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Physics Single Correct Answer Type This section contain 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. and . A changed 1. The space has electromagnetic field which is given as particle having mass m and positive charge q is given velocity ̂ at origin at t=0 sec. The zz coordinate of the particle when it passes through the zz-axis axis is (neglect gravity through motion) (A) (B) (C) (D)
2. An ideal monatomic gas undergoes a cyclic process ABCA as shown in the figure. Graph of pressure versus volume of the cyclic process ABCA is
3. An infinite uniform current carrying wire is kept along zz-axis, carrying current in the directi direction of the positive z-axis. OABCDEFG represents a circle (where all the points are equally
. #5 spaced), whose centre at point (4m, 0m) and radius 4m as shown in the figure. If 123
in S.I unit, then the value of k is
(A) (B) (C) (D)
4 8 3 6
4. An unchanged capacitor C and a value variable resistance R are connected to an ideal source and two resistors with the help of a switch at t =0 as shown in the figure. Initially capacitor is uncharged and switch S is closed at t=0 sec. The graph between for variable. Resistor R for its three different values , !"# % versus time is shown in the figure II. Choose the correct statement (A) $ $ % (B) & & % (C) |!| $ |(| (D) |!| & |(| 5. Three blocks A,B and C whose masses are 9kg,9kg and 18kg respectively as shown in the figure, are released from rest. The coefficient of friction between block A and horizontal surface is 0.5 & the coefficient of friction between block B and the horizontal surface is 0.5. Find the acceleration of block C just after release [take g =10 m/ m/, ]. All strings and pulleys are ideal. (A) (B) (C) (D)
% */, ) - */, ) . */, ) / */, )
6. A plane wave front (wavelength ==0) is falling on YDSE apparatus as shown in the figure. The lower half of it is filled with water (refractive index =1.5) How many maximas can be theoretically obtained on the screen if d= 980 and D=20000 D=200000 (including the maxima at infinity) (A) 245 (B) 246 (C) 122 (D) 123
7. Two identical charged particles each carrying charge q=0.1 mC and of mass m = 10 mg are projected along two parallel lines separated by a distance ‘l’ with equal speed 10 m/s in opposite directions. In the beginning electrostatic interaction between the charges can be ignored due to a large distance between them. The minimum distance between the particles is found to be 12 cm. The value of l is equal to (A) 6 cm (B) 8 cm (C) 12 cm (D) 4 cm 8. A plane sound wave is generated in a medium along positive x-axis, whose equation is given as y= A cos (ωt-kx). If c is the speed of wave in the medium. There is reference frame ‘k’ which is moving with uniform acceleration ‘a’ in the negative direction of x-axis and at t=0 both wave in reference frame ‘k’ is :; = >′] < :; sin[ωt81 ′] :; cos[ωt81 = >′] < :; sin[ωt81 < = >′]
(A) Y= A cos[ωt81 + (B) Y= A (C) Y= A (D) Y= A
Comprehension Type This section contains 3 groups of questions. Each group has 2 multiple choice question based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct. Paragraph for questions 9 and 10 A water tank of height 7.5 m is half full of water. The upper half contains air at atmosphere pressure (A 10- A!). The tank is sealed at the top so that the air within is isolated from the atmosphere. There is a tap (A) at the bottom of the tank through which the water can flow out. The cross-section of the outlet at A is much smaller than the horizontal cross-section of the tank. Ignore any evaporation of water. Take g=10 m/, 9. The speed of efflux of the water through the tap A, when it is initially opened, is approximately (A) 2.5 m/s (B) 8.5 m/s (C) 10.0 m/s (D) 12.5 m/s 10. Assuming that air behaves like an ideal gas and that the temperature of air is constant. Find the maximum height of water remaining in the tank. (A) 4.5 m (B) 3.5 m
(C) 2.5 m (D) 1.5 m Paragraph for questions 11 and 12 In the adjacent figure ‘OX’ is the principal axis of a stationary spherical mirror (either concave mirror or convex mirror). NM is an incident ray, after reflection it passes through the origin O, such that∠DEF 106 . LM is another incident ray, which after reflection passes through point k having coordinates (> , 0), such that∠DEF = 76 . The point P (> , 0) is the pole of the spherical mirror and point C (>% , 0) is the centre of the curvature of spherical mirror. In the figure side of each square is equal to 1cm Answer the following questions, best on the above paragraph. 11. Find the value of > (in cm) (A) √2 (B) √3 (C) 2
(D) √5 12. A point object is moving with velocity ̂ + 4N̂ cm/sec with respect to ground. Find the speed of .
