Rajasthan Public Service Commission 2016
Paper PhysicsII
Ques: 150
Time: 3 Hours
Ques
The method of dimensional analysis can be used to derive which of the following relation




....a. ... .. ... .. ...... ....a.... .... .. ...... ..... .. .... ..




Ques
The pair having the same dimension is
velocity angular velocity
Work, Torque
Angular momentum work
Angular momentum, Linear momentum
... ..... ... ....... .... .. .. ..
..., ..... ...
..... .. ......
..... ....., .....
..... ....., ..... .....
Ques
3
5
4
8
3
5
4
8

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9
9
0
1
9
9
0
1
Ques
Which of the following matrices is a Hermitian matrix




....a. .......g ... .. ... .. ......... ...... ..




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Choose wrong recurrence relation for Hermite Polynomials




...... ..... .. .... ... ........ (........) ..a.... ........




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Ques :17
How many independent components can an antisymmetric tensor of rank two have in n dimensional space




n ...... ....I. ... ........ ..... (....) .. ........... ...... (......) .. ...... ....... ... ..g..





Ques :18
Choose the correct statement for cyclic group
Group of order two may or may not be cyclic.
Group of order three is always a cyclic group.
Group of order four is always a cyclic group.
Group of order four is never a cyclic group.
...... .... (....) .. .... .... ... ......
..... .. .. .... (....) ...... .. .. .... .. .. ..... ..
..... ... .. .... (....) .... ...... .... ..
..... ... .. .... (....) .... ...... .... ..
..... ... .. .... (....) ... .. ...... ..... .... ..
Ques :19
The group formed by three cube roots of unity is
Only Non Abelian
Non Abelian and non cyclic
Abelian and non cyclic
Abelian and cyclic
.... .. ... ......g .. .... (....) ..
.... ........
........ ... .......
...... ....... .......
...... ... ......
Ques :20








Ques :21

Choose the wrong relation for forward difference operator




... ..... ...... (........ ......... ...... .. .... ... ... ......




Ques :22
13.6
15.5
15.9
16.4
13.6
15.5
15.9
16.4
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Ques :24
5
3
zero
4
5
3
.....
4
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Ques :26
From a box containing a white and b black balls, one ball is drawn at random and set aside . The
expexted number of white balls left in the box is





.. ..... ... a .... . b ..... ..... ... . ..... .. .. .... ...`..... ... .. .... ...... .. .. ... .... ..
.. ..... ... ... .... .....g ... ........ ...... ....



Ques :27








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Ques :31
The mass of a body measured in a lift at rest is found to be m. If the lift is going up with an acceleration then
mass of the body in the lift is given by




..... ..... ...... ... .. ..... .. ........ m .... .... .. .... .. ...... a ..... .. ... ... .. .... ...
.. ...... ... ..... .. ........ ....




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Ques :36
The maximum possible angle of scattering for equal masses in laboratory system is




......... ...... ... .... ........ .. ...g .. .... ..... .... ......... ... ..




Ques :37
a symmetric tensor of rank two
an asymmetric tensor of rank two
an asymmetric tensor of rank one
a symmetric tensor of rank one
..... (....) .. .. ...... ...... (......)
..... (....) .. .. ....... ...... (......)
..... (....) .. .. ....... ...... (......)
..... (....) .. .. ...... ...... (......)

Ques :38








Ques :39
If the Lagrangian L is not an explicit function of time then
Hamiltonian H is a constant of motion.
Hamiltonian H is not a constant of motion.
Angular momentum is a constant of motion.
Angular momentum is not a constant of motion.
.... .......... L ... .. ......I. ... . .. ..
......a....... H .... .. ........ .... .. .
......a....... H .... .. ........ ..... .... .. .
..... ..... .... .. ........ .... .. .
..... ..... .... .. ........ ..... .... .. .
Ques :40
The Lagrangian of the simple pendulum is




... .... .. ........... ..




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Ques :42
0.5 cm
4.0 cm
2.0 cm
5.0 cm
0.5 .....
4.0 .....
2.0 .....
5.0 .....

