MH SET 2013: 1 December, Paper II, Physics
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DEC-32213/II 2
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DEC-32213/II
Physics
Paper II
Time Allowed : 75 Minutes] [Maximum Marks : 100
Note : This paper contains Fifty (50) multiple choice questions, each carrying
Two (2) marks. Attempt All questions.
1. Five data points can be exactly fitted →
3. r is the position vector of any point
by using a polynomial of order :
on the surface of a cube of side L.
(A) Five → →
(B) Four
The surface integral ∫∫s r .ds
is :
(C) Three (A) 0
(D) Two (B) ∞
(C) 3L 2
2. A person is confined to move in equal
(D) 3L 3
steps of 1 m in 1 minute along a 4. A (3 × 3) matrix has unequal
straight line. He takes each step eigenvalues a, b and c and its
either to his left or to his right with determinant is D. If a = –1, b = 2
and D = 4, what is the value of c ?
equal probability (random walk in
(A) 1
one-dimension). (B) –1
What is the probability that the (C) –2
(D) 0
person is at his starting point after
5. A matrix M is of the form :
5 minutes ?
0 a
(A) Zero M=
− a * 0
1 If the det M = 1, the most general
(B)
2 value of a is :
(A) cos θ
1
(C) (B) sin θ
8
(C) exp (iθ)
1 (D) cosh θ
(D)
32 where θ is a real parameter.
3 [P.T.O.
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6. The solution of the differential 9. The complex function f ( z) = z is
equation :
singular at :
dy
+ y=x (A) z = ∞
dx
(B) z = 0
is :
(C) z = 1
(A) y = ex (D) z = i
(B) y = x–1 10. Consider an electric charge ‘q’
(C) y = e–x moving at velocity , in an
(D) y = x + 1 otherwise charge-free region
2 containing both an electric field E ,
7. f (t) = e− at is a Gaussian function.
and a magnetic field B , which may
Its Fourier transform is :
depend upon time and position.
(A) Gaussian
Which of the following statements is
(B) Polynomial incorrect ?
(C) Trigonometric (A) The charge experiences a force
(D) Lorentzian F = q (v × B)
1 (B) The force can be derived from
8. f ( z) = 2 , the contour integral of
z +1 a potential
f(z) over a contour C comprising the U = qφ − q(A . v ) + q (A . v ) v2
real axis from –2 to +2 and a with A as the vector potential
(C) The Hamiltonian of the system
semicircle in the upper half of the
is :
complex plane with centre at origin
1
and radius 2 is given by : H= ( p − qA)2 + qφ
2m
(A) 0
where φ is the scalar potential
(B) π (D) The equations of motion are
(C) –π unaltered by gauge
(D) 1 transformations
4
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11. Consider a central force of the form 13. The momentum of inertia I of
F = − kr n . The values of ‘n’ that
a rigid rod of length l about an
result in closed orbits are :
axis passing through one of its
(A) n = –2 and n = 1
ends is :
(B) n = 2, 4, 6, ......
(C) n = 1, 3, 5, 7, .......
(D) n = –1, n = +2
l
12. A satellite is moving in an elliptical
orbit. If v1 and v2 are its maximum
and minimum speeds respectively,
then the eccentricity of the ellipse
is :
Ml 2
(A)
v1 3
(A)
v2
1
v2 (B) Ml2
12
(B) v
1
1
v1 − v2 (C) Ml2
(C) 4
v1 + v2
v1 + v2 4
(D) Ml2
(D) v − v 3
1 2
5 [P.T.O.
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14. Consider a body falling under the 16. If Lagrangian of n-particles system
action of gravitational force F = –mg.
If the effect of air resistance is involves potential V(r), which is
included by including a frictional isotropic in nature, then :
force Fv = − bv and v0 = 0, then the
velocity of the falling body is given (A) The linear momenta of the
by :
n-particles are constants of
− mg
(A) v = motion
b
(B) v = − mgt + b (B) The angular momenta of the
n-particles are constants of
(C)
motion
− bt
− mg m bt (C) The angular momenta of the
(D) v = e +
b m
n-particles are not constants of
15. Due to Coriolis force :
(A) In northern hemisphere, right motion
banks of the rivers are raised
(D) The energy of the system
to a slightly higher level than
the left banks depends on the angular
(B) In southern hemisphere, right momenta alone
banks of the rivers are raised
to a slightly higher level than 17. A triatomic linear molecule AB2 is
the left banks performing small oscillations. The
(C) In northern hemisphere left
atomic displacements in symmetric
banks are raised to a slightly
higher level than the right stretching mode are :
banks
(A) B A B
(D) The river banks are of equal
height in both the northern and (B) B A B
southern hemisphere (C) B A B
[Right and left are defined with
(D) B
respect to direction of river flow] A B
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18. A sphere of radius ‘a’ has a volume 20. At a point at a distance r from the
charge density ρ (r) = A r ½ , where
uniformly charged infinite plane,
‘A’ is a constant and r is the distance
the magnitude of the electric field
from the centre of the sphere. The
is ................. .
