Test Booklet Code & No.

iz'uif=dk dksM o ÿ- C
MAY - 32216/II—C
Paper-II
PHYSICAL SCIENCE
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OMR Sheet No.
MAY - 32216 (To be filled by the Candidate)
Time Allowed : 1¼ Hours] [Maximum Marks : 100
Number of Pages in this Booklet : 16 Number of Questions in this Booklet : 50
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 MAY - 32216/II—C

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 MAY - 32216/II—C
Physical Science
Paper II
Time Allowed : 75 Minutes] [Maximum Marks : 100
Note : This Paper contains Fifty (50) multiple choice questions. Each question
carries Two (2) marks. Attempt All questions.

3. In quantum mechanics three-

1. What is the degeneracy of the third
dimensional normalized wave
excited state for a particle in 3- function ψ(r ) of a particle :
(A) is dimensionless
dimensional isotropic Harmonic
(B) has dimension of (energy ×
oscillator potential. (Ground state is time)
(C) has dimension of energy
not an excited state) : (D) has dimension of (length)–3/2
4. Particles with energy E > V0 are
(A) 10 incident from side with negative x,
on step potential V = 0 for x < 0 and
(B) 6 V = V0 for x > 0.
ψ
= (C
xe) C= *AC
ik2 x
+e +
DeD*D
ik1 x − ik2 x ik1 x
+ Be The wave function is given
T=
A * A + B*B(C) 4 by :
x < 0
(D) 3
x > 0
2. The eigenvalues of a Hermitian Then :
(A) Reflction coefficient R = 0
operator must be :
(B) Tranmission coefficient

(A) Real

(B) Complex (C) Transmission coefficient

(C) Positive

B*B
(D) Negative (D) Reflection coefficient =
A*A

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 MAY - 32216/II—C

5. A constant volume ideal gas 7. A Carnot engine operates between

thermometer is in thermal
600 K and 300 K with ideal gas as
equilibrium with a system A at
working medium. Its maximum
temperature TA and measures a
pressure p A . When the same efficiency will be :

thermometer is brought in thermal

(A) 0.5
equilibrium with another system B,
the measured pressure is The (B) 0.8

temperature of the system B is :

(C) 1.2
(A) T A
(D) 1
(B) TA/2
8. A gaseous sytem of volume V is at
(C) 2T A
pressure p and temperature T. A
(D)
small change ∆V is made in the
6. Consider a process in which the
volume. If ∆Q is the change in the
volume of the system remains
constant and the system is in heat content of the system, the

thermal equilibrium with a heat change ∆u in the internal energy is

reservoir at temperature T. Such a
given by :
process is called :
(A)
(A) isothermal

(B) isobaric isothermal (B)

(C) isochoric adiabatic (C)

(D) isochoric isothermal (D)

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9. The chemical potential, in the 11. Considering the Maxwell-Boltzmann

distribution of speeds of molecules,

classical limit is :
the root mean square speed of a
(A) zero
molecular of mass m, at temperature

(B) negative T is :

(C) positive (A)

(D) complex quantity 8 kT

(B)
πm
(C) 0
10. The partition function zij of two
z
zi 3jkT 2kT
(D)
m
independent systems i and j in m

thermal equilibrium with a reservoir 12. The number of distinct

arrangements of 6 Bosons placed in

at temperature T is given by :
3 energy states are :
(A) zij = zi × zj
(A) 84

(B) zij = zi + zj
(B) 28

(C) zij = (C) 56

(D) zij = zi/zj (D) 3 6

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 MAY - 32216/II—C

13. TTL output of the function generator 15. When two rotary pumps are
is :
connected in parallel to a vacuum
(A) Triangular wave
chamber, the ultimate pressure can
(B) Sine wave

(C) Square wave be achieved is closest to :

(D) Triangular, sine and square

(A) 1 × 10–3 torr
waves

14. In an experiment, the voltage across (B) 0.1 × 10–3 torr

a 10 kΩ resistor is applied to CRO.

(C) 1 × 10–5 torr
The screen shows a sinusoidal signal

of total vertical occupancy 3 cm and

(D) 1 × 10–6 torr
total horizontal occupancy of 2 cm.