Ques :43
Choose the correct property of Poision brackets




..... ...... .. .... .... ....... ......




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The invariance of Lagrangian under spatial translations implies the
conservation of linear momentum
conservation of angular momentum
conservation of energy
conservation of parity
...... ........... .. ........ ........... ... ....a.... ... ............. ..
..
.. ..... .. ......
..... ..... .. ......
..... .. ......
.... .. ......
Ques :48








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Ques :51
Equation E pc is valid
for an electron as well as a photon
for an electron but not for a photon
for a photon but not for an electron
neither for an electron nor for a photon
...... E pc .... .... ..
.. ......... ... .. ..... ....g .. ....
.. ......... .. .... ...... .. ..... .. .... .....
.. ..... .. .... ...... .. ......... .. .... .....

.. .. ......... .. .... .. ... ..... .. ....
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2 m
4 m
6 m
8 m
2 m
4 m
6 m
8 m
Ques :56
0.872 c
0.672 c
0.772 c
0.972 c
0.872 c
0.672 c
0.772 c
0.972 c
Ques :57









Ques :58
A body of mass m moving with velocity v hits another body of same mass moving with same speed v but in the
opposite direction and stick to it . The velocity of the compound body after collision is
Zero
v/2
2v
v/4
v ... .. ....... m ........ ... .. ..... .... ........ ... .... ... .. ........ ..... ... ....... ..
.... ..... .. ...... ... .... .. . ..... .. ... ....... ..... .. ... ....
.....
v/2
2v
v/4
Ques :59
Which of the following is Alembert's principle




.....
.a.... .. ........ ....a. ... .. ... .. ..




Ques :60

1
2
3
4
1
2
3
4
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Ques :64
Muliplication of two linear operators is
always commutative
never commutative
not necessarily commutative
always a unit operator.
.. ..
.. .......g .. ......
.... ... ......... .... .. .
... .. ... ......... ..... .... .. .
... ......... .. .. ...a.. ..... .. .
.... .... ...... .... .. .
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Ques :66
If A and B are self adjoint operators which of the following statements is not true
AB BA is self adjoint
i(AB BA)
is self adjoint
AB is self adjoint only if AB BA
AB will never be self adjoint
.... A ... B ... ...... (...a. .......) ...... .. .. ....a. ... .. ... .. ... .... ..... ..
AB BA ... ...... ....
i(AB BA)
... ...... ....
AB ... ... ...... .... .. AB BA ..
AB ... .. ... ...... ..... ....
Ques :67
Choose the wrong statement for projection operator
Two projection operator are said to be orthogonal if their product is zero
The product of two commutating projection operator is also a projection operator.
The sum of two projection operator is always a projector operator

...... ...... .. .... ... ... ......
.... .. ...... .......g .. ...... ..... .. .. ...... ....a.. ...... .
.. ... ......... ...... .......g .. ...... .. ...... ...... .... .. .
.. ...... .......g .. ... .... ...... ...... .... .. .

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Ques :71
The probability of finding a simple harmonic oscillator in the classical limit is The oscillator is in its normal
state
50%
64%
84%
92%
.. ... ..... .... ... ..... ....a.. .... ... .... ... ......... ..
.... ..... ....... ...... ...
..
50%
64%
84%
92%
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Ques :73
Choose wrong property of Paulispin
matrices




...........
(....) ......... .. .... ... ....... ......




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The ClebschGordon
coefficients are
all real
all imaginary
real and imaginary both
necessarily integer
.............
...... .... ...
... .........
... ...a.....
......... ... ...a..... ....g
...a.. ... .. .......
Ques :76
One dimensional momentum space wave function can be expressed as




.. ...... ..... ....I. .... ... .. ...... .... .... ...... ..




