MH SET 2013: 1 December, Paper III, Physics
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DEC-32313/III 2
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DEC-32313/III
PHYSICS
Paper III
Time Allowed : 2½ Hours] [Maximum Marks : 150
Note : This Paper contains Seventy Five (75) multiple choice questions. Each
question carries Two (2) marks. Attempt All questions.
3. A coin is loaded such that “heads”
1. The polar plot of the equation
occur with twice the frequency as
r = aθ “tails” when it is tossed. A second
coin is an ideal coin. What is the
represents :
probability that when both the coins
(A) circle are tossed simultaneously two “tails”
(B) spiral would occur ?
(C) gaussian (A) 0.167
(D) parabola (B) 0.333
(C) 0.5
2. The minimum order of the
polynomial that fits exactly to 5 data (D) 0.25
set points is : 4. The value of ∇2 (r 2 ) is :
(A) 1 (linear) (A) 3
(B) 2 (quadratic) (B) 6
(C) 4 (quartic) (C) 2r
(D) 5 (quintic) (D) zero
3 [P.T.O.
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5. y(x) satisfies the differential 7. Consider a simple pendulum
equation. oscillating in a plane. The pendulum
bob has mass m and is suspended
d2 y dy
2
− 2 + y = 0 by string of length ‘l’. If θ is the
dx dx
angle made by the string with the
One solution of this equation is Aex.
vertical, then the kinetic energy of
The second linearly independent
the system in plane polar co-
solution is :
ordinates is given by :
(A) e–x
1
(B) xex (A) T = ml2
2
(C) xe–x (B) T = mgl cosθ
(D) x2 + x 1
ml2 θ& 2
(C) T =
2
1
6. f ( z) = , a > 0 . The integral
z 2
+ a2 1
(D) T = m θ& 2
2
of f(z) over a contour comprising the
8. The conjugate momentum pθ of a
real axis a semi-circle of infinite
simple pendulum of mass m
radius in the upper half plane is :
suspended from a support by a string
2π
(A) of length l is given by :
a
2 πi (A) mlθ&
(B)
a
(B) mθ&
π
(C) (C) ml 2θ&
a
(D) ml 2
(D) zero
4
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9. If two particles of equal mass m
10. If a particle of mass m moves under
collide elastically with each other
the action of a gravitational potential
and scatter off, then the following
MG
V(r) = − , then the following
R
statement is correct in the center of
mass frame : statement is correct :
(A) the velocities of the two particles (A) The motion of the system is
are interchanged after the
confined to a plane
collision
(B) The energy of the system is the
(B) the magnitudes of the velocities
only conserved quantity
of the two particles are
unchanged by the collision (C) The motion of the particle is
(C) the two particles move off always bounded
together after the collision
(D) There are no initial conditions
(D) the particle with the larger
for which the particle can be
velocity comes to a rest,
execute uniform circular
whereas the other particle
motion
stays in motion
5 [P.T.O.
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11. Consider the motion of a planet
13. The energy levels of one-
moving about the run under the
action of gravity :
(A) The period of rotation of the dimensional harmonic oscillator
planet around the center of
force is proportional to the 1 2
with potential v( x) = kx are
square of the semi-major axis 2
of the elliptical orbit.
(B) The areal velocity is directly 1
proportional to the angular given by hν n + with n = 0, 1,
2
momentum of the planet
(C) The period of revolution is
proportional to L2. 2, 3.... If the potential is changed to
(D) The area of the elliptical orbit
1 2
is proportional to ‘L’. v(x) = ∞ for x < 0 and v( x) = kx
12. Consider a particle moving under 2
the action of the potential in the for x > 0, the energy levels now, will
figure below :
be given by :
γ(r) E1
3
(A) hν n +
E2 = 0 2
E3 1
(B) 2hν n +
2
E4
Bounded motion is seen at the 1
(C) hν n + , n odd only
energy. 2
(A) E1 + E3
(B) E3 and E4 1
(C) E1 and E4 (D) hν n + , n even only
2
(D) E 2 only
6
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→ → → → 16. A state of a system with spherical
14. The value of operator r . p − p . r
symmetric potential has zero
in quantum mechanics is :
uncertainty in simultaneous
(A) ih
measurements of operators Lx and
(B) zero L y. Which of the following
(C) 3 ih statements is true ?
