them are very high (C) The two genes serve as single unit when it comes to accumulation of mutations within them (D) Then of the two genes one has to be nonfunctional gene for the crossover to occur in between the two
119.
Contractile vacuoles in amoeba (A) Accumulate water and burst upon fusion with the cell membrane releasing water from the cell (B) Are organelles that accumulate nutrients (C) Are responsible for locomotion of amoeba (D) Provide a surface for attachment of ribosomes
120.
During the course of intensive exercise, muscle fatigue occurs because. (A) During exercise entire deposit of glucose is converted to CO2 and H2O (B) O2 deficiency results in accumulation of lactic acid in the muscles (C) O2 deficiency results in accumulation of citric acid in the muscles (D) Excessive utilization of glucose results excessive production of acetyl Co A which is not fully utilized by the TCA cycle (Krebs cycle).
*****
CLASS-XII_STREAM-SB+2_PAGE # 16
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2007 Time : 3Hr.
1.
Max. Marks : 160
In Year 2007, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90),Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2008 Time : 3Hr.
1.
Max. Marks : 160
In Year 2008, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2009 Time : 3Hr.
1.
Max. Marks : 160
In Year 2009, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2010 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2011 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2012 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
YEAR-2008 (KVPY-STREAM-SB+2) PART-I (1 Mark) MATHEMATICS 1.
The equation z2 = z , where z is a complex number, has (A) 4 solution (B) 2 solution (C) no solution (D) infinitely many solutions
10
2.
x 1 x 1 is : The coefficient of the term independent of x in the expansion of 2 / 3 1/ 3 x 1 x x 1/ 2 x (A) 35
3.
(B) 70
(C) 105
If no two of the real numbers a, b, c are equal and (A) abc = 1
(B) a + b + c = 1
(D) 210
a a2
a3 1
b b2
b3 1
2
c3 1
c c
= 0, then :
(C) a + b + c = 0
(D) ab + bc + ca = 0
4.
If the slopes of one of the lines represented by ax2 – 6xy + y2 = 0 is the square of the other for some positive value of a, then a is (A) 1 (B) 2 (C) 4 (D) 8
5.
The number of distinct points common to the curves x2 + 4y2 = 1 and 4x2 + y2 = 4 is (A) 0 (B) 1 (C) 2 (D) 4
6.
An ellipse has its major axis equal to the diameter of a circle and the area of the ellipse is one-third the area of the circle. The eccentricity of the ellipse is : (A)
7.
9.
(B)
2 3
(C)
2 2 3
(D)
1 3
Two perpendicular chords AB and CD of a circle meet at P. If PA = 2, PB = 18 and PC = 4, then the diameter of the circle is : (A)
8.
2 3
5 17 2
(B) 5 17
(C) 20
The value of cos 5º + cos 10º + cos 15º + .......+ cos 355º is (A) 0 (B) 1 (C) – 1
(D) 10 5
(D) 71 cos 5arc
In a square ABCD, points P on BC and Q on CD are such that AP = 4, PQ = 3 and QA = 5. The area of ABCD is (A)
256 15
(B) 16
(C)
256 17
(D)
256 18
CLASS-XII_STREAM-SB+2_PAGE # 17
10.
In a triangle ABC, AD bisects A. Suppose AC = 2, BD = 2, DC = 1. The value of cos B is (A)
11.
12.
6 7
(B)
7 8
(C)
8 9
(D)
9 10
The sides of a triangle are 9x + 1, 6x + 2, 3x + 3, where x is a positive integer. If the area is also an integer, the number of admissible values of x in the set {1, 2, 3........., 20} is : (A) 3 (B) 4 (C) 6 (D) 12
f (1 h) Suppose f is a real function defined on R and hlim exists. Then : 0 h (A) f is not continuous at 1 (B) f is not continuous at 1 but not differentiable at 1 (C) f is differentiable at 1 (D) f is differentiable at 0
13.
14.
Consider the following statements : (I) The derivative of an odd differentiable function is always even. (II) If f(x) is differentiable at a point x0 and g(x) is not differentiable at x0, then f(x) g(x) is not differentiable at x0. Which of the following is true ? (A) I and II are both true (B) I is true and II is false (C) I is false and II is true (D) I and II are both false
sin[ x ] , if [ x ] 0 If f(x) = [ x ] . (Here [x] denotes the integer part of x.) Then xlim f(x) 0 0, if [ x ] 0 (A) is –1
15.
(B) is 0
Let f : [0, ) R be defined by f(x) = x – (A) [ – 1/2, ) x
16.
Let f(x) =
(B) [0, )
x . Then the range of f is
(C) { – 1/4, )
(D) R
t
(B) (– 2, – 1) 1
18.
4
0
The value of
(A)
x +
(D) does not exist
e (t 1)(t 2) dt .Then f(x) decreases in the interval
(A) (– , – 2) 17.
(C) is sin 1
1
(C) (1, 2)
(D) (2, )
x | x |3 / 2 dx is :
4 7
(B)
4 5
(C)
4 3
(D) 0
Let fn(x) = log log ....log(x), where log is repeated n times. Then
x f ( x)f (x)......f 1
2
(A) f11(x) + c
1dx
10 ( x )
(B)
is equal to :
f11( x ) c 11
(C) 10f10(x) + c
(D) 11f11(x) + c
CLASS-XII_STREAM-SB+2_PAGE # 18
19.
The least value of x12 + x22 + x32 where x1, x2, x3 are real numbers satisfying x1 + 2x2 + 3x3 = 4 is 8 (A) (B) 1 (C) 4 (D) 2 7
20.
A coin is tossed until one observes a sequence of exactly three tails. The probability that the experiment comes to an end at 7-th toss is . (A)
7 128
(B)
1 128
(C)
1 32
(D)
5 128
PHYSICS 21.
Super cooled steam suddenly freezes to water. In this process, (A) entropy of the system (steam) decreases, but entropy of the universe increases (B) entropy of the system as well as entropy of environment decreases (C) entropy of the system as well as entropy of the environment increases (D) entropy of the system increases but entropy of the environment decreases
22.
Isothermal compressibility of a substance is defined as : =–
1 V V P T
where the derivative is taken keeping T constant. V : Volume P : Pressure T : Temperature For an ideal gas, equals (A) R (Gas constant) (B) P (C) P–1 (D) P ( is the ratio of specific heats at constant pressure and constant volume = (Cp/ Cv) 23.
Consider two cases : (i) A point charge q at the origin (ii) A uniformly charged solid sphere of radius R (wth its centre at the origin) and total charge q. Given below are graphs of a property X versus distance r from the origin for the two cases. The graphs coincide for r R.
(A) X is electric potential due to point charge/charged sphere. (B) X is magnitude of electric field due to point charge/charged sphere (C) X is electrostatic potential energy of point charge/charged sphere (D) X is charge density in space.
CLASS-XII_STREAM-SB+2_PAGE # 19
24.
One end of a cylindrical solid rod of length L and radius r is clamped in a fixed positon. The other end is turned by an external torque resulting in a twist . The sheer modulus is given by . The twist angle is proportional to : (A) r1/L2 (B) r4/L (C) L/r4 (D) L /r4
25.
A particle of charge q and mass m moves in a cirular orbit with angular momentum given by l . The ratio of its magnetic moment to orbital angular moment l is given by (A)
26.
q m
(B) q
(C)
q 2m
(D) m q
Thermal motion of atoms in a gas causes the spectral line emitted by the atoms to be shifted at random towards both the red and blue. This leads to Doppler broadening of the spectral lines. If f is the frequency of the spectral line and f is a measure of broadening of the line, the ratio
f is proportional to f
(Proportionality constant is given to be dimensionless)
m (A)
kT
(B)
kT m
(C)
mkT
(D)
1 kT c m
27.
Consider a sinusoidal travelling wave along a string, with amplitude A and wave velocity v. The power carried by the wave is proportonal to (A) Av2 (B) AV (C) A2v2 (D) A2 v (The proportionality constant is not dimensionless)
28.
Monochromatic light falls on a pair of slits mounted 24 cm in front of a photographic film. After exposure, the film shows a series of bright bands spaced 0.20 cm apart. The separation between the slits is 6.0 × 10-3 cm. The wavelength of light is : (A) 600 nm (B) 400 nm (C) 500 nm (D) 560 nm
29.
Two clean mercury droplets when pushed into contact spontaneously coalesce to form a single droplet. The single droplet so formed will : (A) Be slightly warmer than the separate pair of droplets (B) Be slightly cooler than the separate pair droplets (C) Have the same temperature as the separate pair of droplets (D) Be warmer or cooler depending on the size of each initial droplet.
30.
The speed of a comet at perihelion (closest to the sun) is 5.6 × 104 ms–1, while its distance from the sun is 9.0 × 1010m. At aphelion (farthest from the sun) its distance is 5.6 × 1012m. The comet’s aphelion speed is : (A) 1.0 km s–1 (B) 900 ms–1 (C) 504 ms–1 (D) 5.6 × 104 ms –1
31.
Consider two wave forms y1 = A cos (k x – t) and y2 = A cos (k x + t) whose superposition forms a standing wave. Here x is in metres and t is in seconds. A node is found at x = 10 m. The longest wavelength possible for this situation is (A) 1 m (B) 40 m (C) 20 m (D) 10 cm
CLASS-XII_STREAM-SB+2_PAGE # 20
32.
The displacement x of a damped oscillator in one dimension is given by x(t) = A e – t sin (t + ) where x is in metres. The SI units of the constants A, , , are respectively (A) m, s–1, s–1, dimensionless (B) m, s, s–1, m (C) m, s–1, s, dimensionless (D) dimensionless, s–1, s–1, dimensionless
33.
In the following reaction, a proton bombards a lithium nucleus at rest producing two -particles : Li7 + 1H1 2 2He4 3 The total rest mass of the products is less than the total rest mass of the reactants by 0.01864 atomic mass unit (amu). By mass-energy conversion formula, 1 amu = 931 MeV approximately. This means that (A) The kinetic energy of the proton 17.4 MeV (B) The total kinetic energy of two - particles is more than the kinetic energy of the proton by 17.4 Mev (C) Each -particle has a kinetic energy of 8.7 MeV. (D) The proton’s kinetic energy is 8.7 MeV more than that of each -article
34.
The radius of the first (n = 1) orbit in Bohr’s model of hydrogen atom is 0.53 × 1010 m. (Planck’s constant h = 6.63 × 10–34 Js, mass of electron = 9.11 × 10–31 kg). The speed of the electron in this orbit is approximately (A) 3.0 × 1010 m s–1 (B) 1.4 × 107 m s –1 (C) 3.5 × 107 m s –1 (D) 2.2 ×107 m s –1
35.
In an electric motor, two parallel wires 60 cm long are separated by a distance of 1.5 cm. The wires have non-magnetic insulation between them. A short circuit in the motor results suddenly in a large current of 4000 A. The currents flow in opposite directions in the two wires. Then (A) There will be a repulsive force of 128 N on each wire (B) There will be an attractive force of 128 N on each wire (C) There will be no force experienced by any wire, since they are insulated. (D) There will be a force along the length of each wire, of magnitude128 N.
36.
Let be the typical de Broglie wavelength associated with an He atom in helium gas at room temperature T (20ºC) and pressure P(1 atmosphere).Let d be the mean separation between helium atoms under these conditions.Then (A) is greater than d under the given T and P. (B) is less than d under the given T and P. (C) is equal to d under the given T and P (D) The ratio of to d has no relation to T or P.
37.
In a plane electromagnetic wave of frequency f traveling in free space with speed c, the electric field magnitude E and magnetic field amplitude B are related ( In S.I. units) by (A) B = fE
38.
(C) B =
E c
(D) E = fB
A resistor R and a capacitor C are connected in series to a 220 V, 50 Hz a.c. source. Let VR and Vc be the r.m.s. voltages across R and C respectively. Then (A) VR = Vc = 220 V
39.
(B) B = cE
(B) VR – Vc = 220 V
(C) Vc – VR = 220 V
(D)
VR2 VC2 = 220 V
Two identical point sources P and Q vibrating in phase with the same amplitude generate sinusoidal waves on a water surface.The sources are 6.5 cm apart. Two nearest points (from P) of destructive interference along PQ are found to be at 0.7 cm and 2.4 cm from P. The total number of points of destructive interference on the line segment PQ is (A) 4 (B) 3 (C) 2 (D) 5
CLASS-XII_STREAM-SB+2_PAGE # 21
40.
An ideal gas is subjected to an isothermal -isochoric cycle 1 – 2 – 3 – 4 – 1 as shown. V
3
4
2
1
T
On the pressure - density (P-) graph, this cycle is represented by
P
P
2
4 3
3
1 4
1
2
(A)
(B)
P
P 2
2 3
3 1
1 4 4
(C)
(A) Graph (A)
(D)
(B) Graph (C)
(C) Graph (B)
(D) Graph (D)
CHEMISTRY 41.
Li metal is a better reducing agent than Na metal because (A) The ionization enthalpy of Li is lower than that of Na (B) The hydration enthalpy of Li is lower than that of Na (C) The ionization enthalpy of Li is higher than that of Na (D) The hydration enthalpy of Li is higher than that of Na
42.
One mole each of the two gases X and Y are stored separately in two cylinders at 25ºC at pressures 1 atm. and 2 atm, respectively. The difference in the compressibilities of the two gases. (kx – ky) is (A) 0.1 atm–1 (B) 0.5 atm–1 (C) 1.0 atm–1 (D) 2.0 atm–1
43.
(S)-lactic acid is OH
OH (A)
(B)
CO2H
OH
OH (C)
CO2H
(D)
CO2H
CO2H
CLASS-XII_STREAM-SB+2_PAGE # 22
44.
45.
The reaction between p-methylbenzaldehyde and NaOH is an example of (A) Aldol condensation reaction
(B) Cannizzarro reaction
(C) Disproportionation reaction
(D) Hydrolysis reaction
A saturated solution of BaSO4 is heated from 25ºC to 35ºC and the conductance of the solution and the solubility of BaSO4 are measured. It is found that : (A) both conductance and solubility increase (B) both conductance and solubility decrease (C) conductance increases but solubility decreases (D) conductance decreases but solubility increases.
46.
An ideal gas is subjected to a cyclic change as shown in the P-V diagram below :
A P
C
B
V The step in which the gas will cool down is along (A) AB 47.
(B) BC
(A) (3Z)-hept-3-en-1-ol
(C) (3Z)-hept-4-en-7-ol
(D) (3E)-hept-4-en-7-ol
is
(B) (3E)-hept-3-en-1-ol
The Lewis acid strength of BF3, BCl3 and BBr3 follows the order. (A) BBr3 > BCl3 > BF3
49.
(D) both BC and CA
The IUPAC name of
OH
48.
(C) both AB and CA
(B) BF3 > BCl3 > BBr3
(C) BCl3 >BBr3 > BF3
(D) BCl3 > BF3 > BBr3
The total number of possible geometrical and optical isomers for [CoCl2(en)2]+ (en = 1, 2-diaminoethane) is (A) 1
50.
(B) 2
(C) 3
(D) 4
In balancing the reaction. xH2S + 2NaNO3 + 2HCl = y S + zNO + kNaCl + 4H2O one would get x,y, z and k, respectively, as (A) 3,3,2 and 2
51.
(B) 2,2,3 and 3
(C) 3,3,4 and 4
(D) 4,4,3 and 3
The overall order of a reaction involving two reactants, X and Y, which follows the rate expression,Rate = k [X]1/3 [Y]2/3 . Where k is the specific rate and [ ] represents concentration, is (A) 2/3
(B) 0
(C) 1/3
(D) 1
CLASS-XII_STREAM-SB+2_PAGE # 23
52.
In a Daniel cell in operation : (A) Electrons flow externally from copper to zinc while anions flow from zinc to copper in solution. (B) Electrons flow externally from zinc to copper while anions flow from zinc to copper in solution. (C) Electrons flow externally from zinc to copper while anions flow from copper to zinc in solution. (D) Electrons flow externally from coppper to zinc while anions flow from copper to zinc in solution.
53.
In the pressure vs. molefraction of benzene curves/lines shown below, the total vapour pressure of an ideal mixture of benzene and toluene will follow the curve/line.
0.5 2 P(bar)
1
3 4
0.0 0.0
(A) 1 54.
(D) [Fe(H2O)6]2+
(B) SO2
(C) SO3
(D) O2
(B) O22– > O2– > O2+
(C) O2– > O22– > O2+
(D) O2+ > O22– > O2–
(B) Polyvinylchloride
(C) Teflon
(D) Bakelite
(B) 200 s
(C) 0.05 s
(D) 100 s
(C) 6
(D) 8
The number of facial atoms in a fcc unit shell is (A) 2
60.
(C) [FeCl4]2–
The half-life of ammonia adsorbed on a Ni surface if the rate of desorption is 6.93 × 10–3 s–1 , is (A) 0.01 s
59.
(B) [Fe(CN)6]3–
A naturally occuring polymer is (A) Amylose
58
(D) 4
The interatomic distance in O2+, O2– , and O22– follow the order (A) O2+ > O2– > O22–
57.
(C) 3
The gas formed when conc. H2SO4 is added to a mixture of NaCl and MnO2, is (A) Cl2
56.
(B) 2
sp3d2 hybridization explains the bonding in (A) [FeCl4]–
55.
1.0
molefraction (benzene)
(B) 3
The maximum amount of work produced by a heat engine operating between 200 K and 800 K, if 100 J of heat is absorbed from the hot reservoir, is (A) 100 J
(B) 75 J
(C) 50 J
(D) 25 J
CLASS-XII_STREAM-SB+2_PAGE # 24
BIOLOGY 61.
62.
Embryonic stem cells are derived from, (A) Inner cell mass of the blastocyst (C) Cells from morula
(B) Outer cell mass of the blastocyst (D) Cells from the placenta
The phase in which meiotic recombination occurs (A) Diplotene (B) Zygotene (C) Pachytene
(D) Diakinesis
63.
SCID (Severe Combined Immuno Defficiency Syndrome) patients do not have (A) T-lymphocytes (B) Platelets (C) Monocytes (D) Erythrocytes
64.
What is the maximum number of hydrogen bonds possible involving a water molecule ? (A) 0 (B) 1 (C) 2 (D) 3
65.
A strand of a nucleic acid having 60% of base A and 30% of base G is (A) B-DNA (B) A-DNA (C) Should be an RNA
(D) Single stranded
66.
Tetracycline, cyclohexamide, and streptomycin inhibit : (A) Transcription (B) Translation (C) Splicing (D) mRNA editing
67.
In the genetic code, a nonsense codon codes for (A) An antisense amino acid (B) A sensible amino acid (C) Does not code for any amino acid (D) Methionine
68.
The dinosaurs became extinct at the end of the following period : (A) Cambrian (B) Cretaceous (C) Ordovician
(D) Silurian
The anticoagulant most commonly used in blood banks is : (A) EDTA (B) Heparin (C) Sodium Citrate
(D) Hirudin
69.
70.
Totipotent cell is (A) A cell which can be differentiated into most of the cell types. (B) A cell which can be differentiated to all cell types to form a complete organism (C) A cell which can be differentiated into only a specific cell type (D) A cell which does not differentiated at all
71.
You have an infection of pneumococcus (a bacteria). Which part of the bacteria may be toxic to your body and causes immunological reaction ? (A) The outer cell wall lipoplysaccharide (B) The plasma membrane of the bacteria (C) bacterial nucleus (D) Polysomes
72.
Three nucleotides form a codon, which can code for a single amino acid. However, the same amino acid can be coded by three different codons. These three codons are collectively called (A) Puncture codons (B) Degenerat codons (C) Nonsense codons (D) Termination codons
73.
The reason for doctor’s advice for vaccination of newborns is : (A) To increase the innate immunity of the baby (B) To increase the acquired immunity of the baby (C) To increase both, the innate and acquired immunity of the baby (D) To protect the baby only against bacterial diseases
CLASS-XII_STREAM-SB+2_PAGE # 25
74.
If you start a bacterial culture with 100 E. coli cells and allow the culture to grow for 2 hours, approximately what would be the total number of E. coli in the culture considering E.coli has a doubling time of 20 minutes. (A) 102 (B) 103 (C) 105 (D) 107
75.
Bacterial Flagellar movement requires (A) Energy through ATP hydrolysis (B) Nutrient gradient (C) Proton gradient coupled to transport (D) Energy through GTP hydeolysis
76.
Which of the following bio-molecules is responsible for the “prion” infectious diseases (A) DNA (B) Protein (C) RNA (D) Lipid
77.
Charles Darwin’s Theory of natural selection was heavily influenced by : (A) Thomas Malthus “An Essay on the Principle of Population” (B) Jean-Bapiste Lamark “Philosophie Zoologique” (C) Issac Newton “Principia” (D) Gregor Mendel “Experiments on Plant Hybridization”
78.
Which one of the following chemical groups is not present in the nascent polypeptide chain of a protein ? (A) Methine (B) Methylene (C) Amide (D) Phosphate
79.
Identify the evolutionarily related proteins : (A) Pepsin & Papain (C) Myoglobin & Hemoglobin
80.
(B) Collagen & Collagenase (D) Lysozyme & Ribozyme
How many peptide linkages are present in a protein with 176 residues ? (A) 174 (B) 175 (C) 176
(D) 177
PART-II (2 Mark) MATHEMATICS 81.
Suppose a, b, c are in arithmetic progression and a2, b2, c2 are in geometric progression. If a < b < c and a + b + c = 3/2, the value of a is :
1 (A)
82.
2
(B)
1
1 1 – 2 2
(C)
3
(D)
1 1 – 3 3
Let y = g(x) be a function whose derivative g'(x) has the following graph. Which of the following values of g is the largest ?
2 1 –1 –2 –3 –4
(A) g(2)
(B) g(3)
1 2 3 4 5
(C) g(4)
(D) g(5)
CLASS-XII_STREAM-SB+2_PAGE # 26
83.
Let ABCDEFGHI be a regular nanogon (9-sided polygon). If AB = x, AC = y, AD = z, then x, y, z are related by (A) z2 = x2 + xy + y2 (B) z = x + y (C) y2 = xz (D) 2y = x + z
84.
If A is a 10 × 10 matrix with entries from the set {0, 1, 2, 3} and if AAT is of the form :
0 * * * * 0 * * * * 0 * * * * 0 the number of such matrices A is : (A) (43)10 (B) (42)10 85.
(A)
1 5 2
(C)
5 2 2
(B)
88.
0
[ x ]e x dx equals :
e e 1
(B)
What is the value of
/2
0
2006
(A)
(C) 1 –
2
e 1
cos1003 xdx
(B)
x x
0
2007
/2
0
1 e
(D)
1 e 1
(D)
2009
cos1004 xdx ?
(C)
2008
e f ( t ) f ( x ) dt is
(A) 0
90.
e2
Let f(x) and g(x) be real polynomials of degree 4 and 3 respectively with leading coefficients 4 and 3 respectively. Then
lim g( x )
89.
2 3 2
(D) not uniquely determinable
The integral
(A)
87.
(D) 1
In an ellipse, O is the centre, AB is the major axis and CD is the minor axis. Suppose the focus between A and O is the ortho-centre of the triangle ACD. The eccentricity of the ellipse is
86.
(C) 410
(B)
(C)
3 16
(D)
The equation of the curve through the origin satisfying the differential equation (A) log 1 tan
(x y) =y 2
(B) log |1 + tan(x + y)| = x
(C) log 1 tan
(x y) =x 2
(D) log |1 + tan(x + y)| = y
4 13
dy = sin(x + y) + cos(x + y) dx
Let A = {1, 2, 3, 4, 5, 6} and f : A A be a bijection. What is the probability that f o f = id, i.e., f is its own inverse ? (A)
19 180
(B)
13 48
(C)
1 720
(D)
5 16
CLASS-XII_STREAM-SB+2_PAGE # 27
PHYSICS 91.
Two stars of masses M1 and M2 form a binary system. The distance between the centres of the stars is d. The orbital period is given by (A)
(B)
(C)
(D)
2 d 3 G(M1 M2 ) 2d3 / 2 G(M1 M2 ) 2d3 / 2 G
M1 M2 , where is the ‘reduced’ mass = M M 1 2
2 d 3 G
92.
A particle is stuck on the rim of a wheel of radius 50 cm. The wheel is rotating with an angular acceleration of 20 rad s–2. If at an instant the angular speed of the wheel is 10 rad s–1, the total linear acceleration of the particle is : (A) 10 ms–2 (B) 50 ms–2 (C) 51 ms–2 (D) 60 ms–2
93.
A beam of 30 keV electrons strikes different targets in different experiments. The lowest wave length cut -off of the continuous spectrum of X-rays generated by beam for any target is
94.
(A) 1.0 × 10– 10 m
(B) 3.0 × 10– 10 m
(C) 4.14 × 10– 11 m
(D) dependent on the nature of the target
A bat flying towards a wall with a speed 9.0 m s–1 emits ultrasound of frequency 90 kHz. (Speed of ultrasonic waves is 340 ms–1) The frequency of ultrasound received by the bat after reflection from the wall is : (A) 90 kHz
95.
(B) 94.9 kHz
(C) 85.4 kHz
(D) 99 kHz
A cylindrical glass vessel of height 18 cm and diameter 8 cm is 4 mm thick. It is covered with a1 mm thick copper lid (Thermal conductivity of copper is 400 W K–1m–1) In a cold environment the water in the vessel has got frozen into 0ºC ice. It is then immersed into a tank of 15ºC water. (Density of ice is 0.92 ×103 kgm–3 and latent heat of fusion of water is 333 x 103 J kg–1) The time taken for the ice to melt completely is (A) 9.2 s
96.
(B) 46 s
(C) 18.4 s
(D) 136 s
An upright cylinder of large base area is filled with water up to height H. Water is flowing out through holes (1, 2 and 3) of equal diameter on the side of the cylinder at heights H/4, H/2 and 3H/4 respectively. Let x1, x2 and x3 be the respective horizontal distance covered by the water flowing out of the holes before hitting the ground. Then (A) x3 > x2 > x1
97.
(B) x3 < x2 < x1
(C) x2 > x1 = x3
(D) x2 > x1 > x3
Ocean tides on the Earth are caused by the gravitational effects of the Moon (for lunar tides) as well as the Sun (for solar tides). If the diameter of the earth were to increase by 20%, then (A) Lunar tides would be strengthened but solar tides would be weakened (B) Lunar tides would be weakened but solar tides would be strengthened (C) Both lunar and solar tides would be strengthened with lunar tides strengthening more than solar tides (D) Both lunar and solar tides would be weakened with lunar tides weakening more than solar tides.
CLASS-XII_STREAM-SB+2_PAGE # 28
98.
The wavelength of radiation emitted by a hydrogen atom when it de-excites from its first excited state to ground state (n = 2 to n = 1) is 121.7 nm. For the analogous transition in a positronium atom (bound state of electron and its antiparticle called positron) the wavelength of radiation will be approximately (A) 243.4 (B) 121.7 (C) 60.85 (D) 0.53
99.
The objective lens of a telescope has a diameter of 12.2 cm. The angular resolution of the telescope at the wavelength of 500 nm is (A) 2 × 10 –9 rad (B) 1.22 × 10 –7 rad (C) 4 × 10 –5 rad (D) 5 × 10 –6 rad
100.
A conducting rod of length 80 cm rotates with its one end fixed at the centre of a circular metallic ring and the other end in contact with the ring. The angular frequency of the rod is 300 s–1. There is a uniform and constant magnetic field of 1.0 T parallel to the axis of rotation. The emf developed between the centre and the ring is : (A) 48 V (B) 192 V (C) 36 V (D) 96 V
CHEMISTRY 101.
The numbers of lone pairs of electrons in XeF2 and XeF4 respectively, are (A) 3 and 3 (B) 2 and 3 (C) 2 and 2 (D) 3 and 2
102.
When 4 moles of N2 gas reacts with 16 moles of H2 gas in 10 lit vessel, 4 moles of ammonia gas is produced in the equilibrium mixture. The equilibrium constant Kc for this reaction in mol–2 lit2 is (A) 0.4 (B) 0.2 (C) 0.8 (D) 1.6
103.
The freezing point of pure benzene is 5.5º C. When 2.9 g of butane is dissolved in 200g of benzene, the freezing point of benzene decreases to 4ºC. To lower the freezing point of benzene by another 1.5ºC, the amount of butane that has to be added to mixture is (A) 5.8 g (B) 2.9 g (C) 1.5 g (D) 8.7 g
104.
X and Y in the following reactions, respectively are SO3H
O
MgBr (i) +
cat
X
Y
(ii) H3O
OH
(A) X =
Q
Q
Y= Q
OH
(B) X =
Q
Y=
Q
OH
(C) X =
Q
Y=
OH Q
OH
(D) X =
Q
Y=
Q = Phenyl group
O
CLASS-XII_STREAM-SB+2_PAGE # 29
105.
The configuration at C-2 and C-5 in the following compound, respectively, are OH 2
5 OH
(A) 2R and 5R 106.
(B) 2S and 5S
(C) 2R and 5S
The cell potential of an electrochemical cell with the cell reaction Zn + 2Ag+ (0.0001M) Zn2+ (0.1 M) + 2Ag, is (A) 1.25 V (B) 1.35 V (C) 1.45 V Given that the standard cell potential is 1.56 V
(D) 2S and 5R
(D) 1.55 V
107.
Methyl chloride reacts with X at high temperature in the presence of a catalyst Y to give Me2SiCl2 as one of the products. The compound can also be formed by reaction of silicon tetrachloride with an organometallic reagent, Z. X, Y, and Z respectively,are (A) Si, Cu, MeMgBr (B) SiO2, Cu, Me2Zn (C) Si, Ni, MeMgBr (D) SiO2, Fe, Me2Zn
108.
A chemical reaction takes place at 625 K with an activation energy barrier, E/R = 500 K. A catalyst when used in the reaction reduces the activation energy barrier to 400 K. The temperature at which the rate constant with and without the catalyst will be same is (A) 300 K (B) 400 K (C) 500 K (D) 600 K
109.
A divalent transition metal ion with valence electron configuration 3d8 forms a complex with cyanide ion. The correct identity of the metal ion, the complex and its geometry, respectively, are (A) Fe2+, [Fe(CN)6]4– , and octahedral (B) Ni2+, [Ni (CN)4]2– and tetrahedral (C) Fe2+, [Fe(CN)6]3– and octahedral (D) Ni2+, [Ni(CN)4]2– and square planar
110.
The number of and particles to be emitted by 238U92 to give 206Pb82 , respectively, are (A) 8 and 6 (B) 4 and 3 (C) 6 and 8 (D) 3 and 4
BIOLOGY 111.
In a double-stranded DNA coding for a protein, in principle, how many codon reading frames are possible? (A) 1 (B) 2 (C) 3 (D) 6
112.
Which of the following is advantage of meiotic recombination in diploids ? (A) Helps in maintaining chromosome length (B) Ensures chromosome segregation (C) Helps chromosomes to attach to the spindle microtubules (D) Ensures new combinations of genetic traits
113.
Plants obtain their nitrogen supply through bacteria of the soil because : (A) Nitrogen is absent in the air and present in the soil (B) Plants do not have a mechanism to absorb gaseous Nitrogen (C) Bacteria are Nitrogen rich (D) Getting nitrogen is a side-effect of a bacterial infection
CLASS-XII_STREAM-SB+2_PAGE # 30
114.
The number of genes in man (Homo sapiens) is X-fold more than in a fly (Drosophila melanogaster). The value of X is (A) 2 (B) 10 (C) 250 (D) 10000
115.
You are supposed to mix a 3000 bp DNA fragment and a 600 bp DNA fragment in 1 : 5 molar ratio. If you take 100 ng of the 3000 bp fragment how much of the 600 bp fragment do you require to get desired ratio (A) 10 ng (B) 100 ng (C) 500 ng (D) 2500 ng
116.
An enzyme that cleaves DNA recognizes an 8 base-pair unique DNA sequence. The probable number of times this enzyme will cleave a 70 kilobase pair random DNA sequence is (A) 1 (B) 2 (C) 3 (D) 4
117.
Mendel’s law of independent assortment when interpreted in a modern context indicates : (A) Alleles are present on the same chromosome, but they assort independently due to recombination (B) Alleles are present on independent chromosomes and these separate and assort independently (C) Alleles are present on independent chromosomes and they can be sorted during meiosis. (D) Alleles are present on the same chromosome and their combination is dependen
118.
Fat absorption in the microvilli is by : (A) Endocytosis (B) Simple diffusion through the plasma membrane (C) Facilitated diffusion (D) Active transport
119.
During the process of photosynthesis (A) Glucose is synthesized during the dark reaction and ATP during the light reaction (B) Glucose and ATP are produced during light and dark reaction (C) Glucose and ATP are produced during the dark reaction (D) Glucose is synthesized during the light reaction and ATP during the dark reaction
120.
Identify the protein with more than one polypeptide chain. (A) Myoglobin (B) Trypsin (C) Immunoglobulin
(D) Lysozyme
CLASS-XII_STREAM-SB+2_PAGE # 31
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2007 Time : 3Hr.
1.
Max. Marks : 160
In Year 2007, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90),Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2008 Time : 3Hr.
1.
Max. Marks : 160
In Year 2008, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2009 Time : 3Hr.
1.
Max. Marks : 160
In Year 2009, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2010 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2011 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2012 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
YEAR-2009 (KVPY-STREAM-SB+2) PART-I (1 Mark) MATHEMATICS 1.
Suppose the sequence a1, a2, a3 ...... is an arithmetic progression of distinct numbers such that the sequence a1, a2, a4, a8...... is a geometric progression. The common ratio of the geometric progression is : (A) 2 (B) 4 (C) a1 (D) not determinable
2.
The positve integer k for which (101)k/2/k! is a maximum is : (A) 9 (B) 10 (C) 11
3.
(D) 101
Let p(x) = a0 + a1x + .......+ anxn be a zero polynomial with integer coefficients. If p( 2 3 6 ) = 0, the smallest possible value of n is : (A) 8 (B) 6
(C) 4
(D) 2
4.
Three players play a total of 9 games. In each game, one person wins and the other two lose ; the winner gets 2 points and the losers get 1 each. The number of ways in which they can play all the 9 games and finish each with a zero score is : (A) 84 (B) 1680 (C) 7056 (D) 0
5.
In a triangle, two vertices are (2, 3) and (4, 0), and its circumcentre is (2, z) for some real number z. The circumradius is :
6 (A)
6.
2 13
(B)
5
(C) 2
(D)
13 6
Consider an ellipse with foci at (5, 15) and (21, 15). If the x-axis is a tangent to the ellipse, then the length of its major axis equals : (A) 17
(B) 34
(C) 13
(D)
416
7.
Let the line 2x + 3y = 18 intersect the y-axis at B. Suppose C ( B), with coordinates (a, b), is a point on the line such that PB = PC, where P = (10, 10). Then 8a + 2b equals : (A) 60 (B) 62 (C) 66 (D) 79
8.
If cosec2( + ) – sin2( – ) + sin2(2 – ) = cos2( – ), where , (0, /2) then sin( – ) is equal to : (A)
9.
If sinx + siny =
(A)
10.
1 2
7 25
(B)
1 2
3 2
(D)
3 2
(D)
24 25
7 1 and cos x + cosy = , the sin(x + y) equals : 5 5
(B)
24 25
The number of solutions to sin x = (A) 1
(C)
(B) 6
(C)
7 25
6 with 0 x 12 is : x (C) 10
(D) 12
CLASS-XII_STREAM-SB+2_PAGE # 32
11.
Define a function f : R R given by :
sin x 2 , for x 0 f(x) = 2 x x ax b, for x 0 Suppose f(x) differentiable on R. Then, (A) a =0, b = 0 (B) a = 1, b = 0 12.