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The first order effect of a time dependent perturbation, varying sinusoidally in time,lead to
absorption of energy only
emission of energy only
emission and absorption of energy
No change of energy
... .. ... .......... ... .. ........... .. ... .. ... .... .... (........) .. .... ..... .....
.... ..
.... ..... ...... ..
.... ..... ........ ..
..... ........ ... ...... ..
..... .. ............ .... ..
Ques :81
Which of the following experiment is a direct evidence for the quantized nature of energy states in atoms
DavissonGermer
experiment
SternGerlach
experiment

FrankHertz
experiment

....a. ... .. ..... ..... ........ ... ..... ........ .. ........... .... .. .... ..... ..
............
.....
.............
.....

......
..... .....
Ques :82
The transition probability per unit time as per Fermi Golden Rule is



.... ...a.. ..... .. ...... ..... ..... ... ...... ... ......... .... ..



Ques :83
The ground state JWKB energy level of freely falling particle in earth's gravitational field is given by [here c
is constant




...... .. ...`..... ..... ... ..... ... .. .... .. .. ... ...... .......a......... (JWKB) ..... .... .. .... c
........ ..




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1
2
3
4
1
2
3
4
Ques :86
For a system of two identical particles each of which can be in one of n quantum states the number of
symmetric states of system are





.. ...... ...g .. ...... .. .... .... ....... .. n ....... ........ ... .. ..... .. .. ...... ... ..
.... .. ...... ... ...... ........ ... ...... ..




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Ques :88
A Dirac particle has a spin of




...... .. .. .... ..





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Ques :90
The d'Alembertian operator is




.....
.a...... ...... ..




Ques :91
A system absorbs 35 J of heat and in the process it does 11 J of work . The system follows another
thermodynamics path to same final state from same initial state and does 15 J of work. The heat transferred

in the process is
39 J
31 J
61 J
35 J
.. ..... ... ...... 35 J ..I.. ........ .. 11 J ..... .... .. . ...... .... ......a.. ... ......
...... .. .... .... ..I....... .. .. 15 J ..... .... .. .. .. .. .. ..I.. ......... .. ... ....
39 J
31 J
61 J
35 J
Ques :92
40 J
72 J
100 J
180 J
40 J
72 J
100 J
180 J
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Ques :94
The combined form of first and second law of thermodynamics is given by
TdS =dU PdV
dQ TdS PdV
dU TdS dQ
TdS dU PdV
..I......... .. .... . ........ ..... .. ....... ... .. ....a. ..a.... ...... ..... .. .... ..
TdS =dU PdV
dQ TdS PdV
dU TdS dQ
TdS dU PdV
Ques :95
One mole of gas expand isothermally to four times of its initial volume. The change in entropy in terms of gas
constant R is
0.602 R
1.387 R
2.774 R
Zero
.. ... ... .... ......... .... .. ... .... .. ....... ... .. ........ .... .. .. ........ ... ...
........ R .. ...g ... ......... ....
0.602 R
1.387 R
2.774 R
.....
Ques :96
Which of the following is not a correct Maxwell's thermodynamics relation




....a. ... .. ... .. .. .... ........ ..I.......... ..a.... ..... ..





Ques :97
Choose the correct statement for Enthalpy
Enthalpy has dimension of entropy.
For an isobaric process the change in enthalpy is equal to change in its internal energy .
Enthalpy remains constant in a reversible isobaric adiabatic process
Enthalpy always increases in a reversible isobaric adiabatic process
......a.. .. .... .... ... ......
......a.. ... ....... ........ .. .... ..
.. ....... ..... .. .... ......a.. ... ......... ....... ..... ... ......... .. ...a. .... ..


Ques :98
Enthalpy pressure P internal energy U and vloume V have a relation given by
H U PV
H U PV
P H UV
U H P V
......a.. ... ........ ..... U ... .... V ... ..a.... .... ..
H U PV
H U PV
P H UV
U H P V
Ques :99









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Ques :101
For equlibrium of a system which is in contact with heat reservoir of constant pressure and temperature the
value of Gibbs Energy
is always zero
must be minimum
must be maximum
always increases
.. ...... ... ...a....... ..... ..... ... . ... .. ..I....... .. ...... ... .. .. .... .... ..... .. ...

