JEST 2020 Question Paper Physics

FOR JEST EXAM PREPARATION

JEST 2020
Question Paper ·
Physics
EXAM YEAR TYPE SUBJECT

JEST 2020 Question Paper Physics

Notes · Sample Papers · Previous Year Papers · Mock Tests

co m .
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PHYSICS
Joint Entrance Screening Test (JEST - 2020)

m
(Booklet Series-D)

om . co
.c e m
e m
PLEASE READ THE INSTRUCTIONS CAREFULLY
l a s
a s a g
Aland Part B contains multiple choice questions and only one of the four options
1. This paper contains three parts: Part A, Part B and Part C
2. Part g
a
in each question is correct. Questions in Part C has integers between 0 and 9999 as
answers.
3. Part A contains 25 questions, and each carries 1 (one) mark for the correct answer and
–1/3 (negative one third) mark for incorrect answer. Part B contains 15 questions and
carry 3 (three) marks each for correct answer and –1 (negative one) mark for incorrect

o m
c
these questions must be answered by integers of. 4 digits each. Note that if the answer is,
answer. Part C contains 10 questions and each carries 3 (three marks). The answer to

e m fill in 0000. If the zeros are not filled in
l a s
agbe credited. There are NO NEGATIVE MARKS
e.g. 5, you must fill in 0005. If it is 0, you must
(where required), the answer will not
for these questions.
4. Only non-programmable scientific calculator is allowed and exchange of calculators
among the candidates is not permitted. Use of other items like electronic diary, writing
pads, pencil box, beeper, cameras, mobile phones, palmtops, laptops, pagers etc. are not

m
permitted inside the examination hall.

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

m . c
c. o
s e m
m a
se l

g
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PART A: 1 Mark Questions
Q1. The persons named A, B, C , D, E , F , G, H , I , J have come for an interview. They are being
called one by one to the interview panel at random. What is the probability that C gives
interview before A and A gives before F ?
1 1 1 1
(a) (b) (c) (d)
6 10 8 4
Q2. The ratio of maximum to minimum resistance that can be obtained with N number of
3   resistors is
(a) N (b) N 2 (c) N 3 (d) N 4
Q3. Consider three infinitely long, straight and coplanar wires which are placed parallel to each
other. The distance between the adjacent wires is d . Each wire carries a current I in the
same direction. Consider points on either side of the middle wire where the magnetic field
vanishes. What is the distance of these points from the middle wire?
2d 2d d d
(a) (b) (c) (d)
3 3 3 3
Q4. A rod consists of two equal sections of length l each with coefficient of thermal
conductivity 1 and  2 , respectively. One end of the rod is kept at a fixed temperature T1

and the other end at a temperature T2 T1  T2  . If  2  21 then the temperature at the

interface is

(a) T 
 2T1  T2  (b) T 
 2T1  T2 
3 3 T1 1 2 T2

(c) T 
T1  2T2  (d) T 
T1  2T2  l l
3 3
Q5. If f  t  is a real and even function of t , which one of the following statements is true

about its Fourier transform F   (here * indicates complex conjugation)?

(a) F      F   (b) F     F  

(c) F     F   (d) F     F   

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Q6. Consider an ideal gas whose entropy is given by
n U V
S   5 R ln  2 R ln  ,
2 n n

m
co
where n is the number of moles,  is a constant, R is the universal gas constant, U is the

.c om
internal energy and V is the volume of the gas. The specific heat at constant pressure is
e m .
e m l a s
s g
then given by

l a a
ag
5 7 3
(a) nR (b) nR (c) nR (d) nR
2 2 2
Q7. A 16 - bit analog to digital converter works in the range 0  1 Volt. The least count of the
converter is
(a) 0.30 mV (b) 15.26 mV (c) 5.44 nV (d) 15.26 V

Q8. A particle in a spherically symmetric potential is known to be in an eigenstate of L2 and L2

m  
c. o
with eigenvalues l  l  1  2 and m , respectively. What is the value of l , m L2x l , m ?

m  l  l  m 
e(b)
s
2 2
 
a
l  l  m2
l
2 2 2
(a)

g
2

(c)
2 2
l  l  m2  a (d)
2 2

l  l  m2 
2 2
Q9. A particle of mass m carrying angular momentum l moves in a central potential
ke  ar
V r    , where k , a are positive constants. If the particle undergoes circular motion,
r

m
what is the equation determining its radius r0 ?

m c. o
c. o m
l2 l2
 ke  ar0 1  ar0 
e
(a)  kar0 e  ar0 (b)

em (c) l  ke la s
mr0 mr0

las 2
l2
ag
g
 ar0
 ke  ar0 1  ar0 
a
(d)
2mr 0 2mr0

m . c
c. o
s e m
m a
se l

g
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Q10. Calculate the collector current and determine whether or not the transistor in figure shown
below is in saturation. Assume VCE  sat   0.2V
RC 1 k 
(a) 6.5 mA , not in saturation
RB  V
 DC  50
CC
(b) 11.5 mA , in saturation
10 k   10V
(c) 11.5 mA , not in saturation VBB
2V
(d) 6.5 mA , in saturation

Q11. Charges are placed as follows: q at  a, a, 0  and   a,  a, 0  and q at  a, a, 0  and

 a, a, 0  . At large distances, how does the electrostatic potential behave as a function of
the distance r from the centre  0, 0, 0  ?