(C) a = 0, b = 1
(D) a = 1, b = 1
The shortest distance from (0, 3) to the parabola y2 = 4x is : (A) 2
(B)
(C) 5
2
(D)
5
13.
Ten trucks, numbered 1 to 10, are carrying packets of sugar. Each packet weighs either 999 gms or 1000 gms and each truck carries only the packets equal weights. The combined weight of 1 packet selected from the first truck, 2 packets from the second, 4 packet from the third, and so on and 29 packets from the tenth truck is1022870 gms. The trucks that have the lighter bags are : (A) 1, 3, 5 (B) 2, 4, 5 (C) 1, 9 (D) 2, 8
14.
What is the value of
1
(A) 1
cos( x ) cos([2x]) dx ? (Here | t | denotes the integral part of the real number t) 0
(B) – 1 1
15.
The value of the limit lim
n 0
(A) 0 16.
(B)
2
(D)
2
(D) 1
2
x10 sin(nx )dx equals : 1 10!
(C)
The area bounded by the parabolas y = x2 and y = 1 – x2 equals : (A)
17.
(C)
2 3
(B)
2 2 3
(C)
1 3
(D)
2 3
A vector which bisects the angle between a 3 i 4k and b = 5 j 12k is :
(A) 39 i – 25 j 8k
5 (B) 3 i 5 j k 8
(C) 39 i 25 j 8k
5 (D) 3 i 5 j k 8
18.
An envelope has space for at most 3 stamps. If you are given three stamps of denomination 1, and three stamps of denomination a (a > 1), the least positive integer for which there is no stamp value is : (A) 7 (B) 8 (C) 9 (D) 10
19.
If m, n are positive integers such that m < n and
d = d (here d | k moeans d is a positive of k), then : d/n
d/m
1
(A)
1
d < d
d/m
d/n
1
(C) 20.
1
d = d
d/m
d/n
1
d > d
d/m
1
(B)
(D) no relationship can be determined
d/n
The number of relation R from an m-element set A to an n-element set B satisfying the condition : (a, b1) R, (a, b2) R b1 = b2 for a A, b1, b2 is : (A) nm (B) 2m + n – 2m – 2n (C) mn (D) (n + 1)m
CLASS-XII_STREAM-SB+2_PAGE # 33
PHYSICS 21.
The relation Cp – Cv = R(Cp, Cv : Molar specific heats at constant pressure, volume) is exactly true for : (A) an ideal mono-atomic gas (B) any ideal gas, whether mono-dia polyatomic (C) any real gas above its critical temperature (D) all real gases
22.
The molecules of air in the room that you are sitting are all experiencing the force of gravity tending to bring them down. The molecules are also frequently and randomly undergoing collisions, which tend to oppose the effect of fall under gravity. The density of air is nearly uniform throughout the room because (A) the mass of the molecules is very small (B) the gravitational potential energy mgh is such lesser than the average thermal energy kT. (C) the gravitational potential enrgy mgh is mush greater the the average thermal energy kT. (D) mgh is nearly of the same magnitude as kT, which results in the cancellation of the two opposing factors. A parallel plate capacitor is charged fully by using a battery. Then without disconnecting the battery, the plates are moved further apart. Then, (A) the charge on the capacitor increases (B) the voltage difference between the plates decreases (C) the capacitance increases (D) the electrostatic energy stored in the capacitor decreases
23.
24.
The five sides of a regular pentagon are represented by vectors A 1 , A 2 , A 3 , A 4 and A 5 , in cyclic order as shown. Corresponding vertices are represented by B1 , B 2 , B 3 , B 4 and B 5 drawn from the centre of the pentagon. A2
A1 B1 B5
B2 A5
B4
B3
A3
A4
Then B 2 + B 3 + B 4 + B 5 = (A) A 1 (B) – A 1 25.
(C) B1
(D) – B1
Four metallic plates each of surface area (of one side) A, are placed at a distance d apart from each other. The two outer plates are connected to a point P and the two inner plates to another point Q as shown in figure. Q
P
Then the capacitance of the system is (A) 0
A 2d
(B) 0
A d
(C) 2 0
A d
(D) 3 0
A d
26.
A progressive wave travelling in positive x-direction given by y = a cos (kx – t) meets a denser surface at x = 0, t = 0. The reflected wave is then given by (A) y = – a sin(kx – ax) (B) y = – a cos(kx + ax) (C) y = a sin (t – kx) (D) y = a cos (kx – t)
27.
A charge Q is spread non uniformly on the surface of a hollow sphere of radius R, such that the charge density is given by = 0 (1 – sin), where is the usual polar angle. The potential at the centre of the sphere is
Q (A) 2 R 0
Q (B) R 0
Q (C) 8 R 0
Q (D) 4 R 0
CLASS-XII_STREAM-SB+2_PAGE # 34
28.
An ideal diatomic gas is heated at constant pressure. The ratio of the work done to the heat supplied is (A)
29.
2 5
(C)
2 7
(D)
4 7
5 27
(B)
5 48
(C)
27 5
(D)
1 3
Two identical conducting spheres carry identical charges. If the spheres are set at a certain distance apart, they repel each other with a force F. A third conducting sphere, identical to the other two, but initially uncharged, is then touched to one sphere, and then to the other before being removed. The forcebetween the original two spheres is now (A)
31.
(B)
In the hydrogen spectrum, the ratio of the wavelengths for Lyman – radiation to Balmer – radiation is (A)
30.
3 5
F 2
(B)
F 4
(C)
3F 4
(D)
3F 8
A small rectangular loop of wire in the plane of the paper is moved with uniform speed across a limited region of uniform magnetic field perpendicular to the plane of the paper, as shown. Uniform magnetic field Initial position
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
x x x x x x x x
Final position
Which graph would best represent the variation of the electric current, I, in the wire with time t ?
I
(A)
(B)
t
I t
I
(C)
32.
I
(D)
t
t
I=0
The moment of inertia of a solid disc made of thin metal of radius R and mass M about one of its diameter is given by
MR 2 . What will be the moment of inertia about this axis if the disc is folded in half about this 4
diameter ? (A)
33.
MR 2 8
(B)
MR 2 2
(C)
MR 2 4
(D) MR2
A plane electromagnetic weve propagating in the direction of the unit vector nˆ with a speed c is described by electric and magnetic field vectors E and B , respectively. Which of the following relations ( in SI units) s) between E and B can be ruled out on dimensional grounds alone ? nˆ E nˆ B (A) E = (B) E cnˆ B (C) B (D) nˆ E B 0 c c
CLASS-XII_STREAM-SB+2_PAGE # 35
34.
A point electric dipole placed at the origin has a potential given by V(r, ) =
p cos 4 0r 2
where is the angle
made by the position vector with the direction of the dipole. Then (A) since the potential vanishes at =
, the electric field is zero everywhere on the = plane 2 2
(B) the electric field everywhere on the =
plane is normal to the plane. 2
(C) the electric field everywhere on the =
plane is along the plane 2
(D) the electric field vanishes on the = 0 35.
A uniform non-deformable cylinder of mass m and radius R is rolling without slipping on a horizontal rough surface. The force of friction is (A) mg, where is the coefficient of sliding friction (B) zero (C) increases with time (D) decreases with time
36.
Consider a one-dimensional potential V(x) as shown in the figure below. A classical particle of mass m moves under its influence and has total energy E as shown.
V(x) E
x
The motion is (A) non-periodic (C) periodic but not simple harmonic
(B) stationary (D) simple harmonic
37.
A source of frequency f is emitting sound waves. If temperature of the medium increases, then (A) wavelength of the sound wave increases (B) speed of the sound wave decreases (C) wavelength of the sound wave decreases (D) amplitude of the sound wave increases
38.
A block of mass m is stationary on a rough plane of mass M inclined at an angle to the horizontal while the whole set up is accelerating upwards at an acceleration a. If the coefficient of friction between the block and the plane is , then the force that the plane exerts on the block is (A) m (g + a) upwards (B) mg cos normal to the plane (C) resultant of mag cos normal to the plane and mg cos along the plane (D) resultant of m (g + a) cos normal to the plane and mg cos along the plane.
CLASS-XII_STREAM-SB+2_PAGE # 36
39.
A stream of charged particles enter into a region with crossed electric and magnetic fields as shown in the figure. On the other side is a screen with a hole that is right on the original path of the particles then, E
B
Charged Particles
(A) no particle can get through the hole (B) all particles can get through the hole (C) only positively charged particles with speed (D) all particles with speed 40.
E can get through the hole B
E can get through the hole. B
A small body is released from a height H of an inclined plane. At the bottom of the plane is a loop of radius R as shown.
H
O R x
Ignoring friction, the minimum H required for the body to just complete the loop ( that is, reach the point O) is (A) 2R
(B)
5R 2
(C) 3R
(D)
7R 2
CHEMISTRY 41.
The gas that has the slowest rate of diffusion among O2, H2, CO2 and CH4 is (A) O2 (B) H2 (C) CO2 (D) CH4
42.
Assuming ideal behaviour the ratio of kinetic energies of 3 g of H2 and 4g of O2 at any temperature is (A) 3 : 4 (B) 1 : 16 (C) 4 : 3 (D) 12 : 1
43.
The IUPAC name for the compound O
Cl
is
Me Me
44.
(A) 1-chloro - 3-methyl- 4-pentanone (C) 5-chloro - 3 - methyl- 2-pentanone
(B) 1-chloro - 2-methyl- 4-pentanone (D) 5-chloro - 2-methyl- 3-pentanone
The shape of the molecule CIF3 is (A) triangular (B) pyramidal
(C) T-shape
(D) linear
CLASS-XII_STREAM-SB+2_PAGE # 37
45.
Among CO32–, OH–, NH3 and HCO3–, the species that acts as a Bronsted acid as well as a Bronsted base is (A) Na2CO3 (B) NH3 (C) OH– (D) HCO3–
46.
The ratio of the heat capacities Cp/Cv for one mole of a gas is 1.67. The gas is : (A) He (B) H2 (C) CO2 (D) CH4
47.
The ion that is isoelectronic with CO is (A) O2+ (B) O2–
48.
49.
(D) N2+
(C) CN–
Among CH4, CO2, H2O and SO2, the bond angle is the highest in (A) CH4 (B) CO2 (C) H2O
(D) SO2
The solvent of choice for carrying out a Grignard reaction is (A) diethyl ether (B) chloroform (C) ethyl acetate
(D) ethanol
50.
The reaction of butanal with n-propylmagnesium bromide gives a (A) chiral secondary alcohol (B) achiral secondary alcohol (C) chiral tertiary alcohol (D) achiral tertiary alcohol
51.
The hybridization of Ni centre in Ni[(PPh3)2Cl2] and [NiCl4]2– respectively are (A) dsp2 and sp3 (B) dsp2 and sp2d (C) sp3 and sp3 (D) sp3 and dsp2
52.
Oxalic acid when treated with potassium permanganate in the presence of an acid, produces (A) O2 (B) C (C) CO (D) CO2
53.
The equilibrium constant for the reaction N2 + 3H2 2NH3 at 400 K is 41. The equilibrium constant for the reaction 1/2N2 + 3/2H2 NH3 at the same temperature will be closest to (A) 41 (B) 20.5 (C) 6.4 (D) 1681
54.
In a one component second order reaction, if the concentration of the reactant is reduced to half, the rate (A) increases two times (B) increases four times (C) decreases to one half (D) decreases to one fourth
55.
The conjugate bases for HCO3– and NH3, respectively, are (A) H2CO3 and NH4+ (B) CO32– and NH2– (C) H2CO3 and NH2–
56.
(D) CO32– and NH4+
Among the following
S CH2 I II the aromatic compounds are (A) I & II (B) I & III 57.
IV
III (C) II & III
(D) II & IV
Among the compounds O
N H I the order of basicity is (A) I > III > II > IV
N
N H
N H
II
III
IV
(B) II > IV > I > III
(C) III > I > IV > II
(D) II > I > III > IV
CLASS-XII_STREAM-SB+2_PAGE # 38
58.
The Newman projection of Me H
Me
H
H H
is known as the (A) eclipsed conformer
(B) staggered conformer (C) skewed conformer
(D) gauche conformer
59.
The half-life of a first order reaction is 30 min. The time required for 75% completion of the same reactionwill be (A) 45 min (B) 60 min (C) 75 min (D) 90 min
60.
The hydrogen ion concentration in a mixture of 10 ml of 0.1 M H2SO4 and 10 ml of 0.1 M KOH solution in water, is (A) 0.1 M (B) 0.05 M (C) 0.2 M (D) 0.02 M
BIOLOGY 61.
62.
During photosynthesis the chemical conversion of water is termed : (A) photolysis (B) hydrolysis (C) hydration
(D) condensation
In the organisms muscle, oxygen is carried by : (A) albumin (B) myosin (C) myoglobin
(D) hemoglobin
63.
Enzymes do the following : (A) make products and reactants of equal energy (B) help the chemical processes by lowering the energy of products (C) reduce the activation barrier and speed up chemical processes (D) hydrolyze all the biopolymers indiscriminately
64.
Glycolysis is : (A) biosynthesis of glucose (C) degradation of glucose
65.
(B) biosynthesis of glycine (D) reaction of glucose with proteins
Plants are attracted to light through the hormonal action of : (A) Gibberelic acid (B) Auxin (C) Chlorophyll
(D) Thiamine
66.
During development, unspecified cells become cells having unique functions. This process is called : (A) evolution (B) differentiation (C) translation (D) replication
67.
The chromosomal attachment site of the spindle microtubule is : (A) centrosome (B) liposome (C) centromere
(D) telomere
Which fo the following diseases is NOT sexually transmitted ? (A) Syphilis (B) Gonorrhoea (C) AIDS
(D) Tuberculosis
68.
69.
This cell organelle consists of two granule-like centrioles and is found in animal cells only. It helps in cell division. What is it called ? (A) centrosome (B) chromosome (C) centromere (D) chromatids
CLASS-XII_STREAM-SB+2_PAGE # 39
70.
Nucleotides are monomers of DNA. What does each nucleotide consist of ? (A) A nitrogenous base and a pentose sugar (B) A nitrogenous base and a phosphate group (C) A pentose sugar and a phosphate group (D) A nitrogenous base, a pentose sugar and a phosphate group
71.
Fetilization in humans usually takes place in : (A) Uterus (B) Graafian follicle
(C) Ovary
(D) Fallopian tube
72.
ELISA, the standard screening test for HIV, detects which of the following ? (A) HIV DNA (B) HIV RNA (C) HIV proteins (D) Antibodies to HIV proteins
73.
Sickle cell anemia is caused by : (A) complete absence of the haemoglobin gene (C) increased affinity of haemoglobin for oxygen
(B) point mutation of the haemoglobin gene (D) truncation of the haemoglobin protein
The natural source of Ti plasmid is : (A) bacteria (B) virus
(C) plants
74.
(D) animals
75.
Earthworms are bisexual but still cross-fertilization is common. This is because : (A) spermatozoa of different earthworms are different (B) spermatozoa and ova mature at different times in the same earthworm (C) ova from other earthworms may be larger (D) sperm and ova from the same earth worm cannot fertilize
76.
One difference between blood and lymph is that : (A) blood contains WBC and lymph contains RBC (B) blood contains RBC and WBC and lymph contains only WBC (C) blood contains RBC and lymph contains WBC (D) blood is liquid while lymph is solid
77.
The abnormal development of which of the following lymphoid organs would result in the most severe immunodeficiency ? (A) Spleen (B) Thymus (C) Tonsil (D) Lymph node
78.
Mitochondria are associated with all of the following functions, EXCEPT : (A) ATP synthesis (B) DNA syntheis (C) Protein synthesis
(D) Protein glycosylation
79.
The probability of having a girl child with blood group O when the parents have blood group A and B is : (A) 0% (B) at least 50% (C) at most 25% (D) exactly 75 %
80.
Wooden doors and windows swell up in the rainy season by : (A) a special type of diffusion called imbibition (B) evaporation of stored water wood (C) conduction of water from walls (D) transpiration
CLASS-XII_STREAM-SB+2_PAGE # 40
PART-II (2 Mark) MATHEMATICS 81.
Let p(x) = a0 + a1x + ........+ anxn. If p(– 2) = – 15, p(– 1) = 1, p(0) = 7, p(1) = 9, p(2) = 13 and p(3) = 25, then the smallest possible value of n is : (A) 5 (B) 4 (C) 3 (D) 2
82.
Let a, b, c be the sides of triangle. If t denotes the expression (a2 + b2 + c2)/(ab + bc + ca), the set of all possible values of t is : (A) {x R| x > 1} (B) {x R | 1 x < 2} (C) {x R | 1 x < 2} (D) {x R | 1 x 2}
83.
The area of the region bounded by y = | x 3 | 4 – 5 and the x-axis is (A) 24.5
84.
(C) 49
1 ( 6 2) 2
(B)
1 ( 5 1) 2
Define a sequence {an}n 0 by an =
87.
(C)
(D)
3
2
1 a n1 for n 1. a0 = cos1. 2
Then lim n 4n(1 – an) equals (A) 2 (B) 2/2 86.
(D) 35 2
The lengths of the sides and the diagonal of an isosceles trapezium from a two-element set {a, b}. If a > b, then a/b equals (A)
85.
(B) 37
(C) /2
The range of the function f(x) = (sin x)sinx defined on (0, ) is (A) (0.1) (B) (e– 1/e , 1) (C) [e– 1/e, 1)
(D)
(D) [e–1/e , 1]
Let A denote the area bounded by the curve y = 1/x and the lines y = 0, x = 1, x = 10, Let B = 1 + 1 1 1 1 , and let C = + + ......+ . Then 9 3 10 2 (A) C < B < A (C) C < A < B and A – C < B – A
1 + 2
....+
88.
(B) A < C < B (D) C < A < B and B – A < A – C
Two points are randomly choses on the circumference of a circle of radius r. The probability that the distance between the two points is at least r is equal to (A)
2
(B) sin r
(C)
2
(D)
2 3
89.
Consider al natural numbers whose decimal expansion has only then even digits 0, 2, 4, 6, 8. Suppose these are arranged in increasing order. If an denotes the n-th number in this sequence, then lim n log an /log n equals : (A) 0 (B) log510 (C) log210 (D) 2
90.
The sum of all absolute values of the differences of the numbers 1, 2, 3......., n, taken two at a time, i.e.
i j
equals :
jin
(A)
n 1 3
(B)
n 3
(C)
n 1 3
(D)
n2 3
CLASS-XII_STREAM-SB+2_PAGE # 41
PHYSICS 91.
A spherical cavity of radius r is carved out of a uniform solid sphere of radius R as shown in the figure.
R r
The distance of the center of mass of the resulting body from that of the solid sphere is given by (A)
92.
(B)
Rr 2
(C) 0
(D)
r3 R 2 Rr r 2
A plano-convex lens made of material of refractive index with radius of curvature R is silvered on the curved side. How far away from the lens-mirror must you place a point object so that the image coincides with the object ? (A)
93.
Rr 2
R
(B) R
(C)
R 1
(D) R
n2a P n moles of a van der Waal gas obeying the equation of state (V – nb) = nRT, where a and b are V 2 gas dependent constants, is made to undergo a cyclic process that is depicted by a rectangle in the PV diagram as shown in the figure. What is the heat absorbed by the gas in one cycle? P P1
P2 V1
94.
V2
V
(A) n(P1 – P2) (V2 – V1)
(B) (P1 – P2) (V2 – V1)
n 2a n 2 a (C) P1 2 P2 2 (V1 – V2) V1 V2
n 2a n 2 a (D) P1 2 P2 2 (V2 – V1) V1 V2
For what value of the resistor X will the equivalent resistance of the two circuits shown be the same ?
R
R 6x
(A) R
6x
R
R
6x
(B) 6R
R x
R 6x
(C) 2R
6x
R
R
6x
(D)
6x
R x
5 1 R 2
CLASS-XII_STREAM-SB+2_PAGE # 42
95.
2 MR2 rolls down a plane 5 inclined at an angle to the horizontal starting from rest. The coefficient of static friction between the sphere and plane is . Then, (A) the sphere will always roll without slipping (B) the sphere will always slide
A solid uniform sphere having a mass M, radius R, and moment of inertia of
(C) the sphere will roll without slipping only if sin
7 2
(D) the sphere will roll without slipping only if tan–1
96.
A cubical box of side a sitting on a rough table-top is pushed horizontally with a gradually increasing force until the box moves. If the force is applied at a height from the table top which is greater than a critical height H, the box topples first. If it is appliced at a height less than H, the box starts sliding first. Then the coefficient of friction between the box and the table top is : (A)
97.
a 2H
(B)
2H a
(C)
a H
(D)
H a
A vehicle is moving with speed v on a curved road of radius r. The coefficient of friction between the vehicle and the road is . The angle of banking needed is given by (A) tan =
98.
7 2
v2 r g v2 r g
v2 r g
(B) tan =
v2 r g
(C) tan =
v2 r g r g v2
(D) tan =
r g v2 r g v2
Two small identical speakers are connected in phase to the same source. The speakers are 3m apart and at ear level. An observer stands at P, 4m in front of one speaker as shown. The sound she hears is least intense when the wavelength is 1 and most intense when the wavelength is 2.
4m
3m
Then possible values of 1 and 2 are : (A) 1 = 1m and 2 = 2m (C) 1 = 2m and 2 = 1m 99.
(B) 1 = 4m and 2 = 3m (D) 1 = 0.5m and 2 = 0.25m
Two small blocks slide without losing contact with the surface along two frictionless tracks 1 and 2, starting at the same time with same initial speed v. Track 1 is perfectly horizontal, while track 2 has a dip in the middle, as shown. V
1
V
2 Start
Finish
Which block reaches the finish line first ? [Hint : Use velocity-time graph to solve] (A) Block on track 1 reaches the finish line first (B) Block on track 2 reaches the finish line first (C) Both blocks reach the finish line at the same time (D) It depends on the length of the dip in the second track, relative to the total length of the tracks.
CLASS-XII_STREAM-SB+2_PAGE # 43
100.
Consider 1 kg of liquid water undergoing change in phase to water vapour at 100ºC. At 100ºC, the vapour pressure 1.01 × 105 Nm2 and the latent heat of vaporization is 22.6 × 105 J kg–1. The density of liquid water is 103 kg m–3 and that of vapour is change is nearly. (A) 1.8 × 105 J kg–1
(B) 20.8 × 105 J kg–1
1 kg m–3. The change in internal energy in this phase 1 .8
(C) 22.6 × 105 J kg–1
(D) 11.3 × 105 J kg–1
CHEMISTRY 101.
If the pH of a mixture of 10 ml of 0.1 M NH4OH and 10 ml of 1 M NH4Cl solution is 8, the pKb value of NH4OH is then closest to (A) 3 (B) 5 (C) 7 (D) 9
102.
A cylinder of cooking gas in a household contains 11.6 kg of butane.The thermochemical reaction for the combustion of butane is 2C4H10(g) + 13O2(g) 8CO2(g) + 10H2O(); H = – 2658 KJ/mol. If the household needs15000 KJ of energy per day, the cooking gas cylinder will last for about (A) 64 days (B) 45 days (C) 20 days (D) 35 days
103.
The addition of 0.643 g of a compound to 50 ml of benzene (density = 0.879 g ml–1) lowers the freezing point from 5.51ºC to 5.03ºC. If the freezing point constant, Kf for benzene is 5.12 K Kg mol –1, the molar mass of the compound is approximately (A) 156 g mol–1 (B) 88 g mol–1 (C) 60 g mol–1 (D) 312 g mol–1
104.
Consider the following electrochemical cell : Zn(s) + 2Ag+(0.04 M) Zn2+(0.28M)+ 2Ag(s). If Ecellº = 2.57 V, then e.m.f. of the cell at 298 K, is (A) 2.5 V (B) 1.5 V (C) 0.5 V (D) – 0.5 V
105.
When Co(II) chloride is dissolved in concentrated HCl a blue solution is obtained. Upon dilution with water, the color changes to pink because (A) CoCl64 – is converted to CoCl63 – (B) CoCl42 – is converted to Co(OH2)62 + 2+ 3+ (C) Co(OH2)6 is converted to Co(OH2)6 (D) CoCl42 – is converted to Co(OH2)63 +
106.
The rate constant for the reaction COCl2(g) CO(g) + Cl2(g) is given by ln [k/(min–1)] = – 11067/T K + 31.33. The temperature at which the rate of this reaction will be doubled from that at 25ºC is (A) 75ºC (B) 100ºC (C) 31ºC (D) 50ºC
107.
Some reactions and their equilibrium constants given below CuCl42– + Br – CuCl3Br2– + Cl – K1 CuCl3Br2– + Br – CuCl2Br22– + Cl – K2 2– – 2– – CuCl2Br2 + Br CuClBr3 + Cl K3 CuClBr32 – + Br – CuBr42– + Cl – K4 The equilibrium constant, K for the reaction CuCl42– + 3Br – CuClBr32– + 3 Cl–, is (B) K1K2K3K4 (C) K1 + K2 + K3 (A) K1K2K3
(D) 1/(K1K2K3)
CLASS-XII_STREAM-SB+2_PAGE # 44
OH Br2 in CS2
108.
NaOH
X
Me-I
Y
In the above sequence of reactions, the major products X and Y are
OH
OMe Br
(A) X =
OH Br
(C) X =
(B) X =
OMe
Y=
OH
Y= Br
(D) X = Br
109.
234
110.
In the following transformation
OH
Br
Y=
OH
OH
OH
Y= Br
OH
Th90 gets converted to 206Pb82 through a series of radioactive decay processes. The number of alpha and beta particles lost in this transformation respectively, are (A) 6 and 6 (B) 6 and 7 (C) 4 and 2 (D) 7 and 6
O O
OH
Me
CO2H
Reagent 1 Reagent 2 OMe
OMe
reagents 1 and 2 are : (A) H2SO4 ; alkaline KMnO4 (C) H3PO4 ; CHCl3/KOH
(B) AlCl3 ; l2 / NaOH (D) KOH;CHCl3 / KOH
BIOLOGY 111.
112.
The mode of action of penicillin is as follows : (A) It inhibits viral replication (C) It inhibits bacterial cell wall synthesis
(B) It enhances immunity (D) It inhibits transcription
Which of the following statements is true for meiosis ? (A) One round of chromosome duplication and one round of cell division (B) One round of chromosome duplication and two rounds of cell division (C) Two rounds of chromosome duplication and one round of cell division (D) Two rounds of chromosome duplication and two rounds of cell division
CLASS-XII_STREAM-SB+2_PAGE # 45
113.
Instead of 3, if 2 bases code for an amino acid, the degeneracy of codons coding for the same amino acid would have : (A) increased (B) decreased (C) remained the same (D) been uncertain
114.
Gregor Mendel showed that unit factors exist in pairs and exhibit as dominant-recessive relationship. These unit factors, in modern terminology, are called : (A) genes (B) alleles (C) Ioci (D) determinants
115.
E.coli has optimal growh temperature of 37ºC. Which of the following in an INCORRECT explanation for this ? (A) The membrane is most permeable at this temperature (B) DNA synthesis makes the least mistakes at this temperature (C) Most enzymes in the cell have the highest activity at this temperature (D) Protein synthesis is most efficient at this temperature
116.
Male offsprings of which of the following couples have the highest chance of haemophilia ? (A) Haemophiliac father and normal, non-carrier mother (B) Haemophiliac father and normal, carrier mother (C) Normal father and normal, carrier mother (D) Normal father and haemophiliac mother
117.
The effect of consumption of excess protein by normal individuals would result in : (A) excretion of excess protein in urine (B) increase in the amount of adipose tissue (C) increase in the synthesis of muscle protein (D) increase in the circulatory plasma proteins
118.
The condition varicose veins in swelling of veins, that occurs due to : (A) loss of elasticity of the muscular layer (B) condition of high blood pressure (C) condition of low blood pressure (D) condition of anoxia
119.
Greatest proportion of photosyntheis in the world is carried out by : (A) trees in the rain forests of the world (B) trees in the temperate forests of the world (C) algae in oceans (D) irrigated crop fields
120.
Energetically unfavourable reactions occur in human cells through : (A) heat energy supplied by the body (B) heat energy released through exercise (C) coupling of energetically favourable reactions with unfavourable ones (D) photosynthesis
CLASS-XII_STREAM-SB+2_PAGE # 46
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2007 Time : 3Hr.
1.
Max. Marks : 160
In Year 2007, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90),Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2008 Time : 3Hr.
1.
Max. Marks : 160
In Year 2008, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2009 Time : 3Hr.
1.
Max. Marks : 160
In Year 2009, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2010 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2011 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2012 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
YEAR-2010 (KVPY-STREAM-SB+2) PART-I (1 Mark) MATHEMATICS
1.
0 i 1 0 , where i2 = –1, and let I denote the identity matrix . Then Let denote the matrix i 0 0 1
I + A + A2 + .............+ A2010 is 0 0 (A) 0 0
2.
0 i (B) i 0
1 i (C) i 1
– 1 0 (D) 0 – 1
Suppose the sides of a triangle from a geometric progression with common ratio r. Then r lies in the interval
– 1 5 (A) 0, 2
1 5 2 5 (B) 2 , 2
– 1 5 1 5 , (C) 2 2
2 5 (D) 2 ,
3.
The number of rectangles that can be obtained by joining four of the twelve vertices of a 12-sided regular polygon is (A) 66 (B) 30 (C) 24 (D) 15
4.
Let 1, and 2 be the cube roots of unity. The least possible degree of a polynomial, with real coefficients, having 22, 3 + 4, 3 + 42 and 5 – –2 as roots is (A) 4 (B) 5 (C) 6 (D) 8
5.
A circle touches the parabola y2 = 4x at (1, 2) and also touches its directrix. the y-coordinate of the point of contact of the circle and the directrix is (A) 2
6.
(B) 2
(C) 2 2
(D) 4
Let ABC be an equilateral triangle; let KLMN be a rectangle with K, L on BC, M on AC and N on AB. Suppose AN / NB = 2 and the area of triangle BKN is 6. The area of the triangle ABC is
7.
(A) 54
(B) 108
(C) 48
(D) not determinable with the above data
Let P be an arbitrary point on the ellipse
x2 a2
y2 b2
1 , a > b > = 0. Suppose F and F are the foci of the 1 2
ellipse. The locus of the centroid of the triangle PF1F2 as P moves on the ellipse is (A) a circle 8.
(B) an ellipse
(C) a parabola
(D) a hyperbola
The number of roots of the equation cos7 – sin6 = 1 that lie in the interval [0, 2] is (A) 2
(B) 3
(C) 4
(D) 8
CLASS-XII_STREAM-SB+2_PAGE # 47
9.
The product (1 + tan 1º) (1 + tan 2º) (1 + tan 3º) ... (1 + tan 45º) equals (A) 221
10.
(B) 222
(C) 223
(D) 224
Let f : R R be a differentiable function such that f (a) = 0 = f (b) and f’(a) f’(b) > 0 for some a < b. Then the minimum number of roots of f’(x) = 0 in the interval (a, b) is (A) 3
11.
(B) 2
(C) 1
(D) 0
The roots of (x – 41)49 + (x – 49)41 + (x – 2009)2009 = 0 are (A) all necessarily real (B) non-real except one positive real root (C) non-real except three positive real roots (D) non-real except for three real roots of which exactly one is positive
12.
The figure shown below is the graph of the derivative of some function y = ƒ (x)
Then (A) f has local minima at x = a, b and a local maximum at x = c (B) f has local minima at x = b, c and a local maximum at x = a (C) f has local minima at x = c, a and a local maximum at x = b (D) the given figure is insufficient to conclude any thing about the local minima and local maxima of f
CLASS-XII_STREAM-SB+2_PAGE # 48
13.
The following figure shows the graph of continuous function y = ƒ (x) on the interval [1, 3]. The points A, B, C have coordinates (1, 1), (3, 2), (2, 3) respectively, and the lines 1 and 2 are parallel, with 1 being tangent to the curve at C. If the area under the graph of y = ƒ (x) from x = 1 to x = 3 is 4 square units, then the area of the shaded region is :
(A) 2
(B) 3
(C) 4
(D) 5
e
14.
n Let n (log x ) dx, where n is a non-negative integer..
1
Then I2011 + 2011 I2010 is equal to
15.
(A) 1000 + 999 998
(B) 889 + 890 891
(C) 100 + 100 99
(D) 53 + 54 52
Consider the regions A = {(x, y) | x2 + y2 100} and B = {(x, y) | sin (x + y) > 0} in the plane. Then the area of the region A B is (A) 10
16.
(B) 100
(C) 100
(D) 50
Three vertices are chosen randomly from the seven vertices of a regular 7–sided polygon. The probability that they form the vertices of an isosceles triangle is (A)
17.
(B)
1 3
(C)
3 7
(D)
3 5
Let u = 2ˆi – ˆj + kˆ , v = – 3 ˆj + 2 kˆ be vectors in R3 and w be a unit vector in the xy-plane. Then the maximum possible value of |( u × v ) . w | is (A)
18.
1 7
5
(B)
12
(C) 13
(D) 17
How many six-digit numbers are there in which no digit is repeated, even digits appear at even places, odd digits appear at odd places and the number is divisible by 4? (A) 3600
(B) 2700
(C) 2160
(D) 1440
CLASS-XII_STREAM-SB+2_PAGE # 49
19.
The number of natural number n in the interval [1005, 2010] for which the polynomial 1 + x + x2 + x3 +.......+ xn–1 divides the polynomial 1 + x2 + x4 + x6 + .........+ x2010 is (A) 0
20.
(B) 100
(C) 503
(D) 1006
Let a0 = 0 and an = 3 an–1 + 1 for n 1. Then the remainder obtained on dividing a2010 by 11 is (A) 0
(B) 7
(C) 3
(D) 4
PHYSICS 21.
A pen of mass m is lying on a piece of paper of mass M placed on a rough table. If the coefficients of friction between the pen and paper, and, the paper and the table are 1 and 2 respectively, then the minimum horizontal force with which the paper has to be pulled for the pen to start slipping is given by :
22.
(A) (m + M) (1 + 2)g
(B) (m 1 + M 2)g
(C) (m 1 + (m + M)2)g
(D) m(1 + 2)g
Two masses m1 and m2 connected by a spring of spring constant k at rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is :
1 m1m 2 (A) T = 2 k m m 2 1
23.
m1 m 2 (B) T = 2 k m m 1 2
(C) T = 2 m1 (D) T = 2 m 2 k k
A bead of mass m is attached to the mid–point of a taut, weightless string of length and placed on a frictionless horizontal table.
Under a small transverse displacement x, as shown, if the tension in the string is T, then the frequency of oscillation is :
(A)
24.
1 2T 2 m
(B)
1 4T 2 m
(C)
1 4T 2 m
(D)
1 2T 2 m
A comet (assumed to be in an elliptical orbit around the sun) is at a distance of 0.4 AU from the sun at the perihelion. If the time period of the comet is 125 years, what is the aphelion distance ? AU : Astronomical Unit. (A) 50 AU
(B) 25 AU
(C) 49.6 AU
(D) 24.6 AU
CLASS-XII_STREAM-SB+2_PAGE # 50
25.
The circuit shown consists of a switch (S), a battery (B) of emf E, a resistance R, and an inductor L.
The current in the circuit at the instant the switch is closed is : (A) E/R 26.
(B) E/(R(1 – e))
(C)
(D) 0
Consider a uniform spherical volume charge distribution of radius R. Which of the following graphs correctly represents the magnitude of the electric field E at a distance r from the center of the sphere ?
(A)
27.
(B)
(C)
(D)
A charge +q is placed somewhere inside the cavity of a thick conducting spherical shell of inner radius R1 and outer radius R2. A charge +Q is placed at a distance r > R2 from the center of the shell. Then the electric field in the hollow cavity.
28.