.... ..... ..
....... .... ......
..... .... ......
.... .... ..
Ques :102
Which of the following is not an example of second order phase transitions

Transition of ferromagnetic to a praramagnetic material at curie point.

Transition of superconductor into ordinary conductor in the absence of magnetic field.
Transition of water into vapour at constant temperature and volume.
....a. ... .. ..... ...... ........ ..... .. ........ ...... (.........) ..... ..

....... ... .. ......a..... ...... .. ......a..... ...... ... .........
...a..... ..... ... ........... ... ........ .. ....... .... ... .........
..... ... . .... .. .... .. ...I. ... .........
Ques :103
The ClausiusClapeyron
equation is




.................
...... ..




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Ques :105
Choose the correct relation between partition function Z and Helmholtz free energy F




........ ... Z . ...a....a... ..... ..... F ... .... ..a.... ......




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Ques :107
Which of the following is not a boson





....a. ... .. ..... ..... ..




Ques :108
Three classical particles are to be distributed in four energy levels . The number of possible ways of
distribution are
81
64
20
12
... ....a.. ...g .. ... ..... .....g ... ........ .... .. . ...... .. .... ......g ... ...... ..
81
64
20
12
Ques :109
The Fermi energy at absolute zero temperature is given by




... ..... ... .. .... ..... ......... ... .... ..




Ques :110
The significance of Bose Einstein
and Fermi Dirac
statistics becomes negligible at
low temperature
low temperature and low pressure

high temperature and low pressure
low temerature and high pressure
............
... ....
...... .......... .. ..... ..... .. .... .. ....
....a. ... ..
....a. ... ... ....a. ... ..
.... ... ... ....a. ... ..
....a. ... ... .... ... ..
Ques :111
The chemical potential for Fermions (FermiDirac
statistics) is
always zero
always negative
always positive
may be negative or positive
........ (....
...... ..........) ... ........ .....
.... ..... .... ..
.... ....... .... ..
.... ....... .... ..
....... .... ....... .. .... ..
Ques :112
The expression for electronic heat capacity is



............ ..I......... .. ...... ..



Ques :113









Ques :114
For shorter wavelengths, Plank's radiation law reduces to
Wien's Law
RayleighJeans
Law
Kirchhoff's Law
Stefan's law
..a. ........... .. .... ...... ........ ..... ...... ..... .. .. ..
... .. .....
.......
.. .....
....... .. .....
....... .. .....
Ques :115
Average energy of a Planck's oscillator is





.. ........
..... ... ... ..... ..




Ques :116
400 K
600 K
300 K
200 K
400 K
600 K
300 K
200 K
Ques :117
At T 0 K the probability that a state 0.50 eV above the Fermi level is occupied is
0.5
Zero


T 0 K .. .... ..... .... .. 0.50 eV ... ..... ...... .. ... .... ... ......... ..
0.5
.....


Ques :118









Ques :119
Chemical potential is defined as



......... ..... .. ....a. ..... .. .......... ..... .... ..



Ques :120









Ques :121
125
73
52
23
125
73
52
23
Ques :122
Nuclear forces are in general
Short ranged, attractive and charge independent
Short ranged, attractive and spin independent
Short ranged, repulsive and spin independent
Long ranged, attractive and charge dependent.
......... .. ......... ..
..a. .... .., ..... ... .... .. ........
..a. .... .., ..... ... .... .. ........
..a. .... .., ......... ... .... .. ........
.... .... .., ..... ... .... .. ....
Ques :123
The masses of neutron and proton are 1.0087 u and 1.0073u respectively . If neutrons and protons combine to
form a helium nucleus of mass 4.0015 u ,then the binding energy of the helium nucleus is
7.1 MeV
20.2 MeV
28.4 MeV
36.5 MeV

...... . ........ .. ........ ..... 1.0073 u . 1.0087 u .. . .... ...... . ........ ...... 4.0015 u ........
.. ........ ...... ..... .. .. ........ ...... ... .... ..... ..
7.1 MeV
20.2 MeV
28.4 MeV
36.5 MeV
Ques :124








