ENTRANCE EXAMINATION, JUNE 2011
QUESTION PAPER BOOKLET

M.Sc. (PHYSICS)
Marks: 75 Time: 2.00 hrs.
Hall Ticket No.:
I. Please enter your Hall Ticket Number on Page 1 of this question paper and on the OMR sheet without fail.
II. Read carefully the following instructions:
1.
This Question paper has two Sections: Section A and Section B

2.
Section A consists of 25 object.ive type questions of one mark each. Thore negative marking of 0.33 mark for every wrong answer. The IIutIks obtained by t.he candidate in this Section will be used for resolving the t.ie CMeS.

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

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


100.


5. Calculators are permit.ted. tablCti are not allowed.
6.
All questions are to be answered.

7.
Hand over both question hooklet and the OMR sheet at the end of the exam­ination.


This book contains 26 pages I
III. Values of physical constants: c=3 x10'mi. h 6.63 x J.• kB 1.36 X 10-23 J/K
• 1.6 X C Ilo 4" X 10-1 Henry/In; 8.85 X 10-12 Farad/In
1

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j ..... 10

SECTION

SinhZ-Z).
iiim lS eqUw to
..
8lnX cos x
A. 0
B.
C. 1/2
D. 1/3
2. If A s.nd B are n x n matrices, which of the following does not equal
A.
B. A2+AB+BA+B2
C.
D.
3.
y
Which of the following functions represents the graph shown above?
A. y l/z
B. y
C. y .-z
D. 1
3
V-10
4. The function
1 _..

,fi.
satisfies
ff'u 1 ff'u
A. at' D
2& Dff'u


B. at
au Dff'u
c. a.,
au ff'u

D.

at
5. Which of the following can represent a coru;ervative force? are unit vectors)
A. C(iy +lZ
B. c(i., +lY
c. c .xyz(i
D. c(ix
6. Consider a body of mass 500 gm connected to two springs as shown in the figure below. The springs are of equal length and spring constant. The body is displaced vertically upward hy a small distance and then left. Which of the following statements is true about the oscillations executed by the body?
:,.X·
•

__-'1111111_.... 500 2IIl

A. Motion is simple hannonic and periodic.
B. Motion is simple harmonic but not periodic.
C. Motion is not simple barmonic but periodic.
D. Motion is neither simple harmonic nor periodic.


f ... IO
4
7. A particle moves in a potential V Air'. The corresponding force is given by
2Ar

A.
Ai"
B. 2r:c
Af
c.
r
Ai"
D.
...
8. A wave traveling on a string is given by
10sin(O. Ix -22t).
The wavelength and frequency of the wave are given by
A. 62.9 em, v 3.5 Hz
B. 31.4 em, v 7 Hz
C. 0.002 em, A 0.3 H.
D. 6.28 em, 35 Hz
9. Lissajous figure produced by two Sille of "'Iual frequency w and equal ampli­tude A but 90° out of phase will be
A. a diagonal line of length A
B. a circle with radius A
C. an ellipse with major axis A
D. a. sine wave
10. As temperature increases, the viscosity of a liquid in general
A. decreases
B. increases
C. initially decreases, passes through a minimum and then increases
D. remains constant
11. Blood Bows through our arteries of radius R with a Bow rate Q. If the arteries become clogged so that the radius IS n>duced by a factor of twu, the Bow rate Q is reduced by
A. a factor of two
B. a factor of four
C. a factor of eight
D. a factor of sixteen
5
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12. A gas has an equation of state PV where P denotes pressure, V denotes volume and e is a coostant. Work done W is obtained by integrating -PrIV between the initial volume, and the final volume, V,. W is proportional to
1 1
A.
V;
B.
C. In


D.
II;
13. Let be the work done during a reversible process. Then is
A. a perfect differential for any process.
B. a perfect differential only for an isothermal process.
C. a perfect. differential only for an adiahatie process.
D. uat", perfect differential for allY process.
14. The partial derivative of temperature with respect to volume kecping en­
tropy coostant, equals


A.
as
p
B.


C.
D.
15. Helmholtz free energy, usually denoted by the symbol F or A is a natural function of
A. temperature T and volume V.
B. entropy S and pressure P.
C. entropy S and volume V.
D. temperature T and pressure P.
6 j ..
16. A plane electromagnetic sinusoidal wave of frequency 40 MHz travels in the X­direction. At some point and at some instant, the electric field h88 its maxi­mum value of 750 NIC and is along the Y-axis. What is the magnetic field jj in magnitude and direction when E ]75ONIC?
A. 2.5 x 10-6 Whim' and along Z-axis
B. 2.5 x 10-6 Whim' and along X-axis
C. 2.5 x 10-6 Whim' and along Y-axis
D. 2.5 x 1011 Whim' and along Z-axis
17. Dominated by diffraction effects, wbat is the angular resolution of a normal human eye (of pupil diameter 2 mm) at a wavelength 600 nm and what is the separation between two points that the human eye cae resolve from a di6tance of 20
A. 0.3 rad and 6
B. 3mradand 6I'm
C. 3radand 60I'm
D. 3x 10-4radand 6mm
18. Which of the following optical components is critical to differentiate between an unpolarizcd light Md a circularly polarized light?
A. Half wave plate
B. Quarter wave plate
C. Polarizer
n. Half wave plate and polarizer
19. A cylinder of radius R with the right side cut at an angle 30· 88 shown in the figure below is kept in a uniform electric field with its axis along the direction of electric field.
•••••••••••••••••••••• -••••••••••.••••••.•.•••210­
E
..............................................•

