ENTRANCE EXAMINATION, FEBRUARY 2013
QUESTION PAPER BOOKLET

M. Sc. (PHYSICS)
Marks: 75 Time: 2.00 hrs. Hall Ticket No.: I

Please enter you Hall TkkBt on Pagp. 1 of this question paper and on the OMR sheet without fail.
II. Read carefully the following instructions:
1.
This Question paper has iJlQ.')ections: Section A and Section B

2.
Section A consists of 25 objective type questions of one mark each. There is negative marking of 0.33 mark for every wrong answer. The marks obtained by the candidate in this Section will be used for resolving the tie cases.

3.
Section B consists of 50 objective type questions of one mark each. There is no negative marking in this Section.

4.
Answers are to be marked on the OMR answer sheet following the instructions provided there upon. An example is shown below


100.
0
5.
Only Scientific Calculators are permitted. Mobile phone based calculators are not permitted. Logarithmic tables are not allowed.

6.
Hand over the OMR answer sheet at the end ofthe examination to the Invigilator.


IThis book contains 24 pages I
III. Values of physical constants: c=3X108 h 6.63 X 10-34 J.s; kB 1.38 X 10-23 J/K e=1.6 x 10-19 f.1o 411" X 10-7 Henry/m; fa 8.85 X 10-12 Farad/m
1


SECTION

1. The function y satisfying the condition f x2 x is given
by
A y x2 2

2
B. y x-2
C. y x2
D. y x2
2. The number of vectors orthogonal to 2J -kis
A. One
B. Two
C. Three
D. Infinite
3. A· (jj x 0 implies that
A. All the three vectors are parallel.
B. All the three vectors are mutually perpendicular.
C. Two of the three vectors are perpendicular
D. The vectors lie in a plane.
4. lim 25 is

A. 00
B. 16
C. 2
D. 0
3


5. For certain motion the plot of velocity versus displacement is shown in figure. The corresponding motion is
velocity
CLlJeriutlic



i 11
B. simple harmonic
C. periodic



D. with constant acceleration
I
displacement

i ..

6. A number is chosen at random from the set of integers .... 1000}. YVhat is the probability that it is divisible by 3 or either 3 or 5 or both]
A. 0.333
B. 0.2
C. 0.1
D. 0.467
7. A particle is moving along the x-axis such that its position at time t is given by 8.4 lOt t3. The most appropriate statement about the motion of this particle is
A. uniform motion
B. uniformly accelerating motion
C. acceleration increasing linearly with time
D. acceleration increasing quadratically with time
8. For small vibrations of a compound pendulum of mass moment of inertia I and distance a of the center of mass from the origin will have time period
A. 21ry'mga/I
1

B. -vI/rrzgo
21r
/Jag

C
T

D. 2rrV
4


9. A bullet of mass m moving with a velocity lOm/s hits a body of mass 3m which is at rest and gets stuck to it. The fraction of the original kinetic energy getting converted into heat is
3
A. ­
4
1

B. ­
3
1

C.
A

5
D. 3

10. A particle of mass 5kg is moved from a point to another point by a constant force given by F 6i 3k where k are the orthogonal unit vectors and force and distance are measured in Newton and meter, respectively. The work done by this force is
A. 5J
B. OJ
C. 4 J
D. 9 J

11. For a flow of a compressible fluid through a narrow tube, the following statement is correct
A. the volume of the fluid crossing any section of the tube is constant.
B. density of the fluid is independent of pressure.
C. mass of the fluid crossing any section of the tube varies with time.
D. mass of the fluid crossing any section of the tube per unit time is constant.
12. A straight cylindrical conductor with radius R carries a current I. The radial depen­dence of the magnetic field inside and outside the cylinder is given by
A. B•



R
R r
r
C. D.
I

·1
R R
r
r
5


13. Let the electric field in a certain region of space be given by Cf'jf00.3 where a has dimension of length and C is a constant. The charge density is given by
A. p= 0
B. p=3C/a3
C. p Cfo/a
D. p= Cffo

14. Four different cases of the interaction energy U between two objects as functions of their separation r are shown schematically in figure. The only attractive interaction is shown in
A. B.
u

r
r
I
C. D.
u1

u
1
i

r
r


15. Three charges +V2q. +V2q are placed at the three corners of an equilateral triangle of side a. The work done in gathering the system of charges is given by
A.
B. (y12
C. -1)q2j(4r.afo)
2(l-V2)q2/(4r.afo)

6




16. Depicted below are two reversible engines, marked 1 and 2. in T-S phase plane. Let I'll and T]2 denote the efficiencies of the engines 1 and respectively. Which of the following statement is correct

