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fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
PH: PHYSICS
2014
GATE Test Paper
Duration: Three Hours

Maximum Marks: 100

Q. 1 – Q. 25 carry one mark each.
Q1. Consider an anti-symmetric tensor Pij with indices i and j running from 1 to 5. The
number of independent components of the tensor is
(A) 3

(B) 10

(C) 9

(D) 6



Cos  sx 
dx , is
2
2
k

x


Q2. The value of the integral 
(A)

 2  ks
e
k2

(B)

  ks
e
k2

2

Q3. The eigenvalues of the matrix  3
0

(A) 5, 2, -2
Q4.

(B) -5, -1, -1

(C)

3
2
0

 ks
e
k

(D)

  ks
e
k

0

0  are
1 
(C) 5, 1, -1

(D) -5, 1, 1

Which of the following is correct expression of probability current density in one
dimension .

i  d *
i  d *
d 
* d 
(B)

.


.
J

 * .


 .

x
2m 
dx
dx 
2m 
dx
dx 
i   * d
d * 
i  * d
d * 
(C) J x 
(D)

.


.
J


.


.




x
2m 
dx
dx 
2m 
dx
dx 
3
Three fermions of spin
is adjusted in one dimensional harmonic oscillator of
2
frequency  what is energy of ground state configuration .

3
5 
7 
(A)
(B)
(C)
(D)
2
2
2
2
(A) J x 

Q.5

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Hauz Khas, New Delhi-16
1

fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

Q6.

Q7.

Which of the following potential will give not give bound state for energy

0 E  .

k
in three dimensional
r

(A) V ( x)  kx 2

(B) V ( r )  

(C) V ( x)  k x

(D) V ( x)  V0 cosh x  V0

Consider Maxwell’s equations in vacuum in the absence of sources. If the solutions to

 



  



these equations are of the form  r , t   0 exp i k.r  t , B r , t   0 exp i k .r  t



where  0 , 0 and k are constant vectors, then



Q8.







(A) k .  0   0  0

(B) k   0   0  0

(C) d dk  0

(D) k  c

Consider an electric field  existing in the interface between a conductor and free space.
Then the electric field  is
(A) external to the conductor and normal to the conductor’s surface
(B) internal to the conductor and normal to the conductor’s surface
(C) external to the conductor and tangential to the conductor’s surface
(D) both external and internal to the conductor and normal to the conductor’s surface

Q9.

The xoy plane carries a uniform surface current of density   50 xˆ A/m. The magnetic
field (in Wb) at the point z = - 0.5 m is
(A) 10  10–6 Wb

Q10.

(B) 1  10 –6 Wb

(C) π  10–6 Wb

(D) 10π  10–6 Wb

A planet of mass m is moving in a circular orbit of radius ‘ a ’ under central force around
the sun of mass M, such that m << M. The kinetic energy of the planet is
(A)

GMm
a

(B) 

GMm
a

(C)

GMm
2a

(D) 

GMm
2a

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Hauz Khas, New Delhi-16
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fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
Q11.

A bead of mass m is slide down smoothly on a wire of shape z = x2 in the (z, x) plane.
The Lagrangian of the bead is .

Q.12

(A)

1 2
mx 1  x 2  mgx 2
2

(B)

1 2
mx 1  4 x 2  mgx 2
2

(C)

1 2
mx 1  x 2  mgx 2
2

(D)

1 2
mx 1  4 x 2  mgx 2
2

















The Lagrangian for a particle in cylindrical coordinates is given to be
L

1
2
m  2   2 2  z 2 / 1  (  /    V (  )
2





where m is the mass of the particle and λ is a constant. Then which of the following is not
a conserved quantity?
(B) m 2

(A) m



(C) mz / 1   /  2
Q.13



(D)

1
2
m  2   2 2  z 2 / 1  (  /    V (  )
2





Consider the Fermi-Dirac distribution function f E  at room temperature (300K) where
E refers to energy. If E F is the Fermi energy, which of the following is true?
(A) f E  is a step function
(B) f E F  has a value ½
(C) States with E  E F are filled completely
(D) f E  is large and tends to infinity as E decreases much below E F

Q.14

2

Find the average value of v x  iv y for ideal gas at temperature T
(A) 0

(B)

kT
m

(C)

2kT
m

(D)

3kT
2m

Q15. ensemble of N three level systems with energies   1, 0, 1 is in thermal equilibrium at
temperature T. Let   kT  1 .
The partition function is given by
(A) (1+cosh2 )

(B) (1+cos2 )

(C) (1+2cosh2 )

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(D) (1+cosh2)
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Q16.