The total electric flux linked with the entire cylinder is
A. 0
B.
C. -7rR'EI2
D. 7rR'E
7
0
20.
A parallel plate capacitor is filled with two dielectrics of dielectric constant and lS shown in the figure below. A is the area of each plate and d is the separation between the plates.

21.
An electron travelling hori•.ontally enters a region as shown in thc figure below whcre a uniform magnctic field is applied perpendicular to the plane of the paper and directcd into. Which onc of the following phrases most accurately describes the motion of the elcctron after it enters the field?



x Xx X
elec1ron
X X XX
• )0.
XX XX XX XX
A. Helical
B. Circular clockwise
C. Circular anticlockwise
D. Elliptical e10ckwise 8 J ....
22. What is the equivalent resistance for the figure given below?
1.50
8

A. 5n
B. 10n
C. 15n
D. 20n
23. An alternating voltage V 50sin(30t) is applied to the primary of a 10:1 step­down transformer and the secondary of this transformer is connected to the input of a half-wave rectifier. The average output volt;ag<> of this rectifier is
A. 5V
B. V
C. V
D. V
24. The ground state energy of a one-dimensional harmonic oscillator is 6.2 eV. If the oscillator undergoes a transition from its n 3 level to n 2 level by emitting a photon, what is the wavelength associat.1d with the photon?
A. 50nm
B. 62nm
C. 100nm
D. 200 nm
25. The de-Broglie wavelength of a neutron (kinetic energy 3/2 kT) at is
A. 1.5 A
B. 2A
C. oA
D. 273 A
9

SECTION

26. Let m and n be positive integers with m n. When 8m +7n is divided by we get remainder 1. When 7m +8n is divided by we get remainder 2. If m-nis divided by the remainder has to be necessarily equal to
A. 2
B. 3
C. 4
D. 1
27. If
x)(log. x){log. (log.
and x oF then x is equal to
A. 12
B. 24
C. 44
D. 48
y
28. The solution of the differential equation dd= x +xy is to be obtained under the
x
condition that y 0 at x O. The solution is given by
A. Y="2x2
B.
C. y


D. "2-1
29. What should be the value of a such that the straight line x+y a will be .. tangent to the circle
A. 1
72
B. V2
C. 2V2
D. 4
10 V..

30. is equal to 1
A.
r
1

B.

1
C.

11
D.
r
31. At very small the expression




(21

x
B.
2
C.
2
D. x
32. 121 where x represents "
A. straight line
B. circle
C. ellipse
D. parabola
33. What shouid be the value of a 60 that the matrix
can berome orthogonal?
A. 1
B.
C. 1
;r.
D.
11

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34. The eigenvalues of the matrix

are given by
A.
B.
C.
D.
35. The commutator of two hermitian matrices is
A. hermitian
B. unitary
C. unti-hermitian
D. orthogonal
36. A mouse of mass m jumps on the outside edge of a freely turning ceiling fan of rotational inertia J and radius R. The ratio of the new angular velocity to the old
one is Riven b.y
J
A.



B.
I

C.
l-mW
I
D.
J mR2
37. A particle of m.... m has a speed v where x is the displacement at time t. Then the force on the particle at time I is proportional to
tl/3
A.
B.
C.
D.

12 V -10

38. A boat of mass m with initial spood v. is launched on a lake. The boat is slowed by the water by a force F where A is a constant. What is the distance the boat sails before it stops?
A. A
B. Less than A
C. Greater than A
D. A(1 v.)
39. A projectile is fired with a velocity v. such that it passes through two points P and Q both at a distance h above the horizontal. The gun has been adjusted for maximum range. The separation of the points P and Q is given by
A. -4gh
B. !!aJ'2gTi
9
C.
D.
40. A particle of mass m starts from rest in a constant gravitationAl field under a frictional force equal to kIllV', wherc k is a constant and v is the instantanooUll velocity. The distance the particle falls in accelerating frOUl the velocity VI to is given by
l -9(Va-....1)2
A
. "ke
B. 2.In
2k


e!y(tI2-I11)2
C.
D. 9 In
2kvl 9
41. A particle at rest is attracted towards a center of force F llCCOrding to the relation F where x is the distance from the centre of force and a is a constant. The time required for the particle to reach the force centre from a distance d is proportional to
dl
A.
B.
c.
d

D.