(A) Such a state can never exist
∂ ∂ ∂
(D) + +
∂x ∂y ∂z (B) The state must be l = 0 state
(C) The state has l = 1 with
15. The ground state energy of a
m = 0
quantum mechanical system is (D) The state can not be an
always : eigenstate of L2 operator
17. Which of the following is an
(A) Suppressed (lowered) due to
eigenfunction of Linear momentum
second order perturbation h ∂
operator , such that it describes
i ∂x
(B) Suppressed (lowered) due to a particle moving in free space in
first order perturbation the direction of negative x-axis, with
zero uncertainty in the linear
(C) Raised due to second order
momentum ?
perturbation (A) cos kx
(B) e ikx
(D) Raised due to first order
(C) ekx
perturbation (D) e –ikx
7 [P.T.O.
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18. The wave function for identical |E B|
20. The dimensions of a quantity µ0
particles is symmetric under particle
are :
interchange. Which of the following
(A) ML2 T–2
is a consequence of this property ?
(B) ML2 T–3
(A) Pauli-Exclusion principle (C) ML0 T–2
(B) Bose-Einstein condensation (D) ML0 T–3
(C) Heisenberg uncertainty 21. An electromagnetic wave going
principle through vacuum is described by
E = E0 cos ( kz − ωt) and
(D) Bohr-correspondence principle
B = B0 cos( kz − ωt) . The relation
19. A point charge q is kept at a distance between E0 and B0 is :
of 2R from the centre of a grounded ω
(A) E0 B0 =
conducting sphere of radius R. The k
image charge and its distance from (B) E0 B0 = ωk
the centre are respectively : (C) E0 K = B0 ω
(D) E0 ω = B0 k
R
(A) − q and
2 22. Electric field at large distance r, from
q R the electric dipole is proportional
(B) − and
2 2 to :
R (A) r2
(C) − q and
4
(B) r–2
q R
(D) − and (C) r–3
2 4
(D) r–4
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23. An electron enters an uniform 25. The Fermi function of a gas of free
electric field region with its velocity electrons has the form :
(A) a = const., ∈ = energy
perpendicular to the direction of the
1
(B)
field. In the field region, the ∈ + a2 a = const., ∈ = energy
2
trajectory of the electron is : a
(C) a = const., ∈ = energy
∈
(A) linear (D) H(∈ < ∈f)
(B) circular where
H (∈ < ∈f) = 1
(C) parabolic
if ∈ ≤ ∈f
(D) helical H (∈ < ∈f) = 0
2 if ∈ ≥ ∈f
e − a∈ 24. An electric field associated with an
26. A perfect gas initially occupies a
electromagnetic radiation is :
volume ‘V’ with the number of
i(kz − ωt)
E = ( ˆxEx + ˆyEy) e . If E y = iE x ,
particles ‘N’ and energy ‘E’. The
then the electromagnetic radiation
volume is now doubled, keeping ‘N’
is : and ‘E’ constant. The change in
(A) plane polarized entropy will be :
(A) NkB ln 2
(B) circularly polarized
(B) NkB ln V
(C) elliptically polarized (C) 2NkB ln V
1
(D) unpolarized (D) NkB ln 2V
2
9 [P.T.O.