(A) depends on both +q and +Q
(B) is zero
(C) is only that due to +Q
(D) is only that due to +q
The following travelling electromagnetic wave Ex = 0, Ey = E0sin(kx + t), Ez = –2E0sin(kx + t) is :
29.
(A) elliptically polarized
(B) linearly polarized
(C) circularly polarized
(D) unpolarized
A point source of light is placed at the bottom of a vessel which is filled with water of refractive index to a height h. If a floating opaque disc has to be placed exactly above it so that the source is invisible from above, the radius of the disc should be : h
h (A) 30.
1
(B)
2
1
h
h (C)
(D)
2
1
2 1
Three transparent media of refractive indices 1,2, 3, respectively, are stacked as shown. A ray of light follows the path shown. No light enters the third medium.
Then : (A) 1 < 2 < 3
(B) 2 < 1 < 3
(C) 1 < 3 < 2
(D) 3 < 1 < 2
CLASS-XII_STREAM-SB+2_PAGE # 51
31.
A nucleus has a half–life of 30 minutes. At 3PM its decay rate was measured as 120,000 counts/sec. What will be the decay rate at 5 PM ?
32.
(A) 120,000 counts/sec.
(B) 60,000 counts/sec.
(C) 30,000 counts/sec.
(D) 7,500 counts/sec.
A block is resting on a shelf that is undergoing vertical simple harmonic oscillations with an amplitude of 2.5 cm. What is the minimum frequency of oscillation of the shelf for which the book will lose contact with the shelf ? (Assume that g = 10 m/s2) (A) 20 Hz
33.
(C) 125.6 Hz
(D) 10 Hz
n2a P A vander Waal's gas obeys the equation of state (V – nb) = nRT. Its internal energy is given by V 2
U = CT –
34.
(B) 3.18 Hz
n2a . The equation of a quasistatic adiabat for this gas is given by : V
(A) TC/nRV = constant
(B) T(C+nR)/nRV = constant
(C) TC/nR (V – nb) = constant
(D) P(C+nR)/nR (V – nb) = constant
An ideal gas is made to undergo a cycle depicted by the PV diagram alongside. The curved line from A to B is an adiabat.
Then : (A) The efficiency of this cycle is given by unity as no heat is released during the cycle (B) Heat is absorbed in the upper part of the straight line path and released in the lower part (C) If T1 and T2 are the maximum and minimum temperatures reached during the cycle, then the efficiency
T2 is given by 1 – T 1 (D) The cycle can only be carried out in the reverse of the direction shown in the figure
35.
A bus driving along at 39.6 kmph is approaching a person who is standing at the bus stop, while honking repeatedly at an interval of 30 seconds. If the speed of sound is 330 ms–1, at what interval will the person hear the horn. (A) 31 sec.
(B) 29 sec.
(C) 30 sec.
(D) The interval will depend on the distance of the bus from the passenger
CLASS-XII_STREAM-SB+2_PAGE # 52
36.
Velocity of sound measured at a given temperature in oxygen and hydrogen is in the ratio : (A) 1 : 4
37.
(B) 4 : 1
(C) 1 : 1
(D) 32 : 1
In Young's double slit experiment, the distance between the two slits is 0.1 mm, the distance between the slits and the screen is 1m and the wavelength of the light used is 600 nm. The intensity at a point on the screen is 75% of the maximum intensity. What is the smallest distance of this point from the central fringe? (A) 1.0 mm
38.
(B) 2.0 mm
(C) 0.5 mm
(D) 1.5 mm
Two masses m1 and m2 are connected by a massless spring of spring constant k and unstretched length . The masses are placed on a frictionless straight channel – which we consider our x-axis. They are initially at rest at x = 0 and x = , respectively. At t = 0, a velocity of v0 is suddenly imparted to the first particle. At a later time t, the center of mass of the two masses is at :
39.
m2 (A) x = m m 1 2
m2 v 0 t m1 (B) x = m m m m 1 2 1 2
m2 v 0 t m2 (C) x = m m m m 1 2 1 2
m1v 0 t m2 (D) x = m m m m 1 2 1 2
A charged particle of charge q and mass m, gets deflected through an angle upon passing through a square region of side a which contains a uniform magnetic field B normal to its plane. Assuming that the particle entered the square at right angles to one side, what is the speed of the particle ? (A)
40.
qB a cot m
(B)
qB a tan m
(C)
qB a cot 2 m
(D)
qB a tan 2 m
A piece of hot copper at 100ºC is plunged into a pond at 30ºC. The copper cools down to 30ºC, while the pond, being huge, stays at its initial temperature. Then : (A) copper loses some entropy, the pond stays at the same entropy (B) copper loses some entropy, and the pond gains exactly the same amount of entropy (C) copper loses entropy, and the pond gains more than this amount of entropy (D) both copper and the pond gain in entropy
CHEMISTRY 41.
The number of isomers of Co(diethylene triamine) Cl3 is. (A) 2
42.
(C) 4
(D) 5
(B) NH3
(C) CN–
(D) I–
(B) 3
(C) 1.5
(D) 1
Among the following, the -acid ligand is : (A) F–
43.
(B) 3
The bond order in O22– is (A) 2
CLASS-XII_STREAM-SB+2_PAGE # 53
44.
The energy of a photon of wavelength = 1 meter is (Planck's constant = 6.626 10–34 J.s, speed of light = 3 108 ms–1) (A) 1.988 10–25 J
45.
(B) 1.988 10–30 J
(C) 1.988 10–28 J
(D) 1.988 10–31 J
The concentration of a substance undergoing a chemical reaction becomes one half of its original value after time t, regardless of the initial concentration. The reaction is an example of a :
46.
(A) zero order reaction
(B) second order reaction
(C) first order reaction
(D) third order reaction
The shape of the molecule CIF3 is : (A) trigonal planar
47.
48.
49.
(C) pyramidal
(D) Y-shaped
Friedal–Crafts acylation is : (A) -acylation of a carbonyl compound
(B) acylation of phenols to generate esters
(C) acylation of aliphatic olefins
(D) acylation of aromatic nucleus
The order of acidity of compounds I–IV, is
I
II
III
IV
(A) I < III < II < IV
(B) III < I < II < IV
(C) IV < I < II < III
(D) II < IV < III < I
(C)
(D)
(C) 11H
(D) 12 H
The most stable conformation for n-butane is
(A)
50.
(B) T-shaped
(B)
In the nuclear reaction 234 90 Th
234 91 Pa + X
X is : (A)
51.
0 1e
(B) 10 e
A concentrated solution of copper sulphate, which is dark blue in colour, is mixed at room temperature with a dilute solution of copper sulphate, which is light blue. For this process (A) Entropy change is positive, but enthalpy change is negative. (B) Entropy and enthalpy changes are both positive. (C) Entropy change is positive and enthalpy does not change. (D) Entropy change is negative and enthalpy change is positive.
CLASS-XII_STREAM-SB+2_PAGE # 54
52.
53.
Increasing the temperature increacses the rate of reaction but does not increase the : (A) number of collisions
(B) activation energy
(C) average energy of collisions
(D) average velocity of the reactant molecules
In metallic solids, the number of atoms for the face centred and the body-centered cubic unit cells, are, respectively. (A) 2,4
54.
(B) 2,2
(C) 4,2
From equation 1 and 2 CO2
CO +
H2 O
H2 +
1 O 2 2 1 O 2 2
[ K c = 9.1 10–12 at 1000°C]
(eq 1)
[ Kc
(eq 2)
1
2
find out Kc for the following equation CO2 + H2 (A) 0.78 55.
(B) 2.0
CO + H2O (C) 16.2
(D) 1.28
(B) [R0] (e–kt)
(C) [R0e]–kt
(D) [R0] (–ekt)
(C)
(D)
The correct structure of PCl3F2 is
(A)
57.
= 7.1 10–12 at 1000°C]
For a first order reaction R P, the rate constant is k. If the initial concentration of R is [R0], the concentration of R at any time 't' is given by the expression. (A) [R0] ekt
56.
(D) 4,4
(B)
The enantiomeric pair among the following four structures is
I
II
III
IV
(A) I & II
(B) I & IV
(C) II & III
(D) II & IV
CLASS-XII_STREAM-SB+2_PAGE # 55
58.
59.
Consider the reaction : 2NO2 (g) 2NO (g) + O2(g). In the figure below, identify the curves X,Y and Z associated with the three species in the reaction
(A) X = NO, Y = O2, Z = NO2
(B) X = O2, Y = NO, Z = NO2
(C) X = NO2, Y = NO , Z = O2
(D) X = O2, Y= NO2, Z = NO
The aromatic carbocation among the following is
(A)
60.
(B)
(C)
(D)
Cyclohexene is reacted with bromine in CCl4 in the dark. The product of the reaction is
(A)
(B)
(C)
(D)
CLASS-XII_STREAM-SB+2_PAGE # 56
BIOLOGY 61.
Ribouncleic Acid (RNA) that catalyze enzymatic reactions are called ribozymes. Which one of the following acts as a ribozyme? (A) Ribosome
62.
(B) Amylase
(C) tRNA
(D) Riboflavin
In 1670, Robert Boyle conducted an experiment wherein he placed a viper (a poisonous snake) in a chamber and rapidly reduced the pressure in that chamber. Which of the following would be true? (A) Gas bubble developed in the tissues of the snake (B) The basal metabolic rate of the snake increased tremendously (C) The venom of the snake was found to decrease in potency (D) The venom of the snake was found to increase in potency
63.
Bacteria can survive by absorbing soluble nutrients via their outer body surface, but animals cannot, because (A) Bacteria cannot ingest particles but animals can (B) Bacteria have cell walls and animals do not (C) Animals have too small a surface area per unit volume as compared to bacteria (D) Animals cannot metabolize soluble nutrients
64.
A horse has 64 chromosomes and a donkey has 62. Mules result from crossing a horse and donkey. State which of the following is INCORRECT? (A) Mules can have either 64, 63 or 62 chromosomes (B) Mules are infertile (C) Mules have well defined gender (male/female) (D) Mules have 63 chromosomes
65.
If the total number of photons falling per unit area of a leaf per minute is kept constant, then which of the following will result in maximum photosynthesis?
66.
67.
(A) Shining green light
(B) Shining sunlight
(C) Shining blue light
(D) Shining ultraviolet light
Path-finding by ants is by means of (A) Visually observing landmarks
(B) Visually observing other ants
(C) Chemical signals between ants
(D) Using the earth's magnetic field
Sometimes urea is fed to ruminates to improve their health. It works by (A) Helping growth of gut microbes that break down cellulose (B) Killing harmful microorganisms in their gut (C) Increasing salt content in the gut (D) Directly stimulating blood cell proliferation
CLASS-XII_STREAM-SB+2_PAGE # 57
68.
If you compare adults of two herbivore species of different sizes, but from the same geographical area, the amount of faeces produced per kg body weight would be (A) More in the smaller one than the larger one (B) More in the larger one than the smaller one (C) Roughly the same amount in both (D) Not possible to predict which would be more
69.
Fruit wrapped in paper ripens faster than when kept in open air because (A) Heat of respiration is retained better (B) A chemical in the paper helps fruit ripening (C) A volatile substance produced by the fruit is retained better and helps in ripening (D) The fruit is cut off from the ambient oxygen which is an inhibitor to fruit ripening.
70.
When a person is suffering form high fever, it is sometimes observed that the skin has a reddish tinge. Why does this happen? (A) Red colour of the skin radiates more heat (B) fever causes the release of a red pigment in the skin (C) There is more blood circulation to the skin to keep the body warm (D) There is more blood circulation to the skin to release heat from the body
71.
Bacteriochlorophylls are photosynthetic pigments found in phototrophic bacteria. Their function is distinct from the plant chlorophylls in that they (A) do not produce oxygen (B) do not conduct photosynthesis (C) absorb only blue light (D) function without a light source
72.
Athletes often experience muscle cramps. Which of the following statements is true about muscle cramps? (A) Muscle cramp is caused due to conversion of pyruvic acid into lactic acid in the cytoplasm (B) Muscle cramp is caused due to conversion of pyruvic acid into lactic acid in the mitochondria (C) Muscle cramp is caused due to nonconversion of glucose to pyruvate in the cytoplasm (D) Muscle cramp is caused due to conversion of pyruvic acid into ethanol in the cytoplasm
73.
A couple went to a doctor and reported that both of them are "carriers" for a particular disorder, their first child is suffering from that disorder and that they are expecting their second child. What is the probability that the new child would be affected by the same disorder? (A) 100% (B) 50% (C) 25% (D) 75%
74.
Of the following combinations of cell biological processes which one is associated with embryogenesis? (A) Mitosis and Meiosis (B) Mitosis and Differentiation (C) Meiosis and Differentiation (D) Differentiation and Reprogramming
75.
Conversion of the Bt toxin produced by Bacillus thuringienesis to its active form in the gut of the insects is mediated by (A) acidic pH of the gut (B) alkaline pH of the gut (C) lipid modification of the protein (D) cleavage by chymotrypsin
CLASS-XII_STREAM-SB+2_PAGE # 58
76.
If you dip a sack full of paddy seeds in water overnight and then keep it out for a couple of days, it feels warm. What generates this heat? (A) Imbibation (B) Exothermic reaction between water and seed coats (C) Friction among seeds due to swelling (D) Respiration
77.
Restriction endonucleases are enzymes that cleave DNA molecules into smaller fragments. Which type of bond do they act on? (A) N-glycosidic Bond (B) Phosphodiester bond (C) Hydrogen bond (D) Disulfide bond
78.
The fluid part of blood flows in and out of capillaries in tissues to exchange nutrients and waste materials. Under which of the following conditions will fluid flow out from the capillaries into the surrounding tissue? (A) When arterial blood pressure exceeds blood osmotic pressure (B) When arterial blood pressure is less than blood osmotic pressure (C) When arterial blood pressure is equal to blood osmotic pressure (D) Arterial blood pressure and blood osmotic pressure have nothing to do with the outflow of fluid from capillaries
79.
The distance between two consecutive DNA base pairs is 0.34 nm. If the length of a chromosome is 1 mm the number of base pairs in the chromosome is approximately (A) 3 million (B) 1.5 million (C) 30 million (D) 6 million
80.
Estimate the order of the speed of propagation of an action potential or nerve impulse (A) nm/s (B) micron/s (C) cm/s (D) m/s
PART-II (2 Mark) MATHEMATICS n
81.
1 1/ 2 Arrange the expansion of x 1/ 4 in decreasing powers of x. Suppose the coefficients of the first 2x three terms form an arithmetic progression. Then the number of terms in the expansion having integer powers of x is (A) 1
82.
(B) 2
(C) 3
(D) more than 3
Let r be a real number and n N be such that the polynomial 2x2 + 2x +1 divides the polynomial (x + 1)n– r. Then (n, r) can be (A) (4000, 41000)
1 (B) 4000, 1000 4
1000 1 , 1000 (C) 4 4
1 (D) 4000, 4000
CLASS-XII_STREAM-SB+2_PAGE # 59
83.
Suppose a, b are real numbers such that ab 0. Which of the following four figures represents the curve (y – ax – b) (bx2 + ay2 – ab) = 0 ?
(A) Fig.1 84.
(B) Fig.2
(C) Fig.3
(D) Fig.4
Among all cyclic quadrilaterals inscribed in a circle of radius R with one of its angles equal to 120º, consider the one with maximum possible area. Its area is (A)
85.
2 R2
(B) 2 R2
(C)
3 R2
(D) 2 3 R 2
The following figure shows the graph of a differentiable function y = ƒ (x) on the interval [a, b] (not containing 0).
Let g(x) = ƒ (x) / x. Which of the following is a possible graph of y = g (x)?
(A) Fig.1
(B) Fig.2
(C) Fig.3
(D) Fig.4
CLASS-XII_STREAM-SB+2_PAGE # 60
86.
Let V1 be the volume of a given right circular cone with O as the centre of the base and A as its apex. Let V2 be the maximum volume of the right circular cone inscribed in the given cone whose apex is O and whose base is parallel to the base of the given cone. Then the ratio V2 / V1 is (A)
3 25
(B)
4 9
(C)
4 27
(D)
8 27
x
87.
Let ƒ : R R be a continuous function satisfying ƒ( x ) x ƒ( t ) dt , for all x R. Then the number of
0
elements in the set S = {x R ƒ (x) = 0 } is (A) 1
(B) 2
(C) 3
(D) 4
2
88.
The value of
min| x – |, cos
–1
(cos x ) dx is
0
(A)
89.
2 4
(B)
2 2
(C)
2 8
(D) 2
Let ABC be a triangle and P be a point inside ABC such that PA 2PB 3PC 0 . The ratio of the area of triangle ABC to that of APC is (A) 2
90.
(B)
3 2
(C)
5 3
(D) 3
Suppose m, n are positive integers such that 6m + 2m+n 3m + 2n = 332. The value of the expression m2 + mn + n2 is (A) 7
(B) 13
(C) 19
(D) 21
PHYSICS 91.
A ball is dropped vertically from a height of h onto a hard surface. If the ball rebounds from the surface with a fraction r of the speed with which it strikes the latter on each impact, what is the net distance travelled by the ball up to the 10th impact ? (A) 2h
92.
1 r 10 1 r
(B) h
1 r 20 1 r 2
(C) 2h
1 r 22 1 r 2
h
(D) 2h
1 r 20 1 r 2
h
A certain planet completes one rotation about its axis in time T. The weight of an object placed at the equator on the planet's surface is a fraction f (f is close to unity) of its weight recorded at a latitude of 60º. The density of the planet (assumed to be a uniform perfect sphere) is given by : (A)
4 f 3 1 f 4GT 2
(B)
4 f 3 1 f 4GT 2
(C)
4 3f 3 1 f 4GT 2
(D)
4 2f 3 1 f 4GT 2
CLASS-XII_STREAM-SB+2_PAGE # 61
93.
Three equal charges +q are placed at the three vertices of an equilateral triangle centred at the origin. They are held in equilibrium by a restoring force of magnitude F(r) = kr directed towards the origin, where k is a constant. What is the distance of the three charges from the origin ? 1 q2 (A) 6 0 k
94.
1/ 3
3 q2 (B) 12 0 k
1/ 3
1 q2 (C) 6 0 k
2/3
3 q2 (D) 4 0 k
2/3
Consider the infinite ladder circuit shown below :
For which angular frequency will the circuit behave like a pure inductance ?
LC (A) 95.
2
R(2 ) 2( 1)
LC
C
(B)
R(2 ) 2( 1)
(C)
R(2 ) 2( 1)
(D)
R(2 ) 2( 1)
x 1 2 kx – V0cos , a 2 where V0,k, a are constants. If the amplitude of oscillation is much smaller than a, the time period is given by
ma 2 ka 2 V0
(B) 2
m k
(C) 2
ma 2 V0
(D) 2
ma 2 ka 2 V0
An ideal gas with heat capacity at constant volume CV undergoes a quasistatic process described by PV in a P–V diagram, where is a constant. The heat capacity of the gas during this process is given by : (A) CV
98.
LC
2L (D)
A particle of mass m undergoes oscillations about x = 0 in a potential given by V(x) =
(A) 2 97.
1 (C)
A narrow parallel beam of light falls on a glass sphere of radius R and refractive index at normal incidence. The distance of the image from the outer edge is given by : (A)
96.
2 (B)
(B) CV +
nR 1
(C) CV + nR
(D) CV +
nR 1 2
3 nR is made to carry out 2 a cycle that is depicted by a triangle in the figure given below : The following statement is true about the cycle : An ideal gas with constant heat capacity CV =
P1V1 (A) The efficiency is given by 1 P V 2
2
1 P1V1 (B) The efficiency is given by 1 2 P V 2
2
(C) Net heat absorbed in the cycle is (P2 – P1) (V2 – V1) (D) Heat absorbed in part AC is given by 2(P2V2 – P1V1) +
1 (P V – P2V1) 2 1 2
CLASS-XII_STREAM-SB+2_PAGE # 62
99.
Two identical particles of mass m and charge q are shot at each other from a very great distance with an initial speed v. The distance of closest approach of these charges is :
q2 (A)
100.
q2 (B)
8 0mv 2
q2
4 0mv 2
(C)
2 0mv 2
(D) 0
At time t = 0, a container has N0 radioactive atoms with a decay constant . In addition, c numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at t = T ? (A)
c exp(–T) – N0exp(–T)
(B)
c exp(–T) + N0exp(–T)
(C)
c (1 – exp(–T)) + N0exp(–T)
(D)
c (1 + exp(–T) + N0exp(–T)
CHEMISTRY 101.
2.52 g of oxalic acid dihydrate was dissolved in 100 mL of water. 10 mL of this solution was diluted is 500 mL. The normality of the final solution and the amount of oxalic acid (mg/mL) in the solution are respectively. (A) 0.16 N, 5.04
102.
(B) 0.08 N, 3.60
(C) 0.04 N, 3.60
(D) 0.02 N, 10.08
Two isomeric compounds I and II are heated with HBr.
I
II
The products obtained are
(A)
(B)
(C)
(D)
CLASS-XII_STREAM-SB+2_PAGE # 63
103.
The number of possible enantiomeric pair(s) produced from the bromination of I and II, respectively, are
(A) 0, 1
104.
105.
(B) 1 , 0
(C) 0, 2
(D) 1, 1
For the reaction A B, H° = 7.5 kJ mol–1 and S° = 25 J mol–1, the value of G° and the temperature, at which the reaction reaches equilibrium are, respectively, (A) 0 kJ mol–1 and 400 K
(B) – 2.5 kJ mol–1 and 400 K
(C) 2.5 kJ mol–1 and 200 K
(D) 0 kJ mol–1 and 300 K
The solubility product of Mg(OH)2 is 1.0 10–12. Concentrated aqueous NaOH solution is added to a 0.01 M aqueous solution of MgCl2. The pH at which precipitation occurs is (A) 7.2
106.
(B) 7.8
(C) 8.0
(D) 9.0
A metal with an atomic radius of 141.4 pm crystallizes in the face centred cubic structure. The volume of the unit cell in pm3 is (A) 2.74 107
107.
(C) 2.19 107
(D) 9.20 107
Identify the cyclic silicate ion given in the figure below
(A) [Si6O24]24– 108.
(B) 6.40 107
(B) [Si6O18]18–
(C) [Si6O18]12–
Diborane is formed the elements as shown in equation (1) 2B (s) + 3H2(g) B2H6(g) Given that H2O () H2O (g) 2B + 3/2 O2 (g) B2O3(s) B2H6(g) + 3 O2 (g) B2O3 (s) + 3 H2O (g) H2(g) + 1/2 O2 (g) H2O () the H0 for the reaction (1) is : (A) 36 kJ (B) 520 kJ (C) 509 kJ
(D) [Si6O24]12–
... (1) H10 = 44 kJ H20 = – 1273 kJ H30 = – 2035 kJ H40 = 286 kJ (D) – 3550 kJ
CLASS-XII_STREAM-SB+2_PAGE # 64
109.
The Crystal Field stabilization Energy (CFSE) and the spin only magnetic moment in Bohr Magneton (BM) for the complex K3[Fe(CN)6] are, respectively. (A) 0.0 and
35 BM
(C) – 0.4 and
110.
(B) – 2.0 and
24 BM
3 BM
(D) – 2.4 and 0 BM
A solution containing 8.0 g of nicotine in 92 g of water freezes 0.925 degrees below the normal freezing point of water. If the molal freezing point depression constant, Kf = 1.85ºC mol–1 then the molar mass of nicotine is : (A) 16
(B) 80
(C) 320
(D) 160
BIOLOGY 111.
A host cell has intracellular bacterial symbionts. If the growth rate of the bacterial symbiont is always 10% higher than that of the host cell, after 10 generations of the host cell the density of bacteria in host cells will increase (A) by 10%
112.
(B) two-fold
(C) ten-fold
(D) hundred-fold
In a diploid organism, there are three different alleles for a particular gene. Of these three alleles one is recessive and the other two alleles exhibit co-dominance. How many phenotypes are possible with this set of alleles? (A) 3
113.
(B) 6
(C) 4
(D) 2
Two students are given two different double stranded DNA molecules of equal length. They are asked to denature the DNA molecules by heating. The DNA given to student A has a following composition of base (A:G:T:C::35:15:35:15). While that given to student B is (A : G : T : C : : 12 : 38 : 12 : 38) Which of the following statements is true? (A) Both the DNA molecules would denature at the same rate (B) The information given is insufficient to draw any conclusion (C) DNA molecule given to student B would denature faster than that of student A (D) DNA molecule given to student A would denature faster than that given to student B
CLASS-XII_STREAM-SB+2_PAGE # 65
114.
The amino acid sequences of a bacterial protein and a human protein carrying out similar function are found to be 60% identical. However, the DNA sequences of the genes coding for these proteins are only 45% identical. This is possible because (A) Protein sequence does not depend on DNA sequence (B) DNA codons having different nucleotides in the third position can code for the same amino acids (C) DNA codons having different nucleotides in the second position can code for the same amino acids (D) Same DNA codons can code for multiple amino acids.
115.
The following DNA sequence (5´ 3´) specifies part of a protein coding sequence, starting from position 1. Which of the following mutations will give rise to a protein that is shorter than the full-length protein?
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
T
G
C
A
A
G
A
T
A
T
A
G
C
T
(A) Deletion of nucleotide 13 (B) Deletion of nucleotide 8 (C) Insertion of a single nucleotide between 3 and 4 (D) Insertion of a single nucleotide between 10 and 11
116.
Which of the following correctly represents the results of an enzymatic reaction? Enzyme is E, Substrate is S and Products are P1 and P2
117.
(A) P1 + S P2 + E
(B) E + S P1 + P2
(C) P1 + P2 + E S
(D) E + S P1 + P2 + E
Four species of birds have different egg colors: [1] while with no markings, [2] pale brown with no markings, [3] grey-brown with dark streaks and spots, [4] pale blue with dark blue-green spots. Based on egg color, which species is most likely to nest in a deep tree hole? (A) 1
118.
(B) 2
(C) 3
(D) 4
Consider a locus with two alleles, A and a, If the frequency of AA is 0.25, what is the frequency of A under Hardy-Weinberg equilibrium? (A) 1
(B) 0.25
(C) 0.5
(D) 0
CLASS-XII_STREAM-SB+2_PAGE # 66
119.
Which of the following graphs accurately represents the insulin levels (Y-axis) in the body as a function of time (X-axis) after eating sugar and bread/roti?
120.
(A)
(B)
(C)
(D)
You marked two ink-spots along the height at the base of a coconut tree and also at the top of the tree. When you examine the spots next year when the tree has grown taller, you will see (A) the two spots at the top have grown more apart than the two spots at the bottom (B) the top two spots have grown less apart than the bottom two spots (C) both sets of spots have grown apart to the same extent (D) both sets of spots remain un-altered.
*****
CLASS-XII_STREAM-SB+2_PAGE # 67
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2007 Time : 3Hr.
1.
Max. Marks : 160
In Year 2007, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90),Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2008 Time : 3Hr.
1.
Max. Marks : 160
In Year 2008, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2009 Time : 3Hr.
1.
Max. Marks : 160
In Year 2009, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2010 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2011 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2012 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
YEAR-2011 (KVPY-STREAM-SB+2) PART-I (1 Mark) MATHEMATICS 1.
Suppose logab + logb a= c. The smallest possible integer value of c for all a,b > 1 is (A) 4 (B) 3 (C) 2 (D) 1
2.
Suppose n is a natural number such that | i + 2i2 + 3i3 + ....+ nin | = 18 1–1 . Then n is. (A) 9 (B) 18 (C) 36
3.
2 . Where i is the square root of
Let P be an m × m matrix such that P2 = P . Then (I+P)n equals (A) I + P (B) I + nP (C) I + 2nP
(D) 72
(D) I + (2n–1)P
4.
Consider the cubic equation x3 + ax2 + bx + c = 0 , where a,b,c are real numbers . Which of the following statements is correct ? (A) If a2 – 2b < 0 , then the equation has one real and two imaginary roots (B) If a2– 2b 0, then the equation has all real roots (C) If a2– 2b > 0, then the equation has all real and distinct roots (D) If 4a3– 27b2 > 0 , then the equation has real and distinct roots
5.
All the points (x,y) in the plane satisfying the equation x2 + 2x sin(xy) + 1 = 0 lie on (A) a pair of straight lines (B) a family of hyperbolas (C) a parabola (D) an ellipse
6.
Let A = (4,0) , B = (0,12) be two points in the plane . The locus of a point C such that the area of triangle ABC is 18 sq.units is (A) (y + 3x + 12)3 = 81 (B) (y + 3x + 81)2 = 12 2 (C) (y + 3x – 12) = 81 (D) (y + 3x – 81)2 = 12
7.
In a rectangle ABCD , the coordinates of A and B are (1,2) and (3,6) respectively and some diameter of the circumscribing circle of ABCD has equation 2x – y + 4 = 0. Then the area of the rectangle is (A) 16
(B) 2 10
(C) 2 5
(D) 20
8.
In the xy–plane , three distinct lines 1,2,3 concur at a point (,0). Further the lines 1,2,3 are normals to the parabola y2 = 6x at the points A = (x1 , y1) , B (x2 , y2) , C = (x3 , y3) respectively . Then we have (A) < – 5 (B) > 3 (C) – 5 < < – 3 (D) 0 < < 3
9.
Let f(x) = cos5x + A cos 4x + Bcos3x + Ccos2x + Dcosx + E. and 2 3 8 9 – f + ..............+ f – f Then T T = f(0) – f + f 5 5 5 5 5 (A) depends on A,B,C,D,E (B) depends on A,C,E, but independent of B and D (C) depends on B,D , but independent of A,C,E (D) is independent of A,B,C,D,E
10.
In triangle ABC , we are given that 3sinA + 4 cosB = 6 and 4sinB + 3cosA = 1. Then the measured of the angle C is (A) 30º (B) 150º (C) 60º (D) 75º
11.
Which of the following intervals is possible domain of the function f(x) = log{x} [x] + log[x] {x} , where [x] is the greatest integer not exceeding x and {x} = x – [x] ? (A) (0,1) (B) (1,2) (C) (2,3) (D) (3,5) CLASS-XII_STREAM-SB+2_PAGE # 68
12.
If f(x) = (2011 + x)n , where x is a real variable and n is a positive integer , then the value of f(0) + f(0) +
f " (0 ) f (n –1)(0) + ......+ is 2! (n – 1)! (A) (2011)n 13.
(B) (2012)n
(C) (2012)n – 1
(D) n(2011)n
The minimum distance between a point on the curve y = ex and a point on the curve y = loge x is
1 (A)
(B)
2
(C)
2
(D) 2 2
3
8
14.
Let f : (2,) N be defined by f(x) = the largest prime factor of [x] , Then
f ( x) dx is equal to 2
(A) 17 15.
(B) 22
(C) 23
(D) 25
Let [x] denote the largest integer not exceeding x and {x} = x – [x]. Then
2012
e cos( { x })
e cos( { x }) e – cos( { x })
0
is equal to (A) 0
16.
1 The value of lim 2 n 4 n – 1 (A)
17.
1 4
(B)
(C) 2012
1 4n 2 – 4
.......... ..
12
(C)
(D) 2012
is 2 2 4n – n 1
4
(D)
6
Two players play the following game : A writes 3,5,6 on three different cards ; B writes 8 ,9,10 on three different cards . Both draw randomly two cards from their collections . Then A computes the product of two numbers he/she has drawn , and B computes the sum of two numbers he/she has drawn . The player getting the larger number wins. What is the probability that A wins ? (A)
18.
(B) 1006
dx
1 3
(B)
5 9
(C)
4 9
(D)
1 9
Let a, b, c be three vectors in the xyz space such that a b = b c = c a 0 . If A,B,C are points with position vectors a, b, c respectively , then the number of possible positions of the centriod of triangle ABC
is (A) 1
(B) 2
(C) 3
(D) 6
19.
The sum of (12 – 1 + 1) (1!) + (22 – 2 + 1)(2!) + .... + (n2 – n + 1)(n!) is (A) (n + 2) ! (B) ( n – 1) ((n + 1) !) + 1 (C) (n + 2)! – 1 (D) n((n + 1)!) – 1
20.
Let X be a nonempty set and let P(X) denote the collection of all subsets of X. Define f : X × P(X) R by 1, x A f(x,A) = .Then f(x , A B) equals 0, x A
(A) f(x, A) + f(x ,B) (B) f(x ,A) + f (x ,B) – 1 (C) f (x , A) + f(x , B) – f (x ,A) f( x ,B) (D) f( x ,A) + | f( x ,A) – f( x ,B) |
CLASS-XII_STREAM-SB+2_PAGE # 69
PHYSICS 21.
A narrow but tall cabin is falling freely near the earth’s surface. Inside the cabin, two small stones A and B are released from rest (relative to the cabin). Initially A is much above the centre of mass and B much below the centre of mass of the cabin. A close observation of the motion of A and B will reveal that : (A) both A and B continue to be exactly at rest relative to the cabin (B) A moves slowly upward and B moves slowly downward relative to the cabin (C) both A and B fall to the bottom of the cabin with constant acceleration due to gravity (D) A and B move slightly towards each other vertically.
22.
Two plates each of mass m are connected by a massless spring as shown :
A weight W is put on the upper plate which compresses the spring further. When W is removed, the entire assembly jumps up. The minimum weight W needed for the assembly to jump up when the weight is removed is just more than : (A) mg (B) 2mg (C) 3mg (D) 4mg 23.
If the speed (v) of the bob in a simple pendulum is plotted against the tangential acceleration (a), the correct graph will be represented by :
(A)
(B)
(C)
(D)
(A) I
(B) II
(C) III
(D) IV
24.
A container with rigid walls is covered with perfectly insulating material. The container is divided into two parts by a partition. One part contains a gas while the other is fully evacuated (vacuum). The partition is suddenly removed. The gas rushes to fill the entire volume and comes to equilibrium after a little time. If the gas is not ideal , (A) the initial internal energy of the gas equals its final internal energy (B) the initial temperature of the gas equals its final temperature (C) the initial pressure of the gas equals to its final pressure (D) the initial entropy of the gas equals to its final entropy
25.
Two bulbs of identical volumes connected by a small capillary are initially filled with an ideal gas at temperature T. Bulb 2 is heated to maintain a temperature 2T while bulb 1 remains at temperature T. Assume throughout that the heat conduction by the capillary is negligible. Then the ratio of the final mass of the gas in bulb 2 to the initial mass of the gas in the same bulb is close to : (A) 1/3 (B) 2/3 (C) 1/3 (D) 1 CLASS-XII_STREAM-SB+2_PAGE # 70
26.
Two rods, one made of copper and the other steel of the same length and cross sectional area are joined together. (The thermal conductivity of copper is 385 J.s–1. m–1. K–1 and steel is 50 J.s–1.m–1.K–1.) If the copper end is held at 100°C and the steel end is held at 0°C, what is the junction temperature (assuming no other heat losses) ? (A) 12°C (B) 50°C (C) 73°C (D) 88°C
27.
Jet aircrafts fly at altitudes above 30,000 ft where the air is very cold at –40°C and the pressure is 0.28 atm. The cabin is maintained at 1 atm pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of 25°C, we will require in addition : (A) a heater to warm the air injected into the cabin (B) an air conditionaer to cool the air injected into the cabin (C) neither a heater nor an air -conditioner : the compressor is sufficient (D) alternatively heating and cooling in the two halves of the compressor cycle.
28.
A speaker emits a sound wave of frequency f0. When it moves towards a stationary observer with speed u, the observer measures a frequency f1. If the speaker is stationary and the observer moves towards it with speed u, the measured frequency is f2. Then : (A) f1 = f2 < f0 (B) f1 > f2 (C) f1 < f2 (D) f1 = f2 > f0
29.
