INDIA(Advance) iNTERNAL TEST SERIES FIITJEE ALL –- JEE CHEMISTRY, MATHEMATICS & PHYSICS SET – A
APT - 5
CODE: 080089.1
Time Allotted: 3 Hours
AI2TS - 5 Maximum Marks: 207
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination Hall before the end of the test.
INSTRUCTIONS Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.
CLASS - XII
A.
General Instructions
B.
Filling of OMR Sheet
C.
Attempt ALL the questions. Answers have to be marked on the OMR sheets. This question paper contains Three Sections. Section-1 is Chemistry, Section-2 is Mathematics and Section-3 is Physics. Each section has two parts: Part-A & Part-C Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.
Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and write in ink your Name, Test Centre and other details at the designated places. OMR sheet contains alphabets, numerals & special characters for marking answers.
Marking Scheme For All Parts.
Part-A (01 – 07) contains 7 Multiple Choice Questions which have only one correct answer. Each question carries +3 marks for correct answer and –1 mark for wrong answer. Part-A (08 – 11) contains 2 Paragraphs. Based upon paragraph, 2 Multiple Choice Questions have to be answered. Each question has only one correct answer and carries +3 marks for correct answer. There is no negative marking. Part-A (12 – 15) contains 4 Multiple Choice Questions which have one or more than one correct answer. Each question carries +4 marks for correct answer. There is no negative marking.
Part-C (01 – 05) contains 5 Numerical Based questions with single digit integer as answer, ranging from 0 to 9 and each question carries +4 marks for correct answer and –1 mark for wrong answer.
Name of the Candidate : ____________________________________________ Batch : ___________________ Date of Examination : ____________________ Enrolment Number : _______________________________________________
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SECTION – 1 (Chemistry) PART – A (Single Correct Choice Type) This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.
+
What is the sum of the number of electrons with = 0 and = 2 present in Cu ion? (A)
2.
(B)
16
(C)
15
(D)
17
Which statement is incorrect for the molecule PCl5? (A) (B) (C) (D)
3.
18
It has trigonal bipyramidal geometry It contains two different sets of P–Cl bonds in terms of bond length 3 Phosphorus undergoes dsp hybridization + In solid state it exists as [PCl4] and [PCl6] ions.
X(g) Products If the initial concentration of X in the above reaction is reduced to half-of its initial value, the half-life is reduced to (A)
4.
1 th of its initial value, what is the order of the reaction? 8
2
(B)
-1
(C)
-2
(D)
1
X(g) Y(g) + Z(g) The concentrations of X, Y and Z gases in the above reaction are same at equilibrium which is established at 6 atm and 40°C. The equilibrium constant Kp is : (A)
0.5 atm
(B)
2 atm
(C)
3 atm
(D)
1.5 atm
Space for rough work
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5.
The electron of hydrogen atom was excited from ground state to a higher orbit. During de-excitation of the electron, photons of six different wavelengths were emitted. If each photon forms a spectral line, how many spectral line will be visible to naked eye? (A)
6.
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4
(B)
2
(C)
1
The greatest angle observed in the following molecule is : (A)
a
(B)
(D)
Cl
7.
c
(D)
H
b
b
c (C)
3
d
C d
F
a H
Graph is given for the following reaction, X(g) Y(g) + Z(g). Choose correct statement regarding the reaction. (A) The unit of rate constant is time-1 t1/2 (in sec)
(B)
It is a second order reaction
(C)
The rate of reaction does not depend on concentration of reactant The rate of reaction decreases with time i.e., with progress of reaction.
(D)
[A0](in M)
Space for rough work
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(Comprehension Type) This section contains 2 paragraphs. Based upon each paragraph 2 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Questions 08 to 09 Read the paragraph carefully and answer the following questions:
Gaseous reactions generally takes place in closed vessels. The reactions proceed towards both direction at equilibrium whatever may be the difference of number of gaseous moles of products and reactants. A 10 litre vessel contains one mole each of SO3 , CO, SO2 and CO2 at 400 K.
SO3 (g) CO(g) SO2 (g) CO2 (g) The above reaction attains equilibrium in the closed 10 L vessel at 400 K. 50%(mole) of reactants undergo reaction at equilibrium. Answer the following questions on the basis of above write up : 8.
If 1, 2, 3, and 4 moles of SO3 ,CO,SO2 and CO2 respectively are taken in a 10 litre vessel and the above reaction takes place in it, then the reaction will proceed towards. (A) (C)
9.
forward direction both direction
(B) (D)
backward direction Unpredictable
(C)
13.136 atm
What is the equilibrium pressure of the system? (A)
11.336 atm
(B)
1.316 atm
(D)
11.846 atm
Paragraph for Questions 10 to 11 Read the paragraph carefully and answer the following questions:
2X(g) 3Y(g) X2 Y3 (g) Data for the above reaction is given below : Expt. No. [X0] in mol L1 1 0.1 2 0.2 3 0.2 10.