For a cubic crystal the diffraction line from the planes with (h2+k2+l2) = 8 is observed at
an angle of diffraction 10.23 0. If only one line is observed at an angle lower than this, the
crystal structure is?
(A) Simple Cubic
(B) Body Centered Cubic
(C) Face Centered Cubic
(D) Diamond Cubic Lattice

Q17.

Consider an ideal Fermi gas, with energy spectrum

(p is momentum), contained in

a box of volume V in space of 3 dimension. Which of the following is correct PV relation
for this system?

Q18.

(A)

(B)

(C)

(D)

Which of the following statement about superconductor is not correct?
(A) With appearance of Meisner effect, resistivity disappear
(B) When superconductivity is destroyed with magnetic field, the material will heat.
(C) Superconductivity occurs in material having high electrical resistivity
(D) Critical temperature (T c) decreases with isotopic mass

Q19. In a He-Ne laser, the laser transition takes place in:

Q20.

(A) He only

(B) Ne only

(C) Ne first, then in He

(D) He first, then in Ne

All vibrations producing a change in the electric dipole moment of a molecule yield
(A) Raman spectra

(B) Infrared spectra

(C) Ultra-violet spectra

(D) X-ray spectra

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Q21. Pick the WRONG statement.
(A) The nuclear force is independent of electric charge

 mc 
(B) The Yukawa potential is proportional to r 1 exp 
r  , where r is the separation
 h 
between two nucleons.
(C) The range of nuclear force is of the order of 10-15 m – 10 -14m
(D) The nucleons interact among each other by the exchange of mesons.

Q.22

In the circuit shown in the figure the Thevenin voltage VTH and Thevenin resistance RTH
as seen by the load between point A and B are respectively
2

12 A


B

(A) 4V , 2

(B) 8V , 3

A


VTH

3

4

RTH

A



B

(C) 12V , 3

(D) 16V , 2

Q.23

How many maximum number of electrons can be adjusted in d orbital of hydrogen
atom …………………..

Q24.

An amplifier has a voltage gain of 500 and input impedance 20 KΩ, without any
feedback. Now a negative feedback with β = 0.1 is applied. Its gain and input impedance
(K ohms) with feedback will respectively be …………………..

Q25.

If the nuclear radius of 27Al is 3.6 Fermi, the approximate nuclear radius of 64Cu in Fermi
is …………………..

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Q. 26 – Q. 55 carry two marks each.

Q.26 The solution of the differential equation for
initial conditions y  0   1.1 and

Q.27

dy
dt

d2y
dy
 2  101 y  10.4e x , subject to the
2
dx
dx

 0.9 , is
x0

(A) e  x ( A cos10 x  B sin10 x )

(B) e  x ( A cos x  B sin x )

(C) e  x ( A cos10 x  B sin10 x )

(D) e x ( A cos10 x  B sin10 x)

A binary star system consists of two stars S1 and S2, with masses m and 2m respectively
separated by a distance r. If both S1 and S2 individually follow circular orbits around the
centre of mass with instantaneous speeds v1 and v2 respectively, the speeds ratio v1/v2 is
…………………….

Q.28

A particle of unit mass moves along the x-axis under the influence of a potential,
2

V  x   x  x  4  . The particle is found to be in stable equilibrium at the point . The time

period of oscillation of the particle is
(A)
Q.29


2

(B) 

(C)

3
2

(D) 2

A parallel plate capacitor has circular plates of radius R. It is being charged by a current I.
Then the magnetic induction B at a point between the plates at a distance R/2 from the
axis of the capacitor is:
(a) B 

0 I ˆ

2R

(b) B 

0 I ˆ

4R

(c) B 

0 I ˆ

6R

(d) B 

1
Q30. Consider a system in the unperturbed state described by the Hamiltonian, H0  
0
0
The system is subjected to a perturbation of the form H '  


0 I ˆ

8R
0
.
1 


, when δ<< 1. The
0 

energy eigenvalues of the perturbed system using the first order perturbation
approximation are
(B) (1 + δ) and (1 - δ)

(A) 1 and (1 + 2δ)
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(C) (1+2 δ) and (1 - δ)

(D) (1+ δ) and (1 - 2δ)

Q31. Consider a two level quantum system with energies  1  0 and  1   . The specific heat
of the system is given by
(A)


e  / k B T
k B T 1  e  / k BT 2

(C) 

Q32.