A plane polarized light passed through successive polarizers which are rotated by 30° with respect to each other in the clockwise direction. Neglecting absorption by the polarizers and given that the first polarizer’s axis is parallel to the plane of polarization of the incident light, the intensity of light at the exit of the fifth polarizer is closest to : (A) same as that of the incident light (B) 17.5% of the incident light (C) 30% of the incident light (D) zero
30.
At 23ºC, a pipe open at both ends resonates at a frequency of 450 hertz. At what frequency does the same pipe resonate on a hot day when the speed of sound is 4 percent higher than it would be at 23º C ? (A) 446 Hz (B) 454 Hz (C) 468 Hz (D) 459 Hz
31.
In a Young’s double slit set-up, light from a laser source falls on a pair of very narrow slits separated by 1.0 micrometer and bright fringes separated by 1.0 millimeter are observed on a distant screen. If the frequency of the laser light is doubled, what will be the separation of the bright fringes ? (A) 0.25 mm (B) 0.5 mm (C) 1.0 mm (D) 2.0 mm
32.
For a domestic AC supply of 220 V at 50 cycles per second, the potential difference between the terminals of a two -pin electric outlet in a room is given by :
33.
(A) V(t) = 220 2 Cos(100t)
(B) V(t) = 220Cos(50t)
(C) V(t) = 220Cos(100t)
(D) V(t) = 220 2 Cos(50t)
In the circuit shown below the resistances are given in ohms and the battery is assumed ideal with emf equal to 3.0 volts. The resistor that dissipates the most power is
(A) R1 34.
(B) R2
(C) R3
(D) R4
An electron collides with a free molecules initially in its ground state. The collision leaves the molecule in a excited state that is metastable and does not decay to the ground state by radiation. Let K be the sum
of the initial kinetic energies of the electron and the molecule, and P the sum of their initial momenta. Let
K’ and P' represent the same physical quantities after the collision. Then (A) K = K’, P P' (B) K’ < K, P P' (C) K = K’, P P'
(D) K’ < K, P P'
CLASS-XII_STREAM-SB+2_PAGE # 71
35.
In the circuit shown, the switch is closed at time t = 0
Which of the graphs shown below best reprsents the voltage across the inductor, as seen on an oscilloscope?
(I)
(II)
(III)
(IV)
(A) I 36.
(B) II
(C) III
(D) IV
Given below are three schematic graphs of potential energy V(r) versus distance r for three atomic particles electron (e), proton (p+) and neutron (n), in the presence of a nucleus at the origin O. The radius of the nucleus is r0. The scale on the V–axis may not be the same for all figures. The correct pairing of each with the corresponding atomic particle is :
(A) (1, n), (2, p+), (3, e–) (C) (1, e–), (2, p+), (3, n)
(B) (1, p+), (2, e–), (3, n) (D) (1, p+), (2, n), (3, e–)
37.
Due to transitions among its first three energy levels, hydrogenic atom emits radiation at three discrete wavelength 1,2 and 3(1 < 2 < 3). Then : (A) 1 = 2 + 3 (B) 1 + 2 = 3 (C) 1/1 + 1/2 = 1/3 (D) 1/1 = 1/2 + 1/3
38.
The total radiative power emitted by spherical blackbody with radius R and temperature T is P. If the radius is doubled and the temperature is halved then the radiative power will be : (A) P/4 (B) P/2 (C) 2P (D) 4P
CLASS-XII_STREAM-SB+2_PAGE # 72
39.
The Quantum Hall Resistance RH is a fundamental constant with dimensions of resistance. If h is Planck’s constant and e the electron charge, then the dimension of RH is the same as : (A) e2/h (B) h/e2 (C) h2/e (D) e/h2
40.
Four students measure the height of a tower. Each student uses a different method and each measures the height many different times. The data for each are plotted below. The measurement with highest precision is :
(A) I
(B) II
(C) III
(D) IV
CHEMISTRY 41.
Ther hybridizations of Ni (CO)4 and [Cr(H2O)6]2+, respectively (A) sp3 and d3sp2 (B) dsp2 and d2sp3 (C) sp3 and d2sp3 (D) dsp2 and sp3 d2
42.
Extraction of silver is achieved by initial complexation of the ore (Argentite) with X followed by reaction with Y, X and Y, respectively, are (A) CN– and Zn (B) CN– and Cu – (C) Cl and Zn (D) Br – and Zn
43.
Assuming ideal behaviour, the enthalpy and volume of mixing of two liquids, respectively, are (A) zero and zero (B) +ve and zero (C) –ve and zero (D) –ve and –ve
44.
At 298 K, the ratio of osmotic pressures of two solutions of a substance with concentrations of 0.01 M and 0.001 M, respectively, is (A) 1 (B) 100 (C) 10 (D) 1000
45.
The rate of gas phase chemical reactions generally increases rapidly with rise in temperature. This is mainly because : (A) the collision frequency increases with temperature. (B) the fraction of molecules having energy in excess of the activation energy increases with temperature. (C) the activation energy decreases with temperature. (D) the average kinetic energy of molecules increases with temperature.
CLASS-XII_STREAM-SB+2_PAGE # 73
46.
Among i-iv :
the compound that does not undergo polymerization under radical initiation, is : (A) i (B) ii (C) iii (D) iv 47.
Two possible stereoisomers for
are : (A) enantiomers
(B) diastereomers
(C) conformers
(D) rotamers
48.
For a process to occur spontaneously. (A) only the entropy of the system must increase. (B) only the entropy of the surrounding must increase. (C) either the entropy of the system or that of the surroundings must increase. (D) the total entropy of the system and the surroundings must increase.
49.
When the size of a spherical nanoparticle decreases from 30 nm to 10 nm, the ratio surface area/volume becomes (A) 1/3 of the original (B) 3 times the original (C) 1/9 of the original (D) 9 times the original
50.
The major product of the following reaction is :
H
(A)
51.
(B)
(C)
(D)
(C) H3O+
(D) H2/Pt
For the transformation
the reagent used is : (A) LiAlH4
(B) H3PO2
52.
The values of the limiting molar conductivity (º) for NaCl, HCl and NaOAc are 126.4. 425.9 and 91.0 S cm2 mol–1 respectively. For HOAC. º in S cm2 mol–1 is : (A) 390.5 (B) 299.5 (C) 208.5 (D) 217.5
53.
To obtain a diffraction peak, for a crystalline solid with interplane distance equal to wavelength of incident X-ray radiation, the angle of incidence should be : (A) 90º (B) 0º (C) 30º (D) 60º
54.
The standard Gibbs free energy change (Gº in kJ mol–1), in a Daniel cell (Eºcell = 1.1 V), when 2 moles of Zn(s) is oxidized at 298 K, is closed to : (A) – 212.3 (B) – 106.2 (C) – 424.6 (D) – 53.1
CLASS-XII_STREAM-SB+2_PAGE # 74
55.
All the products formed in the oxidation of NaBH4 by I2, are : (A) B2H6 and NaI (B) B2H6, H2 and NaI (C) BI3 and NaH
(D) NaBI4 and HI
56.
The spin-only magnetic moments of [Mn(CN)6]4– and [MnBr4]2– in Bohr Magneton, respectively, are : (A) 5.92 and 5.92 (B) 4.89 and 1.73 (C) 1.73 and 5.92 (D) 1.73 and 1.73
57.
In a zero-order reaction, if the initial concentration of the reactant is doubled, the time required for half the reactant to be consumed : (A) increases two-fold (B) increases four-fold (C) decreases by half (D) does not change
58.
The adsorption isothermal for a gas is given by the relation x = ap/(1 + bp) where x is moles of gas adsorbed per gram of the adsorbent, p is the pressure of the gas, and a and b are constants. Then x : (A) increases with p (B) remains unchanged with p (C) decreases with p (D) increases with p at low pressure and the same at high pressure.
59.
The reaction
NaOH / Heat
+ CHCl3 H
is known as : (A) Perkin reaction (C) Reimer-Tiemann reaction 60.
(B) Sandmeyer reaction (D) Cannizzaro reaction
Among i-iii
the boiling point follows the order (A) ii < i < iii (B) iii < ii < i
(C) i < ii < iii
(D) ii < iii < i
CLASS-XII_STREAM-SB+2_PAGE # 75
BIOLOGY 61.
The major constituents of neurofilaments are (A) microtubules (C) actin filaments
(B) intermediate filaments (D) protofilaments
62.
In which phase of the cell cycle are sister chromatids available as template for repair ? (A) G1 phase (B) G2 phase (C) S phase (D) M phase
63.
A person has difficulty in breathing at higher altitudes because (A) oxygen is likely to diffuse from lungs to blood. (B) oxygen is likely to diffuse from blood to lungs (C) partial pressure of O2 is lower than partial pressure of CO2 (D) overall intake of O2 by the blood becomes low.
64.
In humans , the composition of a zygote that will develop into a female is (A) 44A +XX (B) 44A + XY (C) 22 + X (D) 23 A
65.
If you fractionate all the organelles from the cytoplasm of a plant cell. In which one of the following sets of fractions will you find nucleic acids ? (A) nucleus, mitochondria, chloroplast, cytoplasm (B) nucleus, mitochondria, chloroplast, glyoxysome (C) nucleus, chloroplast , cytoplasm and peroxisome (D) nucleus, mitochondria, chloroplast, Golgi bodies
66.
A protein with 100 amino acid residues has been translated based on triplet genetic code. Had the genetic code been quadruplet. the gene that codes for the protein would have been. (A) same in size (B) longer in size by 25% (C) longer in size by 100% (D) shorter in size
67.
If the sequence of base in DNA is 5'- ATGTATCTCAAT- 3', than the sequence of bases in its transcript will be : (A) 5' - TACATAGAGTTA - 3' (B) 5' - UACAUAGAGUUA - 3' (C) 5' - AUGUAUCUCAAU - 3' (D) 5' - AUUGAGAUACAU - 3'
68.
The Na+/K+ pump is present in the plasma membrane of mammalian cells where it (A) expels potassium from the cell (B) expels sodium and potassium from the cell. (C) pumps sodium into the cell. (D) expels sodium from the cell.
69.
The CO2 in the blood is mostly carried (A) by haemoglobin in RBCs (B) in the cytoplasm of WBCs (C) in the plasma as bicrbonate ions (D) by plasma proteins
CLASS-XII_STREAM-SB+2_PAGE # 76
70.
Patients who have undergone organ transplants are given anti-rejection medications to (A) minimize infection (B) stimulate B- macrophage cell interaction (C) prevent T- lymphocyte proliferation (D) adopt the HLA of donor
71.
Saline drip is given to a Cholera patient because (A) NACl kills Vibrio cholera (B) NACl generates ATP (C) Na+ ions stops nerve impulse and hence sensation of pain (D) Na+ ions help in retention of water in body tissue
72.
A water molecule can form a maximum of hydrogen bonds. (A) 1 (B) 2 (C) 3
(D) 4
73.
Circadian Rhythm is an endogenously driven cycle for biochemical, physiological and behavioral processes. In humans, the approximate duration of this 'biological clock' is : (A) 1 Hours (B) 6 Hours (B) 12 Hours (D) 24 Hours
74.
Modern evolutionary theory consists of the concepts of Darwin modified by knowledge concerning : (A) population statistics (B) Mendel's laws (C) the idea of the survival of the fittest (D) competition
75.
Soon after the three germ layers are formed in a developing embryo, the process of organogenesis starts. The human brain is formed from the (A) ectoderm (B) endoderm (C) mesoderm (D) partly endoderm and partly mesoderm
76.
Puffs in the polytene chromosomes of Drosophila melanogaster salivary glands represent (A) transcriptionally active genes (B) transcriptionally inactive genes (C) heterochromatin (D) housekeeping genes
77.
The process of cell death involving DNA cleavage in cells is known as (A) necrosis (B) apoptosis (C) cytokinesis (D) endocytosis
78.
According to the original model of DNA. as proposed by Watson & Crick 1953, DNA is a (A) left handed helix (B) helix that makes a full turn every 70 nm. (C) helix where one turn of DNA contains 20 basepairs (D) two stranded helix where each strand has opposite polarity.
79.
At which stage of meiosis I does crossing over occur ? (A) lepoptene (B) zygotene (C) pachytene (D) diplotene
80.
An electrode is placed in the axioplasm of a mammalian axon and another electrode is placed just outside the axon. The potential difference measured will be (A) 0 (B) – 70mV (B) –70V (D) +70 V
CLASS-XII_STREAM-SB+2_PAGE # 77
PART-II (2 Mark) MATHEMATICS 81.
Let A and B be any two n × n matrices such that the following conditions hold : AB = BA and there exist positive integers k and l such that Ak = I (the identity matrix) and B = 0 (the zero matrix), Then (A) A + B = l (B) det (AB) = 0 (C) det (A + B) 0 (D) (A + B)m = 0 for some integer m
82.
The minimum value of n for which (A) is 101
83.
2 2 4 2 6 2 ....... ( 2n)2 1 2 3 2 5 2 ....... ( 2n – 1)2
(B) is 121
(C) is 151
< 1.01 (D) does not exist
The locus of the point P = (a , b) where a , b are real numbers such that the roots of x3 + ax2 + bx + a = 0 are in arithmetic progression is
84.
(A) an ellipse
(B) a circle
(C) a parabola whose vertex is on the y – axis
(D) a parabola whose vertex is on the x – axis
The smallest possible positive slope of a line whose y–intercept is 5 and which has a common point with he ellipse 9x2 + 16y2 = 144 is (A)
85.
3 4
(B) 1
(C)
4 3
(D)
9 16
Let A = { R | cos2(sin) + sin2(cos) = 1} and B = { R | cos(sin) sin(cos) = 0 }. Then A B (A) is the empty set (B) has exactly one element (C) has more than one but finitely many elements (D) has infinitely many elements
86.
Let f(x) = x3 + ax2 + bx + c , where a,b,c are real numbers. If f(x) has local minimum at x = 1 and a local
maximum at x = –
1 1 and f(2) = 0 , then f ( x ) dx equals 3
–1
(A)
87.
14 3
(B)
– 14 3
(C)
7 3
(D)
–7 3
Let f(x) = x12 – x9 + x4 – x + 1. Which of the following is true ? (A) f is one –one (B) f has a real root (C) f never vanishes (D) f takes only positive values
CLASS-XII_STREAM-SB+2_PAGE # 78
1
88.
x n (1 – x )n For each positive integers n, define fn(x) = minimum n! , n! , for 0 x 1. Let In = fn ( x ) dx, n 1 . 0
Then I n is equal to n1
(A) 2 e – 3
(B) 2 e – 2
(C) 2 e – 1
(D) 2 e
89.
The maximum possible value of x2 + y2 – 4x – 6y , x,y real subject to the condition | x + y | + | x – y | = 4 (A) is 12 (B) is 28 (C) is 72 (D) does not exist
90.
The arithemetic mean and the geometric mean of two distinct 2– digit numbers x and y are two integers one of which can be obtained by reserving the digits of the other (in base 10 representation). Then x + y equals (A) 82 (B) 116 (C) 130 (D) 148
PHYSICS 91.
An isolated sphere of radius R contains uniform volume distribution of positive charge. Which of the curves shown below correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance r from its centre ?
(A) I 92.
(B) II
(C) III
(D) IV
The surface of a planet is found to be uniformly charged. When a particle of mass m and no charge is thrown at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal range L. A particle of mass m and charge q, with the same initial conditions has a range L/2. The range of particle of mass m and charge 2q with the same initial conditions is : (A) L (B) L/2 (C) L/3 (D) L/4
CLASS-XII_STREAM-SB+2_PAGE # 79
93.
Figure below shows a small mass connected to a string, which is attached to a vertical post.If the ball is released when the string is horizontal as shown , the magnitude of the total acceleration (including radial and tangential) of the mass as a function of the angle is
(A) g Sin
(B) g
3 Cos 2 1
(C) g Cos
(D) g
3Sin 2 1
94.
One mole of an ideal gas at intial temprature T, undergoes a quasi–static process during which the volume V is doubled .During the process the internal energy U obeys the equation U = aV3, where a is a constant .The work done during this process is (A) 3RT / 2 (B) 5RT / 2 (C) 5RT / 3 (D) 7RT / 2
95.
A constant amount of an ideal gas undergoes the cyclic process ABCA in the PV diagram shown below.
The path BC is an isothermal .The work done by the gas during one complete cycle , beginning and ending at A is nearly (A) 600 KJ (B) 300 KJ (C) – 300 KJ (D) – 600 KJ 96.
A material is embedded between two glass plates . Refractive index n of the material varies with thickness as shown below .The maximum incident angle (in degrees) on the material for which beam will pass through the material is
(A) 60.0
(B) 53.1
(C) 43.5
(D) 32.3
CLASS-XII_STREAM-SB+2_PAGE # 80
97.
At a distance form a uniformly charged long wire , a charged particle is thrown radially outward with a velocity u in the direction perpendicular to the wire . When the particle reaches a distance 2 from the wire its speed is found to be
2u . The magnitude of the velocity , when it is a distance 4l away from the wire,
is (ignore gravity) (A) 3u 98.
(B) 2 u
(C) 2 2 u
(D) 4 u
A rectangular loop of wire shown below is coplanar with a long wire carrying current I .
The loop is pulled to the right as indicated .What are the directions of the induced current in the loop and the magnetic forces on the left and the right sides of the loop ? Inducded Current Force on left side Force on right side (A) Counterclockwise To the left To the right (B) Clockwise To the left To the right (C) Counter clockwise To the right To the left (D) Clockwise To the right To the left 99.
Two batteries V1 and V2 are connected to three resistors as shown below
If V1 = 2V and V2 = 0V , the current I = 3mA. If V1 = 0V and V2 = 4V , the current I = 4 mA. Now if V1 = 10 V and V2 = 10V , the current I will be (A) 7 mA (B) 15 mA (C) 20 mA (D) 25 mA 100.
y2 + = 1. At point (0, b), the x-component a2 b2 of velocity is u. the y-component of acceleration at this point is : (A) – bu2 / a2 (B) – u2 / a2 (C) – au2 / b2 (D) – u2 / a A particle moves in a plane along an eliptic path given by
x2
CHEMISTRY 101.
XeF6 hydrolyses to give an oxide. The structure of XeF6 and the oxide, respectively are (A) octahedral and tetrahedral (B) distorted octahedral pyramidal (C) octahedral and pyramidal (D) distorted octahedral and tetrahedral
102.
MnO4– oxidizes (i) oxalate ion in acidic medium at 333 K and (ii) HCl. For balanced chemical equations, the rations [MnO4– : C2O42–] in (i) and [MnO4– : HCl] in (ii), respectively, are : (A) 1 : 5 and 2 : 5 (B) 2 : 5 and 1 : 8 (C) 2 : 5 and 1 : 5 (D) 5 : 2 and 1 : 8
103.
If E º Fe 2 / Fe = – 0.440 V and Eº Fe3 / Fe 2 = 0.770 V, then E º Fe3 / Fe is : (A) 0.330 V (B) – 0.037 V (C) – 0.330 V (D) – 1.210 V
104.
The electron in hydrogen atom is in the first Bohr orbit (n = 1). The ratio of transition energies, E(n = 1 n = 3) to E (n = 1 n = 2), is (A) 32/27 (B) 16/27 (C) 32/9 (D) 8/9
CLASS-XII_STREAM-SB+2_PAGE # 81
105.
In the following conversion, (i) MeMgBr
NaOH / I
(ii) H3O
H3O
2 X Y
the major products X and Y, respectively, are :
106.
(A) i (B) ii The reaction sequence,
HNO2 X
(C) iii
(D) iv
(C) iii
(D) iv
Y
the major products X and Y, respectively, are :
(A) i 107.
(B) ii
Optically active (S)--methoxyacetaldehyde on reaction with MeMgX gave a mixture of alcohols. The major diastereomer ‘P’ on treatment with Me1/K2CO3 gave an optically inactive compound. P is :
(A) i
(B) ii
(C) iii
(D) iv
CLASS-XII_STREAM-SB+2_PAGE # 82
108.
At 300 K the vapour pressure of two pure liquids, A and B are 100 and 500 mm Hg, respectively. If in a mixture of A and B, the vapour pressure is 300 mm Hg, the mole fractions of A in the liquid and in the vapour phase, respectively, are : (A) 1/2 and 1/10 (B) 1/4 and 1/6 (C) 1/4 and 1/10 (D) 1/2 and 1/6
109.
The crystal field stabilization energies (CFSE) of high spin and low spin d6 metal complexes in terms of 0, respectively, are : (A) – 0.4 and – 2.4 (B) – 2.4 and – 0.4 (C) – 0.4 and 0.0 (D) – 2.4 and 0.0
110.
Emulsification of 10 ml of oil in water produces 2.4 × 1018 droplets. If the surfaces tension at the oil-water interface is 0.03 Jm–2 and the area of each droplet is 12.5 × 10–16 m2, the energy spent in the formation of oil droplets is : (A) 90 J (B) 30 J (C) 900 J (D) 10 J
BIOLOGY 111.
Which sequence of events gives rise to flaccid guard cells and stomatal closure at night ? (A) low [Glucose ] low osmotic pressure low pH high pCO2 (B) low pH high pCO2 low [Glucose ] low osmotic pressure (C) low osmotic pressure high pCO2 low pH low [Glucose] (D) high pCO2 low pH low [Glucose] low osmotic pressure
112.
Rice has a diploid genome with 2n = 24. If crossing over is stopped in a rice plant and then selfed seeds are collected, will all the offsprings be genetically identical to the parent plant ? (A) yes, because crossing-over is the only source of genetic variation (B) no, because stopping of crossing over automatically increases rate of point mutation (C) yes, only if the parent plant was a completely inbred line (D) yes, only if the parent plant was a hybrid between two prue-bred lines
113.
Rodents can distinguish between many different types of odours. The basis for odour discrimination is that (A) they have a small number of odorant receptors that bind to many different odorant molecules (B) the mechanoreceptors in the nasal cavity are activated by different odorant molecules found in the air passing through the nostrils (C) the part of the brain that processes the sense of smell has many different receptors for odorant molecules (D) a large number of different chemoreceptors are present in the nasal cavity that binds a variety of odorant molecules
114.
Although blood flows through large arteries at high pressure, when the blood reaches small capillaries the pressure decreases because (A) the valves in the arteries regulate at he rate of blood flow into the capillaries (B) the volume of blood in the capillaries is much lesser than that in the arteries (C) the total cross-sectional area of capillaries arising form an artery is much greater than that of the artery (D) elastin fibers in the capillaries help to reduce the arterial pressure
115.
E.coli about to replicate was pulsed with tritiated thymidine for 5 min and then transferred to normal medium . After one cell division which one of the following observations would be correct ? (A) both the strands of DNA will be radioactive (B) one strand of DNA will be radioactive (C) none of the strands will be radioactive (D) half of one strand of DNA will be radioactive
CLASS-XII_STREAM-SB+2_PAGE # 83
116.
Selection of lysine auxotroph (bacteria which requires lysine for growth) from a mixed population of bacteria can be done growing bacterial population in the presence of (A) lysine (B) penicillin (B) lysine and penicillin (D) glucose
117.
Increasing the number of measurements of an experimental variable will (A) increase the standard error of the sample (B) increase the mean of the sample (C) decrease the standard error of the sample (D) result in all of the above
118.
119.
For a human male what is the probability that all the maternal chromosomes will end up in the same gamete ? (A) 1/23 (B) 223 46 (C) 2 (D) (½)23 Nocturnal animal have retinas that contain (A) a high percentage of rods to increase sensitivity to low light conditions (B) a high percentage of cones so that nocturnal color vision can be improved in low light conditions (C) an equal number of rods and cones so that vision can be optimized (D) retinas with the photoreceptor layer present in the front of the eye to increase light sensitivity
120.
The length of one complete turn of a DNA double helix is
(A) 34 A
(B) 34 nm
(C) 3.4 A
(D) 3.4 m
*****
CLASS-XII_STREAM-SB+2_PAGE # 84
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2007 Time : 3Hr.
1.
Max. Marks : 160
In Year 2007, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90),Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2008 Time : 3Hr.
1.
Max. Marks : 160
In Year 2008, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2009 Time : 3Hr.
1.
Max. Marks : 160
In Year 2009, Question Number 1-80 each carries 1 (one) mark, Maths(1-20), Physics (21-40), Chemistry(41-60), Biology(61-80) & Question Number 81 to 125 each carries 2 marks, Maths(81-90), Physics(91-100), Chemistry(101-110), Biology(111-120)
2.
Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.
3.
Write your Name and Roll No. in the space provided in the bottom of this booklet.
4.
Before answering the paper, fill up the required details in the blank space provided in the answer sheet.
5.
Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet.
6.
In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2010 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2011 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
GENERAL INSTRUCTIONS FOR KVPY TEST PAPER, STREAM- SB+2 YEAR : 2012 Time : 3Hr.
Max. Marks : 160
1.
The Question paper consists of two parts (both contain only multiple choice question) for 100 marks. There will be four sections in Part-I (each containing 20 questions) four sections in Part-II (each containing 10 questions). Answer any THREE of the four sections in Part-I and any TWO of the four sections in Part-II.
2.
The composition of the question paper is given in the table below : S No. 1 2 3 4
Subject
Part-I
Part-II
Mathematics
20 questions - 1 mark each
10 questions - 2 mark each
Physics
20 questions - 1 mark each
10 questions - 2 mark each
Chemistry
20 questions - 1 mark each
10 questions - 2 mark each
Biology
20 questions - 1 mark each
10 questions - 2 mark each
3.
The answer paper is machine readable. Do not forget to mention your paper code and Roll Number neatly and clearly in the blank space provided in the Objective Response Sheet (ORS)/Answer Sheet.
4.
For each question, indicate your answer by filling the corresponding oval with a HB pencil only.
5.
For each question there will be four choices given and only one of them is the correct answer. Fill only one oval per question. If you mark more than one oval, it will be considered as an incorrect answer.
6.
There is negative marking for wrong answers. Unanswered questions will not be evaluated and will not be penalized as a wrong answer.
7.
In Part-I each correct answer gets 1 mark and for each incorrect answer 0.25 mark will be deducted. In Part-II each correct answer gets 2 marks and for each incorrect answer 0.5 mark will be deducted.
8.
You are permitted to use a non programable calculator.
9.
Candidates are permitted to carry their question paper after the examination.
YEAR-2012 (KVPY-STREAM-SB+2) PART-I (1 Mark) MATHEMATICS 1.
Three children, each accompanied by a guardian, seek admission in a school. The principal wants to interview all the 6 persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done? (A) 60 (B) 90 (C) 120 (D) 180
2.
In the real number system, the equation (A) no solution (C) exactly four distinct solutions
x 3 – 4 x – 1 + x 8 6 x 1 = 1 has (B) exactly two distinct solutions (D) infinitely many solutions
3.
The maximum value M of 3x + 5x – 9x + 15x – 25x, as x varies over reals, satisfies (A) 3 < M < 5 (B) 0 < M < 2 (C) 9 < M < 25 (D) 5 < M < 9
4.
Suppose two perpendicular tangents can be drawn from the origin to the circle x2 + y2 – 6x – 2py + 17 = 0, for some real p. Then |p| is equal to (A) 0 (B) 3 (C) 5 (D) 17
5.
Let a, b, c be numbers in the set {1, 2, 3, 4, 5, 6} such that the curves y = 2x3 + ax + b and y = 2x3 + cx + d have no point in common. The maximum possible value of (a – c)2 + b – d is (A) 0 (B) 5 (C) 30 (D) 36
6.
Consider the conic ex2 + y2 – 2e2x – 22y + e3 + 3 = e. Suppose P is any point on the conic and S1, S2 are the foci of the conic, then the maximum value of (PS1 + PS2) is (A) e
(B)
e
(C) 2
sin( x a) sin( x a) , then cos( x a) – cos( x a) (A) f(x + 2) = f(x) but f(x + ) f(x) for any 0 < < 2 (B) f is a strictly increasing function (C) f is strictly decreasing function (D) f is a constant function
7.
Let f(x) =
8.
The value of tan 81 – tan 63 – tan27 + tan9 is (A) 0 (B) 2 (C) 3
9.
(D) 2 e
The mid–point of the domain of the function f(x) = (A)
1 4
(B)
3 2
(D) 4
4 2x 5 for real x is (C)
2 3
(D)
2 5
10.
Let n be a natural number and let a be a real number. The number of zeros of x2n+1 – (2n + 1) x + a = 0 in the interval [–1, 1] is (A) 2 if a > 0 (B) 2 if a < 0 (C) at most one for every vale of a (D) at least three for every value of a
11.
Let f : R R be the function f(x) = (x – a1) (x – a2) + (x – a2) (x – a3)+ (x – x3) (x –x1) with a1, a2, a3 R. Then f(x) 0 if and only if (A) at least two of a1, a2, a3 are equal (B) a1 = a2 = a3 (C) a1, a2, a3 are all distinct (D) a1, a2, a3 are all positive and distinct CLASS-XII_STREAM-SB+2_PAGE # 85
/2
12.
The value
(sin x )
2 1
(sin x )
2 1
dx
0 /2
is
dx
0
2 1
(A)
2 1
(B)
2 –1
2 1
2 1
(C)
(D) 2 – 2
2
2012
13.
(sin( x
The value
3
) x 5 1) dx is
– 2012
(A) 2012
14.
(B) 2013
(C) 0
(D) 4024
Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the 5
integral
[ x] { x} dx is 0
(A) 5/2
15.
Let Sn =
(B) 5 n
k 1
(C) 34.5
(D) 35.5
k denote the sum of the first n positive integers. The numbers S1, S2, S3, ....S99 are
written on 99 cards. The probability of drawing a cards with an even number written on it is (A)
16.
(B)
49 100
(C)
49 99
(D)
48 99
A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin? (A)
17.
1 2
41 70
(B)
31 70
(C)
27 70
(D)
1 3
Let H be the orthocentre of an acute–angled triangle ABC and O be its circumcenter. Then HA HB HC (A) is equal to HO
(B) is equal to 3HO
(C) is equal to 2HO
(D) is not a scalar multiple of HO in general
18.
The number of ordered pairs (m,n) where m, n {1, 2, 3, ......, 50}, such that 6m + 9n is a multiple of 5 is (A) 1250 (B) 2500 (C) 625 (D) 500
19.
Suppose a1, a2, a3, ....., a2012 are integers arranged on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even indeced numbers is 3018, what is the sum of all numbers? (A) 0 (B) 1509 (C) 3018 (D) 6036
20.
Let S = 1, 2, 3, ...., n} and A = {(a, b) | 1 a, b n} = S S . A subset B of A is said to be a good subset if (x, x) B for every x S. Then the number of good subsets of A is (A) 1
(B) 2n
(C) 2n(n–1)
(D) 2 n2 CLASS-XII_STREAM-SB+2_PAGE # 86
PHYSICS 21.
An ideal monatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done by the gas is W i . If the process is adiabatic the magnitude of work done by the gas is W a . Which of the following is true (A) W i = W a > 0 (B) W i > W a > 0 (C) W i > W a = 0 (D) W a > W i = 0
22.
The capacitor of capacitance C in the circuit shown is fully charged initially, Resistance is R.
After the switch S is closed, the time taken to reduce the stored energy in the capacitor to half its initial value is : (A)
23.
RC 2
(B) RC ln 2
(C) 2RC ln 2
(D)
RC ln 2 2
A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about its equilibrium shape. By dimensional analysis the ratio
c
can be (Here is
R 3 surface tension, is density, g is acceleration due to gravity, and k is an arbitrary dimensionless constant) (A)
24.
kgR 2
(B)
k R 3 g
(C)
k R 2 g
k (D) g
Seven identical coins are rigidly arranged on a flat table in the pattern shown below so that each coin touches its neighbours. Each coin is a thin disc of mass m and radius r. Note that the moment of inertia of an individual coin about an axis passing through center and perpendicular to the plane of the coin is mr 2 . 2
The moment of inertia of the system of seven coins about an axis that passes through the point P (the centre of the coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is (A)
55 mr2 2
(B)
127 mr2 2
(C)
111 mr2 2
(D) 55 mr2
CLASS-XII_STREAM-SB+2_PAGE # 87
25.
A planet orbits in an elliptical path of eccentricity e around a massive star considered fixed at one of the foci. The point in space where it is closest to the star is denoted by P and the point where it is farthest is denoted by A. Let vP and vA be the respective speeds at P and A. Then
vP 1 e (A) v 1 e A 26.
vP (B) v = 1 A
(C)
vP 1 e2 vA 1 e
(D)
vP 1 e2 v A 1 e2
In a Young's double slit experiment the intensity of light at each slit is 0. Interference pattern is observed along a direction parallel to the line S1 S2 on screen S.
The minimum, maximum, and the intensity averaged over the entire screen are respectively. (A) 0, 40 , 20 (B) 0 , 20 , 30/2 (C) 0, 40 , 0 (D) 0, 20 , 0 27.
A loop carrying current has the shape of a regular polygon of n sides. If R is the distance from the centre to any vertex, then the magnitude of the magnetic induction vector B at the centre of the loop is (A) n
28.
0 tan 2 R n
(B) n
0 2 tan 2 R n
(C)
0 2R
(D)
0 tan R n
A conducting rod of mass m and length is free to move without friction on two parallel long conducting rails, as shown below. There is a resistance R acorss the the rails. In the entire space around, there is a uniform magnetic filed B normal to the plane of the rod and rails. The rod is given an impulsive velocity v0.
1 mv02 2 (A) will be converted fully into heat energy in the resistor (B) will enable rod to continue to move eith velocity v0 since the rails are frictionless (C) will be converted fully into magnetic energy due to induced current (D) will be converted into the work done against the magnetic field Finally, the initial energy
CLASS-XII_STREAM-SB+2_PAGE # 88
29.
A steady current flows through a wire of radius r, length L and resistivity . The current produces heat in the wire. The rate of heat loss in a wire is proportional its surface area. The steady temperature of the wire is independent of (A) L (B) r (C) (D)
30.
The ratio of the speed of sound to the average speed of an air molecule at 300K and 1 atmospheric pressure is close to (A) 1
31.
(B)
300
1 300
(C)
(D) 300
In one model of the election, tho electron of mass me is thought to be a uniformly charged shell of radius R and total charge e, whose electrostatic energy E is equivalent to its mass me via Einstein's mass energy relation E = mec2 . In this model, R is approximately (me = 9.1 × 10–31 kg, c = 3 × 108 m.s–1,
1 = 9 × 109 Farads m–1, magnitude of the electron charge = 1.6 × 10–19 C) 4 0 (A) 1.4 × 10–15 m (B) 2 × 10–13 m (C) 5.3 × 10–11 m (D) 2.8 × 10–35 m 32.
A body is executing simple harmonic motion of amplitude a and period T about the equilibrium position x = 0. Large numbers of snapshots are taken at random of this body in motion. The probability of the body being found in a very small interval x to x + |dx| is highest at (A) x = ± a
(B) x = 0
(C) x = ± a/2
(D) x = ±
a 2
33.
Two identical bodies are made of a material for which the heat capacity increases with temperature One of these is held at a temperature of 100°C while the other one is kept at 0ºC. If the two are brought into contact, then, assuming no heat loss to the environment, the final temperature that they will reach is (A) 50°C (B) more than 50°C (C) less than 50°C (D) 0°C
34.
A particle is acted upon by a force given by F = –x3 – x4 where and are positive constants. At the point x = 0, the particle is (A) in stable equilibrium (B) in unstable equiibrium (C) in neutral equilibrium (D) not in equilibrium
35.
The potential energy of a point particle is given by the expression V(x) = x + sin (x / ). A dimensionless combination of the constants , and is (A)
36.