The front-panel controls of V/div and 16. Noise due to several amplifiers
time/div are on 2 V/div and 2 ms/
connected in series is :
div respectively. Calculate the rms

value of the voltage across the

(A) Additive
resistor :

(A) +3 V (B) Subtractive

(B) –2.1213 V
(C) Multiplicative
(C) +2.1213 V
(D) Logarithmic
(D) –3 V

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17. In which counter for the detection 19. Metallic sodium has a bcc structure.

of the thermal neutrons boron is Its X-ray diffraction pattern does not

introduced in the form of BF3 ? contain lines corresponding to Bragg

plane :
(A) Ionisation chamber
(A) (1 1 0)
(B) Proportional counter
(B) (2 2 2)
(C) G.M. counter
(C) (2 0 0)
(D) Scintillation counter
(D) (2, 2, 1)
18. In the Millikan’s experiments, an oil
20. The movable mirror of Michelson’s
drop carries four electronic charges
interferometer is moved through a
and has a mass of 1.8 × 10–12 g. It
distance of 0.02603 mm. The number
is held almost at rest between two
of fringes shifted across the cross-
horizontal charged plates. 1.8 cm wire of a eyepiece of the telescope,
apart. What voltage must there be if a wavelength of light 5200 Å used

between the two charged plates ? is :

(A) 250 V (A) 100

(B) 300 V (B) 200

(C) 496 V (C) 300

(D) 400
(D) 500 V

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 MAY - 32216/II—C

21. The value of the integral 23. The real part of log (3 + 4i)

is :
∞
sin x
2

∫ x2
dx
−∞
(A) log 2

is :
(B) log 3

π2
(A) (C) log 4
2

(B) 0 (D) log 5

24. Particular integral of the first order

(C)
linear differential equation

(D)

22. The Fourier transform of a Gaussian

function is of the form : is given by :

(A) Exponential
(A)

(B) Lorentzian
(B)

(C) Gaussian
(C)

(D) Screened coulomb

(D)

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 MAY - 32216/II—C
25. Eigenvalues of the matrix 27. If a coin is tossed four times, what

is the probability that two heads and

two tails will result ?

(A)
are :

(A) 1, –1
(B)

(B) –1, –i

(C)
(C) i, –i

(D) 1 + i, 1 – i
(D)
(151iˆ −→→ˆ→ˆj −→1ˆkˆ) ˆ
→
3
∇∫ r̂.×(FFi1F.+=dr
2
∇r 3 →  
8
4
=0j0+= k 0)
1   26. is given by : 28. Which of the following defines a
 | r |1 
conservative force ?

(A) (A)

(B)
(B)

→ (C)
r
(C) 3
r
→
dF
(D) r
(D) =0
dt

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 MAY - 32216/II—C

29. Consider the three vectors : 31. A thin rigid rod of length ‘l’ is
moving inside a sphere of radius
R(R > l) such that both of its ends
are in contact with the inner surface
and of the sphere. The degree of freedom
of the rod are :
(A) Four
Which of the following statements
(B) Three
is true ? (C) Two
(A) are linearly indepen- (D) One

dent 32. For a system shown in figure given

below, the Lagrangian function is
(B) are linearly dependent given by :

(V = 0, at y = 0)
(C) are at right angles to each

other

(D) and are parallel

30. The moment of inertia of a thin disc

of radius R about an axis passing
though its center and perpendicular
to the plane of the disc is :

(A) MR 2
(A)
(B) MR2
1
(B) L = My& 2 + Mgy
2
(C) MR2 1
(C) L = My& − Mg( y − x)
2
2
(D) MR2 (D) L = My& 2 + Mg( y − x)

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34. A particle moves under the action

33. ‘‘Hamiltonian H is not equal to the
1
of force F = − rˆ. The particle
rn
total energy E (sum of kinetic and
moves in a closed orbit, if :

potential energies)’’ holds true for a (A) n = –1 or n = 2

(B) n = 1 or n = –2
system characterized with :
(C) n = –1 or n = –2

(A) conservative forces and time-

(D) n = 1 or n = 2

independent constraints 35. Which of the following statements

holds true for a freely rotating rigid

(B) conservative forces and time- body ?

