JEST 2017 Question Paper Physics

FOR JEST EXAM PREPARATION

JEST 2017
Question Paper ·
Physics
EXAM YEAR TYPE SUBJECT

JEST 2017 Question Paper Physics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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JEST 2017
Part-A: 1-Mark Questions
Q1. A thin air film of thickness d is formed in a glass medium. For normal incidence, the

m
m . co
condition for constructive interference in the reflected beam is (in terms of wavelength
 and integer m  0,1,
c. o 2,... ) se m
(a) 2d   m  1/m a
s e 2  (b) 2d  m
g l
g l ma  1  a
a
(c) 2d  (d) 2   m  1/ 2  d

Q2. Consider the circuit shown in the figure where R1  2.07 k  and R2  1.93 k  . Current

source I delivers 10 mA current. The potential across the diode D is 0.7V . What is the
potential at A ? D A

m
I

co
R1 R2

.
em
s (c) 19.30V
g l a
a
(a) 10.35V (b) 9.65V (d) 4.83V

  x  1   x  3x  2  dx  ?

2 2
Q3.


(a) 1 (b) 2 (c) 5 (d) 7
Q4. A bead of mass M slides along a parabolic wire described by z  2  x 2  y 2  . The wire

rotates with angular velocity  about the z - axis. At what value of  does the bead

o
maintain a constant nonzero height under the action of gravity along  ẑ ?
m
m (d) 4g . c
c. o (a) 3g (b) g (c) 2g
s e m
s em Which one is the image of the complex domain  z xy  1, x  y  0aunder the mapping
g l
a a
Q5.
l
ag f  z   z , if z  x  iy ?
2

(a)  z xy  1, x  y  0 (b)  z x  2, x  y  0

(c)  z y  2x (d)  z y  1x

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Q6. After the detonation of an atom bomb, the spherical ball of gas was found to be of 15
meter radius at a temperature of 3  105 K . Given the adiabatic expansion coefficient
  5 / 3 , what will be the radius of the ball when its temperature reduces to 3  103 K ?
(a) 156 m (b) 50 m (c) 150 m (d) 100 m
Q7. What is Y for the circuit shown below?

A

B Y

C

(a) Y   A  B  B  C  (b) Y   A  B   B  C 

(c) Y   A  B   B  C  (d) Y   A  B   B  C 


Q8. What is the dimension of , where  is a wavefunction in two dimensions?
ix
(a) kg m 1s 2 (b) kg s 2 (c) kg m 2 s 2 (d) kg s 1

Q9. A plane electromagnetic wave propagating in air with E  8iˆ  6 ˆj  5kˆ e  
i t  3 x  4 y 
is 

incident on a perfectly conducting slab positioned at x  0 . E field of the reflected wave
is

 
(a) 8iˆ  6 ˆj  5kˆ e 
i t  3 x  4 y 
 
(b) 8iˆ  6 ˆj  5kˆ e 
i t  3 x  4 y 

(c)  8iˆ  6 ˆj  5kˆ  e  (d)  8iˆ  6 ˆj  5kˆ  e 
i t 3 x  4 y  i t 3 x  4 y 

1 0   10 3i 
Q10. Let     and M    . Similarly, transformation of M to  can be
 0 11  3i 2 
performed by
1  1 3i  1  1 3i 
(a)   (b)  
10  3i 1  9  3i 11 

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1  1 3i  1  1 3i 
(c)   (d)  
10  3i 11 9  3i 1 

 Q1 , Q2 , P1 , P2  and  q1 , q2 , p1 , p2  are two sets of canonical coordinates, where Qi and qi
m
Q11.

om
are the coordinates and Pi and pi are the corresponding conjugate momenta. If P1  q2
. co
.c e m
m
and P2  p1 , then which of the following relations is true?
e l a s
l a s
(a) Q1  q1 , Q2  p2 (b) Q1  p2 , Q2  q1
a g
(c) Qag p , Q  q
1 2 2 1 (d) Q1  q1 , Q2   p2

Q12. Consider magnetic vector potential A and scalar potential  which define the magnetic
   
field B and electric field E . If one adds  to A for a well-defined  , then what

should be added to  so that E remains unchanged up to an arbitrary function of time,
f t  ?
m
 
. co 1  1 

em
(a) (b)  (c) (d) 

s
t t 2 t 2 t

g l a
In the following silicon diode circuit VB  0.7 V  , determine the output voltage
a
Q13.

waveform Vout  for the given input wave.