 2 e  / k B T

1  e



 / k B T 2

(B)

2
e   / k BT
k B T 2 1  e  / kBT 

(D)

2
e   / k BT
k B T 2 1  e  / kBT 2

The internal energy of n moles of a gas is given by E 

3
a
nRT  , where V is the
2
V

volume of the gas at temperature T and a is a positive constant. One mole of the gas in
state (T1, V1) is allowed to expand adiabatically into vacuum to a final state (T2, V2). The
temperature T2 is
(A) 1 

a 1 1
  
R  V2 V1 

(B) 1 

2a 1 1
  
3 R  V2 V1 

(C) 1 

2a 1 1
  
3 R  V2 V1 

(D) 1 

1a 1 1
  
3 R  V2 V1 

Q33. Consider the following circuit in which the current gain βdc of the transistor is 100
and VBE  0.7V . Which one of the following correctly represents the collector current IC
and collector-emitter voltage VCE?

 15 V

(A) 12mA, 0.5V
100 k

(B) 14mA, 1V

900 

(C) 16mA, 2V
(D) 18mA, 3V
100 

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Q.34 For the given circuit the frequency above which the gain will decrease by 20 dB per
decade is
(A) 12 kHz

Vin 

10 k


1000pF

(B) 16 kHz

Vout 


1 k

(C) 18 kHz
(D) 20 kHz

2 k

Q.35 In the circuit shown, the ports Q1 and Q2 are in the state Q1 = 1, Q2 = 0. The circuit is
now subjected to three complete clock pulses. The state of these ports now becomes
Q1
(A) Q2 = 1, Q1 = 0
(B) Q2 = 0, Q1 = 1

1

(C) Q2 = 1, Q1 = 1

Q

1

CLK

(D) Q2 = 0, Q1 = 0

Q.36

J

1

K

J

Q2

Q

CLK

Q

1

K

Q

There are only three bound states for a particle of mass m in a one-dimensional potential
well of the form shown in the figure. The depth V0 of the
potential satisfies

2 2  2
9 2  2
(a)

V

0
ma 2
2ma 2
(c)

2 2  2
8 2  2

V

0
ma 2
ma 2

a/2

V

a/2

 2 2
2 2  2
(b)

V

0
ma 2
ma 2
(d)

x
 V0

2 2  2
50 2  2

V

0
ma 2
ma 2

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Q.37 The equation of a surface of revolution is z  

3 2 3 2
x  y
2
2

 2

The unit normal to the surface at the point A
,0,1 is
 3


Q.38

(A)


2 ˆ
i
k
5
10

(B)


2 ˆ
i
k
5
10

(C)

3ˆ 2 ˆ
i
k
5
5

(D)


2 ˆ
i
k
10
10

0
If f  x   
x  3

for x  3,

(A) s-2e3s

Q.39

then the Laplace transform of f(x) is

for x  3

(B) s2e-3s

(C) s-2

(D) s-2e-3s

A hypothetical semiconductor has a conduction band that can be described by
Ecb = E1 – E2 cos (Ka)
and valence band that can be described by :
Evb = E3 – E4 sin2 (Ka/2)
Where E3 < (E1 – E2) and 



K
a
a

The band gap of the material is

Q.40

(A) E1-E2-E3+E4

(B) E1+E2- E3

(C) E1-E2+E4

(D) 2(E2-E4)

The electron concentration in the conduction band of Ge at 77K is 10 12 cm-3. At this
temperature the electron and hole nobilities are equal, µ = 0.5 x 104 cm2 /V-sec. The
dielectric constant of Ge is 16.
If 100 volts is applied across a 1 cm cube of crystal, the current (mA) flowing in the
sample is …………………..