Rate in mol L1s1 4 × 108 16 × 108 32 × 108
What is the rate constant of the reaction? (A) (C)
11.
[Y0] in mol L1 0.1 0.1 0.2
4 × 106 mol2L s1 2 4 × 105 mol2L s1 2
(B) (D)
4 × 108 mol2L s1 2 4 × 104 mol2L s1 2
Which statement is correct for the half life of X? (A) (B) (C) (D)
It is directly proportional to concentration of X It is inversely proportional to the concentration of X It is directly proportional to the square of concentration of X It is inversely proportional to the square of concentration of X Space for rough work
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(Multi Correct Choice Type) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. 12.
The electronic configuration of an atom is : 2
2
6
2
6
10
2
3
1s 2s 2p 3s 3p 3d 4s 4p
Which of the following statement(s) is/are correct for the atom? (A) (B)
The spin multiplicity of the atom is 4 It contains eight electrons with l = 0
(C)
It’s spin magnetic moment is 2 2B.M It’s tripositive ion contains the electron configuration of an inert gas
(D) 13.
Which of the following statement(s) is/are correct for PF2Cl3?
F F
P Cl
Cl Cl (A) (B) (C) (D) 14.
Fluorine occupy the axial positions of the tbp geometry which triangular plane contains chlorine atoms at vertices and phosphorus at centre It’s dipole moment is zero The orbitals used by phosphorus for hybridization are 3s,3p x,3py which comprises the triangular 2 2 plane with sp hybridization, and 3pz and 3dz which are perpendicular to the plane The structure of the molecule is
2KClO3 s 2KCl s 3O2 g ; H ve The product yield of above reaction can be increased by (A) (C)
15.
(B) (D)
increasing temperature removing KCl
decreasing pressure adding KClO3
The order of a reaction can be changed by (A) (B) (C) (D)
changing concentration using catalyst increasing temperature increasing partial pressure in case of gaseous reactants Space for rough work
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PART – C (Integer Answer Type) This section contains 05 multiple choice questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.
What is the azimuthal quantum number of the unpaired electron of chlorine?
2.
What is the sum of the number of unpaired electrons present in the given species? N, N2, O, O2
3.
The time and concentration graph of the reactant(X) and product(Y) of the following first order reaction is given above. 3X g Y g
If the half-life of the reaction is 4 sec, then the value of ‘t’ in sec. unit is:
Concentration in M
X
Y
t Time in min
4.
NH4Cl s NH3 g HCl g 2
The equilibrium constant Kp of the above reversible reaction is 16 atm at 400 K. What is the equilibrium pressure in atm unit? 5.
How many maximum number of electrons of an atom have the following set of quantum numbers? n = 4, = 0, 1, 2, m = 0, +1, s = -½ Space for rough work
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SECTION – 2 (Mathematics) PART – A (Single Correct Choice Type) This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
1.
4x 3 4x 3 2 cos is 2 6 3 2
The period of the function f x 4 sin4
(A)
3
2
(B)
3
4 2.
(C)
4
4
2
(D)
4
3
3
3
If f x 9x 3 x 1 x , 1 , then the range of f x is ([.] denotes the greatest integer function) (A)
3.
3
0,1,2,3,4,5,6
(B)
0,1,2,3,4,5,6,7
(C)
1,2,3,4,5,6
(D)
1,2,3,4,5,6,7
1 x
If 2 x2 3 , then the number of positive roots of x 2 , (where {x} denotes the
fractional
part of x) is (A) 4.
(C)
, 0 1,
(B)
,
2
(D)
3
(D)
None of these
0 , then S is equal to (C)
, 0 1,
100x 99 sin x , where [.] denotes the greatest integer function, is x
The value of lim x0 sin x 197
(B)
198
(C)
199
The relation R on the set of complex numbers defined by z1Rz2 if and only if (A) (C)
7.
1 1/ x 1
(A) 6.
(B)
If S is the set of all real x for which 1 e (A)
5.
0
reflexive but not symmetric symmetric but not transitive
(B) (D)
(D)
does not exist
z1 z 2 z1 z 2
is real, is
reflexive but not transitive an equivalence relation
The function f x x2 3x 2 cos x is not differentiable at (A)
–1
(B)
0
(C)
1
(D)
2
Space for rough work
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(Comprehension Type) This section contains 2 paragraphs. Based upon each paragraph 2 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Questions 08 to 09 Read the paragraph carefully and answer the following questions:
f x min x x , x x , 2 x 2; g x 2 x 2 , 2 x 2
Let
and
h x
sin x
, 2 x 2 ,
sin x
x0
(where [x] denotes the greatest integer function). On the basis of above information, answer the following questions: 8.
