KUET 2021 Question Paper M.Sc. Physics

FOR KUET EXAM PREPARATION

KUET 2021
Question Paper · M.Sc.
Physics
EXAM YEAR TYPE SUBJECT

KUET 2021 Question Paper M.Sc. Physics

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Sr. No. .............................

ENTRANCE TEST-2021
SCHOOL OF PHYSICAL & MATHEMATICAL SCIENCES

A .com
PHYSICS

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Question Booklet Series

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Total Questions : 60

em a s
Time Allowed : 70 Minutes Roll No. :

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glnecessary
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aBooklet and
fill upathe
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1. Choose the incorrect statement : 4. The Michelson–Morley experiment was designed to
show :
(A) If total linear momentum of a system of particles
is zero, the angular momentum of the system is (A) The difference in the speed of light between
the same around all origins
directions parallel and perpendicular to the
(B) Even if total linear momentum of a system of Earth’s motion
particles is not zero, the angular momentum of
the system is same around all origins (B) The speed of light in vacuum is not invariant

(C) If the total force on a system of particles is zero, (C) That Galilean transformation equations are valid
the torque on the system is the same around all for the speed of light to be invariant
origins

(D) When a rigid body rotates around an axis, every (D) None of the above
particle in the body remains at a fixed distance
5. An astronaut sees two spaceships flying apart with
from the axis
speed 0.99c. The speed of one spaceship as viewed
2. If F is the time-dependent force F = A – Bt, where by the other nearly is :
A and B are positive constants, the velocity v(t) in
terms of A, B, m (mass), v0(initial velocity) and x0(initial (A) 0.99995c
position) is given by :
(B) c
(A) v(t) = v0 + At /m – B t2/2m

(B) v(t) = v0 + At2 /m – B t/2m (C) 0.95555c

(C) v(t) = v0 + B t2/2m (D) 0 c
(D) v(t) = v0– B t2/2m
6. A particle moves in a circular orbit with the potential
3. How far approximately will a small boat move, when energy U(r) = –A/rn, where A > 0. For what values of
a man with mass 64 kg moves from back to front of ‘n’ are the circular orbits stable :
the boat ? Given that length of boat is 2.7 m, its mass
is 92 kg. (Water resistance and tilt of the boat is (A) n > 2
negligible)
(B) n  2
(A) 1.03 m

(B) 1.40 m (C) Only for n = 2

(C) 2.74 m (D) Only for n = 1
(D) 1.10 m

SS-5466–A 2
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A particle of mass ‘m’ is located in the y-z plane at 10. The graph of the function as shown in Fig.1 is best
x = 0, y = 3, z =3. Its moment and products of inertia described by :
y
relative to the origin written in the form of an Inertia
8
matrix are : 6
 2 0  1 4

m
 

co
(A) I = 9m  0 1 0  2

om .
  1 0 1 

c m
x

. e
–4 –2 2 4

em a s
–2

s g l
  1 0  1

l a a
–4
(B) I = 9m  0 1 0 

ag
–6
 1 0 1 

 2 0  1 Fig. 1
  (A) ex cos(x)
(C) I = m  0 1 0 
  1 0 1  (B) e–x cos(x)
(C) ex sin(x)
1 0 1
m
(D) e–x sin(x)

c. o where r is the distance from the origin of the coordinate
 
(D) I = m  0 1 0 
11. If a force F is derivable from a potential function V(r),

e m system, it follows that :
  1 0  1

l a s
g of the (A)  × F = 0
8. A marble of mass 0.1 kg and radius 0.25 m is rolled

a
o
up a plane of angle 30 . If the initial velocity
marble is 2 m/s, the distance ‘d’ it travels up the plane (B)  · F = 0
before it begins to roll back down is equal to : (C)  V
(A) 4 m (D)  2 V= 0
(B) 4/5 m 12. Which of the following expressions for a vector
(C) 4/7 m 
potential A does represent a uniform magnetic field
m
c. o
(D) 4/9 m

om with side L. The moment of inertia around an
of magnitude B along the z-direction ?

c. triangle m
9. A thin sheet of mass M is in the shape of an equilateral 

s e
(A) A  x Bĵ

s em axis through a vertex, perpendicular to the sheet is : la
ag
 1

la
1
(B) A  xB î  y Bˆj

ag
(A) 5/7 ML 2 2 2
(B) 5/12 ML 2  1 1
(C) A   yBî  xBĵ
(C) 5/9 ML2 2 2

(D) 1/2 ML2 (D) A  zBî

SS-5466–A 3 [Turn over
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13. For a particle moving in a central force field, which 16. A square loop of wire (side a) lies on a flat surface, a
one of the following statements is correct ? distance s from a very long straight wire, which carries
a current I as shown in Fig. 2. The flux of B through
(A) The motion is restricted to a plane due to the
the loop is :
conservation of angular momentum a
(B) The motion is restricted to a plane due to the
a
conservation of energy only