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Q.41. Assuming a dispersion relation

under long wavelength approximation for elastic

wave in one dimensional lattice of ferromagnetic system. The lattice specific heat at low
temperature varies as
(A)

Q.42

(B)

(C)

(D)

According to the single particles nuclear shell model, the spin-parity of the ground state
of 178 O is
(A)

Q.43

1
2



(B)

3
2



(C)

3
2



(D)

5
2



The disintegration energy is defined to be the difference in the rest energy between the
initial and final states. Consider the following process: 240
94 Pu 

236
92

U  42 He

The emitted α particle has a kinetic energy 5.17 MeV. The value of the disintegration
energy in MeV is ……………..
Q44. Which of the following fusion reaction give more energy? The nuclear mass of the different
nuclei is as follows
M(

) = 1.00783amu,

M(

M(

) = 3.01603amu,

) = 2.01410amu,

M(

) = 4.02603amu,

M(

) = 3.01605amu,

M(

) = 6.01512amu

and

M(e) = 0.00055amu

(A)

+

(B)
(C)
(D)
Q.45

If λB and λp is the wavelength of the series limit of Bracket and Pfund series respectively.
The ratio of λB and λp will be
(A)

16
25

(B)

25
36

(C)

9
25

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(D)

9
16

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Q.46

A pure rotational Raman spectrum of a linear diatomic molecule is recorded using
electromagnetic radiation of frequency ve. The frequency of two consecutive stokes
(A) ve – 10 B, ve – 14 B

(B) ve – 2 B, ve – 4 B

(C) ve + 10 B, ve + 14 B

(D) ve + 2 B, ve + 4 B

Q.47 The first excited state of nucleus has spin parity 2+ and decays to 1+ ground state by
emitting gamma rays. The possible multipole radiation for the above transition are?
(A) E1, E2, E3

(B) M1, M2, M3

(C) M1, E2, M3

(D) E1, M2, E3.

Common Data Questions
Common Data for Questions 48 and 49
A hydrogen beam is prepared in the state

 r , t  

1

2

3

 Et 
 Et
 Et
exp  i 1  1  r  
exp  i 2   2  r  
exp  i 3   3  r 
14
7
14
  
  
  

where E1, E2, E3 are the energies of the ground state and the first excited state of the



hydrogen atom and 1 r , 2 r , 3 r  are their normalized wave functions respectively.
The beam is incident on a detector which measures their energy. Let E0 be the ionization
energy of the hydrogen atom.
Q48.

what will be probability such that energy is  E0 and 
(A)

Q49.

1 3
,
14 14

(B)

1 9
,
14 14

(C)

E0
respectively .
9

1 1
,
14 14

(D)

3 3
,
14 14

The average energy measured by the detector is given by
(A) – E0

(B) 

3
E0
14

(C) E0

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Phone: 011-26865455/+91-9871145498
Website: www.physicsbyfiziks.com
Email: [email protected]

(D)

3
E0
14

Branch office
Anand Institute of Mathematics,
28-B/6, Jia Sarai, Near IIT
Hauz Khas, New Delhi-16
11

fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
Common Data for Questions 50 and 51
Consider a hetero nuclear diatomic molecule with moment of inertia I .
Q50.

kept at equilibrium temperature T with j total angular

If N no of such molecule

orbital quantum no then write the partition fuction at low temperature .
a) Z  exp( 

2
)
IkT

Z  1  3exp(
Q51.

Z  1  exp(

b)

2
)
IkT

Z  1  3exp(

c)

2
)
IkT

2 2
)
IkT

what will average energy per molecule at higher temperature T
(A) kT

(B) 2kT

(C)

3kT
2

(D)3 kT

Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
Three particles of equal mass m are connected by two identical mass less springs of
stiffness constant k as shown in the figure:
k
Q.52

If x1 , x 2

k

m
m
m
denote the horizontal displacements of the

and x 3

masses from their

respective equilibrium positions, the potential energy of the system is
(A)

1
k x12  x22  x32
2

(C)

1
k x12  2 x 22  x32  2 x 2 x1  x3 
2









(B)

1
k x12  x 22  x 32  x 2  x1  x3 
2

(D)

1
k x12  2 x 22  x32  2 x 2  x1  x 3 
2









Q.53 The normal mode of frequency is given by
(A)

k
k
,
m m

(B)

k 2k
,
m m

(C)

k 3k
,
m m

Head office
fiziks, H.No. 23, G.F, Jia Sarai,
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Email: [email protected]

(D)

k
k
,2
m
m

.

Branch office
Anand Institute of Mathematics,
28-B/6, Jia Sarai, Near IIT
Hauz Khas, New Delhi-16
12

fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
Statement for Linked Answer Questions 54 and 55:
A long solenoid, of radius a, is driven by alternating current, so that the field inside is

sinusoidal: B  t   B0 cos t  zˆ . A circular loop of wire, of radius a and resistance R,
2
is placed inside the solenoid, and coaxial with it.
Q54.

