PUMDET 2023 Question Paper Physics Astrophysics

Subject : PHYSICS/ASTROPHYSICS

(Booklet Number)

Duration : 90 Minutes No. of Questions : 50 Full Marks : 100

INSTRUCTIONS
1. All questions are of objective type having four answer options for each. Only one option is
correct. Correct answer will carry full marks 2. In case of incorrect answer or any
combination of more than one answer, ½ mark will be deducted.
2. Questions must be answered on OMR sheet by darkening the appropriate bubble marked
A, B, C or D.
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respective bubbles.
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5. Write question booklet number and your roll number carefully in the specified locations of
the OMR Sheet. Also fill appropriate bubbles.
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is appeared in Admit Card) in appropriate boxes in the OMR Sheet.
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consequence of such invalidation due to incorrect marking or careless handling by the
candidate will be sole responsibility of candidate.
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the question booklet for rough work.
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Signature of the Candidate : ______________________________
(as in Admit Card)

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Physics/Astrophysics 

SPACE FOR ROUGH WORK

Physics 2 

Physics

1. In a certain culture of bacteria, the rate of increase is proportional to the number present. If
it is found that the number doubles in every 4 hours, how many may be expected at the end
of the 12 hours?

(A) 8 times the original number (B) 4 times the original number

(C) 12 times the original number (D) 10 times the original number

2. Consider the integral 
C
  sin z  2z dz where C is a closed circle of unit radius. The value
C

of the integral will be

(A) 0 (B) 2πi

(C) 4πi (D) sin1


3. The closed line integral of the vector A   x 2  y 2  ˆi  2xyjˆ around a square of side b which
has a corner at the origin, one side on the x-axis and the other side on the y-axis will be

(A) 2b3 (B) 4b3

b3
(C) b3 (D) –
4

2 i
4. Which of the following are eigen values of the matrix   ?
 i 2 

(A) 4, 0 (B) 2, 2

(C) i, –i (D) 1, 3

Physics 3 

5. Consider the following 2nd order differential equation

 x  2   x  1 y  3  x  1 y  2y  0
2

In this equation
(A) x = 1 is a regular singular point (B) x = – 2 is a regular singular point
(C) x = 0 is a irregular singular point (D) x = 1 is a irregular singular point

6. Consider the series
x3 x5 x7
x   
3 5 7
The series converges provided
(A) |x| > 1 (B) |x|  1
(C) |x| < 1 (D) |x|  1

7. The value of the integral  xy 2 dxdy , where R : x 2  y 2  4; x  0 is
R

64
(A) 0 (B) 15
32 4
(C) 15 (D) 15

8.

The component of the unit vector n̂ perpendicular to the plane shown in the figure above is
6iˆ  3jˆ  2kˆ 6iˆ 3i3j
ˆˆ62k
ˆj ˆ 2kˆ 3iˆ 6i6ˆ ˆj22k
ˆj ˆ 3kˆ 6iˆ 2i
2ˆˆj3j
ˆˆ 6kˆ
3k 2iˆ  3jˆ  6kˆ
(A)A A B (B)B (C) (C) (D) (D)
7 7 7 7 7 7 7 7
6iˆ 3i
ˆˆ  62k
3j ˆjˆ 2kˆ 3iˆ  6i
6ˆˆj 22k
ˆjˆ 3kˆ 6iˆ  2i
2ˆj  3j
ˆˆ  6kˆ
3k 2iˆ  3jˆ  6kˆ
B B(C)(C) (C) (D) (D)
(D)
7 7 7 7 7 7 7

Physics 4 

9. Consider the polynomial Bn  x  defined by
te xt
xt 
Bn  x  n
t
 
e  1 n 0 n!
t

Then Bn  x  is [ Bn  x  denotes differentiation of Bn  x  with respect to x]

(A)A nBn  x  A nB
B nnBxn 1 x nBn n1  x1 Bn x
(B)B C C Dn 1n B1n Bxn x D n 1 Bn x

nB
B n nB
xn 1 x C n 1n x 1 Bn  x  C D
B(C)
nB n1 xBn x (D)D  n  1 Bn  x 
n  1nB

A
10. The classical probability of finding a particle is the region 0  x  L is P  x   , where A
L
2
and L are constants. The variance x  x2  x of the position of the particle is
L L
(A)A B 0 C (B) 0 D L
2
L
B 0 (C)C D L (D) L
2 3