13
42. The density of a thin rod of length 1 varies with the distance from one end as

P Po The centre of mass is at a distance
A. 31/4
B. 41/3
C. 1/3
D. 1/2
43. How much work is done around the path shown below by the force F
where A is a constant?
y


A. Ad"
B. AlI'
C. Ad
D. 0
44. A spring-mass Rystcm of mass M suspended from a spring of spring constant "nd equilibrium stretching is equivalent to " simple pendulum of mass m and length
A.
B. It
C. h/2
D.
45. If a pendulum bob is suspended by a string of length L inside a fluid (the bob is 11 times more dense t.han the fluid), the period of small oscillat.ions of the pendulum will be given by
A. 2"
B.
C

• 9"
D.
v,../o
14
46. The dispersion relation for deep water waves is given approximately by
T
gk+ _k3 .
p
The phase velocity and thc group velocity can be equal only when
A. 9 and are equal.
B. 9 is greater than
C. 9 is equal to 2T
p
D. 9 is negligible compared to
47. Standing waves are generated in a pipe with one end closed while the other bcing open. If the length of the pipe is I and speed of sound in air is given by v" the fundamental frequency of the standing wave pattern is given by
A. v./21
B. v./21r/
C. v.11
D. v./41
48. A metallic cube of length 1 m is stretched out uniformly by a force F nonnal to each of its faces. If Y and are the Young's modulus and Poisson's ratio for the material, the deformation of the cube is given by
;lV 3F
A.
V Y
;lV F

B.
V Y
;lV 3F

C.
V Y
;lV F

D.
V Y
49. A soap hubble of radius R has .. unifoTlnly distributed charge q on its surface. The excess pressure inside the bubble is
4T q"
A.
R 321r"oR4
4T

B.

R 321r"oR'
4T

C.
If 161rR'
2T q"
D.
R 321r"oR'
15

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50. Water has a surface tension of 0.4 N/m. In a3 nun diameter vertical tube if the liquid rises 6 mm above the liquid outside the tuhe, what is the contact angle?
A. cos(l1)
B. sin(l1)
C. 008-1(0.11)
D. sin-I (0.11)
51. One thousand water droplets with radius r 1O-6m coalesce to form a single droplet. If the surface tension of water is T 7.5 X 10-2Nm-I, how much energy is liberated when the droplets coalesce?
A. 8.5 x 10-10 J
B. 10-2 J
C. 8.5 X 10-5 J
D. 10-7 J
52. A given quantity of gas is taken from state A to state C quasi-statically and re­versibly by two plLths: A and A B C (see figure below).
p
A
v
During the process A work done by the gas is 60 J lind the heat absorbed
equals 90 J. During the process A B the work done by the gas equals 45
.J. The heat absorbed in this process equals
A. 105J
B. 75J
C. 15J
D. 45J

J ..
16
53. Which of the following is a correct statement of the second law of thermodynamics? entropy; dQ energy gained by the system in the form of heat; dW energy gained by the system in the form of work; temperature; F Helomholtz free energy)
A. dS
B. dS 0
C. dU=dQ+dW
D. dF<W
54. Consider the Ma.xwell -Boltzmann distribution of the velocity of a molecule of an ideal gas. Let the most probable value of the speed of the molecule be denoted by Vm. Let the root-mean-square velocity ofthe molecule be denoted by J(iP). The ratio is given by
A. 2/3
B. 3/2
C. 1
D. .,fii3
55. The entropy S of a system at fixed volume V depends on the absolute temperature
as
S -aT" S.

where b,S. are constants. The heat capacity at constant volume Cv is then given by
A. bTl
B. 3aT' +2bT
C.
D.
56. An insulated chamber is divided into two equal volumes by a partition. The left half contains an ideal gas at temperature T. and the right half is evacuated. A small hole is then opened between the two halves, aJ.lowiug the gas to Bow through, and the system c.omes to "'IuiJihrium. What is the fiual temperature of the system?
A. T.
B. To,
C.

D.

17
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57. A quantity q of energy is transferred in the form of heat from a reservoir at absolute temperature to another reservoir at absolute temperature T" quasi-statically and reversibly. Tbe change in entropy of the combined system is
A.

B.