A. I'll TJ2


i.. .
rl T
B. 771 772


T2
C·TJ!
T, I


I C(S"T 2
52 S
D. TJl T/2
51

17. The internal energyr of a system is expressed by function U(5. where is a constant. The value of is
A. 1
B. 1/3
C.
D. 3/4

18. Let AW be the work done in an infinitesimal reversible process.Which of the following statemet is correct?
A. AW is a perfect differential only in an adiabatic process.
B. A"r is not a perfect differential for all processes.
C. AW is a perfect differential for all processes

D. A Hl is a perfect differential only for an isothermal process.
19. The radius of the Bohr orbit for the ground state of the hydrogen atom is given by
fi2
A.
me2
2
me
f4
B. 1iEo Jfi:2
4
me
C.
4Eofi2
17.2
D
4me2

I

20. The energy eigenstate of a system must necessarily be a
A. A stationary state
B. A state having explicit time dependence.
C. A state having implicit time dependence.
D. A state with no time dependence.

21. The threshold wavelength of potassium is 558 nm. If a light of wavelength 400 nm is incident on it the stopping potential will be given by
A. 8.88 V
B. 0.88 V
C. 88.8 V
D. 2.22 V

22. For an electron having energy 1.5 MeV/c (mass of an electron is 0.5MeV), the velocity is given by
A. 2.92 X 1010 em/sec
B. 2.81 x 1010 em/sec
C. 2.75 x 1010 em/sec
D. 2.50 x 1010 em/sec

23. The impedance at the resonance frequency of a series RLC circuit with L 20 mH, C 0.02 J-tF and R 900 is
A. 00
B. 900
C. 20 kO
D. 40 kO

24. A ray of light is incident at an angle on one of the two perpendicular mirrors as shown in the figure. The incident and emergent rays will be parallel if
A. 0< 7f/2
B. only for 30°
C. only for 45°
D. only for 60°
8



25. A light beam is incident on a sphere with refractive index n at an angle i from air and emerges parallel to the horizontal axis passing through the center of the sphere (see figure). Then
air
A. 30° 60°
B. i 60°
C. i 45°
D. i 30°



SECTION
26. For a unit sphere, with center at the origin, the equation of the tangent plane at the 1
pom .V3' -.J3'.J3 18
A. x z
B.
C.
D. x

27, The divergence of ex xC). where cis a numerical vector, is given by
A. zero
B. IcF
c.
2!cF

D.
-21cF



28. Let 4i). 21) represent the three vertices A. B. C of a triangle ABC. The length of the meridian from C to the side AB is
A. vlO
B. v!f2
C6
D 8

9


29. Which of the following numbers does not lie on the unit circle Izi
A. 201
B. (1
1-Z

C. 3+4i
2

VI +2i
D.
3- 2i
30. The system of linear equations


A. has infinite number of solutions
B. has only trivial solution
C. has a unique solution
D. is inconsistent and has no solution
31. The matrix


is
A. Hermitian
B. antisymmetric

orthogonal

D.
idempotent



32. The coefficient of x4 in the expansion of VI 2x2 is
A.
B. -15/32
C. -65/28
D. -21/128
10

"B-10

33. The value of the line integral J(y2 xy)dx (x2-xy)dy taken along the straight line joining to is
A. 64/3
B. 32/3
C. 16/3
D. 8/3

34. The derivative of the composite function y x is given by
A. (1 x [In


B. x



x


C. x
xx
D. In(1+


35. Given the functions x2, the compositions fog and go f are given by
2 X32
A. f 0 go
32 32

B. f 0 go
C. f 0 go Ixl
D.

36. Consider the differential equation ycot(x) sin(x). The corresponding homoge­neous linear equation has a general solution with C as the integration constant
A. y cos(Cx)
B. y sin(Cx)
C. y C cos(x)
D. y Csin(x)
11



37. The area of the surface obtained by rotating about the x-axis the arc of the curve y x3 from x to x 1 is
A. 21l"( V2
B. 1l"(V2
C. 21l"(2V2
D. rr(2V2

38. A particle, of mass m and charge traveling with a velocity v along the x-axis enters a uniform electric field Ii directed along the y-axis. 'With entry point taken as the origin. the trajectory of the particle is given by
A. y
B. y qEx2/(mv)

C. y qEx2/(2mv2
D. y qEx/(2mv)
39. A uniform magnetic field fj is perpendicular to the plane of a circular wire loop of radius R. The magnitude of the field varies with time according to B Boexp( where Bo and T are constants. The time dependence of the induced e.m.f. in the loop
IS
A.
B. 1 exp( _t2/T2
C.
D. -exp(
40. A stone is thrown with an initial velocity 5m/s such that it covers maximum possible horizontal distance RE on the surface of earth. The same stone is thrown with same initial velocity by a person standing on the moon, making an angle of 1.50 with the surface. Given that acceleration due to gravity on earth's surface is 9 9.8m182 and that on moon's surface is gm =1.6mjs2, the horizontal distance it covers on the moon
IS
A. 0.326 RE
B. 0.326/RE
C. 3.06 RE
D. -0.629 RE
12