(C) The motion is restricted to a plane due to the s
conservation of linear momentum I
Fig.2
(D) The motion is not restricted to a plane

14. The magnetic field of a dipole can be written in the 0 sa
(A) Ia ln 
following coordinate free form : 4  s 

3 0 
[m·r̂ ] r̂  m 
0 sa
(A) 2 (B) Ia ln 2 
4r 4  s 

0  
(B) 3
m·r̂  r̂  m (C)
0 sa
Ia ln 
4r 2  s 
3 0 
(C) 3
m·r̂  r̂  m  0  s2  a 2 
4r Ia l n  
(D) 4
 s 
(D)
1
2
m ·r̂  r̂  m 
4r 17. A stationary iron sphere of radius R carries a charge
15. Which of the following statement is incorrect ? Q and a uniform magnetization M. The magnitude of
angular momentum stored in the electromagnetic fields
(A) Maxwell’s equations in free space are not is :
invariant under Lorentz transformation
2
(A)  M Q R2
(B) Maxwell’s equations in free space are invariant 9 0
under Lorentz transformation
2
(C) Maxwell’s equation show that electromagnetic (B) MQ
9 0
waves travel with the same speed in every inertial
frame 2
(C) MQR
9 0
(D) Maxwell’s equations were able to unify the
theories of electromagnetism and optics 1
(D)  M R2
2 0

SS-5466–A 4
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18. The electromagnetic theory suggests that the electric 22. The van der Waal’s equation of state for an ideal gas
vector of an electromagnetic wave suffers a sudden is given by :
phase change of 180o on reflection from the plane
reflecting surface but the magnetic vector suffers :  a 
 p  2 (V  b)  RT
(A) A phase change of 180o  V 
(B) A phase change of 90o
m
co
The critical constants for such a gas are given as :

om .
(C) A phase change of 270o

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(D) No phase change

m s
2 a 8a

e l a
19. In free space, the Poisson equation for electrostatics (A) VC = b, pc = 2 , TC =

s g
3 27 b 27Rb 2

l a a
becomes :
g
(B) TheaLaplace equation
(A) The Maxwell’s equation ·B  0 1 a 8a
(B) VC = b, pc = 2 , TC =
3 3b 27Rb 2
(C) The steady state continuity equation
(D) The Ampere’s circuital law a 8a
(C) VC = 3b, pc = 2 , TC =
20. For an anisotropic dielectric media, the relative 27 b 27 Rb
permittivity is a :
1 a 8a

m
(A) Vector quantity (D) VC = b, pc = 2 , TC =

o
2 3b Rb2

c
. Which of the following shows the correct relationship
(B) Scalar quantity
(C) Tensor quantity
m
e between the thermodynamical variables ?
s
23.

l a
(D) None of the above because relative permittivity
is only defined for isotropic media
a g    
21. Two ideal polyatomic gases of degrees of freedom T  S   T  S
(A)  p   V    V   p 
f1 and f2 at temperatures T1 and T2 are mixed so that  V  p  p  V
there is no loss of energy. If the masses and the number
of molecules of the two gases are m1, m2 and n1, n2,  T   S   T   S 
respectively, the temperature of the mixture will be : (B)  p   V    V   p 
 V  p  p  V

m
n1f1T1  n 2f 2 T2

om n f T  n f T c. o
(A) n1f1  n 2f 2  p   S   p   V 

c. (B) m
(C)  T   V    S   T 

s e
 S   p  T  S

em la
1 1 1 2 2 2

as ag
n f n f

l
1 1 2 2

g
 p   S   p   V 

a
n fT n f T
1 1 1 2 2 2 (D)  T   V    S   T 
(C)  S  p  T  S
n f n f 1 1 2 2

n1T1  n 2T2
(D) n1f1  n 2f 2

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24. The approximate number of modes of standing 26. Which of the following represents the phase space of
waves in a chamber of volume 100 cm3 in the frequency a linear harmonic oscillator ?
range 4 × 1014 Hz to 4.001 × 1014 Hz are:
px
(where c = 3 × 108m/s ) :