11. A particle is dropped freely from a height H. When it reaches to the ground, it will be

deflected due to the Coriolis force towards

(A) east in northern hemisphere, but west in southern hemisphere

(B) east in southern hemisphere, but west in northern hemisphere

(C) east in both hemisphere

(D) west in both hemisphere

Physics 5 

12. The degrees of freedom of a system of three particles on a line with fixed inter-particle

separations and constrained to move in space is

(A) 6 (B) 4

(C) 7 (D) 5

13. A particle of mass m with speed v approaches a stationary target M. The masses bounce of

each other without any loss in total energy. After collision, the angle between the particles

in the CM frame is

(A) 180 (B) 90

(C) 45 (D) 0

14. Which of the following operators is invariant under Lorentz transformation along x  x

axis?

1 2 2 1 2 2 1 2 2 1 2 2
(A)A A  B 
(B)B 
c 2 t 2 x 2c 2 t 2 x 2 c 2 t 2 x 2c 2 t 2 x 2
2 2 2 2
 1    1     1    1   
(C)C   C    D  (D) D   
 c t x  c t x   c t x  c t x 

15. A particle is oscillating inside the potential V  x   Ax 4 ,  A  0  . If the amplitude of the

oscillation is a 0 , then time period T of oscillation is

1 1
(A) proportional to (B) proportional to
a0 a0

(C) proportional to a 0 2 (D) independent of a 0

Physics 6 

16. A planet of mass m moves in a circular orbit of radius R in the gravitational potential
k
V rr   ,, kk 00  . The orbital angular momentum of the planet is
V
r

(A) 2mkR (B) mkR

(C) mkR (D) 2mkR

17. Lagrangian of a system is given by

1 1
L mx 2  x 2  xxt

2 2

The equation of motion corresponding to the Lagrangian is

(A)A mx   0
  0 A mx   
B mx   x  0
xB 0mx
(B)
  xC 
(C)C mx mxx  0x   x  D  (D)
0 mx xxt
D
 mx 0  xxt
 0

18. An insect flies on a spiral trajectory such that its polar co-ordinates at time t are given by
r  be t ,   t , where b and ω are positive constants. The angle between velocity and
acceleration at time t is

(A) 30° (B) 60°

(C) 45° (D) 90°

19. Consider a unit mass oscillator whose equation of motion is

x  10x  16x  0


This corresponds to

(A) a harmonic oscillator

(B) overdamped harmonic oscillator

(C) underdamped harmonic oscillator

(D) critically damped harmonic oscillator

Physics 7 

20. Which of the following functions represent a travelling wave?

(A)A fA x f x2xvt t 2 v t
 v2 B(B)fB x fvt
x  vt 
2
 2xvt
 
f  xf x v t v t
(C)C C
2 22 2 2 2
f xf2 xv2 2t 2v 2 t 2 
D(D)D

21. The number of cyclic coordinates for a particle falling freely under gravity is

(A) 1 (B) 2

(C) 3 (D) 0

22. A rod of length 10 m, making an angle 30° with x' - axis is at rest in S frame. S frame is

moving with uniform velocity 0.6 c along x – x' axis with respect to S frame. The length of

the rod measured from S frame will be (S and S both are inertial frames)

(A) 9.86 m (B) 7.86 m

(C) 8.54 m (D) 6.84 m

23. Photon gas has an entropy S varying with volume (V) and temperature (T)

[Note energy density  = aT4] as

4 2 3 4 1 1
(A)A S  aVAT S  aV 2 T 3 B S  (B)B 3 S  aVT 3
aVT
3 3 3 3

4 4 2 2
(C)C S  aVT
C 3 S  aVT 3 D S  (D)D 3 S  aVT 3
aVT
3 3 3 3

Physics 8 

24. A hypothetical speed distribution for a sample of N gas molecules is shown below
P(v) = 0 for v > 2V0

How many particles have speeds between 1.2 V0 and 1.9 V0 ?
N 7N
(A) 5 (B) 15
2N N
(C) 21 (D) 8

25. Consider the following reversible cycles represented by right-angled triangle in a T-S
diagram.

The efficiency of the above cycle is
(A) 66% (B) 50%
(C) 33% (D) 25%

26. Consider a system whose three energy levels are given by 0, ε, 2ε. The energy level ε is
two-fold degenerate and the other two are non-degenerate. The average energy of a particle
for KBT >> ε is