41. A body of mass 1 kg is constrained to move along a circle of radius 10 m. At a given instant. its speed is 5 mls and the speed is increasing at the rate of 2.5 m/s2 . The angle between particle's velocity and acceleration is
A. 0°
B. 30"
C. 90°
D. 45°
42. A body of mass 2 kg is suspended from two strings attached to the ceiling and the wall as sho\rrl in the figure. Tensions Ti, T2, T3 in the three strings are given, respectively, by
A. T1 11.3N. T2 19.6N, T3 22.6N
B. T1= 9.6N, T2 22.6N. T3 1l.3N
C. T1 11.6N. T2 40.9N. T3 19.3N


D. T1 11.3JV, T2 7.7I
T3 19.6N
43. A solid cylinder of radius a and mass m rolls down an inclined plane without slipping. The inclined plane' makes an angle a with the ground. The acceleration along the horizontal direction is given by
A. (2g/3)asina
B. mgasina
C. sin a
D. sin a
44. A circular uniform plate has mass m and radius R. A hole of radius r has been drilled in it. The distance between the center of the hole and the center of the circular plate is Z. The moment of inertia of the plate with the hole, about an axis passing through the center of the plate and perpendicular to it is
A. [R2 jR2) (r2 2Z2
B. [R2 R2) (r2
C. [R2 (r2
D. [R2 (r2 /R2 (r2 2Z 2
13


0

45. A vertical rod is rotating with a constant angular velocity w about its own axis. A light inextensible string of length l has one end attached to the top of the rod, while at the other end is a mass m. The string makes an angle with the rod. The tension in the string is given by
A. mw2 l
B. mw2 l
n
rt
V. I/WJ t U
D. m(g +w2

46. A water tank has a hole of area A at its bottom. Water is poured into it, at the speed of v m/s by a tube of cross sectional area A. Then
A. the water level in the tank will keep on rising
B. no water can be stored in the tank

C. the water level will rise to a height and then stop
D. the water level will oscillate

47. A water drop of radius 1O-2m is broken into 1000 equal droplets. If the surface tension of water is 0.075 the gain in surface energy is
A. 7.5 X 10-4J
B. 1X 10-4 J
C. 9.5 X 10-4J
D. 8.5 X10-4J

48. A charge q sits at one corner of a cube as shown in figure. The flux of electrostatic field Ethrough the total shaded area is
z
A.
B.
C. iJ.!(4to)
D.

x
14




49. Three charges are kept on a straight liile as shown in figure. With A and B denoting constants, the potential at a far off point » on the axis is given by
A. Air

+1j -2q
B. A/r2


C. A/rg


a Z.
D. A/r2 B/rg

50. Three distinct materials with dielectric constants given by Kl, K2, and Kg, respectively are arranged between two parallel plates of a capacitor of area as shown in the figure. The effective capacitance of the system is
2€oA K 1K 2Kg
A.
d K1+K2+Kg
B. e= K1 Kg

C. e= €oA K1 K 2Kg
2d 2 K2+Kg

e €oA Kg K2K1
D.
2d 2 K1 K2

51. An infinite ladder network is shown in figure. The effective resistance between points A and B is
10 m 10 20
A. 3(1

A
B. 3(1 y7)Q
C. 3(1
B

D. 3(1 VS)Q 40 4040 40
52. The total current I flowing through the 12 Q resistance is
40


A. B. c. D. 1.8 A 1.2 A 1=1 A 1=0 A 120 14.4V SO
15

B-10

53. In a one dimensional potential well with impenetrable walls occupying the domain x a particle in the lowest energy state has the maximum probability to be found at
A. x 0
B. d/2
C. x d/4
D. x=d
54. According to Bohr's model. the second line of the Balmer series is obtained when there is a transition from n 4 to n 2. The wavelength of the line is given by
A. 486 nm
B. 587 nm
C. 410 nm
D. 520 nm
55. A scientist performing the Compton scattering experiment finds that the incident wave­length Al is shifted by 1.5 percent for the scattering angle of 120°. The wavelength Al is given by
A. 0.242 nm
B. 2.420 nm
C. 24.200 nm
D. 0.024 nm
56. In the conversion of one gram mass into energy, the amount of energy released per hour is
A. 2.0 X 109 kiV
B. 2.5 x 107 kW
C. 3.0 1010 kW
D. 3.5 X lOll kV
.J i. Tvo electrons are ejected in opposir.e directions from a sample of radioactive atoms. Each electron has a speed of 0.67c as measured by a laboratory observer. Their relative velocity is given by
A. 1.34 c
B. 1.19c
C 0.92 c