Vin Vout

m
m c. o
c. o s e m
s em la
gla ag
a

Head office Branch office

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Phone: 011‐26865455/+91‐9871145498 Hauz Khas, New Delhi‐16

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0  /2  3 / 2 2
Vin 3.5 3.5
2.8 2.8
2.1 2.1
1.4 1.4
0.7 0.7
0.0 0.0
0.7 0.7
1.4 1.4
2.1 2.1
2.8 2.8
3.5 3.5
0  /2  3 / 2 2
t

Vout 3.50  /2  3 / 2 2
3.5
2.8 2.8
2.1 2.1
1.4 1.4
0.7 0.7
(a) 0.0 0.0
0.7 0.7
1.4 1.4
2.1 2.1
2.8 2.8
3.5 3.5
0  /2  3 / 2 2
t
0  /2  3 / 2 2
Vout 3.5 3.5
2.8 2.8
2.1 2.1
1.4 1.4
0.7 0.7
(b)
0.0 0.0
0.7 0.7
1.4 1.4
2.1 2.1
2.8 2.8
3.5 3.5
0  /2  3 / 2 2
t

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fiziks, H.No. 40 D, G.F, Jia Sarai, Anand Institute of Mathematics,
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0  /2  3 / 2 2
Vout 3.5 3.5
2.8 2.8
2.1 2.1

m
co
1.4 1.4

om .
0.7 0.7

.c e m
(c) 0.0 0.0
0.7
em
0.7
l a s
l a s
1.4 1.4
a g
ag
2.1 2.1
2.8 2.8
3.5 3.5
0  /2  3 / 2 2
t
0  /2  3 / 2 2
Vout 3.5 3.5
2.8 2.8
2.1 2.1

m
1.4 1.4

co
0.7 0.7
0.0
. 0.0

em
(d)

s
0.7 0.7
1.4
g l a 1.4

a
2.1 2.1
2.8 2.8
3.5 3.5
0  /2  3 / 2 2
t
Q14. 0  x  and 1  x  are respectively are orthonormal wavefunctions of the ground and first
excited states of a one dimensional simple harmonic oscillator. Consider the normalised
wave function   x   c00  x   c11  x  , where c0 and c1 are real. For what values of c0
m
m and c1 will   x  x   x  be maximized?
c. o
c. o (a) c  c  1/ 2 s e m
em (c) c   3 / 2, c  1/ 2 la
(b) c0  c1  1/ 2

las ag
0 1

g
(d) c0   3 / 2, c1  1/ 2
a
0 1

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Q15. Consider the following circuit in steady state condition. Calculate the amount of charge
stored in 1 F and 2 F capacitors respectively.

1 F
4k 

1k  2k 

2F
4k 

6V
(a) 4 C and 8C (b) 8C and 4 C
(c) 3 C and 6 C (d) 6 C and 3 C
Q16. If the mean square fluctuations in energy of a system in equilibrium at temperature T is
proportional to T  , then the energy of the system is proportional to

(a) T   2 (b) T 2 (c) T  1 (d) T 
Q17. Suppose the spin degrees of freedom of a 2 - particle system can be described by a 21 -
dimensional Hilbert subspace. Which among the following could be the spin of one of the
particles?
1 3
(a) (b) 3 (c) (d) 2
2 2
Q18. Water is poured at a rate of R m3 / hour from the top into a cylindrical vessel of diameter

D . The vessel has a small opening of area a  a  D  at the bottom. What should be
the minimum height of the vessel so that water does not overflow?
R2 R2 8R 2
(a)  (b) (c) (d)
2 ga 2 2 gaD 2  D2 g 2

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fiziks, H.No. 40 D, G.F, Jia Sarai, Anand Institute of Mathematics,
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Q19. Suppose that we toss two fair coins hundred times each. The probability that the same
number of heads occur for both coins at the end of the experiment is
2
 100  100 
100 100 100 100
1 1
     
o m
(a)   (b) 2  

m . c
4 n 0  n  4 n0  n 

100 o m
(c)     .c s e
m
2 2
 100 
100 100 100 100
11 1
e a
(d)    
s l


a g
24  n  4  n 
l a
n0 n 0

g

1, 2, 2a ?
Q20. What is the equation of the plane which is tangent to the surface xyz 4 at the point