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27. If the temperature of a black body 30. Three distinguishable particles have
a total energy of 9∈. These particles
enclosure is doubled, the total
are distributed over the energy
number of photons in the enclosure
states with energy 0, ∈, 2∈, 3∈ and
increases by a factor of : 4∈. The total number of microstates
(A) 2 will be :
(B) 4 (A) 3
(B) 1
(C) 6
(C) 10
(D) 8
(D) 6
1
28. Consider a system of spin − 31. The noise figure of an amplifier is
2
particles with magnetic moment µ 3dB. Its noise temperature will be
each. In an applied magnetic field, about :
(A) 145 K
the spin can either be parallel or
(B) 290 K
antiparallel to ‘H’ with equal
(C) 580 K
probability. If there are 10 such (D) 870 K
particles, the total number of 32. Resonance frequency for a free
microstates will be : electron in a magnetic field with
B = 1 tesla is :
(A) 2 10
(A) 28.00 GHz
(B) 10 2
(B) 14.00 GHz
(C) 20 (C) 20.00 GHz
(D) 10 (D) 2.80 GHz
29. For a photon gas, the chemical 33. Which of the following detectors is
used for the measurement of energy
potential is :
of a particle ?
(A) Large and negative
(A) Ionisation chamber
(B) Zero (B) G.M. counter
(C) Equal to Fermi energy (C) Proportional counter
(D) Large and positive (D) Cerenkov counter
10
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34. Which of the following gauge can 37. The minimum value for emitter
measure vacuum in the range bypass capacitor C2 in the following
10–10 to 10–3 torr ? amplifier is..........................[operating
(A) McLeod gauge
frequency 2kHz–10 kHz]
(B) Pirani gauge
(C) Penning gauge
(D) Ionization gauge
R1 22 kΩ RC = 1 kΩ
35. In a Millikan oil-drop experiment, C3
one of the drops falls at speed V C1 Vout
without field and rises at speed V
with field E applied. If the field is 6.8 kΩ
R2
made E/2, the drop will : ~ 560 Ω RE C2
(A) fall with speed V/4
(B) rise with speed V/2
(C) rise with speed 3V/2
(D) remain steady
36. An oscilloscope is on AC mode with
no input. If you touch the input a (A) 1.42 F
fifty Hertz signal is seen on the
screen, what is the origin and how (B) 1.42 mF
does it get coupled to the input ?
(C) 1.42 µF
(A) It originates from the power line
and is coupled through (D) 1.42 PF
conducting air
(B) It originates from the power line 38. What kind of MOSFET mode can be
and is coupled through used in the switching mode ?
capacitor formed with air as
dielectric (A) Depletion mode
(C) Originates from the power (B) Cut-off mode
supply of the oscilloscope
(D) Originates from our body as a (C) Saturation mode
result of electrical activity in
(D) Enhancement mode
the heart
11 [P.T.O.
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39. For a 12-bit A/D converter the range 42. A voltage source VAB = 40 sin ωt
of input signal is 0 to + 10V. The is applied to the terminals A and B
voltage corresponding to 1 LSB of the circuit shown below. The
is : impedance by the circuit across the
(A) 0 terminal A & B is :
(B) 0.0012 V A
(C) 0.0024 V 100 kΩ
(D) 0.833 V 40 sin ωt ~
40. For one of the following conditions, 100 kΩ
clocked J-K flip-flop can be used as
B