(A)  (B) 0
(C) 2.5 (D) 2

Physics 9 

27. In a certain process, the entropy of a substance is known to be equal to S 0 at temperature

T0. If in that process the heat capacity of the substance is C (Constant), then temperature as

a function of entropy S can be expressed as
 S S0 
 S  S0   
T TT
(A)A A 0 T0  B TT0e T0 e  C 
B(B)T
 C 
S S0
 S0  S 
T TT
(C)C C TCe
0e 0 T TT0 T0 
D(D)D 
 C 

28. Consider 1 mole of an ideal gas with internal energy U1 and 1 mole of Van der Waals gas

with internal energy U2. The Van der Waals parameters a and b are positive. Then
 U1U1   U2U 2   U U   U U 
(A)A A   0; 0;   0  0 B(B)B 1  10; 0; 2  20  0
 V V T  T  V V
T T  V VT  T  V V
T T

 U 1U1   U 2U
 2  U 1U1   U 2U 2 
(C)C C    0;0;    0  0     0;0;    0  0
D(D)D
 V VT  T  V VT T  V VT T  V  VT T

29. A gas of molecules, each of mass m is in thermal equilibrium at temperature T. The
velocity components of the molecules along the Cartesian axes are  x ,  y and  z . The

mean value of   x  b y  is
2

3k T3k T 2k T 2k T
(A)A A
1  b12  b B B B(B)B B B
m m m m
1  b12b mBTkmBT
(C)C C
k k 2Tk T
D(D)D1 b1  b B B
m m

30. An EM wave is to pass through an interface separated by two media having dielectric
constants 1 and  2 . If 1 = 2  2 , the wave will be totally reflected if the angle of incidence

is

(A) 0° (B) 60°

(C) 30° (D) 45°

Physics 10 

31. A cube of side a has its edges parallel to x, y and z axis of a rectangular co-ordinate system.
 
A uniform E field is parallel to y axis and a uniform magnetic field B is parallel to z axis.

If S denotes the Poynting vector and U the energy density stored in the cube, then
    dU
A
(A) S  0; UA 0
S  0; U  0 B S  0;(B)B S0 0; 0
dt
 dU   dU 
C S  0;  0 dU D  .S 0;D .S0 0; dU  0
(D)
(C) C
dt S  0;  0 dt
dt dt

32.

Consider the following ray diagram with OA as incident ray. Which of the following
statement is correct, regarding phase change on reflection only.
(A) ray 1 and 2 suffer a phase change of π.
(B) ray 1 suffers a phase change of π and ray 2 does not suffer any phase change.
(C) ray 1 and 2 both do not suffer any phase change.
(D) ray 1 suffers no phase change but ray 2 suffers phase change of π.

33. The components of the electric field of an electromagnetic plane wave are given by
E x  E 0 sin  kz  t 
E y  E 0 cos  kz  t 
Ez  0

Then, the propagation direction of wave and the polarization state are respectively
(A) + z direction, Left circularly polarized
(B) – z direction, Left elliptically polarized
(C) + z direction, Right elliptically polarized
(D) – z direction, Right circularly polarized

Physics 11 

34. The electric field of any region is given by

E  4xiˆ  8yjˆ
The equation of the lines of force is
(A) x2y = constant (B) xy2 = constant
x2 x
(C) = constant (D) = constant
y y2

35. Consider a double slit interference pattern where central maximum contains exactly 9
fringes. How many fringes lie between the 1st and 2nd minima in one side of the central
maximum ?
(A) 4 (B) 3
(C) 5 (D) 8


36. Given uniform magnetic field B  B0 kˆ (B0 = constant), a possible choice for the magnetic

vector potential A is
 
 
 
(A)A A  B0 yiAˆ A  B0 yiˆ B AB (B)
0
B ˆA
yi  ˆ B0 yiˆ  xjˆ
xj
   

(C)C A  B0 Cxiˆ A
 yj 
ˆ B0 xiˆ  yjˆ D A  (D)
BD ˆ A   B0 yiˆ
0 yi

37. A disc of radius R rotates with a constant angular velocity ω about its own axis. The
surface charge density of this disc varies as   r 2 (α is a constant), where r is the
distance from the centre of the disc. The magnetic field intensity at the centre of the disc
will be
 0R 3  R 4 0 R 3
(A)A  0R
3
A B R (B) C
B C D0 D
6 8 3
 0R 3  R0 
3
R4  0 R
0 R
4 3
 0R 3
B R B(C)C0 C D D
(D)
6 6 8 8 3 3

p̂ 2 ˆ ˆ  px
d xp ˆˆ
38. Consider a free particle Hamiltonian operator Ĥ  . Then will be equal
2m dt 2
to