(a) x  2 y  4 z  12 (b) 4 x  2 y  z  12
(c) x  4 y  z  0 (d) 2 x  y  z  6
Q21. If the ground state wavefunction of a particle moving in a one dimensional potential is
 
proportional to exp   x 2 / 2  cosh 2 x , then the potential in suitable units such that

m
  1 , is proportional to

c. o  2x
(a) x 2 (b) x 2  2 2 x tanh

m x  2 2 x coth  2 x 
e(d)
(c) x 2  2 2 x tan  2x
l a s
2

Q22. A possible Lagrangian for a free particle is
a g
1
(a) L  q  q
2 2
(b) L  q  qq
2
(c) L  q 2  q (d) L  q 2 
q
Q23. A rod of mass m and length l is suspended from two massless vertical springs with a
spring constants k1 and k2 . What is the Lagrangian for the system, if x1 and x2 be the
displacements from equilibrium position of the two ends of the rod?
m
m  x1  2 x1 x2  x22   k1 x12  k2 x22
c. o
m 2 1 1

c. o m m
(a)

e
8 2 2

em (b) 2  x  x x  x   14  k  k   x  x  la s
as ag
2 2 2 2

l
1 1 2 2 1 2 1 2

ag (c)  x  x x  x   k x  k x
m
6
2
1
1
2
1 2
1
2
2
2
2
1 1
2
2 2

(d)
2

m 2
x1  2 x1 x2  x22    k1  k2   x12  x22 
1
4

Head office Branch office

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Q24. Two equal positive charges of magnitude  q separated by a distance d are surrounded
by a uniformly charged thin spherical shell of radius 2d bearing a total charge 2q and
centred at the midpoint between the two positive charges. The net electric field at
distance  from the midpoint   d  is

(a) zero (b) proportional to d
(c) proportional to 1/ r 3 (d) proportional to 1/ r 4
px2  pv2
Q25. If the Hamiltonian of a classical particles is H   xy , then x 2  xy  y 2 at
2m
temperature T is equal to
1 3
(a) k BT (b) k BT (c) 2k B T (d) kBT
2 2
Part-B: 3-Mark Questions
Q1. A solid, insulating sphere of radius 1cm has charge 107 C distributed uniformly over its
volume. It is surrounded concentrically by a conducting thick spherical shell of inner
radius 2 cm , outer radius 2.5cm and is charged with 2  107 C . What is the
electrostatic potential in Volts on the surface of the sphere?
Q2. A particle is described by the following Hamiltonian
pˆ 2 1
Hˆ   m 2 xˆ 2   xˆ 4
2m 2
where the quartic term can be treated perturbatively. If E0 and E1 denote the energy

correction of O    to the ground state and the first excited state respectively, what is the

fraction E1 / E0 ?

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Q3. A simple pendulum has a bob of mass 1 kg and charge 1 Coulomb. It is suspended by a
massless string of length 13 m . The time period of small oscillations of this pendulum is


m
T0 . If an electric field E  100 xV
ˆ / m is applied, the time period becomes T . What is the

value of T0 / T  ?
om . co
c m
4

m . x
se
s e g l a
l a a
ag
y l  13 m

E  100 Volt m 1  iˆ
g  10 m sec 2
m  1kg
q  1 Coulomb
Q4. Let a particle of mass 1109 kg , constrained to have one dimensional motion, be

initially at the origin  x  0 m  . The particle is in equilibrium with a thermal bath

 k T  10 J  . What is x o m
c
8
of the particle after a time t  5 s ?
.
2
B

m
eI?
s
I

la
1
,Q5. For the circuit shown below, what is the ratio

g
aR R R
2

R R R R 2R

2R
R 2R 2R 2R I1 2R 2R 2R

I2 E

m
m c. o
c. o A ball of mass 0.1kg and density 2000 kg / m is suspended by a massless
s e m string of
em length 0.5 m under water having density 1000 kg / m . The ball experiences
a a drag force,
3

l
Q6.

las a g
g
3

a     
F  0.2  v  v  , where v and v are the velocities of the ball and water respectively.
d b w b w

What will be the frequency of small oscillations for the motion of pendulum, if the water
is at rest?