image with respect to ground, when it reaches 8% O*, 0O*= (A) (B) (C) (D)
10 cm/s 15 cm/s 20 cm/s 25 cm/s
Paragraph for questions 13 and 14 According to the principle of conservation of linear momentum, if the external force acting on the system is zero, the linear momentum of the system will remain conserve. It means if the centre of mass of a system is initially at rest, it will remain at rest in the absence of external force, i.e. the displacement of centre of mass will be zero. A plank of mass M is placed on a smooth horizontal surface. Two light identical springs each of stiffness k are rigidly connected to struts at the end of the plank as shown in the figure. When springs are in its natural length, their free ends are at a distance of 3l from y axis. A block of mass mis placed on the
plank and pressed against right spring so that it is compressed by 22l.. To keep the block at rest it is connected onnected to the strut by means of a light string. Initially the system is at rest. The right spring is in its natural length. Now the string is burnt. 13. The maximum displacement of plank is (A) (B) (C) (D)
P PQ PQ / PQ
14. Maximum kinetic energy of block m is (A) (B) (C) (D)
PRPQB PRPQB P RPQB P RPQB
Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) ot of which ONE or MORE are correct 15. A system is shown in the figure, which is released from rest. There is no friction between ground and mass 5m. The coefficient of friction between mass 5m and mass 2m is µ.. The coefficient of friction between mass 5m and mass m is also µ. Choose the correctt statement(s) (A) The acceleration of centre of mass of system is zero. (B) The magnitude of acceleration of mass 5m is zero if µ = 0 (C) The tension in the string is
S % √%
if µ =
√%
(D) The magnitude of acceleration of mass 5m is zero if µ =
√%
16. Choose correct statement(s) the regarding photoelectric effect. (A) No matter how small the intensity, if photoelectric emission takes place, the emission is instantaneous. (B) The maximum kinetic energy of a photoelectron does not depend upon the intensity of incident light, if frequency of incident light is kept constant. (C) Threshold frequency depends upon the intensity of incident light. (D) The photoelectric current is inversely proportional to the intensity of incident light and is independent of its frequency. 17. Choose correct statement ement regarding X X-ray
(A) If the target material in a Coolidge tube is changed keeping the acceleration voltage constant, the minimum wavelength of the X X-rays produced will change. (B) X-ray ray do not get deflected on application of electric or magnetic fields. (C) X-ray can ionize a gas. (D) X-ray ray can be reflected, refracted, diffracted and polarized under suitable condition. 18. Two identical discs, each of negligible mass and radius r(, is equal to
%
(A) 3 (B) 6 (C) 8 (D) 9 3. The roots α and β of a quadratic equation are the square of two consecutive natural numbers. The geometric mean of the two roots is 1 greater than the positive difference of the roots. If exactly one root of > − O> + 32 0 lies between α and β, then find the minimum integral value of c (A) 4 (B) 12 (C) 13 (D) None of these 4. Let Ei * denotes a square matrix of order n with entries as follows for 1≤ ≤ ", * = 10; for 1≤ ≤ " 1, *Q , = *,Q = 3 and all other entries in Ei are zero. Let i be the determinant of (A) 0 (B) 1 (C) 2 (D) None of these 5. Let triangle ABC have altitudesℎ: , ℎ , ℎ< from points A, B, C respectively. If ℎ: =8, ℎ =8, ℎ< =10. The perimeter of the triangle formed by joining feet of altitudes of ∆p U is (A) (B) (C)
%√ √ √ -