(A) 0 (B)B p̂
A 0 C D
m m m
2 2 2 2
p̂ p x xˆ
B A 0 B(C)C C D (D)D
m m m m m m

Physics 12 

39. Any eigen function regardless of its energy in an infinite square well is periodic in time
with a period of
2 2
mL mL 4mL 4mL2mL 2mLmL mL
(A)A A B B
(B) C C D D
       

mL 4mL2 4mL2mL2 2mLmL mL
B B(C)C C D (D)D
      2

(m = mass of the particle; L = Length of the well)

40. Eigen functions of the Hamiltonian Ĥ  T̂  V̂ of a harmonic oscillators are

(A) eigen functions of T̂ as well as V̂ (B) eigen function of T̂ but not of V̂

(C) eigen function of V̂ but not of T̂ (D) eigen function of neither T̂ nor V̂

41. Which of the following wave functions is/are not accepted in quantum mechanics?

I.   x   tan x; II.   x   e
x

III.   r, ,    ei /3 IV.   r, ,    ei

(A) I only (B) I and III

(C) II and III (D) I, II, III and IV

42. Let  nm denote the eigen state of hydrogen atom in the usual notation. Consider the state

1
5

2200  3211  7 210  5211 
The above state is an eigen state of

(A) L2 and Lz (B) H and Lz

(C) H, L2 and Lz (D) H only

Physics 13 

43. The band energy of an electron in a crystal for a particular k direction has the form
E  k   A  Bcos ka , where A > 0 and B > 0, and – π < ka < π. The electron has a hole-
like behaviour over the following range of k :
 3      
(A)A  ka  A B  kaka   (B)B C  0ka ka C 0D ka
0 ka   D 0  ka  
2 2 2 2 2 2 4 4
 
B  kaka   B(C)C  0ka ka  C 0D ka
0 ka   (D)D 0  ka  
2 4


44. Consider a rectangular lattice in two dimensions with primitive lattice vectors a1  aiˆ and
 


a 2  2ajˆ . Which of the following represents reciprocal Lattice Vectors b1 , b 2 for this 
lattice ?
          2
(A)A Ab1 b1 ˆi, bˆi,2 b 2  ˆj ˆj B(B)Bb1 b1 ˆi, bˆi,2 b 2  ˆj ˆj
a a 2a 2a a a a a
     
   2       
(C)C Cb1 b0i, ˆ bˆ2 b 2  ˆj ˆj Db1 b1  i, bˆi,2 b 2 ˆj ˆj
ˆ
1  0i, D(D)
a a 2a 2a a a

45. The term symbol for Fe 2 having last shell configuration 3d6 is
(A) 3F (B) 5D
2 4

(C) 5D (D) 2D
0 3/2

46.

Consider the above circuit with a Si diode. The current I in the above circuit is
(A) 1.97 mA (B) 3.02 mA
(C) 2.64 mA (D) 2.07 mA

Physics 14 

47. For the circuit shown below, the output is V0  V1  2V2  3V3

The values of resistances R1, R2 and R3 are respectively
(A) 6 kΩ, 2 kΩ and 3 kΩ (B) 2 kΩ, 6 kΩ and 3 kΩ
(C) 6 kΩ, 3 kΩ and 2 kΩ (D) 6 kΩ, 3 kΩ and 3 kΩ

48. On the basis of extreme single particle shell model, the ground state spin parity of 21 Sc 45
will be
       
(A)A    3  5  (B)B C    7  5  5
3 5 7
A B   C D    D  
2  2  2   2  2   2  2  2
      
 3  5   5  7   7  5  (D)D  
5
B   B(C)C   C D   
 2  2   2  2   2  2  2

49. Consider a strong interaction:    p     X . The z component of Isospin (I3) of X is

1 1
(A) 2 (B) –2

(C) +1 (D) –1


50. In the quark model, the  , a spin –3/2 resonance of charge +2, consists of which of the
following combinations of quarks?
(A) uuu (B) uud
(C) ddd (D) ud
____________

Physics 15 

SPACE FOR ROUGH WORK

Physics 16 