Head office Branch office

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e
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m a s
Phone: 011‐26865455/+91‐9871145498 Hauz Khas, New Delhi‐16

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Q7. Suppose that the number of microstates available to a system of N particles depends on
N and the combined variable UV 2 , where U is the internal energy and V is the volume
of the system. The system initially has volume 2m3 and energy 200 J . It undergoes an

isentropic expansion to volume 4m3 . What is the final pressure of the system in SI units?
Q8. The temperature in a rectangular plate bounded by the lines, x  0, y  0, x  3 and y  5

is T  xy 2  x 2 y  100 . What is the maximum temperature difference between two points
on the plate?
Q9. A sphere of inner radius 1cm and outer radius 2 cm , centered at origin has a volume
K
charge density  0  , where K is a nonzero constant and r is the radial distance. A
4 r

point charge of magnitude 103 C is placed at the origin. For what value of K in units of

C / m 2 the electric field inside shell is constant?
Q10. If x̂  t  be the position operator at a time t in the Heisenberg picture for a particle

pˆ 2 1
described by the Hamiltonian, Hˆ   m 2 xˆ 2 what is ei  t 0 xˆ  t  xˆ  0  0 in units of
2m 2

where 0 is the ground state?
2m
Part-C: 3-Mark Questions
Q1. Consider a grounded conducting plane which is infinitely extended perpendicular to the
y -axis at y  0 . If an infinite line of charge per unit length  runs parallel to x -axis at
y  d , then surface charge density on the conducting plane is
 d  d
(a) (b)
 x  d 2  z2 
2
 x  d 2  z2 
2

 d  d
(c) (d)
  x  d 2  z2 
2
2  x  d 2  z 2 
2

Head office Branch office
fiziks, H.No. 40 D, G.F, Jia Sarai, Anand Institute of Mathematics,
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Q2. A system of particles on N lattice sites is in equilibrium at temperature T and chemical
potential  . Multiple occupancy of the sites is forbidden. The binding energy of a particle
at each site is   . The probability of no site being occupied is
m
1 e 
om . co
  
1

.c m
(a) (b)

e
 N 1    
1 e
N
1  e     

e m
 
l a s
a s a g
1 gel
   
1 1 e

a
(c) (d)
1 e 
    
N  N 1    


 x 1
Q3. The integral I   dx is
1  x 
1 2

   
(a) (b) (c) (d)
2 2 2 2 2

m
co


.
Q4. For an electric field E  k xxˆ where k is a non-zero constant, total charge enclosed by

e m
las
the cube as shown below is z

ag
l O y
l
l
l
x
 3  1
m
(b) k 0 l 5/ 2

c. o
(a) 0

m
c. o (c) k  l  5  1 (d) k  l  2  1
em
5/ 2 5/ 2

em la s
0 0

las ag
ag

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e
28‐B/6, Jia Sarai, Near IIT

m a s
Phone: 011‐26865455/+91‐9871145498 Hauz Khas, New Delhi‐16

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Q5. Consider a point particle A of mass mA colliding elastically with another point particle

mB
B of mass mB at rest, where   . After collision, the ratio of the kinetic energy of
mA
particle B to the initial kinetic energy of particle A is given by
4 2
(a) (b)
1 1
 2 
 
2 1
(c) (d)
 2
1 

Q6. Two classical particles are distributed among N   2  sites on a ring. Each site can

accommodate only one particle. If two particles occupy two nearest neighbour sites, then
the energy of the system is increased by  . The average energy of the system at
temperature T is
2  e   2 N  e 
(a) (b)
 N  3  2e    N  3  2e  
 2  e  
(c) (d)
N  N  2   2e  
Q7. Consider a 741 operational amplifier circuit as shown below, where VCC  VEE  15V

and R  2.2 k  . If vI  2mV , what is the value of v0 with respect to the ground?
R

R R

V CC
R

741
  vo
vl
V
EE

(a) 1 mV (b) 2 mV (c) 3 mV (d) 4 mV

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fiziks, H.No. 40 D, G.F, Jia Sarai, Anand Institute of Mathematics,
Near IIT, Hauz Khas, New Delhi‐16 28‐B/6, Jia Sarai, Near IIT
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1
Q8. The Fourier transform of the function up to proportionality constant is
x  3x 2  2
4