(D) None of these 6. The number of permutations of > , >, >%, … … . . >i, of 1,2,3 … . .100 such that the cyclic sum of ∑i |> >Q | (with >iQ > ) is minimum, is (A) 100.2)/ (B) 99. 2)) (C) 2. 3)/ (D) None of these
7. If → +uw +→ ,→ +→ + uw ,→ +uw +uw =36, where →,→ !"# → are three vectors then the : %< < %: < : % : < →→ →→ →→ :. : :. :. < → →→ →→¡ is value of ¡→ :. . . < →→ →→ →→ (A) 4 (B) 6
:. <
- + (> + O> % + #> + |> + ¢ touches the line L:y mx+n at x=1,2,3. Find the area bounded by these graph? (A) (B) (C)
% % %
(D) None of these Comprehension Type This section contains 3 paragraphs. Based upon paragraph 2 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 9 to 10 Read the following write up carefully and answer the following questions: There are ‘n’ black identical balls and two identical red balls in a bag. One by one, balls are drawn at random out of the bag. Kartikey wins as soon as two black balls are drawn and Farhan wins as soon as two red balls are drawn. The game continues until one of the two wins. Let J(n) and F(n) be the two probabilities that Kartikey and Farhan win, respectively. 9. The value of F(1) + F(2)+……..F(2013) is (A) (B) (C)
% %) -
(D) None of these 10. The value of limi→¥ ∏¨ §(q) is (A) (B) (C)
%
(D) None of these Paragraph for Question Nos. 11 to 12 Read the following write up carefully and answer the following questions:
Let P(x) be a polynomial with real coefficient such that R> + > + 1B PR> 1B=R> > + 1B P(x) ∀ > ∈ R and P (1) =3 11. If 1 !" 8 Qª( )=dx + 1 !" (> + 1) dx = (« − 5"4) then value of k is
(A) 10 (B) 8
(C) 12 (D) None of these
i
12. Let 5i =1 A(> ) + A(> − 1) dx. If (k+1) 5i = 2(1 + 5i ), then the value of n is (k, n∈ F)
(A) (B) (C) (D)
1 2 4 None of these
Paragraph for Question Nos. 13 to 14 A variable circle touches straight line x=y and cut off a constant length of 2√2 units from x+y=0. The locus of centre of circles is curve C. 13. The eccentricity of curve C is (A) √2 (B) √3 (C) 2 (D) 3 14. The line x+2y=1 intersects the curve C at P and Q (where P is above x-axis). The centre of circle which touches the curve C at P and passes through Q is (A) 8 , =
(B) 8 , =
(C) 8 ,
(D)
=
8 , =
Multiple Correct Answer(s) Type This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE are correct. i ` ¬ ;
15. Consider a function f(x) = 10 is drawn through P(0,0) to meet the lines ® :2x+y-1=0 and ® :2x+y-6=0 at A and B respectively. From A, a line perpendicular to L is drawn meeting the parallelogram pp
is formed. The equation of line L is obtained so that the area of the parallelogram pp
is least. (A) The equation of line L is 3x-y=0 (B) The equation of line L is 3y-x=0 (C) The minimum area of parallelogram pp
is 5 (D) The minimum area of parallelogram pp
is 5
t : Q %Q
17. Let f(x)=¯( > + (> + 1, > = 1 (| Oa""ae, ! > = 1, ℎ|" °ℎOℎ a¢ ℎ| (1 + ln O. !" (> − 1)) /(²³ ) 1$1
house is √2012 on both days. (A) |´| 1
(B) |´|
-
(C) Re R´ B
(D) Re R´ B
20. Let ¢: R0,1) → (0,1) be the strictly monotonic polynomial function such that for every positive integer ‘n’ and odd positive integer ! < 2i , there exists an odd positive integer ( < 2i such :
that 8¶ = = ¶ , which of the following may be correct?
(A) ¢ · (>) ≠ 0 ∀ > ∈ (0, 1) (B) ¢ · (>) = 0 ¢aq ,a*| > ∈ (0, 1)
(C) ¢ · 8= = 1
(D) ¢ · 8= = −1
ANSWERS Q. No. 1 2 3 4 5
Physics A C B B C
Chemistry B D D C C
Mathematics A C B B B
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A A A B C B B B D A,B,C,D A,B B,C,D A,C,D A,D B,D
B C C B B B D B C B,C,D A,B,D C,D C,D A,B,C,D B,C
A A B B C C B A C A,D A,D A,B,C,D A,C,D A,C A,C,D
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