(B)
2
(C)
(D)
A ball of mass m suspended from a rigid support by an inextensible massless string is released from a height h above its lowest point. At its lowest point it colIides elastically with a block of mass 2m at rest on a frictionless surface. Neglect the dimensions of the ball and the block. After the collision the ball rises to a maximum height of
(A)
h 3
(B)
h 2
(C)
h 8
(D)
h 9
CLASS-XII_STREAM-SB+2_PAGE # 89
37.
A particle released from rest is falling through a thick fluid under gravity. The fluid exerts a resistive force on the particle proportional to the square of its speed. Which one of the following graphs best depicts the variation of is speed v with time t?
(A)
(B)
(C)
(D)
38.
A cylindrical steel rod of length 0.10m and thermal conductivity 50 W.m–1.K–1 is welded end to end to copper rod of thermal conductivity 400 W.m–1.K–1 and of the same area of cross section but 0.20 m long. The free end of the steel rod is maintained at 100°C and that of the copper rod at 0°C. Assuming that the rods are perfectly insulated from the surrounding the temperature at the junction of the two rods is (A) 20°C (B) 30°C (C) 40°C (D) 50°C
39.
A parent nucleus X is decaying into daughter nucleus Y which in turn decays to Z. The half lives of X and Y are 4000 years and 20 years respectively. In a certain sample, it is found that the number of Y nuclei hardly changes with time. If the number of X nuclei in the sample is 4 × 1020 , the number of Y nuclei present in it is (A) 2 × 1017 (B) 2 × 1020 (C) 4 × 1023 (D) 4 × 1020
40.
An unpolarized beam of light of intensity 0 passes through two linear polarizers making an angle of 30° with respect to each other. The emergent beam will have an intensity. (A)
3 0 4
(B)
3 0 4
(C)
3 0 8
(D)
0 8
CHEMISTRY 41.
42.
43.
44.
Among the following, the species with the highest bond order is : (A) O2 (B) F2 (C) O2+
(D) F2–
The molecule with non-zero dipole moment is : (A) BCl3 (B) BeCl2
(D) NCl3
(C) CCl4
For a one-electron atom, the set of allowed quantum numbers is : (A) n = 1, = 0, m = 0, ms = +½
(B) n = 1, = 1, m = 0, ms = +½
(C) n = 1, = 0, m = –1, ms = –½
(D) n = 1, = 1, m = 1, ms = –½
In the reaction of benzene with an electrophile E+, the structure of the intermediate -complex can be represented as :
(A)
(B)
(C)
(D)
CLASS-XII_STREAM-SB+2_PAGE # 90
45.
The most stable conformation of 2, 3-dibromobutane is :
(A)
(B)
(C)
(D)
46.
Typical electronic energy gaps in molecules are about 1.0 eV. In terms of temperature, the gap is closest to: (A) 102 K (B) 104 K (C) 103 K (D) 105 K
47.
The major final product in the following reaction is : 1) CH MgBr
3 CH3CH2CN
2) H3O
(A)
(B)
(C)
(D)
48.
A zero-order reaction, A Product, with an initial concentration [A]0 has a half-life of 0.2 s. If one starts with the concentration 2[A]0, then the half-life is : (A) 0.1 s (B) 0.4 s (C) 0.2 s (D) 0.8 s
49.
The isoelectronic pair of ions is : (A) Sc2+ and V3+ (B) Mn3+ and Fe2+
50.
(C) Mn2+ and Fe3+
(D) Ni3+ and Fe2+
(C)
(D)
(C)
(D)
The major product in the following reaction is : NaNH
2
(A)
51.
(B)
The major product of the following reaction is : Conc.HBr
(A)
(B)
CLASS-XII_STREAM-SB+2_PAGE # 91
52.
The oxidation state of cobalt in the following molecule is :
(A) 3
(B) 1
(C) 2
(D) 0
53.
The pKa of a weak acid is 5.85. The concentrations of the acid and its conjugate base are equal at a pH of: (A) 6.85 (B) 5.85 (C) 4.85 (D) 7.85
54.
For a tetrahedral complex [MCl4]2–, the spin-only magnetic moment is 3.83 BM. The element M is : (A) Co (B) Cu (C) Mn (D) Fe
55.
Among the following graphs showing variation of rate (k) with temperature (T) for a reaction, the one that exhibits Arrhenius behavior over the entire temperature range is :
(A)
56.
57.
58.
(B)
(C)
(D)
The reaction that gives the following molecule as the major product is
(A)
(B)
(C)
(D)
The C–O bond length in CO, CO2 and CO32– follows the order : (A) CO < CO2 < CO32– (B) CO2 < CO32– < CO (C) CO > CO2 > CO32–
(D) CO32– < CO2 < CO
The equilibrium constant for the following reactions are K1 and K2, respectively. 2P(g) + 3Cl2(g) 2PCl3(g) PCl3(g) + Cl2(g) PCl5(g) The the equilibrium constant for the reaction 2P(g) + 5Cl2(g) 2PCl5(g) is : (A) K1K2 (B) K1K22
(C) K12K22
(D) K12K2 CLASS-XII_STREAM-SB+2_PAGE # 92
59.
The major product of the following reaction is : AlCl
3 + (CH3C)2CHCH2Cl
60.
(A)
(B)
(C)
(D)
Doping silicon with boron produces a : (A) n-type semiconductor (C) p-type semiconductor
(B) metallic conductor (D) insulator
BIOLOGY 61.
The disorders that arise when the immune system destroys 'self' cells are called autoimmmune disorders. Which of the following would be classified under this (A) rheumatoid arthritis (B) asthma (C) rhintis (D) eczema
62.
Which of the following class of immunoglobulins can trigger the complement cascade ? (A) IgA (B) IgM (C) IgD (D) IgE
63.
Diabetes insipidus is due to (A) hypersecretion of vasoperssin (C) hypersecretion of insulin
(B) Hyposecretion of insulin (D) hyposecretion of vasopressin
64.
Fossils are most often found in which kind of rocks ? (A) meteorites (B) sedimentary rocks (C) igneous rocks (D) metamorphic rocks
65.
Peptic ulcers are caused by (A) a fungus, Candida albicans (B) a virus, cytomegalo virus (C) a parasite, Trypanosoma brucei (D) a bacterium, Helicobacter pylori
66.
Transfer RNA (tRNA) (A) is present in the ribosomes and provides structural integrity (B) usually has clover leaf-like structure (C) carries genetic information from DNA to ribosomes (D) codes for proteins
67.
Some animals excrete uric acid in urine (uricotelic) as it requires very little water. This is an adaptation to conserve water loss. Which animals among the following are most likely to be uricotelic? (A) fishes (B) amphibians (C) birds (D) mammals
68.
A ripe mango, kept with unripe mangoes causes their ripening. This is due to the release of a gaseous plant hormone (A) auxin (B) gibberlin (C) cytokinine (D) ethylene
CLASS-XII_STREAM-SB+2_PAGE # 93
69.
Human chromosomes undergo structural changes during the cell cycle. Chromosomal structure can be best visualized if a chromosome is isolated from a cell at (A) G1 phase (B) S phase (C) G2 phase (D) M phase
70.
By which of the following mechanisms is glucose reabsorbed from the glomerular filtrate by the kidney tubule (A) osmosis (B) diffusion (C) active transport (D) passiver transport
71.
In mammals, the hormones secreted by the pituitary, the master gland, is itself regulated by (A) Hypothalamus (B) median cortex (C) pineal gland (D) cerebrum
72.
Which of the following is true for TCA cycle in eukaryotes (A) takes place in mitochondrion (B) produces no ATP (C) takes place in Golgi complex (D) independent of electron transport chain
73.
A hormone molecule binds to a specific protein on the plasma membrane inducing a signal. The protein it binds to it called (A) ligand (B) antibody (C) receptor (D) histone
74.
DNA mutations that do not cause my functional change in the protein product are known as (A) nonsense mutations (B) missense mutations (C) deletion mutations (D) silent mutations
75.
Plant roots are usually devoid of chlorophyll and cannot perform photosynthesis. However, three are exceptions. Which of the following plant root can perform photosynthesis (A) Arabidopsis (B) Tinospora (C) Rice (D) Hibiscus
76.
Vitamin A deficiency leads to night-blindness. Which of the following is the reason for the disease ? (A) rod cells are not converted to cone cells (B) rhodopsin pigment of rod cells is defective (C) melanin pigment is not synthesized in cone cells (D) cornea of eye gets dried
77.
In Dengue virus infection, patients often develop haemorrhagic fever due to internal bleeding. This happens due to the reduction of (A) platelets (B) RBCs (C) WBCs (D) lymphocytes
78.
If the sequence of bases in sense strand of DNA is 5'-GTTCATCG-3, then the sequence ofd bases in its RNA transcript would be (A) 5'-GTTCATCG-3' (B) 5'GUUCAUCG-3 (C) 5'CAAGTAGC-3' (D) 5'CAAGUAGC -3
79.
A refilex aciton is a quick involuntary response to stimulus. Which of the following is an example of BOTH, unconditioned and conditioned reflex (A) knee jerk reflex (B) secretion of saliva in response to the aroma of food (C) sneezing reflex (D) contration of the pupil in response to bright light
80.
In a food chain such as grass deer lion, the energy cost of respiration as a proportion of total assimilated energy at each level would be (A) 60%- 30%-20% (B) 20%- 30%-60% (C) 20%- 60%-30% (D) 30%- 30%-30% CLASS-XII_STREAM-SB+2_PAGE # 94
PART-II (2 Marks)
MATHEMATICS 81.
Suppose a, b, c are real numbers, and each of the equations x2 + 2ax + b2 = 0 and x2 + 2bx + c2 = 0 has two distinct real roots. Then the equation x2 + 2cx + a2 = 0 has (A) two distinct positive real roots (B) two equal roots (C) one positive and one negative root (D) no real roots
82.
The coefficient of x2012 in
(1 x 2 )(1 x )
(A) 2010
(B) 2011
83.
325 36
(B)
6
(B)
36 325
(C)
13 25
5 6
(D)
25 13
1 cosx = sin2(x + ) is 2 4
(C)
(D) 2
(B) P(1) 0
(C) P(1) 0
(D)
Define a sequence (an) by a1 = 5, an = a1a2 ... an–1 + 4 for n > 1. Then lim
n
(A) equals
1 2
(B) equal 1
87.
(D) 2013
A polynomila P(x) with real coefficients has the property that P(x) 0 for all x. Suppose P(0) = 1 and P(0) = – 1. What can you say about P(1)? (A) P(1) 0
86.
(C) 2012
The sum of all x [0, ] which satisfy the equation sinx + (A)
85.
is
Let (x, y) be a variable point on the curve 4x2 + 9y2 – 8x – 36y + 15 = 0. Then min (x2 – 2x + y2 – 4y + 5) + max(x2 – 2x + y2 – 4y + 5) is (A)
84.
1 x
The value of the integral
cos 2 x
1 a
x
(C) equals
2 5
1 –1 < P(1) < 2 2
an an 1 (D) does not exists
dx , where a > 0, is
–
(A) 88.
(B) a
(C)
2
(D) 2
Consider L=
3
2012 +
3
2013 + ... +
3
3011
R=
3
2013 +
3
2014 + ... +
3
3012
3012
and I =
3 x dx .
2012
(A) L + R < 2I
(B) L + R = 2I
(C) L + R > 2I
(D)
LR = I
CLASS-XII_STREAM-SB+2_PAGE # 95
89.
A man tosses a coin 10 times, scoring 1 point for each head and 2 points for each tail. Let P(K) be the
1 is 2 (D) 17
probability of scroing at least K points. The largest value of K such that P(K) > (A) 14
90.
(B) 15
(C) 16
x 1 for all x 1. Let f1(x) = f(x), f2(x) = f (f(x)) and generally fn(x) = f(fn–1(x)) for n > 1. Let P = x 1 f1(2) f2(3) f3(4) f4(5) which of the following is a multiple of P (A) 125 (B) 375 (C) 250 (D) 147 Let f(x) =
PHYSICS 91.
The total energy of a black body radiation source is collected for five minutes and used to heat water. The temperature of the water increases from 10.0°C to 11.0°C. The absolute temperature of the black body is doubled and its surface area halved and the experiment repeated for the same time. Which of the following statements would be most nearly correct? (A) The temperature of the water would increase from 10.0°C to a final temperature of 12°C (B) The temperature of the water would increase from 10.0°C to a final temperature of 18°C (C) The temperature of the water would increase from 10.0°C to a final temperature of 14°C (D) The temperature of the water would increase from 10.0°C to a final temperature of 11°C
92.
A small asteroid is orbiting around the sun in a circular orbit of radius r0 with speed V0. A rocket is launched from the asteroid with speed V = V0 where V is the speed relative to the sun. The highest value of for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effect of other planets) (A)
93.
(B) 2
2
(C)
(D) 1
3
A radioactive nucleus A has a single decay mode with half life A. Another radioactive nucleus B has two decay modes 1 and 2. If decay mode 2 were absent, the half life of B would have been A/2. If decay mode
B 1 were absent, the half life of B would have been 3 A. If the actual half life of B is B , then the ratio A is (A)
3 7
(B)
7 2
(C)
7 3
(D) 1
94.
A stream of photons having energy 3 eV each impinges on a potassium surface. The work function of potassium is 2.3 eV. The emerging photo-electrons are slowed down by a copper plate placed 5 mm away. If the potential difference between the two metal plates is 1V, the maximum distance the electrons can move away from the potassium surface before being turned back is (A) 3.5 mm (B) 1.5 mm (C) 2.5 mm (D) 5.0 mm
95.
Consider three concentric metallic spheres A, B and C of radii a, b, c respectively where a 0. Then which of the following is false?
10.
x
(A) xlim xsin(1/x) f(x) = M
(B) xlim sin(f(x)) = sin M
(C) xlim xsin(e–x) f(x) = M
(D) lim
x
sin x .f ( x ) 0 x
For x, t R let pt(x) = (sint)x2 – (2cost)x + sint 1
be a family of quadratic polynomials in x with variable coefficients. Let A(t) =
p ( x)dx . Which of the t
0
following statements are true? (I) A(t) < 0 for all t. (III) A(t) = 0 for infinitely many t. (A) (I) and (II) only (B) (II) and (III) only
(II) A(t) has infinitely many critical points. (IV) A’(t) < 0 for all t. (C) (III) and (IV) only (D) (IV) and (I) only CLASS-XII_STREAM-SB+2_PAGE # 101
11.
Let f(x) =
2 x x 2 and g(x) = cos x. Which of the following statements are true? (I) Domain of f((g(x))2) = Domain of f(g(x)) (II) Domain of f(g(x)) + g(f(x)) = Domain of g(f(x)) (III) Domain of f(g(x)) = Domain of f(g(x)) (IV) Domain of g((f(x))3) = Domain of f(g(x)) (A) Only (I) (B) Only (I) and (II) (C) Only (III) and (IV) (D) Only (I) and (IV) x
12.
For real x with – 10 x 10 define f(x) =
2
[t]
dt , where for a real number r we denote by [r] the largest
10
integer less than or equal to r. The number of points of discontinutiy of f in the interval (–10,10) is (A) 0 (B) 10 (C) 18 (D) 19 13.
For a real number x let [x] denote the largest integer less than or equal to x and {x} = x – [x]. The n
smallest possible integer value of n for which
xxdx exceeds 2013 is 1
(A) 63 14.
(B) 64
4 2 (B) 8 2
4 2 (C) 4 2
4 2 (D) 4 2
A box contains coupons labeled 1, 2, 3....n. A coupon is picked at random and the number x is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is y. Then the probability that one of the numbers x, y divides the other is (in the options below [r] denotes the largest integer less than or equal to r) (A)
16.
(D) 91
The area bounded by the curve y = cos x, the line joining (–/4, cos(–/4)) and (0, 2) and the line joining (/4, cos(/4)) and (0, 2) is
4 2 (A) 8 2 15.
(C) 90
1 2
(B)
1
n
n 2 n k 1 k
(C)
1 1 n n2
n
n k k 1
(D)
1 2 n n2
n
n
k k 1
Let n 3. A list of numbers 0 < x1 < x2 < ... < xn has mean and standard deviatiion . A new list of numbers is made as follows : y1 = 0, y2 = x2, ....,yn–1 = xn–1, yn = x1 + xn. The mean and the standard deviation of the new list are ˆ and ˆ . Which of the following is necessarily true?
17.
(A) = ˆ , ˆ
(B) = ˆ , ˆ
(C) = ˆ
(D) may or may not be equal to ˆ
Let 1, 2 , 3 , 4 be unit vectors in the xy -plane, one each in the interior of the four quadrants. Which of the following statements is necessarily true?
(A) 0 1 2 3 4
(B) There exist i, j with 1 i < j 4 such i j is in the first quadrant
(C) There exist i, j with 1 i < j 4 such that i . j < 0 (D) There exist i, j with 1 i < j 4 such that i . j > 0 18.
The number of integers n with 100 n 999 and containing at most two distinct digits is (A) 252 (B) 280 (C) 324 (D) 360 CLASS-XII_STREAM-SB+2_PAGE # 102
19.
For an integer n let Sn = {n + 1, n + 2, ....., n + 18}. Which of the following is true for all n 10? (A) Sn has a multiple of 19 (B) Sn has a prime (C) Sn has at least four multiples of 5 (D) Sn has at most six primes
20.
Let P be a closed polygon with 10 sides and 10 vertices (assume that the sides do not intersect except at the vertices). Let k be the number of interior angles of P that are greater than 180°. The maximum possible value of k is (A) 3 (B) 5 (C) 7 (D) 9
PHYSICS 21.
Consider an initially neutral hollow conducting spherical shell with inner radius r and outer radius 2r. A point charge +Q is now placed inside the shell at a distance r/2 from the centre. The shell is then grounded by connecting the outer surface to the earth. P is an external point at a distance 2r from the point charge +Q on the line passing through the centre and the point charge +Q as shown in the figure.
The magnitude of the force on a test charge +q placed at P will be
1 qQ (A) 4 2 0 4r 22.
1 9qQ (B) 4 2 0 100r
1 4qQ (C) 4 2 0 25r
(D) 0
Consider the circuit shown in the figure below :
All the resistors are identical. The charge stored in the capacitor, once it is fully charged, is (A) 0 23.
(B)
5 CV 13
(C)
2 CV 3
(D)
5 CV 8
A nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If M(A, Z) denotes the mass of a single neutral atom of an element with mass number A and atomic number Z, then the minimal condition that the decay
X AZ YZA1 – v e will occur is (me denotes the mass of the particle and the neutrino mass mv can be neglected) : (A) M(A, Z) > M(A, Z + 1 ) + me (B) M(A, Z) > M(A, Z + 1) (C) M(A, Z) > M(A, Z + 1) + Zme (D) M(A,Z) > M(A, Z + 1) – me
CLASS-XII_STREAM-SB+2_PAGE # 103
24.
The equation of state of n moles of a non-ideal gas can be approximated by the equation 2 P n a V nb nRT V 2 where a and b are constants characteristic of the gas. Which of the following can represent the equation of a quasistatic adiabat for this gas (Assume that CV, the molar heat capacity at constant volume, is independent of temperature)?
25.
(A) T( V nb)R / C V = constant
(B) T( V nb)C V / R = constant
ab R / CV constant (C) T 2 V nb V R
n 2ab V nbCV / R constant T (D) 2 V R
A blackbox (BB) which may contain a combination of electrical circuit elements (resistor, capacitor or inductor) is connected with other external circuit elements as shown below in the figure (a). After the switch (S) is closed at time t = 0, the current (I) as a function of time (t) is shown in the figure (b).
From this we can infer that the blackbox contains (A) A resistor and a capacitor in series (C) A resistor and an inductor in series 26.
(B) A resistor and a capacitor in parallel (D) A resistor and an inductor in parallel
In a photocell circuit the stopping potential, V0, is a measure of the maximum kinetic energy of the photoelectrons. The following graph shows experimentally measured values of stopping potential versus frequency v of incident light.
The values of Plank’s constant and the work function as determined from the graph are (taking the magnitude of electronic charge to be e = 1.6 × 10–19 C) (A) 6.4 × 10–34 Js, 2.0 eV (B) 6.0 × 10–34 Js, 2.0 eV –34 (C) 6.4 × 10 Js, 3.2 eV (D) 6.0 × 10–34 Js, 3.2 eV 27.
An engine moving away from a vertical cliff blows a born at a frequency f. Its speed is 0.5% of the speed of sound in air. The frequency of the reflected sound received at the engine is (A) 0.990 f (B) 0.995 f (C) 1.005 f (D) 1.010 f
CLASS-XII_STREAM-SB+2_PAGE # 104
28.
An arangement with a pair of quarter circular coils of radii r and R with a common centre C and carrying a current I is shown.
The permeability of free space is 0. The magnetic field at C is (A) 0 I(1/r – 1/R)/8 into the page (B) 0 I (1/r – 1/R)/8 out of the page (C) 0 I(1/r + 1/R)/8 out of the page (D) 0 I(1/r + 1/R)/8 into the page 29.
The circuit shown has been connected for a long time. The voltage across the capacitor is
(A) 1.2 V 30.
(B) 2.0 V
(C) 2.4 V
(D) 4.0 V
A wheel of radius R with an axle of radius R/2 is shown in the figure and is free to rotate about a frictionless axis through its centre and perpendicular to the page. Three forces (F, F, 2F) are exerted tangentially to the repective rims as shown in the figure.
The magnitude of the net torque acting on the system is nearly (A) 3.5FR (B) 3.2 FR (C) 2.5 FR
(D) 1.5 FR
31.
Two species of radioactive atoms are mixed in equal number. The disintegration of the first species is and of the second is /3. After a long time the mixture will behave as a species with mean life of approximately (A) 0.70/ (B) 2.10/ (C) 1.00/ (D) 0.52/
32.
The bulk modulus of a gas is defined as B = –VdP/dV. For an adiabatic process the variation of B is proportional to Pn. For an idea gas, n is (A) 0
(B) 1
(C)
5 2
(D) 2 CLASS-XII_STREAM-SB+2_PAGE # 105
33.
Photons of energy 7 eV are incident on two metals A and B with work functions 6 eV and 3 eV respectively. The minimum de Broglie wavelengths of the emitted photoelectrons with maximum energies are A and B, respectively where A/B is nearly (A) 0.5 (B) 1.4 (C) 4.0 (D) 2.0
34.
An electron enters a chamber in which a uniform magnetic field is present as shown. Ignore gravity. During its motion inside the chamber. (A) the force on the electron remains constant (B) the kinetic energy of the electron remains constant (C) the momentum of the electron remains constant (D) the speed of the electron increases at a uniform rate
35.
A ray of light incident on a glass sphere (refractive index
36.
Young-Laplace law states that the excess pressure inside a soap bubble of radius R is given by P = 4/R where is the coefficient of surface tension of the soap. The number E0 is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of g, the acceleration due to gravity, , the density of the surrounding fluid, and a characterstic length scale L which could be the radius of the bubble. A possible expression for E0 is
3 ) suffers total internal reflection before emerging out exactly parallel to the incident ray. The angle of incidence was (A) 75° (B) 30° (C) 45° (D) 60°
(A) 37.
g L3
L2 (B) g
gL2 (C)
gL2 (D)
A plank is resting on a horizontal ground in the northern hemisphere of the Earth at a 45° latitude. Let the angular speed of the Earth be and its radius re. The magnitude of the frictional force on the plank will be (A) mre2
(B)
mre 2 2
(C)
mre 2 2
(D) Zero
38.
The average distance between molecules of an ideal gas at STP is approximately of the order of (A) 1 nm (B) 100 nm (C) 100 cm (D) 1 m
39.
A point particle of mass 0.5 kg is moving along the x-axis under a force described by the potential energy V shown below. It is projected towards the right from the origin with a speed v. What is the minimum value of v for which the particle will escape infinitely fasr away from the origin ?
(A) 2 2 ms–1 (C) 4 ms–1
(B) 2 ms–1 (D) The particle will never escape
CLASS-XII_STREAM-SB+2_PAGE # 106
40.
The figure below shows pressure variation in two different sound waves in air with time at a given position. Both the figures are drawn to the same scale.
Which of the following statements is true? (A) Wave 1 has lower frequency and smaller amplitude compared to wave 2 (B) Wave 1 has higher frequency and greater amplitude compared to wave 2 (C) Wave 1 has shroter wavelength and greater amplitude compared to wave 2 (D) Wave 1 has shorter wavelength and smaller amplitude compared to wave 2
CHEMISTRY 41.
Among the following, the set of isoelectronic ions is : (A) Na+, Mg2+, F—, Cl— (B) Na+, Ca2+, F—, O2— (C) Na+, Mg2+, F—, O2—
(D) Na+, K+, S2—, Cl—
42.
For a zero-order reaction with rate constant k, the slope of the plot of reactant concentration against time is: (A) k/2.303 (B) k (C) –k/2.303 (D) – k
43.
The compound which reacts with excess bromine to produce 2, 4, 6-tribromophenol, is : (A) 1, 3-cyclohexadiene (B) 1, 3-cyclohexanedione (C) salicylic acid (D) cyclohexanone
44.
Ethyl acetate reacts with NH2NHCONH2 to form : (A) CH3CONHCONHNH2 (C) CH3CONHNHCONH2
45.
(B) CH3CON(NH2)CONH2 (D) CH3CH2NHNHCONH2
The variation of solubility of four different gases (G1, G2, etc.) in a given solvent with pressure at a constant temperature is shown in the plot.
The gas with the highest value of Henry’s law constant is (A) G4 (B) G2 (C) G3
(D) G1 CLASS-XII_STREAM-SB+2_PAGE # 107
46.
For the reaction, the concentration of A decreases from 0.06 to 0.03 mol L–1 and that of B –1 rises from 0 to 0.06 mol L at equilibrium. The values of n and the equilibrium constant for the reaction, respectively, are : (A) 2 and 0.12 (B) 2 and 1.2 (C) 3 and 0.12 (D) 3 and 1.2
47.
The reaction of ethyl methyl ketone with Cl2/excess OH– gives the following major product : (A) ClCH2CH2COCH3 (B) CH3CH2COCCl3 (C) ClCH2CH2COCH2Cl (D) CH3CCl2COCH2Cl
48.
The compound that readily tautomerizes is : (A) CH3COCH2CO2C2H5 (B) CH3COCH2CH2CH3
(C) CH3COCH2CH2CH3
(D) (CH3)3CCOC(CH3)3
49.
Hydrolysis of BCl3 gives X which on treatment with sodium carbonate produces Y, X and Y, respectively, are (A) H3BO3 and NaBO2 (B) H3BO3 and Na2B4O7 (C) B2O3 and NaBO2 (D) B2O3 and Na2B4O7
50.
The numbers of lone pair(s) on Xe in XeF2 and XeF4 are, respectively : (A) 2 and 3 (B) 4 and 1 (C) 3 and 2
(D) 4 and 2
51.
The entropy change in the isothermal reversible expansion of 2 moles of an ideal gas from 10 to 100 L at 300 K is : (A) 42.3 JK–1 (B) 35.8 J K–1 (C) 38.3 J K–1 (D) 32.3 J K–1
52.
D-Glucose upon treatment with bromine-water gives :
(A)
(B)
(C)
(D)
53.
In the structure of borax, the numbers of boron atoms and B-O-B units, respectively, are : (A) 4 and 5 (B) 4 and 3 (C) 5 and 4 (D) 5 and 3
54.
The number of peptide bonds in the compound is :
(A) 1 55.
(B) 2
(C) 3
(D) 4
For the isothermal reversible expansion of an ideal gas : (A) H > 0 and U = 0 (B) H > 0 and U < 0 (C) H = 0 and U = 0
(D) H = 0 and U > 0
56.
If the angle of incidence of X-ray of wavelength 3Å which produces a second order diffracted beam from the (100) planes in a simple cubic lattice with interlayer spacing a = 6 Å is 30°, the angle of incidence that produ ces a first-order diffracted beam from the (200) planes is : (A) 15° (B) 45° (C) 30° (D) 60°
57.
The number of ions produced in water by dissolution of the complex having the empirical formular, COCl34NH3, is : (A) 1 (B) 2 (C) 4 (D) 3
58.
The spin-only magnetic moments of [Fe(NH3)6]3+ and [FeF6]3– in BM are, respectively, (A) 1.73 and 1.73 (B) 5.92 and 1.73 (C) 1.73 and 5.92 (D) 5.92 and 5.92
CLASS-XII_STREAM-SB+2_PAGE # 108
59.
The order of SN1 reactivity in aqueous acetic acid solution for the compounds is :
(A) 1 > 2 > 3 60.
(B) 1 > 3 > 2
(C) 3 > 2 > 1
(D) 3 > 1 > 2
An ionic compound is formed between a metal M and a non-metal Y. If M occupies half the octahedral voids in the cubic close-packed arrangement formed by Y, the chemical formula of the ionic compound is: (A) MY (B) MY2 (C) M2Y (D) MY3
BIOLOGY 61.
Human fetal haemoglobin differs from the adult haemoglobin in that it has (A) higher affinity for oxygen (B) lower affinity for oxygen (C) two subunits only (D) is glycosylated
62.
Nucleolus is an organelle responsible for the production of (A) carbohydrates (B) messenger RNA (C) lipids
(D) ribosomal RNA
63.
The sequences of four DNA molecules are given below: i. TATATATATATATA ii. TTTCCCGGGAAA ATATATATATATAT AAAGGGCCCTTT iii. TTGCGTTGCCC iv. GCCGGATCCGGC AACGCAACGGG CGGCCTAGGCCG Which one of these DNA moelcules will have the highest melting temperature (Tm)? (A) i (B) ii (C) iii (D) iv
64.
If DNA codons are ATG GAA, insertion of thymine after the first codon results in, (A) non-sense mutation (B) mis-sense mutation (C) frameshift mutation (D) silent mutation
65.
Genetic content of a cell reduces to half during (A) meiotic prophase I (B) mitotic prophase
66.
67.
(C) meiotic prophase II
(D) meiotic telophase
Which one of the following techniques is used for the detection of proteins ? (A) Northern blotting (B) Western blotting (C) Southern blotting
(D) In-situ hybridization
Fission yeasts are (A) Archaebacteria
(D) Eukaryotes
(B) Eubacteria
(C) Prokaryotes
68.
In green leaves, the light and dark reactions occur in (A) stroma and grana respectively (B) grana and stroma respectively (C) cristae and matrix respectively (D) both occur in cytoplasm
69.
According to Mendel, ..................................... segregate and ........................... assort independently. (A) alleles of a gene; alleles of different genes (B) alleles of different genes; alleles of a gene (C) dominanat traits; recessive traits (D) recessive traits; recessive traits
70.
The two enzymatic activities associated with RUBISCO are (A) oxidase and oxygenase (B) oxygenase and carboxylase (C) oxidase and carboxylase (D) oxygenase and carbamylation
71.
Chlorofluorocarbons (CFCs) are belived to be associated with cancers because, (A) CFCs react with DNA and cause mutations (B) CFCs react with proteins involved in DNA repair (C) CFCs destroy the ozone layer and permit harmful UV rays to reach the earth (D) CFCs react with DNA polymerase and reduce fidelity of DNA replication
72.
Morphogenetic movements take place predominantly during the following embryonic stage (A) blastula (B) Morula (C) Gastrula (D) Fertilized eggs CLASS-XII_STREAM-SB+2_PAGE # 109
73. 74.
75.
The only organ which is capable of producing Fructose in humans is (A) liver (B) pancreas (C) seminal vesicles
(D) muscle
Stroke could be prevented/treated with (A) balanced diet (B) clotting factors
(C) insulin
(D) blood thinners
In orange and lemon, the edible part of the fruit is (A) placenta (C) hairs of the ovary wall
(B) thalamus (D) succulent Mesocap
76.
Which one of the following statements about nitrogenase is correct? (A) It is sensitive to CO2 and therefore present in isolated nodules. (B) It requires O2 and therefore functional during the day (C) It is sensitive to O2 and therefore is functional in anaerobic environments (D) It is sensitive to light and therefore functions only in dark.
77.
Part of epidermis that keeps out unwanted particles is called (A) columnar epithelium (B) squamous epithelium (C) ciliated epithelium (D) cuboidal epithelium
78.
Species that are most effective at colonising new habitats show (A) low reproductive ability (B) high dispersal ability (C) slow growth and maturation (D) high competitive ability
79.
In a large isolated population, alleles p and q at a locus are at Hardy Weinberg equilibrium. The frequencies are p = 0.6 and q = 0.4. The proportion of the heterozygous genotype in the population is (A) 0.24 (B) 1 (C) 0.48 (D) 0.12
80.
In vertebrates ‘glycogen’ is stored chiefly in (A) heart and blood (B) spleen and stomach
(C) bones and lymph
(D) liver and muscles
PART-II Two Mark Questions MATHEMATICS 81.
82.
1 Let f(x) be a non-constant polynomial with real coefficients such that f = 100 and f(x) 100 for all 2 real x. Which of the following statements is NOT necessarily true ? (A) The coefficient of the highest degree term in f(x) is negative (B) f(x) has at least two real roots (C) If x 1/2 then f(x) < 100 (D) At least one of the coefficients of f(x) is bigger than 50.
Let a, b, c, d be real numbers such that n
(ak
3
bk 2 ck d) n 4
k 1
for every natural number n. Then | a | + | b | + | C | + | d | is equal to (A) 15 (B) 16 (C) 31 83.
(D) 32
The vertices of the base of an isosceles triangle lie on a parabola y2 = 4x and the base is a part of the line y = 2x – 4. If the third vertex of the triangle lies on the x-axis, its coordinates are 5 (A) ,0 2
7 (B) ,0 2
9 (C) ,0 2
11 (D) ,0 2
CLASS-XII_STREAM-SB+2_PAGE # 110
84.
In a triangle ABC, let G denote its centroid and let M, N be points in the interiors of the segments AB, AC, respectively, such that M, G, N are collinear. If r denotes the ratio of the area of triangle AMN to the area of ABC then (A) r = 1/2 (B) r > 1/2 (C) 4/9 r < 1/2 (D) 4/9 < r
85.
Let XY be the diameter of a semicircle with centre O. Let A be a variable point on the semicircle and B another point on the semicircle such that AB is parallel to XY. The value of BOY for which the inradius of triangle AOB is maximum, is
1 5 1 (A) cos 2
86.
Let f(x) = 1+ (A) 0
87.
1 5 1 (B) sin 2
3
(D)
x x2 x3 x 4 . The number of real roots of f(x) = 0 is 1! 2! 3! 4! (B) 1 (C) 2
5
(D) 4
Suppose that the earth is a sphere of radius 6400 kilometers. The height from the earth’s surface from where exactly a fourth of the earth’s surface is visible, is (A) 3200 km
88.
(C)
(B) 3200 2 km
(C) 3200 3 km
(D) 6400 km
Let n be a positive integer. For a real number x, let [x] denote the largest integer not exceeding x and n 1
{x} = x – [x]. Then
1
(A) loge(n)
x[ x ] dx is equal to x (B)
1 n 1
(C)
n n 1
(D) 1
1 1 .... 2 n
89.
A box contains coupons labelled 1,2,...,100. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be x1, x2,....,x5. What is the probability that x1 > x2 > x3 and x3 < x4 < x5? (A) 1/120 (B) 1/60 (C) 1/20 (D) 1/10
90.
In a tournament with five teams, each team plays against every other team exctly once. Each game is won by one of the playing teams and the winning team scores one point, while the losing team scores zero. Which of the following is NOT necessarily true? (A) There are at least two teams which have at most two points each. (B) There are at least two teams which have at least two points each. (C) There are at most three teams which have at least threee points each (D) There are at most four teams which have at most two points each
PHYSICS 91.
A bullet of mass m is fired horizontally into a large sphere of mass M and radius R resting on a smooth horizontal table.