(a) 2 exp   k 2   exp  2k 2  (b) 2 exp   k   exp  2 k  
  m  (d) 2 exp   2k   exp  2k 
. c om
o
2 exp  k  exp  2 k
m
2 2

c
(c)

1 m . s e
 I  s3e      
 
g l a
If   la a
g
x y z
  , where  ’s are the Pauli matrices and I is the identity
a
Q9.
2
matrix, then the trace of  2017 is
1
(a) 22017 (b) 22017 (c) 1 (d)
2
Q10. A cylinder at temperature T  0 is separated into two compartments A and B by a free
sliding piston. Compartments A and B are filled by Fermi gases made of spin 1/ 2 and

o m
. c
3 / 2 particles respectively. If particles in both the compartments have same mass, the

e m
s
ratio of equilibrium density of the gas in compartment A to that of gas in compartment
B is
g l a
(a) 1 (b)
1 a (c)
1
(d)
1
32 / 5 22 / 5 22 / 3
Q11. What is the DC base current (approximated to nearest integer value in  A ) for the
following n - p - n silicon transistor circuit, given R1  75 , R2  4.0 k , R3  2.1 k ,

R4  2.6 k , R5  6.0 k , R6  6.8 k , C1  1 F , C2  2 F , VC  15V  dc  75 ?

m
c. o
C3 R1

m
c. o s e m
em
R5

s la
ag 
R4 C1

la
R6

g
R2

a
 C2
VC R3

(a) 20 (b) 24 (c) 16 (d) 32

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m . c
fiziks, H.No. 40 D, G.F, Jia Sarai, Anand Institute of Mathematics,

c. o m
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e
28‐B/6, Jia Sarai, Near IIT

m a s
Phone: 011‐26865455/+91‐9871145498 Hauz Khas, New Delhi‐16

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Q12. Consider a particle confined by a potential V  x   k x , where k is a positive constant.

The spectrum En of the system, within the WKB approximation is proportional to
3/ 2 2/3 1/ 2 4/3
 1  1  1  1
(a)  n   (b)  n   (c)  n   (d)  n  
 2  2  2  2
Q13. Consider the Hamiltonian
1 0 0 0 0 1 
   
H t     0 2 0    t  0 0 0 
 0 0 3  1 0 2 
   
The time dependent function   t    for t  0 and zero for t  0 . Find

 t  0  t  0 , where   t  0  is the normalised ground state of the system at
2

a time t  0 and   t  0  is the state of the system at t  0 .

(a)
1
2
1  cos  2 t   (b)
1
2
1  cos  t  

(c)
1
2
1  sin  2 t   (d)
1
2
1  sin  t  
Q14. The function f  x   cosh x which exists in the range   x   is periodically repeated

between x   2m  1  and  2m  1  , where m   to  . Using Fourier series,

indicate the correct relation at x  0

 1  1    1  2 
n n
 

(a)    1 (b) 
n  1  n2 2  cosh   n  1  n2 cosh 

 1  1  1  
n n

 

(c)  2 (d)    1
n  1 n 2
sinh  n 1 1 n 2
2  sinh  

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fiziks, H.No. 40 D, G.F, Jia Sarai, Anand Institute of Mathematics,
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Q15. A toy car is made from a rectangular block of mass M and four disk wheels of mass m
and radii r . The car is attached to a vertical wall by a massless horizontal spring with
spring constant k and constrained to move perpendicular to the wall. The coefficient of

m
co
static friction between the wheel of the car and the floor is  . The maximum amplitude
of oscillations of the o m m .
c. car above which the wheels start slipping is se
 g  M  2emm l a
s
la mk
 M  4m  g M  m 
g
2 2

(a)
g
(b)
a
a
Mk

 g  M  m  g  M  4m  M  6m 
2

(c) (d)
2mk 2mk

m
. co
s em
g l a
a

m
m c. o
c. o s e m
s em la
gla ag
a

Head office Branch office

m . c
fiziks, H.No. 40 D, G.F, Jia Sarai, Anand Institute of Mathematics,

c. o m
Near IIT, Hauz Khas, New Delhi‐16
e
28‐B/6, Jia Sarai, Near IIT

m a s
Phone: 011‐26865455/+91‐9871145498 Hauz Khas, New Delhi‐16

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