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Ques :127
According to the liquid drop model when a nucleus is bombarded by neutrons the compound nucleus attains
the given shapes in sequence
ellipsoidal spherical dumbbell
spherical ,ellipsoidal dumbbell
spherical ,dumbbell,
ellipsoidal
dumbbell,
ellipsoidal spherical
.. ...... .. .........g ... ....... .... .... .. .. ... .... ........ .. ...... ....... ...... ...... ....a.
.... .... .... ..
........... ....... ..a...
....... ,........... ..a...
....... ,..a..., ...........
..a..., ........... .......
Ques :128








Ques :129

According to shell model
Nucleons have continous energy states
Nucleons are held in equilibrium under symmetric nuclear forces.
There is no spinorbit
coupling in nucleus.
Nucleons move independently in a central filed.
... .... .. ......
.......... ... ..... ...... ... .... ..
...... ......... ...g .. .... .......... ...a....... ... .... ..
.......... ... ... .........
...... ..... .... ..
.......... ......... ..... ... ....... ... .. .... .... ..
Ques :130
1
1
1
1
1


1

1
1
1
1
1


1

Ques :131
Reflection invariance
Rotational invariance
Gauge invariance
Both Reflection and Rotational invariance
........ ....a....
...... ....a....
... ....a....
........ ... ...... ....a.... ....g

Ques :132








Ques :133
6.42 keV
3.21 MeV
6.42 MeV
3.21 keV
6.42 keV
3.21 MeV
6.42 MeV
3.21 keV
Ques :134









Ques :135
The ground state of deutron may be taken to be a mixture of




........ ... ... ...... .. ... ........ .. ...... ... .... .., .. ...




Ques :136









Ques :137
The spin of Baryons is




........ .. ..... (....) .... ..




Ques :138
Choose the wrong statement for Leptons
The spin of every lepton is 1/2 .
Charged leptons are negatively charged particle.
All leptons are stable particles.
All leptons are acted upon by weak forces.
....... .. .... ... ... ......
... ....... .. .... 1/2 .... .. .
....... ....... ......... .... .. .
... ....... ...... .. .. .
... ....... .. ...... .. ..... .... .. .
Ques :139
charge conservation law
law of conservation of Baryon number
Both charge conservation law and law of conservation of strangeness.
Both conservation law of strangeness and law of conservation of isospin.
.... ...... ..... ..

........ ...... ...... ..... ..
.... ...... ..... ... ........ ...... ..... ....g ..
........ ...... ..... ... ........ ...... (.... .....) ...... ..... ....g ..
Ques :140
29.8 MeV
34.0 MeV
4.1 MeV
39.0 MeV
29.8 MeV
34.0 MeV
4.1 MeV
39.0 MeV
Ques :141
The quark structure of neutron is
u u d
u u s
d d u
d d s
........ ... ....... ...... ..
u u d
u u s
d d u
d d s
Ques :142
GamowTeller
selection rules for Beta decay are




.... ... .. .... ........
... ..... ....a. ..





Ques :143








Ques :144
is always zero
increase with Z but independent of A
decrease with Z but independent of A
increase with Z and A.
.... ..... .... ..
Z .. ... .... .. ....... A .. ....... ..... ....
Z .. ... .... .. ....... A .. ....... ..... ....
Z . A .. ... .... ..
Ques :145









Ques :146








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Positronium is the bound state of an electron and a positron. The most probable decay product of any such
state of positronium with zero spin is
Consider states of zero orbital angular momentum only
4 photon
2 photon
0 photon
1 photon
............ .. ......... . .. ........ ... ... ...... .. . ..... .... ... ............ ...... ..
....... ......... ...... ...... ..
.... ..... ..... ..... ..... .. ........
4 .....
2 .....
0 .....
1 .....
Ques :148
Which one of the following is not a magic nuclei




....a. ... .. ... .. ..... ...... ..... ..




Ques :149
GellmannNishijima
relation is given by



.........
....... ..a.... ..




Ques :150