DIVIDE BY.2 circuit when the pulse
(A) 50 kΩ
train to be divided is applied at clock
input : (B) 100 kΩ
(A) J = 1, K = 1 and the flip-flop
(C) 150 kΩ
should have active HIGH inputs
(B) J = 1, K = 1 and the flip-flop (D) 200 kΩ
should have active LOW inputs 43. For the logic circuit shown in figure
(C) J = 0, K = 0 and the flip-flop the required input condition (A, B,
should have active HIGH inputs C) to make the output X = 1 is :
(D) J = 0, K = 0 and the flip-flop
should have active LOW inputs
41. The following can be used a delay
circuit :
(A) Astable multivibrator
(A) 1, 0, 1
(B) Bistable multivibrator
(B) 0, 0, 1
(C) Schmitt trigger circuit (C) 1, 1, 1
(D) Monostable multivibrator (D) 0, 1, 1
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44. Estimate the values of Ic, Vc in the 46. The following circuit acts as a :
following circuit :
RB
D1
A
Vout
B
D2 RE
(A) NAND gate
(A) Ic = 5.17 mA Vc = 0 V
(B) NOR gate
(B) Ic = 98 µA Vc = 392 mV
(C) Ic = 4 mA Vc = 16 V (C) AND gate
(D) Ic = 4 mA Vc = 4.7 V
(D) OR gate
45. The output voltage for the following
Op-Amp circuit is :
47. The shortest wavelength of spectral
R1 = 10 kΩ Rf = 12 kΩ
+3V line in Lyman series is 912 Å. The
R2 = 10 kΩ
–2V – shortest wavelength of the spectral
R3 = 10 kΩ Ro
+4V +
line of the Paschen series will be :
(A) 8208 Å
(B) 8028 Å
(A) – 3.6 V
(B) + 3.6 V (C) 8828 Å
(C) + 4.2
(D) – 4.2 (D) 8820 Å
13 [P.T.O.
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48. The normal modes of vibration of 51. Transition for the sodium D2 line
(589.0 nm) is :
CO2 molecule are observed at 1330
(A)
2
P32 → 2S1 2
cm–1, 667cm–1 (doubly degenerate)
and 2349 cm–1. The total zero point (B)
2
P1 2 → 2S1 2
energy of the CO2 molecule is : (C)
2
D3 2 → 2P1 2
(A) 31.1 eV (D)
2
D5 2 → 2P3 2
(B) 0.031 eV 52. How many electrons can be put in
(C) 0.311 eV an atomic shell corresponding to
(D) 3.11 eV n = 5 ?
[data : h = 6.625 × 10–34 J.s, (A) 10
c = 3×108m/s] (B) 24
49. How many normal modes of (C) 36
vibration does the water molecule (D) 50
possess ? 53. How many spectral lines appear in
the Zeeman splitting of D3 2 → P1 2
2 3
(A) 9
transition of sodium ?
(B) 3
(A) 2
(C) 4
(B) 3
(D) 6
(C) 1
50. Transition for the sodium D1 line
(D) 4
(589.6 nm) is :
54. What is the ground state of a helium
(A)
2
P3 2 → S 1 2
2
atom ?
2
(B)
2
P1 2 → 2
S1 2 (A) P1 2
(B) 1S0
(C)
2
D3 2 → 2P1 2 1
(C) S12
(D)
2
D5 2 → 2
P3 2 (D) 2S0
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57. The magnetic susceptibility of a
55. Consider a hydrogen atom whose
paramagnetic substance shows the
electron is in the state with quantum following behaviour as a function of
numbers n = 3, l = 2. To what lower ‘T’.
(A) Hyperbolic behaviour
states are radiative transitions
(B) Parabolic behaviour
possible ? (C) is identically zero
(A) n = 3, l = 1 and n = 2, l = 1 (D) shows constant behaviour
58. The plasma frequency ωp for the
(B) n = 3, l = 2 and n = 2, l = 0
electron gas is :
(C) n = 2, l = 0 and n = 1, l = 0 1
(A) ∝
m
(D) n = 3, l = 0 and n = 1, l = 0 (B) ∝ m
(C)
56. A three level system of atoms has
∝m 2
(D) independent of m,
N1 atoms in level E1, N2 in level
where m is the mass of electron.