(A) 1.5 × 1014 x
(A)
(B) 1.5 × 1012

(C) 1.5 × 1010

(D) 1.5 × 1014
px
25. Which of the following statement is not correct ?
x
(A) Stefan-Boltzmann law states that the total rate (B)
of emission of radiant energy by a body per unit
area is related to energy density as fourth power
of its temperature
px
(B) Rayleigh-Jeans formula for the distribution of
energy treats blackbody radiation as standing x
electromagnetic waves which arise due to (C)

multiple reflections at the walls of the enclosure
and each mode

(C) According to Planck, blackbody radiation
chamber is filled up not only with radiation but px

also with the molecules of a perfect gas, which
exchange energy via resonators of molecular x
(D)
dimensions

(D) According to Rayleigh-Jeans formula the energy
density of Blackbody spectrum within the
wavelength range  and  + d  is directly
proportional to the fourth power of the
wavelength

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27. There are two identical particles and each particle can 29. The coefficient of viscosity for a gas having velocity
be in one of the three possible quantum states of gradient in a direction normal to the direction of mass
energies 0,  and 3. The number of microstates of motion is given by :
the system for Maxwell-Boltzmann, Bose-Einstein and
1 2
Fermi-Dirac statistics are respectively : (A)  = m nv

m
3

om . co
m
(A) 6,6,3
c
1

. e
(B)  = mn v

m a s
3
(B) 3,6,3
s e g l
(C) 3,3,6g l a 1
a
a
(C)  = mn 2 v
3

(D) 6,6,6 1
(D)  = mnv2
3
28. For a Fermi–Dirac system, the thermodynamic
where m is the molecular mass, v is the average
probability of distributing N indistinguishable particles
speed and  is the mean free path of a molecule.

m
into various energy states subject to Pauli principle is

c. o
given by : 30. Choose the incorrect statement :

s em (A) A real gas shows deviation from perfect gas
(A)  i
g i!
g l a
a
n i! (g i  n i )! behaviour at high pressures

(B) The temperature above which a gas cannot be
ni!
(B)  i g ! (g  n )! liquefied by applying pressure is known as critical
i i i
temperature
(n i  g i  1)!
(C)  i n ! (g  1)! (C) Every gas undergoing Joule–Thomson expansion

m
i i

c. o
at a temperature below the inversion temperature

m
c. o m
shows cooling

e
gi!

s
(D)  i n ! (g  n )!

s em la
i i i

ag
(D) van der Waals’ equation is inconsistent with the

gla
a
Where n represents the number of particle in ith state statement that all gases approach ideal gas
i

and g , the degeneracy of the state. behaviour at low pressures
i

SS-5466–A 7 [Turn over
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31. Fig.3 shows the p-V diagram of an ideal engine. 33. Which of the following statements is CORRECT for
Assuming all the processes to be quasi-static and heat a common emitter amplifier circuit ?
capacity at constant pressure, Cp to be constant. Then (A) There is 180o phase shift between input and
the efficiency of such an ideal engine is given by : output voltages
p (B) Both p-n junctions are forward biased

b (C) There is 90o phase shift between input and output
pb c
voltages
(D) There is no phase shift between input and output

pa voltages
d
a
V 34. For an ideal Fermi gas in three dimensions, the Fermi
Fig. 3
energy f is proportional to n , where n is the number
1

 pa   of electrons per unit volume , then  is equal to :
(A)  = 1 –  
 pb  (A) 2/3
1 (B) 1/3
 pa  
(B)  = 1 –   (C) 1/2
 pb 
(D) 2

 pa  35. The order of magnitude of the energy gap of a typical
(C)  = 1 –  
 pb  semiconductor is :
1 (A) 1 MeV
 p a  1
(D)  = 1 –   (B) 10 eV
 pb 
(C) 1 eV
32. Which of the following equations correctly represents
(D) 10–3 eV
the change in the entropy of an ideal gas ?
36. If the group velocity of waves in a certain medium is
 T2   V2  vg , while its phase velocity is v, then which of the
(A) S = CV ln  T  + R ln  V 
 1  1 following is not correct :

 T2   p2  (A) For a normal dispersive medium, v > vg
(B) S = Cp ln  T  – R ln  p  (B) For a non-dispersive medium, v = vg
 1  1
(C) For an anomalously dispersive medium, v < vg
 V2   p2 
(C) S = Cp ln  V  + CV ln  p  dv
 1  1 (D) For a normal dispersive medium, <0
d
(D) All the above where  represents the wavelength.