The sum of all the roots of the equation g x h x 0 is (A)
9.
Positive
(B)
Negative
(C)
Zero
(D)
None of these
The set of values of ‘a’ such that the equation f x a 0 has exactly eight real and distinct roots is (A)
1 2
a 0,
(B)
1 2
a 0,
(C)
a 0, 1
(D)
a 0, 1
Space for rough work
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Paragraph for Questions 10 to 11 Read the paragraph carefully and answer the following questions:
A circular arc of radius 1 subtends an angle of x radians, 0 x
, as shown in the figure. The point R 2
is the intersection of the two tangent lines at P and Q. Let T (x) be the area of triangle PQR and let S(x) be the area of the shaded region. R P
1
Q x 1 O
On the basis of above information, answer the following questions:
10.
The value of lim
(A)
11.
T x
x0 S x
1/2
is
(B)
2/3
(C)
1
(D)
3/2
(B)
1/3
(C)
½
(D)
2/3
2
The value of S ' is (A)
–1
Space for rough work
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(Multi Correct Choice Type) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. 12.
If f x 2x sinx and g x 3 x, then (A) (C)
range of gof is R both f and g are one – one
(B) (D)
gof is one – one both f and g are onto
13. Which of the following functions are periodic?
f x sin x sin x
(A)
14.
lim x x
(A)
15.
lim x0
x 1 x
2
(B)
x 1 1 t dt,x 2
If f x 0
(A) (B) (C) (D)
(D)
1
2 x 3x 10 3 3
where [.] denotes the greatest integer function.
equals
ln 1 x x x
1 sinx 1 sec x 1 cos x 1 cos ec x
p x x x
h x max sinx,cos x
(C)
g x
(B)
5x 1, x 2
lim x0
1 cos x x
2
(C)
lim x0
1 x 1 x
(D)
lim x0
x 2
x x 2x
, then
f(x) is not continuous at x = 2 f (x) is continuous but not differentiable at x = 2 f (x) is differentiable everywhere the right derivative of f x at x = 2 does not exist Space for rough work
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PART – C (Integer Answer Type) This section contains 05 multiple choice questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).
1.
1 sin3 x , x 2 2 3 cos x If f x a, is continuous at x , then the value of x 2 2 b 1 sin x , x 2x 2 2
2.
If f x f y f
3.
1/3
b a
is
3f 3 f x xy for all x,y R , xy 1 and lim is 2 , then the value of x0 x f ' 2 1 xy
If f x
sin
1
1 x .cos1 1 x , then the value of 2 x.1 x
18 2
lim f x is (where {x} denotes the x0
fractional part of x)
x x x cos tan is . The value of 4 12 3
The fundamental period of the function f x sin 4.
is (where [.] denotes the greatest integer function)
6
5.
x 2
The number of solutions of sin 2x x 2 2 1 is Space for rough work
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SECTION – 3 (Physics) PART – A (Single Correct Choice Type) This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1.
(A)
cos
1
5
(B)
cos
12 2.
1
5
(C)
cos
13
1 12
(D)
cos
1
13
7 13
A person walking at the rate of 3km/hour, the rain appears to fall vertically when he increase his to 0 speed 6 km/hr it appears to meet him at angle of 45 with vertical. The speed of rain is (A)
3.
If vectors P, Q and R have magnitude 5, 12 and 13 units and P Q R , the angle between Q and R is
3 2 km / hr
(B)
3
km / hr
(C)
2
6 2 km / hr
(D)
2 3 km / hr
A particle is projected from ground At a height of 0.4 m from the ground, the velocity of a projectile in
vector form is v (6iˆ 2ˆj) m/s (the x-axis is horizontal and y-axis is vertically upwards). The angle of 2 projection is (g = 10 m/s ) : (A) 4.
45°
(B)
60°
(C)
30°
(D)
–1
tan (3/4)
A spring has a length l1 when tension in it is n1(in N). It has a length l2 when tension is n2 (in N). Find its spring constant : (A)
(n2l2 – n11 l ) (l1 – l2 )
(B)
(n1 – n2 ) (l1 – l2 )
(C)
(n2 – n1) (l1 – l2 )
(D)
(n11 l – n2l2 ) (l1 – l2 )
Space for rough work
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5.
A block of mass 2 kg rests on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is (A)
6.
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9.8 N
(B)
0.79.8 3N
(C)
9.8 3 N
(D)
0.7 × 9.8 N
Force acting on a particle moving in a straight line varies with the velocity of the particle as F=
K
. Here, K is a constant. The work done by the this force in time t is:
v
(A)
K v
7.