ω
dL
dt
dependent constraints (A) and are perpendicular to

each other
(C) dissipative forces and time-
(B) and are parallel to each

independent constraints other

(D) for every system irrespective of (C) and are antiparallel to

each other
the nature of forces and
(D) and do not have 0
constraints
specific relationship

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 MAY - 32216/II—C

36. A particle is at rest in a rotating 38. The Ampere’s law in the case of free
frame of reference. The space takes the form :
pseudoforce(s) acting on the particle
(A)
is(are) :
→
(A) None of these → → → ∂E
(B) ∇ × B = µ0 J + ∈0 µ0
∂t
(B) Only the Coriolis force
→
(C) Only the centrifugal force
→ → ∂E
(C) ∇ × B = ∈0 µ0
∂t
(D) Both the centrifugal and
→
Coriolis forces
→ → → ∂E
(D) ∇ × B = µ0 J − ∈0 µ0
∂t
37. The electric field of an
39. An electric charge +Q is placed at
electromagnetic wave propagating

in the free space is given by : the center of a cube of sides 10 cm.

The electric flux emanating

from each of the face of the cube

→
Then the wave vector k is given is :
by :
Q
(A) ∈
0
(A)

(B)
 3 1 
(B) 400 π  2 xˆ − 2 yˆ 
  Q
(C) 6 ∈
0
(C)
10Q
(D) (D) ∈0

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 MAY - 32216/II—C

40. A field at certain point in the space

42. A plane polarized EM wave of
is expressed as the potential
frequency ω is incident at an angle
function Then

the potential V at point (2, –1, 1)

θ in a rectangular wave guide of
is :
resonant frequency ω mn . Then
(A) 15 V

energy carried by the wave

(B) 13 V

(C) 0 V propagating inside the cavity will

(D) 8 V
δVs→= 3 xc→2→
z − xy→3
+ z. propagate with the group velocity
nˆ122 ×− (D
(D D12) +.×nˆDˆ12
1 )==δδs s/ /∈
n12 ∈
00
 ω mn 41. The electric displacement vector at
2
1− 
 ω  of :
the interface of two dielectric media

with unit normal vector n̂12 from

(A)
medium 1 to 2 and free surface

charge density is given by : ω mn

(B) c 1 −
ω
(A)
c
(B) ω 
(C) 1 −  mn 
 ω 
(C)
2
 ω mn 
(D) c 1 − 
(D)  ω 

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 MAY - 32216/II—C
43. A plane polarized electromagnetic
wave is incident normally on an 45. The electric field of an elecro-
interface separating two dielectrics
with intrinsic impedance equal to z1 magnetic wave is described by the
and z 2 . The reflection and
transmission (Fresnel’s) coefficients relation :
(R and T), respectively, are given
as : → → →
E(r, t) = (eˆ1E1 + eˆ2E2 ) . ei ( k . r − ωt)
2 z2 z2 − z1
(A) z + z and z + z
1 2 1 2
where eˆ1 and eˆ2 are two mutually

(B) and
orthogonal unit vectors both

(C) and perpendicular to and E2 are

2 z2 z1 + z2 the electric field components along

(D) z + z and z − z
1 2 1 2

44. If the divergence of a vector the two directions. What type of

potential at a point in the
polarization state does this wave
fluid is non-zero and takes positive
value, then which of the following represent ?
is correct ?
(A) The fluid is expanding (A) Plane polarized
(B) The fluid density is decreasing
with time (B) Left circularly polarized

(C) The point acts as a source of

(C) Right circularly polarized
fluid
(D) Statements (A), (B) and (C) all
(D) Elliptically polarized
are correct

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 MAY - 32216/II—C

46. A harmonic oscillator is perturbed 48. a and a + are annihilation and

creation operators for one
by a perturbation potential dimensional harmonic oscillator.
The ground state energy of the Then equals :

oscillator to a first order in (A)

perturbation is : (B) (n + 1)2 | n >

(C) n(n + 1)| n >

(A) (D)

49. The ground state energy shift

due to a non-zero perturbing
(B)
potential is zero in first order
perturbation.Which of the following
3 is correct ?
(C) hω + α
2ih
2 (A) ∆E > 0 in second order
3aa ω3+ +
∂| >a∂| n >n∂> 
hα xn (.a
n+ 1)|
n
 ∂2x ++ α∂y + ∂z  perturbation
hω (B) ∆E = 0 in second order
(D) + α3
2 perturbation
→ → → → (C) ∆E < 0 in second order
47. The value of operator r . p − p . r
perturbation
in quantum mechanics is :
(D) ∆E = 0 in all orders of
perturbation
(A) ih
50. The parity of wave function ψ is
(B) zero associated with which of the
following transformation ?
(C) (A) Space inversion
(B) Space translation

(D) (C) Space rotation

(D) Space exchange of two particles

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 MAY - 32216/II—C

ROUGH WORK

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