D. 0.87 c
16

58. An unstable particle of rest energy 1000 MeV decays into a J.l-meson and a neutrino with a mean life 1O-8sec, when at rest. If the particle has a momentum of 1000 MeV/ c the mean decay distance is given by
A. 140 cm
B. 200 cm
C. 300 cm
D. 420 cm
59. Let mHe, mp, mn me represent the masses of 4He nucleus, proton, neutron and electron, respectively. These masses satisfy the following relation
A. mHe 2(mp mn me)
B. mHe 2(mp mn)
C. mHe 2(mp mn)
D. mHe 2(mp mn)
60. An experiment shows that a given radioactive element emits 100 a particles/minute initially and after 10 seconds the rate becomes 10 a particles/minute. The half life period of this a-emitter (upto 2nd decimal place) is
A. 3.00 sec.
B. 0.33 sec.
C. 30.00 sec.
D. 0.03 sec.
61. An electron is mov.ing with a speed c/2 where c is the velocity of light. The electron mass will
A. remain constant
B. become double
C. become 33% more of its rest mass
D. becomes 15% more of its rest mass
17


B-j
62. A piece of metal at 400 K with heat capacity of 1000 JK-1 is pushed into a heat bath at lOOK and cooled. The change in entropy of the universe is
A. -1386 JK-l
B. 3000 JK-l
C. 1614 JK-1
D. zero JK-l
63. Partial derivative of P with respect to S at constant i.e., v equals
A.




p

B.



C.
v

D.



64. An ideal gas at pressure P is heated to twice its temperature keeping its volume
constant. It is then cooled to its original temperature at constant pressure. The work done is
A. 2PV
B. p2JV
C. PV
D. PV/2
65. The turns ratio of a transformer required to match an 80 n source to a 320 nload is
A. 80
B. 20
C. 4
D. 2
18


B-.1 0
66.
The filtering action offered by the resonant circuit shown in the figure is

67.
A coil which has an inductance of 40 mR and a resistance of 2n is connected together to form a RL series circuit. If they are connected to a 20V DC supply, the time constant of the RL series circuit is


A. High Pass
B. c. Low Pass Band Pass Source L Load
D. Band Stop

A. 20ms
B. 200 ms
C. 100 ms
D. 1000 ms
68. A germanium diode is operated at 20°C. A reverse bias of -1.5 V results in a current of 70 p,A. Assuming that the temperature remains constant, the reverse saturation current is approximately
A. 60 p,A
B. 60nA
C. 35 p,A
D. -60 p,A
69. A 10 V battery, 250n resistor and a Zener diode are connected in series such that the Zener diode is reverse biased. If the Zener breakdown voltage is 5V, the current flowing through this diode is
A. 40 rnA
B. 20 rnA
C. 25 rnA
D. 10 rnA
19




70. The minimum value of the base current IB required to saturate the transistor shown in figure is given by
A. 0.2 rnA
B. 10 rnA
C. 1.2 rnA
D. 0.12 rnA

71. The superposition of two oscillations given by y A[sin(w1t) sin(w2t)] is periodic if only the frequencies satisfy the relation
A. wI!w2 is a real number
B. WI!W2 is an integer
C. wI!W2 is rational
D. wI!W2 is irrational
72. A body executes simple harmonic motion about the origin with amplitude A 13 em and period T 12 see. At time t =0it is at x 13 em. The shortest time of passage from x 6.5 em to x -6.5 em is
A. 4sec
B. 3 sec
C. 2 sec
D. 1 sec
73. The profile of a wave at time t 0 and at t see with A 1 em, B em-2 and v 2 em see-1 is shown in figure. The wave can be represented by the expression

I
A. y I
t=1sec
y Ae-B //......... •...

B.
g J I
Ae-Blx-vt!lx+vt) I
C. Y
..

04 ..j j
..
y

D. :I
i

I .... L '..........,..

I

1 23
20·r
B-l0
74. A glass (with refractive index 1.5) hemisphere in air with radius of curvature 8 em has a spot P at x em. Viewed along x from the right. the spot will be imaged by the spherical surface at x
y

t
R=8cm


A. 6.2cm
B 5.8 em
C. 4.8 em

3.2 ern

75. A ray of light is incident at an angle 60° on an interface between glass with refractive index 1.5 and a liquid with refractive index n. The ray will be totally internally re­flected only if

A. n
B

C. n>v!3
D. n 3v!3/4
21