2
.t
(B)
2Kt
(C)
Kt
(D)
2Kt v
2
Acceleration time graph of a particle is shown. Work done by all the forces acting on the particle on the particle of mass m in time interval from t1 to t2 while a1 is the acceleration at time t1, is given by :
(A)
ma12 3 3 (t 2 – t1 ) 4t1
(C)
ma1 4 4 (t 2 – t1 ) 2 4t1
2
(B)
2
(D)
ma1 4 4 (t 2 – t1 ) 2 8t1 ma1 2t1
2 2 (t 2 – t1 )
Space for rough work
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(Comprehension Type) This section contains 2 paragraphs. Based upon each paragraph 2 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Questions 08 to 09 Read the paragraph carefully and answer the following questions:
Taking y – axis along line of greatest slope of the given inclined plane and x – axis perpendicular to it as shown in figure. A body is projected along the inclined plane with 0 speed 10 m/s at an angle 53 with x – axis from origin O ( g = 2 10 m/s )
y
10 m/s 53
0
x
O 37
8.
Speed of body after t = 2 sec is (A)
9.
0
2 10 m / s
(B)
42 m / s
(C)
13 m / s
(D)
2 13 m / s
(D)
3.6 sec
Time after which body is moving perpendicular to initial direction is (approx) (A)
2.1 sec
(B)
1.8 sec
(C)
3 sec
Paragraph for Questions 10 to 11 Read the paragraph carefully and answer the following questions:
A block of mass 6 kg is kept on a rough horizontal surface and is pulled by time varying force F = Kt –1 where K = 5Ns , acting at an angle 37° with horizontal. It is observed that motion of block has started at t 2 2 = 4 sec. and just after that acceleration of block is 2/3 m/s (g = 10 m/s ). 10.
Co-efficient of static friction between block & surface is (A)
11.
2/3
(B)
1/3
(C)
4/5
(D)
3/4
(D)
233 m/s 2
Velocity of block when it breaks off the surface is equal to (A)
218 m/s
(B)
128 m/s
(C)
112 m/s
Space for rough work
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(Multi Correct Choice Type) This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. 12.
A ball of mass m is attached to the lower end of light vertical spring of force constant k. The upper end of the spring is fixed. The ball is released form rest with the spring at its normal (unstretched) length, and comes to rest again after descending through a distance x. Then, (A) (B) (C) (D)
13.
x = mg/k x = 2mg/k The ball will have no acceleration at the position where it has descended through x/2. The ball will have an upward acceleration equal to g at its lowermost position
A bead is sliding down a smooth, massless rod PQ attached on the circumference of a vertical circle of radius R. The bead starts from rest from P : (A)
Time taken by bead to go from P to Q is 2
R cos g
14.
Time taken by bead to go from P to Q is
(C)
The velocity of bead when it reaches centre of circle is 2g R cos
(D)
The velocity of bead when it reaches centre of circle is 2 gR cos
2
g cos
The potential energy of a particle moving along x-axis is given by U = 20 + 5sin(4x) where U is in J and x is in metre under the action of conservative force : (A) (C)
15.
R
(B)
at x = 7/8m, particle is at equilibrium. x = 3/8m, particle is at equilibrium.
(B) (D)
at x = 7/8 m, particle is not at equilibrium. x = 3/8 m, particle is not at equilibrium.
S1, S2 and S3 are the different sizes of windows 1, 2 and 3 respectively, placed in a vertical plane. A particle is thrown up in that vertical plane. Find the correct options :
(A) (B) (C) (D)
average speed of the particle passing the windows may be equal if S1 < S2 < S3 average speed of the particle passing the windows may be equal if S1 > S2 > S3 if S1 = S2 = S3, the change in speed of the particle while crossing the windows will satisfy V1 < V2 < V3 if S1 = S2 = S3 , the time taken by particle to cross the windows will satisfy t1 < t2 < t3 Space for rough work
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PART – C (Integer Answer Type) This section contains 05 multiple choice questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.
In the figure, find the minimum value of mass ‘m’ (in kg) of the rod so that the block of mass M =12 kg remains stationary on the inclined 2 plane (take g = 10 m/s ) assume there is no friction between rod and block
rod m
= 0.5
M
37
2.
3.
Two blocks of masses 6 kg and 4 kg connected by a rope of mass 4 kg are resting on frictionless floor as shown. If a constant force of 21 Newton is applied to 6 kg block, tension (In N) in the rope at point B is (CB BA = 1 : 1)
4 kg Q
0
6 kg C
Potential energy of a particle moving along x-axis is given by U =
B
A
P
21N
x3 9x 2 20x . Find out 3 2
position of stable equilibrium state. 4.
3 kg is placed horizontally. The length of rod 2
In a hemispherical shell of radius R, a rod of mass
is R. Find the normal reaction at any end of the rod (in N). 5.
Power supplied to a particle of mass 2 kg varies with time as P
3t
2
2
W. Here t in second. If velocity
of particle at t = 0 is v=0. Find the velocity (in m/sec) of the particle at time t = 2Sec. Space for rough work
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