electric field magnitude at a distance
(A) 0
r < a from the centre varies with
r as : (B) inversely proportional to r
(A)
−1 (C) inversely proportional to r2
r2
1 (D) independent of r
(B)
r2
21. A particle enters uniform constant
3
(C)
r2 magnetic field region with its initial
(D) r −2
velocity parallel to the field
19. A point charge of magnitude ‘q’ is
direction. Which of the following
at a distance ‘d’ from grounded
statements about its velocity is
conducting infinite plane. The
correct ?
electrostatic energy stored in the
system is ............... . (A) There is change only in
(A) 0 magnitude
− q2 (B) There is change only in
(B)
4 π ∈0 d
direction
2
−q
(C) (C) There is change in both
8 π ∈0 d
magnitude and direction
− q2
(D)
16π ∈0 d (D) There is no change
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22. Which of the following represents 24. Which of the following relations
Coulomb gauge condition ? describes the conservative character
of electrostatic field E ?
(A) ∇ . A = 0
ρ
(A) ∇.E =
(B) ∇ × A = 0 ∈0
(B) ∇ × E = 0
∂φ
(C) ∇ . A = − ∈0 µ0 ∂ρ
∂t (C) ∇ . J + =0
∂t
(D) ∇ × A = B
∂E
(D) ∇ × B = µ0 J + ∈0 µ0
∂t
23. Current ‘I’ flows through a circular
25. An electromagnetic wave is
wire loop of radius ‘a’. The radius
propagating with speed ‘c’. The
of the wire is ‘r’. The volume current
associated electric and magnetic
density at a point in the wire
is ............... . fields share the energy of this
electromagnetic wave in the
(A) 0
ratio ............... .
I
(B) π a2
(A) 1 : 1
I (B) c : 1
(C)
π r2
(C) 1 : c
I
(D) (D) 1 : c2
(2πa) (π r 2 )
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26. If [ x, p] = ih , the value of [ x3 , p]
28. Which of the following is an eigen
is :
(A) 2 ih x 2 function of Lz ?
(B) −2 ih x 2
(A) cos φ
(C) 3 ih x 2
(D) −3 ih x 2 (B) sin φ
Ψ(x)
(C) cos2 φ
+a
x (D) e2iφ
–a
27.
29. Consider a particle of mass m
moving in the potential,
The figure shows one of the possible
1
energy eigen functions Ψ(x) for a V( x) = ∞ for x ≤ 0
2
1
particle in infinite square well = mω 2 x2 for x > 0
2
potential V = 0 for |x| < a and
V = ∞ for |x| > a. If the energy eigen- The ground state wave function
value of this state is 2 eV, what is
Ψ0(x) of the particle is given by :
the energy eigen-value of the
particle in the ground state ? 2
(A) ψ 0 ( x) = N 0 x e−αx
(A) 0 eV
2
(B) ψ 0 ( x) = N 0 e−αx
(B) eV
2
1 (C) ψ 0 ( x) = N 0 x e+αx
(C) eV
2
2
(D) 1 eV (D) ψ 0 ( x) = N 0 e+αx
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30. The Pauli matrices : 32. What is the degeneracy of the
0 1 0 −i third excited state of a particle in
σx = , σy =
i 0
,
1 0 3-dimensional isotropic harmonic
1 0 oscillator potential ?
σz =
0 −1
.
(Note : The ground state is not an
(A) Anticommute
excited state.)