SS-5466–A 8
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co m .
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as 37. Stern-Gerlach experiment verified the : ag
41. Which of the following statement is not correct ?
(A) Quantization of angular momentum (A) The interference pattern in Young’s two slit
(B) Existence of electron spin experiment is based on the principle of division
(C) That atoms can align themselves in a magnetic of wave front
field only in a few directions

m
(B) The interference pattern in Michelson

co
(D) All the above

om .
interferometer is based on the principle of

.c e m
38. An atom is placed in a magnetic field B. The change

m s
division of amplitude

e l a
in the energy of the atom is :

l a s a g
(C) A Michelson interferometer is basically a

(B) E =g–g(2L + S) . B
(A) E = –g(L + 2S) . B

a
multi-wave interferometer

(C) 0 (D) Two-wave interference is characterized by a
(D) E = –g( L + S) . B sinusoidal variation of light intensity with phase

39. The average power o f a harmonic wave, difference between the interfering waves
y = A sin (kx – t), propagating with velocity, v, along 42. When a plane wave is incident normally on N parallel
a stretched string having mass per unit length, µ, is

m
slits, the intensity distribution according to the

. co
given by :
Fraunhofer diffraction is given by :

em
2 2 2
(A)  A v sin (kx – t)

l a s sin 2  2

g
(B) 2A2v cos2(kx – t) (A) I = I0 sin N

a
sin 
 2 2
(C) Av
2 sin 2  sin 2 N
(B) I = I0
(D) Zero 2 cos2 
40. Consider a standing wave, y = 2A cos(t) sin (kx)
sin 2  sin 2 N
n (C) I = I0
with ‘n’ antinodes, on a string of length L. If k = , 2 sin 2 
L

m
c. o
then which of the following is not correct :
m
sin 2 

c. o
cos2 

m
(D) I = I0

e
2
(A) The average energy of the wave is directly 

em la s
proportional to A2

las ag
(B) The average energy of the wave is directly b sin  d sin 
where,  = and  = , and
g
proportional to n2
a
 
(C) The average energy of the wave is inversely
 is the wavelength  , is the angle of diffraction ‘b’
proportional to L
(D) The average energy of the wave is inversely represents the width of each slit and ‘d’ is the separation
proportional to n2 between two slits.

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43. Consider the following statements : 45. Consider the following three experiments :
(1) In the process of diffraction from a circular (a) The x component of the position of an electron
aperture, if the source of light is at a finite distance is measured to within ±x and simultaneously
from the diffracting aperture, then the wave fronts the x component of its momentum is measured
falling on the aperture are spherical wave fronts. to within ±px
(2) Fresnel type of diffraction is defined such that
(b) The x component of the position of an electron
distance between the source or the observation
is measured to within ±x and then later the
screen or both of them are at finite distances from
x component of its momentum is measured to
the diffracting aperture.
within ±px
(3) If the source of light or the observation screen
or both of them are at infinite distances from the (c) The x component of the position of an electron
diffracting aperture, then diffraction falls under is measured to within ±x and simultaneously
the category of Fresnel type of diffraction. the y component of its momentum is measured
(4) If the source of light is at a finite distance from to within ±py.
the diffracting aperture, then the wave fronts In which of these cases does the Uncertainty Principle
falling on the aperture or reaching the screen will NOT impose a limitation on the outcome of the
be plane wave fronts. experiment ?
Which of the above statement/s are true ?
(A) (a) only
(A) All the statements from (1) to (4) are true
(B) (a) and (b) only
(B) Only the statement (2) is true (C) (b) and (c) only
(C) Only the statements (1) and (2) are true (D) (c) only

(D) None of the above 46. A beam of particles is incident from the negative x
direction on a potential energy step at x = 0. When
44. X rays of wavelength 0.24 nm are Compton-scattered
x < 0, the potential energy of the particles is zero and
and the scattered beam is observed at an angle of 60o
for x > 0 the potential energy has the constant positive
relative to the incident beam. The energy of the
value U0. In the region x < 0, the particles have a
scattered X-ray photons is :
kinetic energy K that is smaller than U0. What is the
(A) 5.14 keV form of the wave function in the region x > 0 ?

(B) 514 eV (A) Aekx + Be–kx

(B) Aeikx + Be–ikx
(C) 5141 keV
4
(C) Aeikx
(D) 5.1 × 10 keV
(D) Ae–ikx

SS-5466–A 10
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47. The list of excited states to which the 4p state can 50. A certain insulator has an energy gap of 6.0 eV.
make downward transitions are : A visible light in the wavelength range 400 to 700 nm
falls on this material. Now choose the correct
(A) 4p  3s , 4p  4s , 4p  2s , 4p  1s
statement :
(B) 4p  3s , 4p  2s , 4p  1s , 4p  3d
(A) The material will strongly absorb the visible light