The Magnetic flux through the loop is,
(A)

1 2
 a B0 sin  t 
4

(B)  a 2 B0 sin t 

(C)  a 2 B0 cos  t 

(D)

1 2
 a B0 cos  t 
4

Q55. Then the amplitude of current induced in the loop is
(A)

 a 2 B0
2R

(B)

 a 2 B0
3R

(C)

 a 2 B0
4R

Head office
fiziks, H.No. 23, G.F, Jia Sarai,
Near IIT, Hauz Khas, New Delhi-16
Phone: 011-26865455/+91-9871145498
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Email: [email protected]

(D)

 a 2 B0
5R

Branch office
Anand Institute of Mathematics,
28-B/6, Jia Sarai, Near IIT
Hauz Khas, New Delhi-16
13

fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
General Aptitude (GA) Questions
Q.56 – Q.60 carry one mark each

Q.56

Choose the grammatically INCORRECT sentence:
(a) They gave us the money back less the service charges of Three Hundred rupees.
(b) This country’s expenditure is not less than that of Bangladesh.
(c) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a
lesser sum.
(d) This country’s expenditure on educational reforms is very less.

Q.57. Which one of the following options is the closest in meaning to the word given below?
Mitigate
(a) Diminish

Q.58

(b) Divulge

(c) Dedicate

(d) Denote

Choose the most appropriate alternative from the options given below to complete the
following sentence:
Despite several ––––––––– the mission succeeded in its attempt to resolve the
conflict.
(a) attempts

Q.59

(b) setbacks

(c) meetings

(d) delegations

T he cost function for a product in a firm is given by 5q2, where q is the amount of
production. The firm can sell the product at a market price of Rs50 per unit. The number
of units to be produced by the firm such that the profit is maximized is
(a) 5

Q.60

(b) 10

(c) 15

(d) 25

Choose the most appropriate alternative from the options given below to complete the
following sentence:
Suresh’s dog is the one ––––––––– was hurt in the stampede.
(a) that

(b) which

(c) who

Head office
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Phone: 011-26865455/+91-9871145498
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Email: [email protected]

(d) whom
Branch office
Anand Institute of Mathematics,
28-B/6, Jia Sarai, Near IIT
Hauz Khas, New Delhi-16
14

fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
Q.61 – Q.65 carry two marks each.

Q.61

Which of the following assertions are CORRECT?
P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
(a) P, Q

Q.62

(b) Q, R

(c) P, R

(d) R, S

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X
supplies
60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a
quality test. The ones that pass the quality test are considered reliable. Of X’s shock
absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is
made by Y is
(a) 0.288

Q.63

(b) 0.334

(c) 0.667

(d) 0.720

A political party orders an arch for the entrance to the ground in which the annual
convention is
being held. The profile of the arch follows the equation y = 2x – 0.1x2 where y is the
height of the
arch in meters. The maximum possible height of the arch is
(a) 8 meters

(b) 10 meters

(c) 12 meters

Head office
fiziks, H.No. 23, G.F, Jia Sarai,
Near IIT, Hauz Khas, New Delhi-16
Phone: 011-26865455/+91-9871145498
Website: www.physicsbyfiziks.com
Email: [email protected]

(d) 14 meters

Branch office
Anand Institute of Mathematics,
28-B/6, Jia Sarai, Near IIT
Hauz Khas, New Delhi-16
15

fiziks
Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES
Q.64

Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct
personal interviews to collect and collate economic data. Requirements: High Schoolpass, must be available for Day, Evening and Saturday work. Transportation paid,
expenses reimbursed.
Which one of the following is the best inference from the above advertisement?
(a) Gender-discriminatory
(b) Xenophobic
(c) Not designed to make the post attractive
(d) Not gender-discriminatory

Q.65

Given the sequence of terms, AD CG FK JP, the next term is
(a) OV

(b) OW

(c) PV

Head office
fiziks, H.No. 23, G.F, Jia Sarai,
Near IIT, Hauz Khas, New Delhi-16
Phone: 011-26865455/+91-9871145498
Website: www.physicsbyfiziks.com
Email: [email protected]

(d) PW

Branch office
Anand Institute of Mathematics,
28-B/6, Jia Sarai, Near IIT
Hauz Khas, New Delhi-16
16

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