The bullet hits the sphere at a height h from the table and sticks to its surface. If the sphere starts rolling without slippng immediately on impact, then (A)
h 4m 3M R 2m M
(B)
h m 3M R m 2M
(C)
h 10m 7M R 5m M
(D)
h 4m 3M R mM
CLASS-XII_STREAM-SB+2_PAGE # 111
92.
A small boy is throwing a ball towards a wall 6 in front of him. He releases the ball at a height of 1.4 m from the ground. The ball bounces from the wall at a height of 3 m, rebounds from the ground and reaches the boy’s hand exactly at the point of release. Assuming the two bounces (one from the wall and the other from the ground) to be perfectly elastic, how far ahead of the boy did the ball bounce from the ground? (A) 1.5m (B) 2.5 m (C) 3.5 m (D) 4.5 m
93.
In the P-V diagram below the dashed curved line is an adiabat.
For a process that is described by a straight line joining two points X and Y on the adiabat (solid line in the diagram) heat is : (hint : Consider the variations in temperature from X to Y along the straitght line) (A) absorbed throughtout from X to Y (B) released throughout from X to Y (C) absorbed from X up to an intermediate point Z (not shown in the figure) and then released from Z to Y (D) released from X up to an intermediate point Z (not shown in the figure) and then absorbed from Z to Y 94.
A singly ionized helium atom in an excited state (n = 4) emits a photon of energy 2.6 eV. Given that the ground state energy of hydrogen atom is –13.6 eV, the energy (Et) and quantum number (n) of the resulting state are respectively, (A) Et = – 13.6eV, n = 1 (B) Et = – 6.0 eV, n = 3 (C) Et = – 6.0 eV, n = 2 (D) Et = – 13.6 eV, n = 2
95.
The figure below shows a circuit and its input voltage vi as function of time t.
Assuming the diodes to be ideal, which of the following graphs depicts the output voltage v0 as function of time t ?
(A)
96.
(B)
(C)
(D)
A ball is rolling without slipping in a spherical shallow bowl (radius R) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled, the period of oscillation
(A) increases slightly (C) is increased by a factor of 2
(B) is reduced by a factor of 1/2 (D) decreases slightly
CLASS-XII_STREAM-SB+2_PAGE # 112
97.
A solid sphere rolls without slipping, first horizontal and then up to a point X at height h on an inclined plane before rolling down, as shown.
The initial horizontal speed of the sphere is (A) 98.
10gh / 7
7gh / 5
(B) 10 J
5gh / 7
(D)
2gh
(C) 20 J
(D) 30 J
A block of mass m slides from rest at a height H on a frictionless inclined plane as shown in the figure. It travels a distance d across a rough horizontal surface with coefficient of kinetic friction , and compresses a spring of spring k by a distance x before coming to rest momentarily. Then the spring extends and the block travels back attaining a final height of h. Then
(A) h = H –2(d + x) (C) h = H –2d + kx2/mg 100.
(C)
The three processes in a thermodynamic cycle shown in the figure are : Process 1 2 is isothermal; Process 2 3 is isochoric (volume remains constant); Process 3 1 is adiabatic. The total work done by the ideal gas in this cycle is 10 J. The internal energy decreases by 20 J in the isochoric process. The work done by the gas in the adiabatic process is –20 J. The heat added to the system in the isothermal process is
(A) 0 J 99.
(B)
(B) h = H + 2(d + x) (D) = H – 2(d + x) + kx2/ 2mg
A metallic prong consists of 4 rods made of the same material, cross-section and same lengths as shown. The three forked ends are kept at 100° C and the handle end is at 0°C. The temperature of the junction is
(A) 25°C
(B) 50°C
(C) 60°
(D) 75°C
CLASS-XII_STREAM-SB+2_PAGE # 113
CHEMISTRY 101.
The major product obtained in the reaction of aniline with acetic anhydride is NHCOCH3
NH2
NHCOCH3
(B) H3C
(A)
(D) H3C
(C)
O
O
102.
The maximum number of isomers that can result from monobromination of 2-methyl-2-pentene with Nbromosuccinimide in boiling CCl4 is (A) 1 (B) 2 (C) 3 (D) 4
103.
The compound X (C7H9N) reacts with benzensulfonyl chloride to give Y (C13H13NO2S) which is insoluble in alkali. The compound X is
NH2 (A)
NH2
NH2
NH CH3
(B)
CH3
(C)
(D)
CH3
H3C
104.
In 108 g of water, 18 g of a non-volatile compound is dissolved. At 100°C the vapor pressure of the solution is 750 mm Hg. Assuming that the compound does not undergo association or dissociation, the molar mass of the compound in g mol–1 is (A) 128 (B) 182 (C) 152 (D) 228
105.
The standard electrode potential of Zn2+/Zn is –0.76 V and that of Ca2+/Cu is 0.34 V. The emf (V) and the free energy change (kJ mol–1), respectively, for a Daniel cell will be (A) – 0.42 and 81 (B) 1.1 and –213 (C) –1.1 and 213 (D) 0.42 and –81
106.
Consider the equilibria (1) and (2) with equilibrium constants K1 and K2, respectively SO2(g) +
1 O (g) 2 2
2SO3(g)
SO3(g)
.... (1)
2SO2(g) + O2(g)
.... (2)
K1 and K2 are related as (A) 2K1 = K22
(B) K12 =
1 K2
(C) K22 =
1 K1
2 (D) K2 =
K 12
107.
Aqueous solution of metallic nitrate X reacts with NH4OH to form Y which dissolves in excess NH4OH. The resulting complex is reduced by acetaldehyde to deposit the metal. X and Y, respectively, are (A) Cs(NO3) and CsOH (B) Zn(NO3)2 and ZnO (C) AgNO3 and Ag2O (D) Mg(NO3)2 and Mg(OH)2
108.
The density of eq. wt of a metal are 10.5 g cm–3 and 100, respectively. The time required for a current of 3 amp to deposit a 0.005 mm thick layer of the same metal on an area of 80 cm2 is closest to (A) 120 s (B) 135 s (C) 67.5 s (D) 270 s
109.
The amount of Na2S2O3.5H2O required to completely reduce 100 mL of 0.25 N iodine solution, is (A) 6.20 g (B) 9.30 g (C) 3.10 g (D) 7.75 g
110.
In aqueous solution, [Co(H2O)6]2+ (X) reacts with molecular oxygen in the presence of excess liquor NH3 to give a new complex Y. The number of unpaired electrons in X and Y are, respectively (A) 3, 1 (B) 3, 0 (C) 3, 3 (D) 7, 0
CLASS-XII_STREAM-SB+2_PAGE # 114
BIOLOGY 111.
109 bacteria were spread on an agar plate containing penicillin. After incubation overnight at 37°C, 10 bacterial colonies were observed on the plate. That the colonies are likely to be resistant to penicillin can be tested by (A) measuring their growth rate (B) observing the colour of the colonies (C) checking their ability to grow on another plate containing penicillin. (D) checking their ability to cause disease
112.
Watson and Crick model of DNA is (A) B-form DNA with a spiral length of 34 Å and a diameter of 20 Å (B) A-form DNA with a spiral length of 15 Å and a diameter of 20 Å (C) Z-form DNA with a spiral length of 34 Å and a diameter of 20 Å (D) B-form DNA with a spiral length of 28 Å and a diameter of 14 Å
113.
Eco RI and Rsa I restriction endonucleases require 6 bp and 4 bp sequences respectively for cleavage. In a 10 kb DNA fragment how many probable cleavage sites are present for these enzymes (A) 0 Eco RI and 10 Rsa I (B) 1 Eco RI and 29 Rsa I (C) 4 Eco RI and 69 Rsa I (D) 2 Eco RI and 39 Rsa I
114.
From an early amphibian embryo the cells that would give rise to skin in adults were transplanted into the developing brain region of another embryo. The transplanted cells developed into brain tissue in the recipient embryo. What do you infer from this experiment? (A) Cell fate is permanently determined during early embryonic development. (B) Developmental fate of donor cells is influenced by the surrounding cells. (C) Developmental fate of donor cells is not influenced by recipient cells. (D) Any cell which is transplanted into another embryo always develops into a brain.
115.
Presence of plastids in Plasmodium suggests (A) it is a plant species (B) it is a parasite with a cynobacterium as an endosymbiont (C) it is a parasite with a archebacterium as an endosymbiont (D) it is a plant species with a archebacterium as an endosymbiont
116.
The figure below demonstrates the growth curves of two organisms A and B growing in the same area. What kind of relation exists between A and B?
Increase in biomass
organism A only organism B only organism B in presence of A organism A in presence of B
Time
(A) Competition
(B) Symbiosis
(C) Commensalisms
(D) Mutualism
CLASS-XII_STREAM-SB+2_PAGE # 115
117.
A scientist has cloned an 8 Kb fragment of a mouse gene into the Eco RI site of a vector of 6 Kb size. The cloned DNA has no other Eco RI site within. Digestions of the cloned DNA is shown below.
Which one of the following sets of DNA fragments generated by digestion with both Eco RI and Bam HI as shown in (iii) is from the gene? (A) 1 Kb and 4 Kb (B) 1 Kb and 2.5 Kb (C) 1 Kb and 3 Kb (D) 1 Kb and 3.5 Kb 118.
Brown fat is a specialised adipose tissue with abundant mitochondria and rich blood supply. Brown fat (A) insulates animals that are acclimatised to cold. (B) is the major source of heat production of birds. (C) provides energy to muscles. (D) produces heat without producing ATP.
119.
In some species, individuals forego reproduction and help bring up another individual’s offspring. Such altruistic behaviour CANNOT be explained by which of the following? (A) An individual helps relatives only and gets indirect genetic benefits. (B) The individual benefits because it can later inherit the breeding position. (C) The individual benefits because it gets access to resources, such as food and security from predators, in return. (D) The species benefits from a reduction in competition among offspring.
120.
Lions in India are currently restricted to Gir, Gujarat. Efforts are being made to move them to other parts of the country. This is because they are MOST susceptible to extinction due to infectious diseases under the following conditions when present as (A) several small, isolated populations (B) one large population (C) several large, connected populations (D) several large, isolated populations
CLASS-XII_STREAM-SB+2_PAGE # 116
KISHORE VAIGYANIK PROTSAHAN YOJANA - 2014 Date : 02-11-2014
Duration : 3 Hours
Max. Marks : 160
STREAM - SB/SX GENERAL INSTRUCTIONS •
The Test Booklet consists of 120 questions.
•
There are Two parts in the question paper. The distribution of marks subjectwise in each part is as under for each correct response.
MARKING SCHEME : PART-I : MATHEMATICS Question No. 1 to 20 consist of ONE (1) mark for each correct response. PHYSICS Question No. 21 to 40 consist of ONE (1) mark for each correct response. CHEMISTRY Question No. 41 to 60 consist of ONE (1) mark for each correct response. BIOLOGY Question No. 61 to 80 consist of ONE (1) mark for each correct response.
PART-II : MATHEMATICS Question No. 81 to 90 consist of TWO (2) marks for each correct response. PHYSICS Question No. 91 to 100 consist of TWO (2) marks for each correct response. CHEMISTRY Question No. 101 to 110 consist of TWO (2) marks for each correct response. BIOLOGY Question No. 111 to 120 consist of TWO (2) marks for each correct response.
YEAR-2014 (KVPY-STREAM-SB/SX)
PART-I One Mark Questions MATHEMATICS 1.
Let C0 be a circle of radius 1.for n 1 , let Cn be a circle whose area equals the area of a square inscribed in Cn-1.Then
i0
Area Ci equals :
(A) 2 2.
(B)
(C)
1 2
(D)
2 2
For a real number r we denote by [r] the largest integer less than or equal to r. If x,y are real numbers with x,y 1 then which of the following statements is always true ? (A) [x+y] [x]+[y]
3.
2 2
(C) [2x] 2[x]
(B) [xy] [x][y]
x x (D) y y
n For each positive integer n, let A n max r | 0 r n . Then the number of elements n is
1,2,3,........20 An for which 1.9 A 2 is : n 1 (A) 9 4.
(B) 10
(D) 12
Let b, d>0. The locus of all points P(r,) for which the line OP (where O is the origin) cuts the line rsin=b in Q such that PQ=d is : (A) (r d)sin b
5.
(C) 11
(B) (r d)sin b
(C) (r d)cos b
(D) (r d)cos b
Let C be the circle x2 + y2 = 1 in the xy-plane. For each t 0 , let Lt be the line passing through (0,1) and (t,0). Note that Lt intersects C in two points, one of which is (0,1). Let Qt be the other point. As t varies between 1 and 1 2 , the collection of points Qt sweeps out an arc on C. The angle subtended by this are at (0,0) is : (A)
6.
8
(B)
4
(C)
3
(D)
3 8
In a ellipse, its foci and the ends of its major axis are equally spaced, if the length its semi-minor axis is
2 2 , then the length of its semi-major axis is : (A) 4 7.
(C) 10
(D) 3
Let ABC be a triangle such that AB=BC. Let F be the midpoint of AB and X be a point on BC such that FX is perpendicular to AB. If BX=3XC then the ratio BC/AC equals : (A)
8.
(B) 2 3
3
(B)
2
(C)
3 2
4 The number of solutions to the equation cos x
(A) 6
(B) 4
(C) 2
(D) 1 1 1 sin4 x in the interval 0,2 is : 2 cos x sin2 x (D) 0 CLASS-XII_STREAM-SB+2_PAGE # 117
9.
Consider the function
x 5 f x x 2 1
if x 2 if x 2
Then f(f(x)) is discontinuous (A) at all real numbers (C) at exactly one value of x 10.
(B) at exactly two values of x (D) at exactly three values of x
For a real number x let [x] denote the largest number less than or equal to x. for x R let f(x) [x]sin x . Then : (A) f is differentiable on R (B) f is symmetric about the line x=0
(C)
3
f x dx 0 3
(D) For each real , the equation f(x)-=0 has infinitely many roots. 11.
Let f : 0, R be defined as sin x, if x is irrational and x 0, f x 2 tan x, if x is rational and x 0,
The number of points in[0, ] at which the function f is continuous is : (A) 6 (B) 4 (C) 2
(D) 0
1
12.
Let f : [0,1] [0, ) be a continuous function such that
f x dx 10 . Which of the following state0
ments is NOT necessarily true ? 1
1 x (A) e f x dx 10
(B)
f x
1 x
2
dx 10
0
0
1
1 2
(C) 10 sin 100x f x dx 10
(D) f x dx 100
0
0
x
13.
A continuous function f : R R satisfies the equation f x x f t dt . 0
Which of the following options is true ? (A) f(x+y) = f(x) + f (y) (C) f(x+y) = f(x) + f(y) + f(x)f(y) 14.
(B) f (x+y) = f(x)f(y) (D) f(x+y) = f(xy)
For a real number x let [x] denote the largest integer less than or equal to x and {x} = x - [x]. Let n be a n
positive integer. Then cos 2[x] x dx is equal to : 0
(A) 0
(B) 1
(C) n
(D) 2n-1
15.
Two persons A and B throw a (fair) die (six-faced cube with faces numbered from 1 to 6) alternately, starting with A. The first person to get an outcome different from the previous one by the opponent wins. The probability that B wins is : (A) 5/6 (B) 6/7 (C) 7/8 (D) 8/9
16.
Let n 3 .A list of numbers x1,x 2 ,.........xn has mean and standard deviation . A new list of numbers
y1,y 2 ,..........yn is made as follows : y1
x1 x 2 x1 x 2 , y2 and y j x for j 3,4,.......n . The mean 2 2
and the standard deviation of the list are ˆ and ˆ . Then which of the following is necessarily true ? (A) ˆ and ˆ
(B) ˆ and ˆ
(C) ˆ
(D) ˆ CLASS-XII_STREAM-SB+2_PAGE # 118
17.
What is the angle subtended by an edge of a regular tetrahedron at its center ? 1 1 (B) cos 2
1 1 (A) cos 2
1 1 (C) cos 3
1 1 (D) cos 3
18.
Let S = {(a,b):a,b Z,0 a,b 18}. The number of elements (x,y) in S such that 3x + 4y + 5 is divisible by 19 is : (A) 38 (B) 19 (C) 18 (D) 1
19.
For a real number r let [r] denote the largest integer less than or equal to r. Let a > 1 be a real number which is not an integer, and let k be the smallest positive integer such that [ak]>[a]k. then which of the following statements is always true ? (A) k 2 a 1
20.
2
(B) k a 1
4
(C) k 2[a ] 1
(D) k
1 1 a [a]
Let X be a set of 5 elements. The number d of ordered pairs (A,B) of subsets of X such that
A ,B ,A B satisfies : (A) 50 d 100
(B) 101 d 150
(C) 151 d 200
(D) 201 d
PHYSICS 21.
A uniform thin rod of length 2L and mass m lies on a horizontal table. A horizontal inpulse J is given to the rod at one end. There is no friction. The total K.E. of the rod just after the impulse will be : (A) J2/2m (B) J2/m (C) 2J2/m (D) 6J2/m
22.
A solid cylinder P rolls without slipping from rest down an inclined plane attaining a speed vp at the bottom. Another smooth solid cyclinder Q of same mass and dimensions slides without friction from rest
vp down the inclined plane attaining a speed vq at the bottom. The ratio of the speeds v is : q 3 (A) 4
3 (B) 2
2 (C) 3
4 (D) 3
23.
A body moves in a circular orbit of radius R under the action of a central force. Potential due to the central force is given by V(r) = kr (k is a positive constant). period of revolution of the body is proportional to : (A) R1/2 (B) R-1/2 (C) R-3/2 (D) R-5/2
24.
A simple pendulum is attached to a block which slides without friction down an inclined plane (ABC) having an angle of inclination as shown
while the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string is : (A) at angle to the perpendicular to the inclined plane AC. (B) parallel to the inclined plane AC. (C) vertically downwards. (D) perpendicular to the inclined plane AC. CLASS-XII_STREAM-SB+2_PAGE # 119
25.
Water containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross- section. In this region the bubbles : (A) move with greater speed and are smaller than in the rest of the pipe (B) move with greater speed and are larger in size than in the rest of the pipe (C) move with lesser speed and are smaller than in the rest of the pipe. (D) move with lesser speed and are of the same size as in the rest of the pipe
26.
A solid expands upon heating because : (A) the potential energy of interaction between atoms in the solid is asymmetric about the equilbrium positions of atoms (B) the frequency of vibration of the atoms increases (C) the heating generates a thermal gradient between opposite sides (D) a fluid called the caloric flows into the interatomic spacing of the solid during heating thereby expanding it.
27.
Consider two thermometers T1 and T2 of equal length which can be used to measure temperature over the range 1 to 2. T1 contains mercury as thermometric liquid while T2 contains bromine. The volumes of the two liquids are the same at the temperature 1.The volumetric coefficients of expansion of mercury and bromine are 18 × 10-5 K-1 and 108 × 10-5 K-1, respectively. The increase in length of each liquid is the same for the same increase in temperature. If the diameters of the capillary tubes of the two thermometers are d1 and d2 respectively, then the ratio d1:d2 would be closest to : (A) 6.0 (B) 2.5 (C) 0.5 (D) 0.4
28.
An ideal gas follows aprocess described by PV2=C from (P1,V1,T1) to (P2,V2,T2)(C is a constant). Then (A) if P1 > P2 then T2 > T1 (B) if V2 > V1 then T2 < T1 (C) if V2 > V1 then T2 > T1 (D) if P1 > P2 then V2 > V2
29.
A whistle emitting a loud sound of frequency 540 Hz is whirled in a horizontal circle of radius 2m and at a constant angular speed of 15rad/s. The speed of sound is 330 m/s. The ratio of the highest to the lowest frequency heard by a listener standing at rest at a large distance from the center of the circle is : (A) 1.0 (B) 1.1 (C) 1.2 (D) 1.4
30.
Monochromatic light passes through a prism. Compares to that in air, inside the prism the light’s (A) speed and wavelength are different but frequency remains same. (B) speed and frequency are different but wavelength remains same. (C) frequency and wavelength are different but speed remains same. (D) speed,wavelength and frequency are all different.
31.
The flat face of a plano-convex lens of focel length 10 cm is silvered. A point source placed 30 cm in front of the curved surface will produce a : (A) real image 15 cm away from the lens (B) real image 6 cm away from the lens (C) virtual image 15 cm away from the lens (D) Virtual image 6 cm away from the lens
32.
Two identical metallic square loops L1 and L2 are placed next to each other with their sides parallel on a smooth horizontal table. Loop L1 is fixed and a current which increases as a function of time is passed through it.Then loop L2 : (A) rotates about its center of mass (B) moves towards L1 (C) remains stationary (D) moves away from L1
33.
An electron enters a parallel plate capacitor with horizontal speed and is found to deflect by angle on leaving the capacitor as shown. It is found that tan = 0.4 and gravity is negligible
If the initial horizontal speed is doubled,then tan will be : (A) 0.1 (B) 0.2 (C) 0.8
(D) 1.6 CLASS-XII_STREAM-SB+2_PAGE # 120
34.
Consider a spherical shell of radius R with a total charge +q uniformly spread on its surface (center of the chell lies at the origin x = 0). Two point charges, +q and -q are brought, one after the other, from far away and placed at x = -a/2 and x = +a/2 (a EII and AI > AII
(B) EII > EI and AII > AI
(C) EI > EII and AII > AI
(D) EII > EI and AI > AII
(D) Na I ln k II 1/T
Ni(CO)4 is : (A) tetrahedral and paramagnetic (C) tetrahedral and diamagnetic
(B) square planar and diamagnetic (D) square planar and paramagnetic
In the following reactions :
1. ozonolysis
X
2. OH
the major product X is : O
O O
O
(A)
(B)
(C)
(D) O
49.
Given the structure od D-(+)-glucose as : CHO H
OH H
HO H
OH
H
OH CH2OH
The structure of L-(-)- glucose is : CHO
CHO
(A)
HO
H
HO
HO
H
H
H
OH
H
OH CH2OH
(B)
H OH
HO
H
HO
H CH2 OH
CHO
CHO
(C)
H
OH
HO
HO
H
H
H
OH H
HO CH2OH
(D)
H OH H
HO H
OH CH2OH
CLASS-XII_STREAM-SB+2_PAGE # 122
50.
In a cubic close packed structure, fractional contributions of an atom at the corner and at the face in the unit cell are, respectively : (A) 1/8 and 1/2 (B) 1/2 and 1/4 (C) 1/4 and 1/2 (D) 1/4 and 1/8
51.
The equilibrium constant Kc of the reaction 2A B C is 0.5 at 25°C and i atm. The reaction will proceed in the backward direction when concentrations [A], [B] and [C] are respectively : (A) 10-3, 10-2 and 10-2 M (B) 10-1, 10-2 and 10-2 M (C) 10-2, 10-2 and 10-3 M (D) 10-2, 10-3 and 10-3 M
52.
Major products formed in the reaction of t-butyl methyl ether with HI are :
(A)
(B)
(C)
(D)
53.
If the molar conductivities (in S cm2 mol-1) of NaCl, KCl and NaOH at infinite dilution are 126, 150 and 250 respectively, the molar conductivity of KOH (in S cm2 mol-1) : (A) 526 (B) 226 (C) 26 (D) 274
54.
4-Formylbenzoic acid on treatment with one equivalent of hydraine followed by heating with alcoholic KOH gives the major product :
(A)
(B)
(C)
(D)
55.
Two elements, X and Y, have atomic numbers 33 and 17 respectively. The milecular formula of a stable compound formed between then is (A) XY (B) XY2 (C) XY3 (D) XY4
56.
The number of moles of KMnO4 required to oxidize one equivalent of Kl in the presence of sulfuric acid is (A) 5 (B) 2 (C) 1/2 (D) 1/5
57.
Three successive measurements in an experiment gave value 10.9, 11.4042 and 11.42 the correct way of reporting the average value is (A) 11.2080 (B) 11.21 (C) 11.2 (D) 11
58.
The latent heat of melting of ice at 0 °C is 6 kJ mol-1. The entropy change during the melting in J K-1 is closest to (A) 22 (B) 11 (C) -11 (D) -22
CLASS-XII_STREAM-SB+2_PAGE # 123
59.
The major product of the following reaction
is
60.
(A)
(B)
(C)
(D)
The energies of dxy and d2z orbitals in octahedral and tetrahedral transition metal complexes are such that (A) E (dxy) > E (dz2) in both tetrahedral and octahedral complexes (B) E (dxy) < E (dz2) in both tetrahedral and octahedral complexes (C) E (dxy) > E (dz2) in tetrahedral abut E (dxy) < E (dz2) in octahedral complexes (D) E (dxy) < E (dz2) in tetrahedral abut E (dxy) < E (dz2) in octahedral complexes
BIOLOGY 61.
In which of the following types of glands is the decretion collected inside the cell and discharged by disintegration of intire gland ? (A) Apocrine (B) Merocrine (C) Holocrine (D) Epicrine
62.
Which one of the following interactions does NOT promote coevolution ? (A) Commensalism (B) Mutualism (C) Parasitism
(D) Interspecific competition
Stratification is more common in which of the following ? (A) Deciduous forest (B) Tropical rain forest (C) Temperate forest
(D) Tropical savannah
Where is the 3rd ventricle of the brain located? (A) Cerebrum (B) Cerebellum
(D) Diencephalon
63.
64.
(C) Pons varoli
65.
Which of the following is the final product of a gene ? (A) a polypeptide (B) an RNA only (C) either polypeptide or RNA (D) a nucleotide only
66.
Forelimbs of whales,bats,humans and cheetah are examples of which of the following processes? (A) Divergent evolution (B) Convergent evolution (C) Adaptation (D) Saltation
67.
Which of the following results from conjugation in paramecium ? (A) Cell death (B) Cell division (C) Budding
68.
(D) Recombination
In an experiment investigating photoperiodic response, the leaves of a plant are removed.what is the most likely outcome ? (A) Photoperiodism is not affected (B) Photoperiodic response does not occur (C) The plant starts flowering (D) The plant starts to grow taller
CLASS-XII_STREAM-SB+2_PAGE # 124
69.
70.
71.
72.
73.
74.
Testosterone is secreted by which endocrine part of testis? (A) Leydig cells (B) Seminiferous tubules (C) Tunica albugenia
(D) Sertoli cells
The mutation of a purine to a pyrimidine is known as: (A) transition (B) frame shift (C) nonsense
(D) transversion
Which of the following is secreted at the ends of an axon ? (A) Ascorbic acid (B) Acetic acid (C) Acetyl choline
(D) Acetyl CoA
A bacterial colony is produced from : (A) a single bacterium by its repetitive division (C) clumping of two to three bacteria
(B) multiple bacterium without replication (D) a single bacterium without cell division
Rhinoviruses are the causative agents of : (A) Diarrhoea (B) AIDS
(C) Dengue
What is the genetic material of Ebola virus ? (A) Single-Standard DNA (C) Single-Standard RNA
(D) Common Cold
(B) Double-Standard RNA (D) Double-Standard DNA
75.
Name the terminal acceptor of electrons in the mitochondrial electron transport chain : (A) Nitrate (B) Fumarate (C) Succinate (D) Oxygen
76.
Two tubes labeled ‘P’and ’Q’ contain food stuff. Tube ‘P’gave positive test with Benedict’s solution while tube ‘Q’ gave positive test with Nitric acid. Which of the foloowing is correct ? (A) Tube ‘P’ contains sugar;tube ‘Q’ contains protein (B) Tube ‘P’ contains protein;tube ‘Q’ contains sugar (C) Both tube ‘P’ and tube ‘Q’ contain sugar (D) Both tube ‘P’ and tube ‘Q’ contain protein
77.
How many linear DNA fragments will be produced when a circular plasmid is digested with a restriction enzyme having 3 sites ? (A) 4 (B) 5 (C) 3 (D) 2
78.
If the humidity of the atmosphere suddenly increases substantially, the water flow in the xylem will : (A) increase (B) decrease (C) remain unaltered (D) increase sharply and then reduce slowiny to the pre-existing level
79.
Which one of the following is the complementary sequence for the DNA with 5’-CGTACTA-3’ (A) 5’-TAGTACG-3’ (B) 5’-ATCATGC-3’ (C) 5’-UTCUTGC-3’ (D) 5’-GCUAGCA-3’
80.
A diploid plant has 14 chromosomes,but its egg cell has 6 chromosomes. Which one of the following is the most likely explanation of this ? (A) Non-disjunction in meiosis I and II (B) Non-disjunction in meiosis I (C) Non-disjunction in meiosis (D) Normal meiosis
CLASS-XII_STREAM-SB+2_PAGE # 125
PART-II Two Mark Questions MATHEMATICS 81.
Let n 3 be an integer. For a permutation =(a1,a2,....an) of (1,2,...,n) we let f (x) = anxn-1+an1+...+a x+a .Let S be the sum of the roots of f (x) = 0 and let S denote the sum over all permutation 2 1 of (1,2,....,n) of the number S . Then (A) S < -n! (B) -n! < S < 0 (C) 0 < S < n! (D) n! < S
82.
If n is a positive integer and 1 is a cube root of unity, the number of possible values of
n
(A) 2
(B) 3
(C) 4
n k is k ek 0
(D) 6
83.
Suppose a parabola y = ax2 + bx + c has two x intercepts one positive and one negative, and its vertex is (2,2). Then which of the following is true (A) ab > 0 (B) bc > 0 (C) ca > 0 (D) a + b + c > 0
84.
Let n 3 and let C1, C2,....Cn, be circles with radii r1,r2,...,rn, respectively. Assume that Ci and Ci+1 touch externally for 1 i n-1. It is also given that the x-axis and the line y = 2 2 x+10 are tangential to each of the circles. Then r1,r2,.....,rn are in (A) An arithmetic progression with common difference 3+ 2 (B) A geometric progression with common ratio 3+ 2 (C) An arithetic progression with common diffrence 2+ 3 (D) A geometric progression with common ratio 2+ 3
85.
86.
The under of integers n for which 3x3 - 25x+n = 0 has three real roots is (A) 1 (B) 25 (C) 55
An ellipse inscribed in a semi-circle touches the circular are at two distinct points and also touches the bounding diameter. its major axis is parallel to the bounding diameter. When the ellipse has the maximum possible area, its eccentricity is
1
(A)
(B)
2 / 2
87.
Let In =
x
n
0
/2 (A) e 1
88.
(D) Infinite
1 2
(C)
1
(D)
3
2 3
I I cos x dx, where n is a non negative int eger . Then n 2 n n 2 equal n! (n 2)!
2
(B) e / 2 1
/2 (C) e
2
(D) e /2
For a real number x let [x] denote the largest integer less than or equal to x. The smallest positive n
integer n for which the integral
[x][
x ]dx exceeds 60 is
1
(A) 8 89.
(C) 10
(D) [602/3]
Choose a number n uniformly at random from the set {1,2,...100}. Choose one of the first seven days of the year 2014 at random and consider n consencutive days among the chosen n days, the number of Sunday is different from the number of Mondays? (A)
90.
(B) 9
1 2
(B)
2 7
(C)
12 49
(D)
43 175
Lets S = {(a,b)}Ia,b Z, 0 a,b, 18}. The number of lines in R2 passing through (0,0) and exactly one other point in S is (A) 16 (B) 22 (C) 28 (D) 32 CLASS-XII_STREAM-SB+2_PAGE # 126
PHYSICS 91.
A solid sphere spinning about a horizontal axis with an angular velocity is placed on a horizontal surface. Subsequently it rolls without slipping with an angular velocity of (A) 2 /5 (B) 7 /5 (C) 2 /7 (D)
92.
Consider the system shown below F
X
Y
A horizontal force F is applied to a block X of mass 8 kg such that the block Y of mass 2kg adjacent to it does not slip downwards under gravity. There is no friction between the horizontal plane and the base of the block X. The coefficient of friction between the surfaces of blocks X and Y is 0.5. Take acceleration due to gravity to be 10ms-2. The minimum value of F is (A) 200N (B) 160N (C) 40N (D) 240N 93.
The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is (A) 90° (B) 60° (C) 45° (D) 30°
94.
One mole of a monoatomic ideal gas is expanded by a process described by PV3 = C where C is a constant. The heat capacity of the gas during the process is given by (R is the gas constant)
5 3 R (C) R (D) R 2 2 A concave mirror of radius of curvature R has a circular outline of radius r. A circular disk is to be placed normal to the axis at the focus so that it collects all the light that is reflected from the mirror from a beam parallel to the axis. for r 0 3x (x – 2a) > 0 (x – 2a) > 0 [ x > 0] x > 2a So, a 0.
CLASS-XII_STREAM-SB+2_PAGE # 136
3
14.
xcos 2 x xdx 1
2
3
= cos 2 x 1dx + 1
2 cos 2 x 2dx
2
2
=
15.
sin 2 x 1 2
=
2 4 [1 0] [1 0]
=
6 .
1
3
sin 2 x 2 + 2 2
2
Let A =
1 {(2n + 1) (2n + 2) ------- (2n + n)}1/n n
log A =
( 2n n) ( 2n 1) ( 2n 2) ( 2n 3 ) 1 ..... lim log n n n n n n
log A =
1 2 2 n 1 lim log 2 n 2 n 2 n ..... 2 n n n 1
log A =
log( 2 x )dx 0
1
log A = x log( 2 x) x 2 log(2 x) 0 log A = [log 3 – 1 + 2 log 3 – 2 log2] log A = [log 3 – loge + log 9 – log4] log A = [log (27/4e)] A = (27/4e). 16.
V1 + V2 + V3 = 0
V1 V2 = ? V1 V2 = – V3
V V . V V = V . V 1
2
2
V1
1
2
3
2
3
2
+ V2 + 2V2 . V2 = V3
1 + 1 + 2V2 . V2 = 1 2V2 . V2 = – 1 V2 . V2 =
1 2
CLASS-XII_STREAM-SB+2_PAGE # 137
2
V1 V2
2
= V1
2
+ V2 – 2 V1 . V2
1 2 =1+1+1=3 =1+1–2×
2
V1 V2
=3
V1 V2 =
17.
Total number of possible cases = 4 + 3 + 2 + 1 = 10 Favourable cases = {(H T T H T),(T H T H T ), (T T H H T ), (T T T H H)} Total number of favourable cases = 4
18.
3.
p(4th toss is a head) =
4 10
=
2 . 5
a + b + c = even Case 1 : All taken are even : 5C3 = 10 Case 2 : One even + 2 odd : 5C1 × 5C2 = 50 Total = 10 + 50 = 60.
19.
2log(x – 2y) = logx + logy log(x – 2y)2 = log(xy) (x – 2y)2 = xy x2 + 4y2 – 4xy = xy x2 + 4y2 – 5xy = 0 x2 – 4xy – xy + 4y2 = 0 x(x – 4y) – y (x – 4y) = 0 (x – y)(x – 4y) = 0 x = y (N.P.), x = 4y
x y = 4. 20.
Let x, y and z are 2n, n2 – 1 & n2 +1. Let x = 2n, y = n2 – 1 and z = n2 +1. Option (A) : 2 does not divide x . Clearly 2 divides x. So option (A) is not true. Ex : 8, 15 and 17 are pythogorean triplet. 2 divides 8. Option (B) : 2 does not divide z(x + y) (n2 + 1)(2n + n2 – 1) which is an odd number so, 2 does not divides z(x + y). So, option (B) is true. Option (C) : 4 divides x + y + z Ex : 5, 12, 13 are the pythogorean triplet. Clearly 5 + 12 + 13 = 30, and 4 does not divides 30. So, option (C) is not true. Option (D) : 8 divides x + y + z Ex : 8, 15, 17 are the pythogorean triplet. Clearly 8 + 15 + 17 = 40, and 8 divides 40. So, option (B) is true. CLASS-XII_STREAM-SB+2_PAGE # 138
PHYSICS 21.
By work energy theorem, W = K mgh – wf = 0 wf = mgh
22.