m
co
(C) 4p  3s , 4p  4s , 4p  2s , 4p  4d

c om m .
(B) The material will not absorb the visible light

. e
(D) 4p  3s , 4p  2s , 4p  1s , 4p  2d

48. For a molecule, therem
e l a s
s g
(C) The material shines when the light falls on it
a
are three different types of excited

l a
agorder according to the amount of energy
states : electronic, vibrational and rotational. Put these
(D) The material will strongly absorb the infrared light
in increasing
generally required for each type of excitation : 51. At the lowest temperatures, the molar heat capacity
(A) Vibrational, electronic, rotational of metals can be explained primarily by the application
of :
(B) Vibrational, rotational, electronic
(A) The equipartition theorem

m
(C) Electronic, vibrational, rotational

c. o (B) Fermi-Dirac statistics of electrons
m (C) Bose-Einstein statistics of vibrating atoms
(D) Rotational, vibrational, electronic

s e
 (T), to its Fermi energy at absolute zero, la(0), is
49. The ratio of Fermi energy of a metal at temperature T,
f

approximately equal to : ag f
(D) Maxwell-Boltzmann statistics

(A) 1 52. The temperature at which the lattice and electronic
heat capacities of copper become equal to each
2
(B) kT other (Take Debye temperature, TD = 343 K and
12
Fermi energy = 7.03 eV) :

m
m c. o
 2  kT 

c. o m
(C) 1 12   (0)  (A) 300 K

s e
  f 

s em    kT   la
ag
(B) 273 K

la
2

g
2

a
(D) 1  12   (0)   (C) 4.2 K
   f

(D) 3.2 K

SS-5466–A 11 [Turn over
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53. Which of the following statement is not correct 55. In a p-n junction at room temperature, the ratio
regarding the Nuclear Fusion ? between the current with a forward bias of 2 V to the
current with a forward bias of 1V is (approximately) :
(A) Nuclei produced in the reaction are usually highly
radioactive (A) 1.7 × 1019

(B) Energy release can be as large as several MeV (B) 1.7 × 1017
per reacting nucleon
(C) 2.1 × 1015
(C) It is usually necessary to overcome a Coulomb
barrier for the reaction to occur (D) 2.1 × 1019

(D) Reacting nuclei come from commonly available 56. Choose the incorrect statement :
chemical elements
(A) The small-signal hybrid-pi model applies to
54. In the decays and reactions of elementary particles, transistors operating in the forward-active mode
which of the following conservation laws is not in linear amplifier circuits
followed strictly ?
(B) The cut-off frequency of a transistor is the
(A) In any process, the lepton numbers for frequency at which the magnitude of the
electron-type leptons, muon-type leptons and common-emitter current gain becomes equal
tau-type leptons must each remain constant to 100

(B) In any process, the total baryon number must (C) The frequency response of a transistor amplifier
remain constant
is a function of the emitter–base junction

(C) In processes governed by the strong or capacitance charging time

electromagnetic interactions, the total strangeness
(D) When a transistor is biased in the forward-active
must remain constant
mode of operation, the current at one terminal
(D) In processes governed by the weak interaction, of the transistor (collector current) is controlled
the strangeness must remain constant by the voltage applied across the other two
terminals of the transistor (base–emitter voltage)

SS-5466–A 12
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57. A typical transistor with  = 100, has a base-to- 59. A certain common emitter amplifier has a voltage gain
collector leakage current, ICBO, of 5µA. If the transistor of 100. If the emitter bypass capacitor is removed :
is connected for common-emitter operation then the
(A) The circuit will become unstable
collector current for IB = 40 µA :

(B) The voltage gain will decrease

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(A) 4.5 mA

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(C) The voltage gain will increase

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(B) 5.4 mA

e m l a s
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(D) The Q-point will shift.

l a a
(C) 1.5 mA

(D) 4.5ag
µA
60. A Voltage-divider bias :

(A) Cannot be independent of dc
58. The bandwidth of an amplifier is determined by :

(B) Is not widely used
(A) The mid range gain

(C) Requires fewer components than all the other
(B) The critical frequencies

om
methods
(C) The input capacitance
m.c (D) Can be essentially independent of 
s e
a
dc

(D) The roll-off rate
g l
a

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c. o s e m
s em la
gla ag
a

SS-5466–A 13 [Turn over
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ROUGH WORK

SS-5466–A 14
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as ROUGH WORK ag

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.c e m
e m l a s
l a s a g
ag

m
. co
s em
g l a
a

m
m c. o
c. o s e m
s em la
gla ag
a

SS-5466–A 15 [Turn over
163


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c. o s e m
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