C. q
log
D.

58. What is tbe group velocity for an electromagnetic wave in water if tbe refractive indcx of water at 20'C is 1.3311 for A 656.3 om and is 1.3314 for A =643.8 nm?
A. 2.28 x108 m/sec
B. 1.14 x108 m/sec
C. 4.56 x108 111/Sec
D. 7.60 x m/sec
59. An electromagnetic wave is obtained by superposition of two waves having tbe 8ame amplitude and rigbt and left-hand circular polarizations as given below:
EL iEoCOS wt +]sinwt
En iEocos(wt
If tbe initial pbase difference betwecn the waves is what are the characteristic of l.lie resultant wave?
A. Linearly polarized with E forming angle 6 with the x-axis
B. Linearly polarized with E forming angle witb the x-axis
C. LineAorly polAorized witb Eforming angle with the x-axis
D. Right circularly polarized
60. The ordinary and extraordinary refractive inclices of quartz are "0 1.54424 and 1.552335 at 589.3 nm. What sbould be the tbickness of the quartz plate if it bas to function as a quarter wave plate?
A. 64.68
B. 32.34
C. 8.0851=
D. 16.171-'01
18
61. A 633 nm He-Ne laser light passes through a narrow slit and tbe resulting diffraction pattern is obeerved on a screen kept 6 m away from tbe source. If tbe distance between the centers of the first minima on either side of the central maximum on tbe screen is 32 mm, bow wide is the slot?
A. 0.24mm
B. 0.12 mm
C. 0.36 mm
D. O.48mm
62. A cylindrical glass rod of refractive index ",=1.52 is immersed in water (refractive index .... 1.33). One end of the glass rod has a polished herni-spherical surface with radius R=2 em. A small object is placed at a distance 8 em to the left of the vertex of the berni-spherical surface. The image distance and the magnification

are given by

A.
-10.65 em; m +4.66

B.
..I -21.3 em; m +2.33

C.
-31.95 em; m +3.50

D.
+21.3 cm; m -2.33


63. A glass plane-convex lens has its flat side toward the object. The convex side h.. a radius of curvature of 30.0 em. The index of refraction of the glass for violet light =400 nm) is 1.537, and that for red light 700 mo) is 1.517. Tbe colour purple is a mixture of red and violet. If a purple object is placed SO.O em from this lens, where are the red and violet images formed?
A. -211 em -185 em
B. 185 em " 211 em
C. 211 em; 185 em
D. 15.96 em s:. 13.88 em
19

V-10

64. What is the equivalent capacitance between A and
2jlF

I ""F I
I ""F


A. 2IJF
B. 3"F
C. 4IJF
D. 6IJF
65. The equivalent resistance between the two points A and B is given by
R
R
A
B


A. Rq
B. Rq iR
C. R.. =3R
D. n..
66. A 5 II.F' capacitor is charged by II 12 V battery through II resistance of The total amount of heat dissipated by the resistance during the charging process is equa.! to
A. 36 mJ
B. 3.6 wJ
C. 360 mJ
D. 0.36 lllJ
20 V-fO

67. A parallel circular plate capacitor with radius 10 em is getting charged by an increasing voltage. The displacement current density is 0.5 pAlm'. The magnetic field at a distance of 5 cm from the axis (point of the capacitor plate is approximately


......


v
A. 1.6 X 10-14 T
B. 0.5 X 10-14 T
C. 10 X 10-14 T
D. 0T
68. The electric potentia.! in the xy-plane in a certain region of 6pa<:e is given by where x and y arc in meters and V is in volts and Cis .. constant. What is the magnitude of the y-component of the electric field at the point
A. 0Vim
B. 18C Vim
c. 24C Vim
D. 30C Vim
69. A circular ring of radius a has a line charge density P Po sec." where 8 is measured with respect to a fixed radius. The potential at the centre is equal to
A. po/a
B. "po/a
C.
"Po
D. 0
70. A particle of mass M at rest decays into two particles of m8SSC6 Il.IId m. having nonzero velocities. The ratio of de-Broglie wavelengths of the particles is
A. mdm.
B. mo/ml
c. I
D. Jmdmo
21

71. For large principle quantum number the spacing between two neighbouring coergy levels of a hydrogen atom is proportional to
A. lin
B. lin'
C. lin'
D.
72. A particle is confined in a one-dimensional box of length I. Its ground state wave function is given by
fi .
VI SID ,forO<x<1 ,for
The expectation value of the momcotum operator will respect to the above wave function is equal to
A. 1
B. 0.5
C. 1/2
D. 0
73. The current JD flowing through the silicon diode shown below is given in the first approximation by
10KD 10Ke
11.4V


A. 0rnA
B. 0.33 rnA
C. 0.38 rnA
D. 0.4.3 rnA
22

74. The current flowing through the zener diode shown in the figure below (with the Zener breakdown voltage equal to 6 is

V.

V..
13
IV
A. OmA
B. 7mA
C. 8.3 rnA
D. 13mA
75. The half life of thorium is 1.4x1010 years. What is the time required for 10% of a sample of thorium to disintegrate?
A. 2.13 x 10· years
B. 2.13 x years
C. 2.13 x 10" years
D. 2.13 x lOS years
23

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