E2 and N3 in level E3. If N2 > N1
59. The energy dissipated per second in
> N 3 and E 1 < E 2 < E 3, laser a dielectric per unit volume is
emission is possible between the proportional to :
levels : (A) ω
1
(A) E3 → E1 (B)
ω
(B) E2 → E1 (C) ω2
1
(C) E3 → E2 (D)
ω2
(D) E2 → E3 where ω is the angular frequency
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62. The first Brillouin zone of the body-
60. The probability of occupation of an
centered cubic lattice is :
energy level E, when E – EF = kT,
(A) truncated octahedron
is :
(B) rhombohedron
(A) 0.73 (C) tetrahedron
(B) 0.63 (D) rhombic dodecahedron
63. The magnetic field B inside a super-
(C) 0.27
conductor maintained at a
(D) 0.50 temperature T less than the critical
temperature Tc :
61. A unit cell of a cubic lattice has an
(A) behaves linearly as a function
edge of 3.6Å. How many unit cells
of the applied field H , up to a
are present in a lump of 1cm3 ? critical field Hc
(B) vanishes identically upto the
(A) 2.14 × 1022
critical field Hc
(B) 1.42 × 1023
(C) is a non-zero constant below Hc
(C) 6.00 × 1012 (D) shows parabolic behaviour
below Hc and a gap above Hc
(D) 6.00 × 1023
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66. In a semiconductor, the effective
64. Above Curie temperature, the
masses of holes and electrons are
ferromagnetic material exhibits
identical. The position of the Fermi
B-H curve in the form of :
level at absolute zero temperature
(A) B–H loop is :
(A) near the top of the valence band
(B) Straight line
(B) near the bottom of the
(C) Circle
conduction band
(D) Ellipse
(C) midway between valence and
65. A d.c. voltage of 1 µV applied across conduction bands
a junction formed by sandwiching a (D) below the valence band
thin layer of insulator between two 67. Among the following nuclei, which
superconductors causes rf current has the maximum binding energy
per nucleon ?
oscillations of a frequency of :
16
8 O , 56
26 Fe
208
, 82 235
Pb , 92 U
(A) 48.36 MHz
16
(A) 8 O
(B) 4836.00 MHz
56
(B) 26 Fe
(C) 4.836 MHz 208
(C) 82 Pb
(D) 483.6 MHz (D) 235
U
92
17 [P.T.O.
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238
68. Radius of nucleus 27Al is 3.6 Fermi. 70. The decay chain for the 92 U nucleus
involves eight α-decays and six
The approximate nuclear radius of
β– decays. The final nucleus at the
64Cu is :
end of the process will have :
(A) 8.5 Fermi
(A) Z = 88, A = 206
(B) 7.2 Fermi
(B) Z = 84, A = 224
(C) 4.8 Fermi (C) Z = 82, A = 206
(D) 3.6 Fermi (D) Z = 76, A = 200
69. The magic numbers in nuclear 71. Which of the following particles was
assumed to be involved in β-decay
physics arise mainly due to :
process, in order to explain
(A) dipole-dipole interaction
continuous spectrum of β-rays ?
(B) spin-orbit interaction
(A) Higg’s Boson
(C) short range character of nuclear
(B) Neutrino
force
(C) Pion
(D) coulomb interaction (D) Muon
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72. Which of the following statements 74. What is the possible values of Iso
is true for a compound nuclear
Spin -I and its Z-component I3 for
reaction ?
(A) The formation of the compound the following system of a particle
nucleus and its break-up are
_
independent π + p
(B) The break-up of compound
1
(A) I3 = − , I = 1
nucleus is instantaneous (very 2
short life time)
1 3
(B) I3 = − , I =
(C) The break-up of a compound 2 2
nucleus depends on the channel
3 1
of its formation (C) I3 = − , I = −
2 2
(D) The Q-value of compound 1 1
(D) I3 = , I =
nuclear reaction is always 2 2
negative
75. The quark structure of ∆++ is :
73. According to the liquid-drop model,
the surface energy part is (A) UUU
proportional to :
(A) A2/3 (B) UdU
(B) A1/3
(C) SSS
(C) A
(D) A 2 (D) ddd
19 [P.T.O.
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ROUGH WORK
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Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.