E = –13.6 ×
z2 n
2
= – 13.6 ×
4 = 54.4eV Ans (D) 1
2E 23.
E VFB deflected in –x direction (Ans.B) P P1 I
25.
P2
45º
I
90º
By Malus's law, I=cos245º initensity after P1
I 2 initensity after P2 I = Icos245 =
I2 =
I1 I cos245 = Ans : B 2 4
26.
Due to inertia ballon displace in the direction of motion of the bus.
27.
(D) As for hydrogen like atom
1 1 1 R.z 2 2 2 n1 n2 So,
28.
(Here z = 1, same for deuterium and hydrogen)
1 will be same for deuterium as that for hydrogen.
Bulk modulus, B =
P V V
As in isothermal process, PV = K On differentiating, PdV + VdP = 0
V P V P P Hence B = P = P P
CLASS-XII_STREAM-SB+2_PAGE # 139
29.
2 From brewster’s law tan = 1
30.
Cheaking dimensionally all the formula g L [L] 2 [L2 T 2 ] 2 T
and
g [MLT 2 ] [L1T 2 ] [ML3 ] [L]
1/ 2
= [L2T–2]
(dimension of v2)
2 [M1L1T 2 ][L1] = [L2T–2] [L][ML3 ] Only (A) option is correct dimensionally 33.
As v & d depends on frame of referance but change in KE and hence heat does not depend. V
34.
V>> 2gr
B
v
36.
x
2v
A
B
v
C 2v
2v vB = v0 1 c vC = vo 1
v c
2v cos VA = V0 1 c VA > VC > VB (Answer : C)
37.
By dalton's law of partion pressure.
38.
Ein = 0 Eout =
(Ans : D)
KQ r2
KQ KQ = const. Vout = R r X is for electric field versus distance graph Y is for potential versus distance graph Ans. is (B) Vin =
kq 39.
Enet = 2 Enet =
2
( x y 2 )3 / 2
[ x]
2kq x2
CLASS-XII_STREAM-SB+2_PAGE # 140
CHEMISTRY 41.
For weak acid [H+] = C [H+] = 0.1 × 0.1 [H+] = 10–2 pH = –log[H+] pH = –log[10–2] pH = 2
42.
N
O O
it has two donor side [O & N] –
43.
H3O+ sp3 hybridisation, due to presence of 1 p structure is trigonal pyramidal.
45.
(D) Ba > Ca > Mg > Be Solubility increases down the group due to increase of size of cation.
46.
C > Be > B > Li Zeff I E
47.
Dipole moment µ = e × d F
Be µ=0
F
48.
[NiCl4]2– is tetrahedral.
50.
mvr =
51.
(A) both valencies of one double bonded C-atom are occupied by the same group (H).
52.
p-nitrophenol –I & –M
nh 2
where n = 1, 2, 3 -------
-o-nitrophenol –I & –M ( intramolecular H-bond)
CH2 – O – COR
54.
(A) CH – O – COR
m-nitrophenol –I
CH2 – OH + 3NaOH
CH2 – O – COR
3RCOONa + CH – OH Salt of fatty acid CH2 – OH glycerol
55.
(B) Branching surface area vanderwaals’ forces b.p.
CLASS-XII_STREAM-SB+2_PAGE # 141
56.
(C) Zn/NaOH 2
58.
NO2
Zn/NaOH
N=N
CH3 – CH2 – CH(OH) – COOH
OH COOH
59.
(C)
[contains phenolic group]
60.
(B) stability of carbanions
– & –M & M
PART-II (2 Mark) MATHEMATICS 81.
ab = 2 (a + b) ab 1 ab 2 1 1 1 a b 2
...... (i)
bc = 3( b + c) bc 1 bc 3 1 1 1 b c 3
...... (ii)
ca = 4( c + a) ca 1 ca 4 1 1 1 c a 4
...... (iii)
Add (i), (ii) and (iii) 1 1 1 1 1 1 2 a b c 2 3 4 1 1 1 643 a b c 24 1 1 1 13 a b c 24
...... (iv)
From (i) and (iv) c = 24
CLASS-XII_STREAM-SB+2_PAGE # 142
From (ii) and (iv) a=
24 5
From (iii) and (iv) b=
24 7
So, value of 5a + 7b + c = 24 + 24 + 24 = 72. 82.
x2 + ax + b = 0 + = – a, = b x4 + ax3 + cx2 + dx + e = 0 Roots are + , – , – + and – – Sum of roots = – a + + – – + – – = – a a = 0 + = 0 Sum of roots taken two at a time = + c ( + ) ( – ) + ( – ) (– + ) + (– + )(– – ) + (– – ) ( + ) + ( + ) (– + ) + ( – ) (– + ) = c 0 – ( + )2 + 0 + 0 + 0 – ( + )2 = c – 2( – )2 = c – 2[2 + 2 – 2] = c – 2[( + )2 – 2 – 2] = c – 2[– 4] = c c = 8 c = 8b 0 Product of roots taken three at a time = – d ( + ) ( – ) (– + ) + ( + ) (– + )(– – ) + (– – ) ( + ) + ( + ) (– + ) (– + ) (– + ) = – d 0+0+0+0=–d d=0 Product of roots = e ( + )( – )(– + )(– – ) = e e=0 So, c = 0 is the false statement
83. y = 3x Q y = 2x P O
PQ = 5 Let point Q is (x, 3x)
CLASS-XII_STREAM-SB+2_PAGE # 143
Given QP = 5 and QP line 2x – y = 0
2x 3 x
=5
4 1 x= 5 5
Therefore point Q is ( 5 5 , 15 5 ) 2
OQ =
2
5 5 15 5
=
125 1125
=
1250
= 25 2 In OPQ OQ2 = OP2 + PQ2
2
25 2
= OP2 + (5)2
1250 – 25 = OP2 OP2 = 1225 OP = 35 cm. 84.
s(s b) (s a )(s c )
cot
B = 2
cot
s(s c ) C = ( s a)(s b) 2
cot
s(s b) (s a)(s c )
B C cot = 2 2
s(s c ) (s a)(s b)
s 2 (s b)(s c )
cot
B C cot = 2 2
cot
B C cot = 2 2
cot
s B C cot = sa 2 2
(s a)2 (s b)(s c ) s2 ( s a) 2
Given : b + c = 3a
s=
a 3a abc = = 2a. 2 2
cot
2a 2a B C cot = = = 2. 2 a a a 2 2
CLASS-XII_STREAM-SB+2_PAGE # 144
85.
D
C F E
B
A
Given : AE = EF = FC =
AC 3
Let,
AB = BC = CD = DA = x
Then,
AC =
2x
Let BE = a In AEB
2x 2 x 2 a2 9 cos 45º = 2x 2 .x 3
11x 2 a2 9 1 = 2 2x 2 2 3
2x 2 11x 2 = – a2 3 9
a2 =
11x 2 2x 2 – 9 3
a2 =
11x 2 6 x 2 5x 2 = 9 9
a=
5 x 3
Similarily BF = a =
5x . 3
In BEF BE = BF =
and
EF =
5x 3
2x 3
CLASS-XII_STREAM-SB+2_PAGE # 145
cos =
BE 2 BF 2 EF 2 2BE BF
5 x 2 5 x 2 2x 2 9 9 9 cos = 5x 5x 2 3 3
8x 2 9 cos = 10 x 2 9
tan =
86. D
A
x
=
8 4 = . 10 5
3 . 4 x
C
B
2007
v = Volume of box = (2007 – 2x)2 × x dv = 2(2007 – 2x)(– 2x) + (2007 – 2x)2 dx
= (2007 – 2x)[– 4x + 2007 – 2x] = (2007 – 2x) (2007 – 6x) For the maximum volume dv =0 dx
(2007 – 2x)(2007 – 6x) = 0 x= d2 v dx 2
2007 2007 or x = 6 2
= (2007 – 6x) (– 2) + (2007 – 2x) (– 6) = – 4014 + 12x – 12042 + 12x = 24x – 16056
d2 v 2007 dx 2 2007 = 24 × – 16056 x 6 6
= 8028 – 16056 < 0
Volume is maximum when x =
2007 669 = cm. 6 2
CLASS-XII_STREAM-SB+2_PAGE # 146
87.
S = y2 – 4x S (0, 2) = 4, S (1/2, 5/2) = 25/4 – 2 = 17/4, S (5/2, 9/2) = 81/4 – 20/2 = 41/4 and S (1, 3) = 9 – 4 = 5 It is clear that (0, 2) is closest to parabola y2 = 4x.
88.
or 2
e
e
2
e
or 2
I 1.
and –
x + 4 x > 0 for all x < 0 So, range of f is [0, ). x
16.
f(x) =
t
e (t 1)(t 2) dt 0
f’(x) = ex(x – 1)(x – 2) For decreasing f’(x) < 0 ex(x – 1)(x – 2) < 0 (x – 1)(x – 2) < 0 x (1, 2). 1
17.
x | x |3 / 2 dx
1 0
=
1 0
=
[ ex > 0]
1
x( x )3 / 2 dx +
1
x 5 / 2 ( 1)3 / 2 dx + 0
= (– 1)
3/2
x( x )3 / 2 dx
0 1
x 5 / 2 dx
0
1
x7 / 2 x7 / 2 + 7 / 2 –1 7 / 2 0
= (– 1)3/2
2 2 [0 – (– 1)7/2] + [1 – 0] 7 7
= – (– 1)5
2 2 2 2 4 + = + = . 7 7 7 7 7
CLASS-XII_STREAM-SB+2_PAGE # 157
18.
x f ( x)f (x)......f 1
10 ( x )
2
1 dx
Let f11(x) = t
dx x f1( x )f2 ( x )......f10 ( x ) = dt
1.dt
=t+C = f11(x) + C.
19.
Applying AM and GM condition : x1 2x 2 3 x 3 6 x1x 2 x 3 1 / 3 3 4 6 x1x 2 x 3 1/ 3 3
Cubing both sides
64 6 x1x 2 x 3 27 x1x 2 x 3
32 81
Now also
x1 x 2 x 3 2 2 2 x1 x 2 x 3 3
2
2
2
2
2
2
x1 x 2 x 3 32 3 81 210 x1 + x2 + x3 3 38 2
2
2
2
2
2
1/ 3
2/3
1/ 3
x1 + x2 + x3
38 2 9 9
x 12 + x 22 + x 32
24 0 .6 9
1/ 3
x 12 + x 22 + x 32 1 . 6 So, according options least value is 2. 20.
12 3 4 5 6 7 at each position two posibility i.e. either H or T So total posible outcomes = 27 As we want three tails is sequence and it happened at 7th turn. So at position 5, 6, 7 we have tails and position 4 must have head otherwise our requirement is fullfilled at position 6. So, the position 1, 2, 3 can have anything i.e. H/T = 23 To get tail at 1, 2,3 position we have only one probability. So, total favourable cases = 23 – 1 = 7 required probability =
7 27
=
7 . 128
CLASS-XII_STREAM-SB+2_PAGE # 158
PHYSICS 22.
PV = nRT PdV + VdP = 0
1 dV 1 V dP P = P–1 –
23.
(Answer is C)
1 for point charge r2 Force solid sphere
E
Inside the sphere E r and out side the sphere E
24.
=
r2
L r 4
So, = 25.
1
L r 4
Angular momentum, = mvr Magnetic moment, = IA = nqr2 =
qr 2 2
v vqr 2 = 2r qr 2 vqr q 2mvr 2m
or
26.
kT c m
(Answer is C)
2 2 1/ 2
ML T = LT M 1
1/ 2
= [M0L0T0]
which dimensionally satisfies
1 kT f = c m f 27.
(Answer is D)
Average power, = Av2
28.
Wave length, =
1 2 2 v Aw w 2 (Answer is A)
d 0.2 6 103 = 0.5 × 10–4 m D 24
= 5 × 10–5 cm = 500 nm
(Answer is B)
29.
(B)
30.
By angular momentum conservation m1v1r1 = m2v2r2 ( m1 = m2 )
So, v2 =
5.6 10 4 9 1010 5.6 1012
= 900 m/s (Answer is B)
CLASS-XII_STREAM-SB+2_PAGE # 159
31.
y = y1 + y2 = 2A cos (2Kx) cos(2cost) x = 0, y = 0 (Ans. C)
20m
32.
A m (some as x)
1 sec–1 t
1 sec–1 t = angle(dimensionless) 33.
34.
(Answer is A)
KE = 0.01864 × 931 = 17.4 Mev KEf – KEi = 17.4 Mev As proton is at rest (B) option is correct
mv 2 kq1q2 2 r r kq1q2 mr
v=
v = 1.6 × 10–19
9 10 9 9.11 10 31 0.53 10 10
v = 2.24 × 106 m/s
(Answer is D)
I
35.
F
F=
F=
F
0 1 2 2d 4 10 7 4000 4000 60 10 2 2 1.5 10 2
F = 128N repulsion
(Answer is B)
37.
(C)
38.
Phase different between VR and VC is 90º so,
VR2 VC2 = 220
(Answer is D)
39.
Distance between to consecutive destructive interference is 1.7cm, so total number of points of destructive interference on the line PQ is 4. (Answer is A)
40.
(D)
CLASS-XII_STREAM-SB+2_PAGE # 160
CHEMISTRY 41.
The ionization energy or enthalpy of Na is less than that of Li but the hydration enthalpy of Li is higher than that of Na. Difference between ionization enthalpy of both is less than difference between their hydration enthalpy so overall oxidation potential of Li is greater than Na. Therefore Li metal is a better reducing agent than Na metal.
42.
Compressibility K = Kx – Ky =
1 P
1 1 – 1 2
= 0.5 atm–1 OH
43. CO2H
44.
2CH3
CHO
conc. NaOH
CH3
CH2OH + CH3
COOH
Cannizzarro reaction 45.
On heating solution becomes unsaturated solubility and conductance both are increase.
46.
According to graph, segment BC represents isobaric process. It means pressure is constant so according to Charle’s law V T [on constant pressure] From B to C volume decreases so temperature will also decreases.
H 6
H 3
4
1
47. 7
5
OH
2
when same groups present in same side of the double bond then geometrical isomer is known as Z – isomer. Due to back donation electron defficiency of [B] almost neutral.
+
+ Cl
Cl
Cl 49.
en
Co Cl trans
en
en
Co en cis/d
/////////////////////////
48.
+
Cl Cl Co
en
en
CLASS-XII_STREAM-SB+2_PAGE # 161
50.
xH2S + 2NaNO3 +2HCl yS + zNO + k NaCl + 4H2O Put the following values of variables in above equation x = 3, y = 3, z = 2, k = 2 3H2S + 2NaNO3 + 2HCl 3S + 2NO + 2NaCl + 4H2O
51.
R = k [X]1/3 [Y]2/3 order of reaction =
1 2 + =1 3 3
52.
Because Zn has higher oxidation potential than Cu,So Zn loses its electrons at an anode and convert in Zn2+ ions and come into the solution. These electrons flow externally from zinc to Cu by wire.
53.
Because ideal mixture of benzene and toluene follows Raoult’s law according to Raoult’s law Pmix = PA + PB Pmix = XAPAº + XBPBº Pmix = XAPAº + (1 – XA) PBº Pmix = XA(PAº – PBº) + PBº This is a linear equation, by comparing with y = mx + c y = Pmix x = XA m = PAº – PBº c = PBº according to above data graph will be like following -
PBº Pmix PAº XA = 0 XA = 1 XA molefraction (benzene )
54.
sp3d2 hybridization explains the bonding of complex which has C.N. (co-ordination number) 6 so answer may be either [Fe(CN)6]3– or [Fe(H2O)6]2+. But H2O is a weak ligand and CN– is a strong ligand. Because weak ligand form an outer orbital complex with metal ion and this is possible when sp3d2 hybridization takes place.
55.
2NaCl + H2SO4 Na2SO4 + 2HCl MnO2 + 4HCl MnCl2 + 2H2O + Cl2
56.
Bond order =
1 [N – Na] 2 b
CLASS-XII_STREAM-SB+2_PAGE # 162
B.O. of O2+ =
1 [10 – 5] = 2.5 2
Nb = no. of electrons present in BMO
1 [10 – 7] = 1.5 Na = no. of electrons present in ABMO 2 1 B.O. of O22– = [10 – 8] = 1 2 1 Inter atomic distance B.O order of inter atomic distance ; O22– > O2– > O2+ B.O. of O2– =
57.
amylose [it is a part of starch]
58
t1/ 2 = t1/2 =
59.
60.
0.693 K 0.693
6.93 10 – 3
t1/2 = 100 s Because unit cell has six faces and every facial atom is a part of two unit cell. It means only half part of one facial atom belongs to one unit cell. 1 so, total no. of facial atoms in fcc unit cell = 6 × =3 2 =
W T1 – T2 = Q1 T1
W 800 – 200 800 100
W = 75 J
PART-II (2 Mark) MATHEMATICS 81.
a=A– d b=A c=A+d a + b + c = 3A = A=
3 2
1 =b 2
a+b+c= a+c= b2 =
3 2
3 3 1 –b= – =1 2 2 2
....(i)
a 2c 2 2
1 = ± ac 2 When
ac = c=
1 4
1 4a
...(ii)
CLASS-XII_STREAM-SB+2_PAGE # 163
From (i) & (ii) 1 =1 4a 4a2 – 4a + 1 = 0 (2a – 1)2 = 0 2a – 1 = 0
a+
1 2 By this we get a=b=c But a < b < c, so we take a=
When
– ac =
1 4
1 4a
c=
....(iii)
from (i) & (iii) a–
1 =1 4a
4a2 – 4a – 1 = 0 a=
=
4 16 16 8
44 2 1 2 = 8 2
as b > a
a=
1 2 2
82.
g’(x) is changing its slope from positive to negative as it passes through g(2). So, g(2) is largest.
83.
92 × 180º = 140º B = 9
1 = 2 =
D
x
180 º 140 º = 20º 2
z 3
C
3 = 140 – 2 = 120º In ACD
y 2 x 2 z2 cos 120º = 2xy
2
y A
x
1 x
B
y 2 x 2 z2 1 = 2xy 2 – xy = y2 + x2 – z2 z2 = x 2 + y2 + xy
CLASS-XII_STREAM-SB+2_PAGE # 164
84.
0 * * * * 0 * * * * 0 * T AA = * * * 0 As the diagonal element of resulting matrix are zero. multiplication R1 of A and C1 of AT (i.e. = R1 of A) = 0 It is possible only when all element in R1 of A is zero In the same way we can say that element of all 10 rown of A is zero so for the above condition we can formm only 1 matrix i.e. A = null matrix.
(0, b) C E
85.
(– a, 0) A
(0, 0) O
(–ae, 0)
F
B
D (0, – b)
(i)
As line DE and AC are so product of there slope = – 1.
b 0 b × =–1 0 ae a b b × =–1 ae a 2
b e= a (ii) and line CF and AD are also b0 b 0 × =–1 0 ae 0a
b b × =–1 ae a 2
b e= a (iii) and line AO is to CD 00 2b × –1 0a 0
2
b From (i) & (ii) case e = a But in (iii) case ‘e’ cannot be determined. So, we can not determined uniquely.
86.
0
[ x ]e x dx =
= 0 + e x
1
0e 0
2 1
x
2
dx +
1
(1) e x dx +
3
2e 2
x
dx + ......
x 3 2
+ 2e + .........
= – (e–2 – e–1) – 2(e–3 – e–2) – 3(e–4 – e–3) ......... = e–1 + e– 2 + e–3 ............
=
1 e1
+
1 e2
+
1 e3
+ ..........
S =
1 e 1 1 e
=
1 . e 1
CLASS-XII_STREAM-SB+2_PAGE # 165
87.
/2
0
=
cos1003 xdx
lim g( x )
x
lim
lim x
= 89.
=
2008
e f ( t ) dt
e
g' ( x )
=
2 1004
0 f(x)
x
=
=
e f ( t ) f ( x ) dt x
=
cos1004 xdx
0
g( x )
=
0
(1002 1000 998 .....2) (1003 1001 .....1) × 1003 1001 ....... 1 1004 1002 ....... 2 2
x
88.
/2
lim 0
x
lim 0
x
x
0
e f ( t ) g( x )e f ( x )
f ' ( x )e f ( x )
g( x ) f ' (x) 3 x 3 ..... 16 x 3 ....
3 . 16
dy = sin(x + y) + cos(x + y) dx let x + y = u Differentiating wrt x
1+
dy du = dx dx
dy du = –1 dx dx
dy = sin(x + y) + cos(x + y) dx
du – 1 = sinu + cosu dx du = sinu + cosu + 1 dx du dx sin u cos u 1 Integrating both sides du
sin u cos u 1 dx
CLASS-XII_STREAM-SB+2_PAGE # 166
du
2 tan u / 2 2
1 tan u / 2
1 tan 2 u / 2 2
1 tan u / 2
dx 1
sec 2 (u / 2)du
2 tan u / 2 1 tan
2
u / 2 1 tan 2 u / 2
sec 2 (u / 2)du dx 2 tan u / 2 2
sec 2 (u / 2)du dx 2(tan u / 2 1)
dx
Put 1+ tanu/2 = t (1/2)sec2u/2du = dt
dt dx t
log |t| = x + c log |1+ tanu/2| = x + c log 1 tan
(x y) =x+c 2
It passes through origin. log1 = 0 + c c = 0. So, log 1 tan 90.
(x y) = x. 2
Total mappings of bijection is 6 !. for self inverse 4! 6 C 4 2! 2! 2!
6! 2! 2! 2! 3! + 2 pairing
P=
2 going to their own value
+
6 C2 1 4 going to their own value
= 76
76 19 = . 720 180
CLASS-XII_STREAM-SB+2_PAGE # 167
PHYSICS d 91.
M2
M1 r1
r2
M1r1 = M2r2 and r1 + r2 = d
M2 d so r1 = M M 1 2 2r1 T = v 1
........(i)
........(ii)
Here
M1v12 = r1
GM1M2 d2
GM2r1
or v1 =
d
From (ii) T=
T=
T=
2r1d GM2r1
2d r1 GM2 2d
T=
GM2
M2d M1 M2
2d3 / 2 G(M1 M2 )
92.
a = r = 20 × 0.5 = 10 m/s2
93.
For min
(Answer is B)
hc min = K.E. min =
hc K.E.
6.6 10 34 3 10 8 min = 30 10 3 1.6 10 19 = 4.14 × 10–111 m
CLASS-XII_STREAM-SB+2_PAGE # 168
94.
95.
V V0 340 9 App. frequency, N = V V N 340 9 90 S N = 94.9 kHz
Mass of water, m =
kg 10 3 m = × 18×10–2 × (3.96)2 × 10–4 × 0.92 ×103 mLf =
t = 96.
18 (3.96 )2 0.92
mL f t = KA ( ) 1 2
KA (1 2 ) t
18(3.96)2 0.92 333 103 10 3
t = 9.2 s
103 400 (3.96)2 15
(Answer is A)
Range, R = 2 (H h) h (i) h = H/4 HH X1 = 2 H 44
3H/4 H/2 2
3 X1 = H 2 (ii) h = H/2 X2 = H (iii) h = 3H/4 X3 = H
3
H/4
1 X2
3 2
X1= x3
X2 > X1 = X3 (Answer is C)
CHEMISTRY 101.
Xe contains 8 electrons in its outermost shell or valence shell. In XeF2, Xe uses 2 electrons for bonds so it contains 3 p. In XeF4., Xe uses 4 electrons for bonds, so it contains 2 p.
N2 + 3H2
102. initial moles
4
2NH3
16
0
at equilibrium
[according to question ammonia gas is produced = 4 mol] 2 = 4 put the value of = 2 4–2
16 – 3 × 2
2
10
4
concentration 2 at equilibrium V
10 V
4 V
moles at equilibrium
2×2
CLASS-XII_STREAM-SB+2_PAGE # 169
KC
=
[NH3 ]2 [N2 ][H2 ]3 2
4 V = 2 10 3 V V = =
42 2 10 3 8
× V2
× (10)2
10 3
(V = 10L]
= 0.8 mol–2 lit2 103.
Kw 0 Depression in freezing point TF = m W 0 In given two cases m0, W and K are constants so TF w0 ( TF )1 ( w 0 )1 = ( TF )2 ( w 0 )2 5.5 – 4 2.9 = 5.5 – 2.5 2.9 x 1.5 2.9 = 3 2.9 x x = 2.9 g I
105.
OH II 2
2R and 5R III
'
III ' 5
II
OH I '
106.
Zn + 2Ag+ (0.0001M) Zn2+ (0.1M) + 2Ag by nernst equation Ecell = Eº –
[ Zn2 ][ Ag]2 0.059 log10 [ Ag ]2 [ Zn] n
[Ag] = [Zn] = 1 Ecell = Eº –
[ Zn2 ] 0.059 log10 [ Ag ]2 2
Ecell = 1.56 –
(0.1) 0.059 log10 ( 0 . 0001)2 2
Ecell = 1.56 – 0.2065 Ecell 1.35 V 107.
Cu(Y)
(CH3)2SiCl2 2CH3Cl + Si (X)
SiCl4 + 2CH3MgBr (CH3)2SiCl2 + 2Mg(Br)Cl (Z) CLASS-XII_STREAM-SB+2_PAGE # 170
108.
according to Arrhenius theory K = Ae
–
E RT
according to question K is same in both cases, so
E1 E2 RT1 = RT2 E1 and T1 are activation energy and temp. in absence of catalyst
400 500 = T2 625
E2 and T2 are activation energy and temp. in presence of catalyst
T2 = 500K 109.
28
Ni [Ar]3d84s24p0
Ni2+ [Ar]3d8 4s0 4p0
[Ar] because CN– is a strong ligand ,so pairing of electrons takes place.
[Ar] dsp2 hybridization
[Ar] 2
dsp hybridized Unhybridized orbitals orbitals
In dsp2 hybridization geometry of complex is square planar.
110.
238 206 82 Pb 92 U
x 24He y –01e
by balancing of mass no. 238 = 206 + 4x + 0y x=8 by balancing of nuclear charge 92 = 82 + 2x – 1y 92 = 82 + 2 × 8 – y y=6
*****
CLASS-XII_STREAM-SB+2_PAGE # 171
HINTS & SOLUTIONS (YEAR-2009) ANSWER KEY Que s. Ans. Que s.
1 A 16
2
3
B 17
4
C 18
5
B 19
6
D 20
B 21
7 D 22
8 A 23
9 A 24
10
11
12
13
14
15
C 25
B
B
D
C
A
26
27
28
29
30
Ans.
B
C
B
C
D
B
B
D
D
C
C
Que s.
31
32
33
34
35
36
37
38
39
40
41
D 42
C 43
A 44
D 45
Ans.
D 46
C 47
A 48
B 49
B 50
C 51
A 52
A 53
A 54
B 55
C 56
D 57
C 58
C 59
D 60
A 61
C 62
B 63
A 64
B 65
A 66
D 67
C 68
D 69
B 70
D 71
A 72
D 73
B 74
B 75
A 76
C 77
C 78
C 79
B 80
B 81
C 82
D 83
A 84
D 85
D 86
D 87
B 88
A 89
B 90
Ans. B Que s. 91 D Ans. Que s. 106 C Ans.
B 92 A
D 93 B
C 94 C
A 95 D
C 96 A
B 97 C
C 98 C
B 99 B
B 100 B
D 101 B
C 102 D
D 103 A
B 104 A
C 105 B
107 A
108 C
109 D
110 B
111 C
112 B
113 A
114 B
115 A
116 D
117 B
118 A
119 C
120 C
Que s. Ans. Que s. Ans. Que s.
PART-I (1 Mark) MATHEMATICS 1.
Given : a1, a2, a3 .........AP and a1, a2, a4, a8 ......GP. Let common difference of A.P. = d a2 = a1 + d a4 = a1 + 3d a8 = a1 + 7d
a8 a2 a4 = = a1 a2 a4 = r a1 d a1 3d a1 7d a1 = a1 d = a1 3d = r (a1 + d)2 = a1(a1 + 3d) a12 + d2 + 2 a1d = a12 + 3a1 d d2 = a1 d
(d 0)
d = a1
....(i)
a2 a1 d Hence, a = r ; a =r 1 1 a1 a1 =r a1
(using (i))
r = 2.
CLASS-XII_STREAM-SB+2_PAGE # 172
2.
Tk 101 till k = 10 Tk –1 k Tk > Tk–1 Let k = 11 T11 < T10 T10 is maximum at k = 10.
3.
x=
2+ 3+ 6 2
2
x 2 = 3 6
x2 + 2 – 2 2 = 9 + 6 2 x2 – 7 = 8 2 (x2 – 7)2 = 64 × 2 So, smallest possible value of n is 4. 4.
Let the three players are A, B, C. Now, each player get 0 score after playing 9 games. It happened only when each player wins 3 games and loss 6. So, A win 3 games out of 9 9C3 B win 3 games out of remaining 6 6C3 C win 3 games out of remaining 3 3C3 So, required way = 9C3 × 6C3 × 3C3 =
9 8 7 6! 6 5 4 3! × ×1 3 2 1 6! 3 2 1 3!
= 1680. A (2, 3)
5.
O (2, z) B (4, 0)
C (x, y)
O is circumcenter OA = OB = OC = circumradius (2 – 2)2 + (z– 3)2 = (4 – 2)2 + (0 – z)2 z2 + 9 – 6z = 4 + z2 9 – 6z = 4 5 = 6z 5 =z 6
Circumcenter =
5 13 . ( z 3 ) 2 ( 2 2) 2 = | z – 3 | = 6 3 = 6
CLASS-XII_STREAM-SB+2_PAGE # 173
6. (5, 15) L(21, 15) P
P'
A
5 21 15 15 , Mid point of PP’ = 2 2 L = (13, 15) Point A will be (13, 0) By property PA + PA’ = 2a
PA =
(13 5)2 (0 15 )2 =
64 225
=
289 = 17 cm
PA’ = =
(13 21) 2 (0 15) 2 64 225
=
289 = 17 cm 2a = PA + PA’ 2a = 17 + 17 2a = 34 cm So, length of major axis = 2a = 34 cm. 7.
P (10, 10)
B (0, 6)
2x + 3y = 18
C (a, b)
PB = PC (10 – 0)2 + (10 – 6)2 = (a – 10)2 + (b – 10)2 100 + 16 = a2 + 100 – 20a + b2 + 100 – 20b a2 + b2 – 20a – 20b + 84 = 0 ....(i) Also (a, b) i.e. on 2x + 3y = 18 2a + 3b = 18
3b 2 Using equation (i) a=9–
2
3b 3b – 20b + 84 = 0 9 + b2 – 20 9 2 2
81 +
9b2 – 27b + b2 – 180 + 30b – 20b + 84 = 0 4
13b 2 – 17b – 15 = 0 4 13b2 – 68b – 60 = 0
CLASS-XII_STREAM-SB+2_PAGE # 174
13b2 – 78b + 10b – 60 = 0 13b(b – 6) + 10 (b – 6) = 0 10 13
b = 6 or b =
When b = 6, then a = 9 –
When b =
10 3 10 30 132 , then a = 9 + =9+ = 13 2 13 26 13
132 10 +2× 13 13
8a + 2b = 8 ×
1056 20 79 . 13
=
8.
36 =0 2
cosec2( + ) – sin2( – ) + sin2(2 – ) = cos2( – ) cosec2( + ) + sin2(2 – ) =
cos 2 ( ) sin 2 ( ) 1
cosec2( + ) = 1 – sin2(2 – ) cosec2( + ) = cos2(2 – ) Minimum value of cosec2( + ) is 1 and maximum value of cos2(2 – ) is 1. They will be equal for the value 1.
2
.....(i)
2 – = 0 By adding (i) & (ii)
.....(ii)
+=
2
3 =
9.
=
6
=
3
sin( – ) = sin (
sinx + siny =
7 5
cos x + cosy =
1 – ) = – sin ( ) = . 6 3 6 2
....(1) 1 5
....(2)
By (1)2 + (2)2 we get 2 + 2sinx siny + 2 cosx cosy = 2
CLASS-XII_STREAM-SB+2_PAGE # 175
sinx siny + cosx cosy = 0 cos(x – y) = 0 x – y = 90º By (1) × (2) we get sinx cosx + sinx cosy + siny cosx + siny cosy =
7 25
sin(90 + y)cosx + sin(x + y) + sin(x – 90) cos y =
7 25
cosy cosx + sin(x + y) – cosx cosy = sin(x + y) =
7 25
7 . 25
10.
6 x
y=
(1, 1) 1 0 y = sin x Clearly, curve meet each other twice in
11.
2 – 3 4 – 5 6 – 7 8 – 9 10 – 11
Total 10 Times.
f(x) is differentiable on R. So, it will be contincous on R. Continuity at x = 0 LHL 2 lim– sin x x 0 x Put x = 0 – h, then h 0 2 lim sin(0 h) h0 h
lim sin h h = 0 h h RHL h0
lim x2 + ax + b
x 0
Put x = 0 + h, then h 0
lim h2 + ah + b = b
h0
Value of f(x) at x = 0 f(0) = b.
CLASS-XII_STREAM-SB+2_PAGE # 176
f(x) is contineous at x = 0 LHL = RHL = f(0) 0=b=b b=0 Differentiability at x = 0 LHD
lim
f ( 0 h ) f ( 0) h
lim
sinh 2 b h h
h0
h0
2 lim sin h = 1 h0 h2 RHD
lim f (0 h) f (0) h
h0
2 lim h ah b – b h0 h
lim h(h a ) = a. h f(x)is differentiable at x = 0, LHD = RHD a = 1. h0
12.
Let point p(x1, y1) is on the curve y2 = 4x. 2
y12 = 4x1 x1 =
y1 4
( x1 0) 2 ( y1 3 ) 2
PA =
AP2 = x12 + y12 – 6y1 + 9 AP2 = x12 + y12 – 6y1 + 9 Let AP = z z2 = x12 + y12 – 6y1 + 9 2
y12 2 z = 4 + y12 – 6y1 + 9 4
z2 =
y1 + y12 – 6y1 + 9 16
Diff. w.r.t. y1 3 dz 4 y1 2z dy = + 2y1 – 6 16 1
3 dz y 2z dy = 1 + 2y1 – 6 1 4 3
=
y1 8 y1 24 4
dz 2z dy = (y1 – 2) (y12 + 2y1 + 12) 1
CLASS-XII_STREAM-SB+2_PAGE # 177
For the critical points
dz dy 1 = 0 (y1 – 2)(y12 + 2y1 + 12) = 0 y1 = 2 y12 = 4x1 (2)2 = 4x1 x1 = 1.
dz 2 dy 1
2
d2 z
+ 2z
2
dy 1
= (y12 + 2y1 + 12) + (y1 – 2) ( 2y1 + 2) = y12 + 2y1 + 12 + 2y12 – 4y1 + 2y1 – 4 = 3y12 + 8.
dz when y1 = 2 and dy = 0 1 d2 z 2
dy 1
>0
z is min at (1, 2)
Minimum distance = (1 0)2 (2 3)2 = 13.
1 1 =
2.
We can find the answer through option as the sum of weight of packet taken from trucks is 1022870 gm and its unit digit is 0. The truck that have heavier bags have unit digit 0. So, the truck have lighter bags in which the sum of weight of bags must have unit digit 0. So, according to option D. i.e. truck no. 2, 8 Track 2 have 21 bags and total weight = 21 × 999 gm = .......8 gm Truck have 27 bags and total weight = 27 × 999 = 128 × 999 gm = ......2 gm So, the unit digit of the weight contain by truck 2, 8 together is 0. 1
14.
cos( x ) cos([2x]) dx 0
1/ 2
1
cos( x ) cos 0 dx +
=
=
=
sin x
0 1/ 2
0
1/ 2
cos( x ) cos dx
1
cos( x ) dx – 1/ 2
1/ 2
cos( x ) dx 1
– 0
sin x
1/ 2
1 1 = – 0
=
2 .