(B) Commute
(C) Neither commute nor anti- (A) 10
commute
(D) Commute as well as anti- (B) 6
commute (C) 4
31. A system, with an unperturbed
Hamiltonian ∧H 0 is subject to a (D) 3
perturbation H1 where :
33. In scattering theory, the Born
15 0 0
∧ approximation and partial wave
H 0 = E0 0 3 0
analysis are usually used for :
0 0 3
(A) Both approximations are used
0 0 0
∧ E0 for low energy scattering
and H1 = 0 0 1
100
0 1 0 (B) Born approximation for high
The eigenvalue of the non- energy and partial wave
degenerate state upto first order in analysis for low energy
perturbation is given by : scattering
1
(A) 15 + E (C) Both approximations are used
100 0
for high energy scattering
1
(B) E (D) Born approximation for low
100 0
energy and partial wave
(C) 15 E0
analysis for high energy
1
(D) 3 + E scattering
100 0
10
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35. The Gibbs’ free energy ‘G’ of a system
34. Consider a system of three non-
maintained at a temperature ‘T’
interacting identical spin ½ particles satisfies the following relation with
the pressure ‘P’, the volume ‘V’, the
that are in the same spin states internal energy ‘U’ and the entropy
‘S’ of the system :
| s, ms > ≡ |½, ½ > and confined to (A) G = PV – TS
(B) G = U + PV – TS
move in a one-dimensional infinite
(C) G = U – PV + TS
potential well of length a, V(X) = 0 (D) S = –kB ln G
36. A gas chamber has a volume of
for 0 < x < a and V(X) = ∞ for other 0.1 m3 and is filled with helium gas
at a pressure of 5 × 106 Pa. Another
values of x. The ground state energy
chamber has a volume of 0.15 m3
and is filled with helium gas at a
E of the system is given by :
pressure of 6 × 10 6 Pa. A tap
connecting the two chambers is then
3 π 2h 2
(A) E = opened. Assuming that helium is a
2ma2
monatomic ideal gas and the walls
5 π 2h 2 of the chambers to be adiabatic and
(B) E =
2ma2 rigid, the final pressure of the system
will be :
2 2
7π h
(C) E = (A) 5.5 × 106 Pa
ma2
(B) 5.6 × 106 Pa
(C) 5.4 × 106 Pa
5 π 2h 2
(D) E = (D) 5 × 106 Pa
ma2
11 [P.T.O.
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37. Consider a system of N non-
39. The critical temperature TC for the
interacting atoms, each having an
Bose-Einstein condensation depends
orbital angular momentum J = 2.
A constant magnetic field H is on the density ‘n’ of the gas as :
applied along the z-axis. The total
(A) n1/3
number of microstates of the system
is :
(B) n2/3
(A) 5N
(C) n
(B) N5
(C) 2N (D) n4/3
(D) 5N 40. The Fermi wave-vector KF of an
38. Two identical indistinguishable ideal gas of N molecules enclosed in
particles are to be distributed over
a volume V at T = 0ºK, obeys the
three energy states. The number of
relation :
ways of distribution for Fermi gas
1/3
and Bose gas, respectively, will N
(A) K F = (const)
V
be :
(B) K F = (const) (N/V )
2
(A) 1, 3
1/2
(B) 6, 3 N
(C) K F = (const)
V
(C) 3, 6
2 N
(D) K F = (const)
(D) 1, 6 V
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41. Consider a paramagnetic salt with 43. Surface barrier detector (SBD) is
used for the detection of .............. .
1
N magnetic ions each with spin . (A) Alpha particles
2
(B) Beta particles
At T = 0, in the presence of an
(C) Gamma radiation
external magnetic field H : (D) Neutron
(A) All the spins will be parallel 44. A well directed white beam of X-rays
to H is incident on a single crystal. The
transmission beam will show :
(B) All the spins will be antiparallel
(A) spots arranged in a regular
to H pattern
(C) Half of the spins will be parallel (B) a ring pattern
to H and half of them (C) a random distribution of spots
(D) extended lines
antiparallel to H
45. In a Q-meter, a distributed
=−3
xx 1=
C πC/ 2
4 (D) The spins will be randomly
2 capacitance of coil is measured by
2 oriented changing the capacitance of a
tuning capacitor. The values of
42. The Stefan-Boltzmann law for the
tuning capacitors are C1 and C2 for
radiation of energy from a black
resonant frequencies f1 and 2f 1
body is given by u ∝ T x , where u respectively. The value of distributed
is the energy density and T is the capacitance is :
temperature of the black body. Here (A)
x is given by :
C1 − 2C2
(A) (B)
3
(B) C1 − 4C2
(C)
3
(C)
C1 − 3C2
(D) (D)
2
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46. Lasing transition in He – Ne laser 49. The vapour diffusion pump works in
giving red light occurs in the
the following region of air flow :
following levels :
(A) 3d → 2 p (A) molecular flow
(B)
(C) (B) turbulent flow
(D)
(C) lamellar flow
47. The noise generated from the
movement of charge carriers as they (D) viscous flow
cross the p-n junction or arrive at
50. When the phase difference between
electrode surface is :
(A) thermal noise the voltage applied to the X and Y
(B) flicker noise
plates of CRO is equal to 180º, the
(C) shot noise
shape of the Lissajous figure
(D) environmental noise
48. The body-centered cell of a crystal observed on the screen of CRO is :
has two atoms of the same kind
(A) A straight line with a positive
located at (0, 0, 0) and (½, ½, ½).
Its crystal structure factor F in terms slope
of atomic scattering factor f when
(B) A straight line with a negative
(h + k + l) is even is :
(A) F = 2f slope
(B) F = 0
(C) Ellipse
(C) F = f
(D) F = 4f (D) Circle
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ROUGH WORK
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ROUGH WORK
16Official key not published for this paper.
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Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.