CLASS-XII_STREAM-SB+2_PAGE # 178
1
cos(nx )x 9 dx cos(nx)x10 10 + n n 0 1
15.
IN =
0
=
1 1 10 sin(nx )x 9 9 sin(nx )x 8 dx 0+ n n n 0 n 0
=
1 10 9 sin(nx )x 8 dx 2 n 0
1 10 ! sin(nx )dx = 10 n 0
= 0 as Denom
16.
y = x2 & y = 1 – x2 Point of intersections of graphs x2 = 1 – x2 2x2 = 1
1 x=±
2
1 1 1 1 , and , . Point of intersections = 2 2 2 2 Area under graph : 1/ 2
x
=
2
(1 x )2
1 / 2
1/ 2
=
1 /
1/ 2
3 2x 1 = 2x x 1/ 3 2 2
2 =2×
=2 17.
6 2
26 6 2
1 2 4
=
2
3 2
=
2 2 . 3
a 3 i 4k and b = 5 j 12k
2 2 2 a (3)2 4 5 and b (5) 12 13
Therefore, a vector which bisects the angle is 13 3 i 4k + 5 ( 5 j 12k ) = 39 i 25 j 8k .
CLASS-XII_STREAM-SB+2_PAGE # 179
19.
Let M 2 x1 .3 x 2 .5 x 3 ...... , N 2 y1 .3 y 2 .5 y 3 ...... xi & yi w x1
5 x3 – 1 2 y1 – 1 3 y 2 – 1 5 – 1 ....... = 2 – 1 3 – 1 .........
3 x2 – 1 3 –1
d = d 22 ––11
d/m
d/N
x2 1 x1 – 1 1 – 1 2 3 .... 1 / 2 – 1 1 / 3 – 1 1/ d 1 y1 1 y 2 d/M 1/ d = 2 – 1 3 – 1 .... d/N 1 / 2 – 1 1 / 3 – 1
(2 x1 – 1)(3 x 2 – 1).....
2 x1 3 x 2 .....
20.
m C0
(2
y1
m C1 n
– 1)(3
y2
– 1)......
=
N 1. M
2 y1 3 y 2
m C2 n 2 mC m n m (1 + n)m
only one element from A
PHYSICS 27.
Sphere is hollow so potential inside sphere will be same as that on surface.
28.
Heat supplied Q = dU + W PV = RT PdV = RdT
(at constant pressure)
PdV R Q = CVdT + PdV dT =
PdV + PdV R Work done at constant pressue, W = PdV Q = CV
Q W
CV
PdV PdV R PdV
Q CV 1 W R
(For diatomic gos, CV =
5 R) 2
Q 5R 1 W 2R Q 7 W 2
W 2 Q 7
CLASS-XII_STREAM-SB+2_PAGE # 180
29.
1 1 1 R 2 2 For lyman series 2 1 1 1 1 R 2 2 For balmer series 3 2
(
1 1 94 ) 4 9 36
3/4 3 9 27 = 5 / 36 1 5 5
5 27
A
B
q
q
30.
q q and 2 2
charge divides
Than, on touching
q sphere to q 2
Charge divides
q / 2 q 3q 2 4
force between
3q q R 4 2
f=
f=
unchanged
K 3q2 8R 2 3 kq2 3 F × 8 R2 8
31.
Intially block enters in the magnetic field rate of change of flux will be constant so constant current will induce, when it moves inside the magnetic field there is no change in magnetic flux, current I = 0, when it use the filed the rate of the change in flux will be again constant between in decreasing order so constant current will induced on opposite.
32.
No change in moment of inertia
34. E
–q
A
O
+q
Electric field at each point of OA obtained to it and opposite to direction of dipole moment.
CLASS-XII_STREAM-SB+2_PAGE # 181
38.
a
m
Total force in upward direction m × (g + a) because mass m is stationary on inclined plane and whole system is accelerated with acceletration a in upward direction. 39.
Force of positve charge = Electric force + Magnetic force F = (qE + qVB) This force is in upward direction so no any particle will pass through the hole.
40.
Potential energy at H height = Kinetic energy at the lowest point of circular path. mgH =
1 mv2 2
To complete the circular motion minmum velocity at lowest point will be V = mgH =
H=
5gR
1 m (5gR) 2
5 R 2
CHEMISTRY 41.
According to Graham’s law
1 Rate of diffusion
Molar mass
due to highest molar mass of CO2 rate of diffusion is slowest.
42.
Moles of H2 =
3 4 , Moles of O2 = 2 32
Kinetic energy of n moles of gas =
3 nRT 2
3 n1RT 2 Kinetic energy of hydrogen so, = 3 Kinetic energy of oxygen n 2RT 2 n1 = n 2 =
3/2 4 / 32
= 12 : 1 CLASS-XII_STREAM-SB+2_PAGE # 182
44.
ClF3 sp3d hybridisation, but due to presence of two lp on central atom Cl, according to VSEPR theory shape is ‘T’
45.
HCO3– + H+ H2CO3 Bronsted base HCO3– H+ + CO32– Bronsted acid
47.
Isoelectronic means same no. of electrons CO has 6 + 8 = 14 electrons CN– has 6 + 7 + 1 = 14 electrons
48.
CO2, due to sp hybridisation bond angle = 180º
49.
Diethyl ether, because it is inert towards the Grignard reagent
50.
CH3 – CH2 – CH2 – CHO + CH3 – CH2 – CH2 – MgBr
H
H +
CH3 – CH2 – CH2 – C – CH2 – CH2 – CH3
H3O
CH3 – CH2 – CH2 – C – CH2 – CH2 – CH3
OMgBr 51.
[Ni (PPh3)2 Cl2] [NiCl4]2–
52.
OH Achiral Secondary alcohol
dsp2 hybridisation, because PPh3 is strong ligand hence pairing of electrons takes place sp3 hybridisation, because Cl– is weak ligand hence pairing of electrons is not takes place
16H++ 2MnO4– + 5COO– COO–
53.
Suppose equilibrium constant for the following reaction is K1 N2 + 3H2
2NH3
; K1 =
[NH3 ]2
-------- (i)
[N2 ][H2 ]3
and equilibrium constant for the following reaction is K2 [NH3 ] 1 3 N2 + H2 NH3 ; K2 = [N ]1/ 2 [H ]3 / 2 2 2 2 2 square the both side of equation (ii)
K22 =
[NH3 ]2 [N2 ][H2 ]3
K22 = k1 K2 =
-------- (ii)
[by equation (i)
k1
K2 = 41 K2 = 6.4
[ K1 = 41]
CLASS-XII_STREAM-SB+2_PAGE # 183
54.
Suppose reaction is 2A Product according to rate law Rate R = k [A]2
[ A ]12 R1 or R = [ A ]22 2 R1 [A]12 according to question R = 2 2 [A]1 2
[ A ]1 [ A]2 2
R1 R =4 2 R2 =
55.
R1 4
HCO3– H+ + CO32– Conjugate base NH3 H+ + NH2– Conjugate base
56.
57.
(II) & (IV) Because both have close system of conjugated double bond and follow Huckel’s (4n+2) e– rule.
••
N H p of N takes part in resonance with conjugated double bonds, so it is not easily available on N for the protonation.
N ••
p is not taken part in resonance so easily available for the protonation.
O ••
N H due to high E.N. of O availability of p on N decreases.
••
N H No extra effect, so availability of p on N increases.
CLASS-XII_STREAM-SB+2_PAGE # 184
58.
Gauche conformer. because angle between same groups is 60º
59.
Suppose initial quantity = No after 75% completion of the reaction remaining quantity N = No ×
T=
No 2.303 log N K
T=
No 2.303 log N / 4 K o
T=
1.386 -------- (i) K
T1/2 =
K=
25 N = o 100 4
0.693 K
0.693 -------- (ii) 30
so by equation (i) and (ii) T=
1.386 0.693 / 30
T = 60 min.
60.
Concentration of H+ ions in H2SO4 solution = 2 × 0.1 = 0.2 M So no. of moles of H+ ions in 10 ml H2SO4 solution =
0.2 10 = 0.002 1000
concentration of OH– ions in 0.1 KOH solution = 1 × 0.1 = 0.1 M So no. of moles of OH ions in 10 ml KOH –
solution =
0.1 10 1000
= 0.001 after mixing remaining moles of H+ ions
= 0.002 – 0.001 = 0.001
+
so concentration of H ions in mixture of solutions =
0.001 × 1000 = 0.05 M 10 10
CLASS-XII_STREAM-SB+2_PAGE # 185
PART-II (2 Mark) MATHEMATICS 81.
p(x) = a0 + a1x + ........+ anxn p(0) = 7 a0 = 7 p(1) = a0 + a1 + a2 + ............+ an = 9 p(– 1) = a0 – a1 + a2 ........... = 1 p(2) = a0 + 2a1 + 4a2 + .......... = 13 p(– 2) = a0 – 2a1 + 4a2 ........... = – 15 p(1) + p(– 1) = 2[a0 + a2 + .........] = 10 a0 + a2 + a4 = 5 .....(1) 7 + a2 + a4 = 5 a2 + a4 = – 2 .....(2) p(2) + p(– 2) = 13 – 15 2(a0 + 4a2 + .........) = – 2 a0 + 4a2 + 16a4 = – 1 4a2 + 16a4 = – 8 .....(2) p(3) = 25 a0 + 3a1 + 9a2 + ........ = 25 a0 + 3a1 + 9a2 + 27a3 + 81a4 + 243a5 = 25 From (1) and (2)
.....(3)
4a2 + 4a4 = – 8 4a2 + 16a4 = – 8 – – + a4 = 0 and a2 = – 2 Smallest possible value of n is 3. 2
82.
(a – b )
2
0
abc
a 1 ab
|a – b| < c ...... (1) |b – c| < a ...... (2) |c – a| < b ...... (3) Squaring and adding a2 + b2 + c2 < 2ab + 2bc + 2ca
[Triangle inequalities]
a2 2 ab So, b [1,2). 83.
y = | x 3 | 4 – 5 When, x < – 1 y=|3–x–4|–5 y=–x–1–5 y=–x–6 When –1 x < 3 y=|3–x–4|–5 = | – x – 1| – 5 =x+1–5 =x–4 When, 3 x < 7 y = |x – 7| – 5 y=7–x–5 y=2–x
12 –6
–
3
–1
7
O
x
–
6 x
2– x
–4
x
–
12
–5
CLASS-XII_STREAM-SB+2_PAGE # 186
When, x 7 y = | x – 7| – 5 =x–7–5 = x – 12. Area bounded region 1
=
3
( x 6 )dx
+
6
7
( x 4 )dx
+
1
12
( 2 x )dx +
3
1
3
( x 12)dx 7
7
12
x2 x2 x2 x2 2 x 6 x 4 x 12 x = + + + 2 2 6 2 1 2 7 3
49 9 1 36 9 1 144 49 6 – 36 + 12 – 4 + 14 144 – 84 – 6 + = 2 2 2 2 2 2 2 2
=
11 15 9 21 3 119 – 18 – – – – – 72 + 2 2 2 2 2 2
=
130 48 – – 90 2 2
= 65 – 24 – 90 = 49 sq. unit.
A 84.
b
a
b
C
a
D
cos =
B
b
b a2 b2 a2 = 2 a 2ab
cos(180º – ) =
– cos =
cos =
....(i)
b2 b2 a2 2b 2
2b 2 a 2 2b 2
a 2 2b 2
....(ii)
2b 2
From (i) & (ii) a 2 2b 2 2b
2
=
b 2a
3
a a –2 –1=0 b b
CLASS-XII_STREAM-SB+2_PAGE # 187
a =x b
Let
x3 – 2x – 1 = 0 (x + 1)(x2 – x –1) = 0 x = – 1 or x =
1 1 4( 1)(1) 2
1 5 2 x cannot be negative
x=
=
85.
1 ( 5 1) 2
an =
1 a n1 2
a1 =
1 a0 2
a1 =
1 cos 2
2 cos 2 a1 =
2
a1 = cos
2
1 a1 2
a2 =
=
2
1 cos
2
2
2 cos 2 =
4
2 = cos
22
an = cos
2n
lim 4n(1 – a ) n
n
lim 4n 1 cos 2n
n
CLASS-XII_STREAM-SB+2_PAGE # 188
lim 4n × 2sin2
2 n 1
n
2 2n 2 sin2
2
lim
n
2n 1
×
2
n 1
2
n 1
2n 1
sin2
2
n 1
n 1
2 lim × 2 2n 1 2n 1
n
2 . 2
= 86.
f(x) = (sin x)sinx f(x) = e sin x log sin x Minimum value of sinxlog(sinx) is 0. Maximum value of (sin x)sinx is e0 = 1. Maximum value of sinxlog(sinx) is – Minimum value of (sin x)sinx is 10
87.
1 . e
1 e
e .
1
x dx 1
=
10
log x
1
= log10 = 2.303
1 1 + ....+ 9 2 = 1 + 0.5 + 0.33 + 0.25 + 0.20 + 0.16 + 0.14 + 0.12 + 0.11 2.81
B=1+
1 1 1 + ....+ + 2.81 – 1 + 0.1 =1.91 9 10 2 So, C < A < B and B – A 0.51, A – C = 2.303 – 1.91 0.40. So, B – A > A – C.
C=
r
A
88.
D
B
r
60º
r
r
60º
r
r
C
As we want the distance between two point is at least r. Now when the point A, B are at distance r.Then the angle made arc BA is 60º. Now as chord AB come closer to centre the length of chord AB is increased that is it is greater than r and the angle is also increases i.e. from 60º to 180º and now when chord AB move way from centre then the length of chord AB decreases , when chord AB reach CD the length of AB equal to r and the angle chang from 180º to 60º CLASS-XII_STREAM-SB+2_PAGE # 189
So, the angle required for desired conditions = 2(180 – 60) = 240 Total angle for all around the circle = 360º So, required propability = 89.
240 2 = 360 3
Let aN be pth digit no.
4(5P –1) 4(5P – 1) 1 a + ar > ar2
r2 – r – 1 < 0
1 5 r 2 ,
Case 2 : Case 3 :
r = 1 equilateral triangle r a
r2 + r – 1 > 0
– 1 5 – 1 5 , r 2 2
1 5 2 5 r lies in the interval 2 , 2 . 3.
Number of diagonals passing through centre = 6 Number of rectangles = 6C2 = 15
4.
22, 3 + 4, 3 + 42, 5 – – 2 –1–
3 i , 1 + 2 3 i , 1 – 2 3 i, 6
where =
– 1 3 i 2 – 1 – 3 i , = 2 2
1 + 2 3 i , 1 – 2 3 i are conjugate of each other.. 5.
Least possible degree = 5
Tangent at (2, 1) y.2 = 2 (x + 1) y=x+1 x–y+1 =0 equation to circle (x – 1)2 + (y – 2)2 + (x – y + 1) = 0 putting x = – 1 4 + (y – 1)2 + (– y) = 0 y2 – 4y – y + 8 = 0 D=0 (+ 4)2 = 32 y=
( 4) D 4
y=
4 2 0 =±2 2 2
CLASS-XII_STREAM-SB+2_PAGE # 197
6.
BKN = 6 BN 1 BKN 1 AN 2 AB 3 APB 9 BN 1
9 ×6 1
APB =
=
ABC = 108.
7.
x2 a2
h=
a2
y2
=1, a>b>0
b2
x y , k= 3 3
(3h)2
8.
54 1
(3k )2 b2
= 1 which is ellipse
7 6 cos 1sin 1
1
LH.S is less than or equal 1 while R.H.S is greater or equal to 1 possible when
9.
cos = 1
= 0, 2
and sin = 0
(1 + tan 1º) (1+ tan 2º) .........(1+ tan 45º) (1 + tan A) (1 + tan B) = 2
if A + B = 45º
Ans = 223
10.
f is differentiable function . f (a) f(b) > 0
f is increasing at x = a and b
or
f is decreasing at x = a and b
minimum number of roots of f (a) = 0 in (a, b) is 2,
CLASS-XII_STREAM-SB+2_PAGE # 198
11.
When x is less than 49 then f(x) has negative value. Which is not possible. when x > 49 then f(x) = 49 (x – 41)48 + 41 (x – 49)40 + 2009 (x – 2009)2008 so sing of f(x) does not change f(x) > 0 non real except one positive root.
12.
f (x) is given smooth curve hence differentiable i- given domain By first derivative test x = a, c is point of local maxima x = b is point of local minima 3
13.
f ( x )dx 4 i
shaded area = Trapezium Area – Area under curve
5 7 (3 – 1) 2 2 = –4=2 2
e
14.
n =
n
(log x ) .dx 1
n = x (log x )
n
e
e 1
–
i
n(log x )n –1 .x dx x
n = (e – 0) – n n–1
CLASS-XII_STREAM-SB+2_PAGE # 199
n + n n–1 = e 2011 + 2011 2010 = e
15.
100 + 100 99 = e
x2 + y2 100
Area bounded = 100
sin (x + y) > 0 Hence common area of region bounded = 50 as in half the region sin (x + y) > 0 and in other half sin (x + y) < 0
16.
n(S) = 7C3 = 35
n () = 7 + 7 + 7 = 21
ˆi 17.
ˆj
P () =
21 3 35 5
kˆ
2 –1 1 = ˆi (–2 3) – ˆj( 4 ) kˆ (–6) = u v = 0 –3 2
(u v ).w ,
53
greatest when x2 + y2 = 1 fmax. = 17
Ans. (D)
18.
Number of ways = 4P2 × 4P2 × 10 = 1440
19.
1 + x2 + x4 + .........+ x2010 =
1 – ( x 2 )1006 1– x2
=
1 – ( x1006 ) 2 (1 x )(1 – x )
=
(1 x1006 ) (1 – x1006 ) (1 – x ) (1 x )
= (1 + x1006)
(1 – x 503 ) (1 x 503 ) (1 – x ) (1 x )
= (1 + x1006) (1 + x + x2 + ...............+ x502) (1 – x + x2 – x3 + ............ + x502)
n – 1 = 502
n = 503
CLASS-XII_STREAM-SB+2_PAGE # 200
20.
an = 3an–1 + 1 = 3(3an–2 + 1) + 1 = 32 an–2 + 3 + 1 = 32 (3an–3 + 1) + 3 + 1 = 33 an–3 + 32 + 3 + 1 aN = 3n a0 + 3N–1 + 3N–2 + .... 1 Method - I a2010 = (1 + 3 + 32 + 33 + 34) + ....... + 32009 = (1 + 3 + 32 + 33 + 34)+ 35 (1 + 3 + 32 + 33 + 34)+ 310 (1 + 3 + 32 + 34 + 35) +.....+32005 (1+ 3 + 32 + 33 + 34) each (1 + 3 + 32 + 33 + 34) is divisble by Method-II a2010 =
32010 – 1 35402 – 1 (243)402 – 1 (242 1)402 – 1 2 2 2 2
= 11 k (k I) Hence remainder is 0
PHYSICS
21.
F – 1mg – 2(m + M)g = M.
1mg m
F = 1mg + 2(M + m)g + 1Mg = 1g(M + m) + 2g(m + M) = (1g + 2g) (M + m)
22.
m1m2 1 T = 2 m m k 2 1 we can use concept of reduced mass.
23.
2T cos = – ma ;
If
x 2a h>3
2
=
320 25
8 5 8 5 5 8 5
2 5 = 16 here
4a = 6, 2a = 3
CLASS-XII_STREAM-SB+2_PAGE # 220
9.
(C) f(x) = cos5x + A cos 4x + Bcos3x + Ccos2x + Dcosx + E f( – x) = – cos5x + Acos4x – B cos3x + C cos2x – D cos x + E f (x) – f( – x) = 2 [A cos4x + C cos2x + E) for x = 0 f(0) – f() = 2(1 + B + D) ...... (i) at x =
at x =
4 3 = 2 | –1 + B cos , f – f + D cos | ...... (ii) 5 5 5 5 5
2 6 1 B cos D cos 5 5
2 3 2 – f =2 , f 5 5 5
f( + x) = – cos5x + A cos4x – B cos5x + C cos2x – D cosx + E f ( – x) = f ( + x)
..... (iii)
...... (iv)
9 2 8 3 7 T = f(0) – f() – f 5 f 5 + f 5 f 5 – f 5 f 5 +
4 6 f f 5 5
2 8 =f from equation iind f 5 5 9 f = f 3 3 3 7 4 6 = f and f = f f 5 5 5 5
4 2 3 So T = f(0) – f() – 2 f 5 – f 5 f 5 – f 5 from equation 1, 2 & 3 T = 2(1 + B + D) – 2 [–1 + B cos
3 6 2 + Dcos | + 2 [ 1 + B cos + D cos ] 5 5 5 5
Will depend on B and D only 10.
(B) 3sinA + 4cosB = 6 ...... (i) 3 cosA + 4sinB = 1 .......(ii) Squaring and adding , we get 9 + 16 + 24 sin(A+B) = 37
1 2 1 sin( – C) = 2 sin(A+B) =
sin C =
11.
(C) [x] > 1 [x] 2 x2 But x cannot integers Possible domain = (2,3)
12.
(C) f(0) + f(0) +
(2011) +
1 2
f " (0 ) f (n –1)(0) + ......+ 2! (n – 1)!
n(2011)n –1 n(n – 1)(2011)n – 2 n(n – 1)...2! (2011)' , ...... n – 1! 1! 2!
= nC02011 + nC12011n–1 + .... + nCn–1(2011) + nCn (2011)0 – 1 = (2011 + 1)n – 1 = 2012n – 1
CLASS-XII_STREAM-SB+2_PAGE # 221
13.
(B)
Point where slope of tangent is 1 of the curve y = ex is y = ex = 1 x=0 (0,1) and for y = lnx point is (1,0) required minimum distance is 8
14.
(B)
2
4
3
f ( x ) dx =
2
2
f ( x ) dx
3 f ( x) dx
8
+ ...... +
7 f ( x ) dx
= 2 + 3 + 2 + 5 + 3 + 7 = 22
e cos x
1
15.
(B) I = 2012
0e
cos x
e cos x
dx
e cos x cos x e cos x 0 e 1
again I = 2012
dx
1
dx
2I = 2012
I = 1006
16.
0
1 (D) lim 2 n 4 n – 1 n
4n – r 2
n
1
1 = 2 1
=
1
0
r 2n 1– 2n
2
dx
0
2 2 4n – n 1
2
lim
n r 1
4n 2 – 4
.......... ..
1
= nlim r 1
=
1
1–
x2 4
dx 4 – x2 1
1 x = sin 2 0 CLASS-XII_STREAM-SB+2_PAGE # 222
17.
(C) E1 : A wins when A takes out 3 & 6 and B takes out 8 & 9 1 1 1 × = 3 3 9 E2 : A wins when A takes out 5 & 6 and B takes out any two no. 1 1 P (E2) = × 1 = 3 3
P (E1) =
Required probability = 18.
(A) a b b c c a ab bc 0 ab cb 0 a c b 0 a c b a c b (bc ) = ca a c c = c a a c c a a c a c 0 (1 + ) ( a c ) = 0 From (ii) a c b abc 0
........(i)
........(ii)
= –1
abc 0 centroid of ABC = 3
n
19.
1 1 4 + = 9 3 9
2 (B) r r 1 r !
r 1
Tr = [(r + 1) (r – 1) – (r – 2)] r! Tr = (r – 1) (r + 1)! – (r – 2) (r!) but r = 1, 2, .............., n Tr = 1 + (n + 1)! (n – 1) 20.
1, x A (C) If f (x , A B) = 0, x A Case (i) x A, x B then, f(x, A) + f(x, B) – f(x, A) f(x, B) = 1 + 0 – 0 = 1 Case (ii) x A, x B f(x, A) + f(x, B) – f(x, A) f(x, B) = 0 + 1 – 0 = 1 Case (iii) x A, x B f(x, A) + f(x, B) – f(x, A) f(x, B) = 0 + 0 – 0 = 0 Case (iv) x A and x B f(x, A) + f(x, B) – f(x, A) f(x, B) = 1 + 1 – 1 = 1 CLASS-XII_STREAM-SB+2_PAGE # 223
f(x, A B) = f(x, A) + f(x, B) – f(x, A) f(x, B)
Aliter
1, x A B If f (x , A) = 0, x A B Option A is rejected because x (AB) ,then f(x,A) + f(x,B) = 1+ 1 = 2 which can’t be attained by f.
Option B is rejected baecuse if x A B , then f(x,A) + f(x,B) –1 = 0 + 0 –1 = –1 which can’t be attained by f . Also option D is rejected because if x A , then f(x,A) + |f(x,A) – f(x,B)| = 1 + |1 – 0| = 2 Which is also unattainble
PHYSICS 21.
(A) acceleration of cabin is g relative acceleration of A and B w.r.t. cabin is zero so both A and B continue to be exactly at rest relative to the cabin.
22.
(B) k k k = mg
23.
(A) v = A 2 r 2 from (i) and (ii)
W
v2 2 A 2
mg
a2 4 A 2
W = 2mg
...(i)
a = 2r
...(ii)
1
It is the equation of ellipse 24.
(A) Work done in this process is zero so that (Ui = Uf)
25.
(B) Using mole conservation 2n = n1 + n2 ...(i) PV = n1RT ...(ii) PV = n2R(2T) ...(iii) n1 = 2n2 2n = 2n2 + n2 2n
n2 = 3
26.
(D)
;
M2 f 2n / 3 2 M2i n 3
dQ dT KA dt dx
K1A( T 100 ) K 2 A (0 T )
K1(T – 100) = K2(–T) K1T – K1 × 100 = –K2T T(K1 + K2 ) = K1 × 100 385 100 = 88°C 435
T= 27.
(B) P1- T= constant
CLASS-XII_STREAM-SB+2_PAGE # 224
T1 P 1 T P 2 2
233K T
7/5
1
(7 / 5)1
0.28 1
233
T=
(0.28 )2 / 5
466 J
So that we will required in addition an air conditionaer to cool the air injected into the cabin
28.
v
(C) f1 = v u f0 v u
f2 = v f0
...(i) ...(ii)
f1 v 2 f2 v 2 u2 v2 f1 = f2 2 2 v u
f2 > f1 29.
(C) = 0 (cos2)4 3 = 0 × 4
4
= 30% of 0
30.
nv
(C) f = 2 f’ =
n v' 2
f v v f ' v ' 1.04 v
f’ = (1.04)(450) = 468 Hz 31.
(D) × 1 1 2 2
f11 = f22 f1 2 f1 2 f2 1 2f1 1 1 2 2 1 1 1 2 2
2 = 2 1 = 2.0 mm 32.
(A) V = V0 cost CLASS-XII_STREAM-SB+2_PAGE # 225
Vrms =
V0 2
V0 = 220 2 Volt = 50 × 2 rad/sec = 100 rad/sec. v = 220 2 Cos(100t) 33.
(A) Current through R1 is maximum so power dissipates at R1 is maximum.
34.
(B) Momentum is conserved during collision so P P' . But some part of kinetic energy is stored in excited state So K’ < K
35.
(D) Potential difference across inductor during current growth is v = v0e–t/
36.
(A) Neutron is chargeless so graph is (1) Proton is positive charge so graph is (2) and for e– graph is (3)
37.
(D) R 9 1
1
8
1 1 3R R 1 2 4 4 1 1 1 5R 5R R 3 4 9 9 4 36
1 1 1 1 2 3
38.
(A)
P P'
AT 4 T 4 A 2
4
P 4 P'
P’ =
P 4
V i
V. i
P
h 2 i e
39.
(B) RH =
40.
(A) From given graph highest precision that means sharpness is maximum in graph (I)
2
i
2
CLASS-XII_STREAM-SB+2_PAGE # 226
CHEMISTRY 41.
(C) 2,2,2 2,2 Ni(CO)4 Ni : [Ar] 3d8 4s2 = t 2g e g
CO is a strong filed ligand
Cr (H2O)6+2 Cr+2 : [Ar] 3d4 45°
octahedral complex : d2sp3 42.
(A) Ag+ + 2CN– [Ag(CN)2]– 2[Ag(CN)2]– + Zn+2 [Zn(CN)4]–2 + 2Ag+
43.
(A) Ideal mixture H = 0 V = 0
44.
(C) = CRT
45.
(B) Energy distribution at two different temperatures
46.
(D)
1 0.01 2 = 0.001 = 10
The radical formed as intermediate
or
is unstable , where as in all other
cases resonance stabilised radicals are formed. 47.
(A)
The given compound is chiral and the possible stereoisomers are enatiomer to each other. 48.
(D) According to second law of thermodynamics, for spontaniety
:
SUNIV > 0
CLASS-XII_STREAM-SB+2_PAGE # 227
49.
(B) r1 = 30 nm
r2 = 10 nm
2 surface area 3 = 4r = 3 volume r 4r 3
(3 / r2 ) 30 (3 / r1 ) = 10 = 3 50.
(C) The reaction is example of Pinacole – Pinacolone reaction with classical ring expanssion rearrangement.
51.
(B) H3PO2 a mild reducing agent is used to remove the diazonium group with H.
52.
(A)
0NaOAc + 0HCl – 0NaCl = 0AOAC 53.
(D)
BRAGG’S Law 2dsin = n d = , n = 1
1 = 30° 2 angle of incidence = 60° sin =
54.
(C) Zn Zn+2 + 2e– 2mol 2mol 4mol G° = –nFE°cell = – 4 × 96500 × 1.1 = – 424.6 kJ/mol
55.
(B) 2NaBH4 + 2 2Na + B2H6 + H2
56.
(C) [Mn(CN)6]–4 & [(Mn/Br)4]–2 Mn+2 in both Mn+2 : [Ar]3d5 4s With CN– : With Br– : Magnetic moments :
1(1 2) BM &
5 (5 2) BM
CLASS-XII_STREAM-SB+2_PAGE # 228
57.
(A) Half life of zero order reactions initial concentration of the reactant.
58.
(D)
59.
(C)
60.
(C) Due to intramolecular H-bonding boiling point of (ii) is less than (iii) but greater than (i).
PART-II (2 Mark) MATHEMATICS 81.
82.
(B) AK = I B = 0 |AB| = 0
|A|K = 1 |B| = 0
(C) Let 12 + 22 + .......+ (2n–1)2 = x and c =
n
(4r 2 – 4r 1) = 3 (4n
2
– 1)
12 2 2 ...... (2n)2 – x < 1.01 x 2n(2n 1) ( 4n 1) < 2.01 6x n (2n 1) ( 4n 1) n 3 ( 4n 2 – 1) < 2.01 3
( 4n 1) < 2.01 (2n – 1)
4n + 1 < (2.01) (2n – 1) 4n + 1 < 4.02 n – 2.01 3.01 < 0.02 n
301 KC Reaction move in backward direction
Ans.
(A)
52.
SN-1 Reaction, more stable carbocation is formed
Ans.
(C)
53.
Ans. (D)
54.
Wolf kishner Reduction
Ans.
(B)
55.
Compound is AsCl3
Ans.
(C)
56.
Valency factor of KMnO4 = 5 5e- + MnO4- + 8H+ Mn+2 + 4H2O
Ans.
(D)
Ea 1 R T
57.
Ans. (C)
58.
H 6000 J S = T 213k 22J/K.mol
Ans.
(A)
59.
Ullmann reaction
Ans.
(A)
60.
Energy of t2g orbitals < eg orbitals in octahedral complexes Ans. (C)
Ans.
(D)
CLASS-XII_STREAM-SB+2_PAGE # 280
PART-II Two Mark Questions MATHEMATICS 81.
Ans-(A) n
82.
e
n
k wk
2
n
1 w
e
R0
e
n
w
when n is multiplying of 3, then S=e, 1/e when n is not multiple of three,then s= e1/ 2 e1/ 2 Ans- (C) 83.
y = ax2 + bx + c a > 0, b < 0, c < 0 Also y(1) = a + b + c < 0 Ans-(B)
84.
Sin
1
r1 r 2 AP1 AP2
3
AP2 AP1 r1 r2
r2 3 r1 3 r1 r2 r2 ( 3 1) r1
3 1
r2 2 3 r1 85.
Ans- (D)
Let f(x) = 3x3 - 25x f’(x) = 9x2 - 25 5 3 f(-5/3) = 250/9 27.7 f(5/3) = -250/9 -27.7 n can take 55 values
f’(x) = 0
86.
Ans-( )
87.
Sol- In
/2
0
Ans-(C)
xn cos xdx n
In +n(n-1)In-2 = 2
.......(1)
I n 2 !I In In 2 n 2 n Also = n! n 2 ! n 2 n 2 n!
n ( 2) = n 2 n!
2 = e 1 2
Ans- (A)
CLASS-XII_STREAM-SB+2_PAGE # 281
88.
Sol-
n
1
n
[x][ x ]dx 2dx ............ 1
= 50
for n = 8
66
for n = 9
Ans - (B) 89.
Ans- (B), Check for n = 1, 2 , 3,......
90.
Sol- No correct Option (1,17), (2,17),(3,17),(4,17),(4,17),(6,17),(7,17)_ _ _ _ _ _ _ (16,17),(18,17) = 17 points Also (17,1), (17,2), _ _ _ _ _ _ _ _ _ _ _ _ _ (17,16), (17,18) = 17 points So there are more then 34 points. Ans-()
PHYSICS Initial
Final
w V=W'R
91. A
From cons. of anguler momentum about A
v=
2Rw 7
92.
Ans. (A)
93.
Tmax - mg =
W’ =
2w 7
mv 2 ....(i) R from energy cons. ki + ui = kf + uf
1 O + mg (R-R cos ) = mv2+0 2 V2 = 2gR (1-cos ) Put in eq. (i) Tmax = 3mg - 2mg cos
Ans.
(C)
Tmin Tmax mg cos V mg
mg
Tmax Tmin =4 Ans.
=60° (B)
94.
Heat cap. is define as C = Cv + C=
R 1
3 R R R 2 1 3
Ans.
(D)
95.
Ans. (A)
96.
Ans. (C)
CLASS-XII_STREAM-SB+2_PAGE # 282
97.
At steady state capacitor will belave as open circuit So charge store in 1 F = 1×4 = 4 C in 2 F = 2 × 4 = 8 C Ans. B
98.
F=
2P C
;
mg =
99.
E = + eV
;
E = + e (.9)
;
1.1E = + e(.9)
.1E = .3e
;
E = 3eV put
;
2.4eV
100.
2 1.5 103 3 108
;
(MLoT-2 -4) = (ML2T-1) (ML2T-2 -1) (LT T-1) Solving we get
m = 10-6kg
Ans.
(C)
Ans.
(B)
Ans.
(D)
Ans.
(B)
Ans.
(C)
Ans.
(D)
Ans.
(B)
CHEMISTRY 101.
Ans. (A)
102.
d=
PM RT M = 123
dRT P acetic acid exist as dimer
M=
103.
E = H - (PV) = H - ngRT
104.
Ans. (C)
105.
N2 (g) + 2H2(g) N2H4(g)
= 106.
(BDE)
Reacant
(BDE)Pr oducts
Vk+ + VCl- = 133 + 181 KCl form FCC Lattice 2(VK+ + VCl-) = a = edge length of unit cell V = a3
107. Ans.
K2Cr2O7+6FeSO4+ 7H2SO4 Cr2(SO4)3 + 3Fe2 (SO4)3+ K2SO4 + 7H2O (B)
108.
EoCell = SRP cathode - SRP anode = -0.44 - (-0.74) = 0.3V o G = - nF E Cell (n = 6 ele )
109.
Ans. (A)
110.
XeF6 + 3H2O XeO3 + 6HF XeO3 is SP3 hybrid and pyramidal (C)
Ans.
Ans.
(C)
CLASS-XII_STREAM-SB+2_PAGE # 283
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