(a) 1/ r 3 (b) 1/ r 2 (c) 1/ r (d) 1/ r 4
Q12. An n  n Hermitian matrix A is not a multiple of the identity matrix. Which one of the
following statements is always true?

(a) nTr  A2   TrA  (b) nTr  A2   TrA 
2 2

(c) nTr  A 2   TrA  (d) Tr  A2   n TrA 
2 2

Q13. A ring of radius 0.5 m has a gap of 0.002 m . If the ring carries a charge of 1.0 C
distributed uniformly along it, then the electric field at the centre of the ring is
 
(a) 7.5  10 7 NC 1  
 
1
 
(b) 7.2  10 NC
7

 
 
(c) 6.2  10 7 NC 1  
 
 

(d) 6.5 10 7 NC 1     

Q14. Consider a system of two particles at temperature T   . Each of them can occupy three
different quantum energy levels having energies 0, and 2  , and both of them cannot
occupy the same energy level. What is the average energy of the system?
3
(a)  (b) (c) 2  (d) 4 
2

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3
Q15. If x and y have the joint probability distribution f  x, y    xy for 0  x, y  1 , and
4
1
f  x, y   0 otherwise. What is the probability that y assumes a value greater than
m
,

co
2

given that x is equalotom .
.c 2 m
1

se
s em (b) 7 g l a
16 la a
6 8 9

g
(a) (c) (d)

a function of an electron in one dimension is given by
16 16 16
Q16. The wave
 0, for x  0
  x  
2 3e
x
1  e  , for x  0
x

The ratio between the expected position x and the most probable position xm is

m
c. o
(a) 0.856 (b) 1.563 (c) 2.784 (d) 3.567

m The surface of the
Q17. A particle is to slide along the horizontal circular path on the inner

e
sspeed of the particle (in
a
surface of the funnel as shown in the figure.
funnel is frictionless. What must be lthe
g
terms of r and  ) if it is to executeathis motion?
r

(a) rg sin 

(b) rg cos  

(c) rg tan 

rg cot 
o m
c
(d)
Q18. m . and are
c. o connected by a millivoltmeter. What is the reading of the millivoltmeter m
e when a train
Two rails of a railroad track are insulated from each other and from the ground,

em l s
a component of the
las a g
g
travels at the speed 90 km / hr down the track? Assume that the vertical

a earth’s magnetic field is 0.2 gauss and that the tracks are separated by two meters. Use
1 gauss  10 4 Tesla  10 4 V  sec / m 2
(a) 10 (b) 1 (c) 0.2 (d) 180

m . c
c. o
s e m
m a
se l

g
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Q19. A particle of mass m moves in a one-dimensional potential V  x   F0 x , where F0 is a

positive constant. Given the initial conditions, x  0   x0  0 and x  0   0 , which one of

the following statements is correct?
(a) The particle undergoes simple harmonic motion about the origin with frequency
F0
  2
mx0

1 F0
(b) The angular frequency of oscillations of the particle is   
2 2mx0

(c) The particle begins from rest and is accelerated along the positive x -axis such that
x0  F0t 2
x t  
2m
(d) The angular frequency of oscillations of the particle is independent of its mass
Q20. A carbon rod of resistance Rc and a metal rod of resistance Rm are connected in series. Let

their linear temperature coefficients of resistivity have magnitudes  c and  m ,
respectively. The condition that the net resistance would be independent of temperature is
Rc  m Rm  m
(a) Rc  Rm (b)  c   m (c)  (d) 
Rm  c Rc  c
Q21. The 2 ' s compliment of 1111 1111 is
(a) 0000 0001 (b) 0000 0000 (c) 1111 1111 (d) 1000 0000
Q22. Two tuning forks A and B are struck instantaneously to obtain Lissajous figures. The
figures go through a complete cycle in 20 s . Fork A is located with wax, so that the cycle
period changes to 10 s . If the frequency of fork B is 256.10 Hz , what is the frequency of
fork A after loading?
(a) 256.00 Hz (b) 256.05 Hz (c) 256.15 Hz (d) 256.20 Hz
Q23. Consider a classical harmonic oscillator in thermal equilibrium at a temperature T . If the
spring constant is changed to twice its value isothermally, then the amount of work done on
the system is
ln 2
(a) k BT ln 2 (b) k BT (c) 2k BT ln 2 (d)  k BT ln 2
2

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Q24. The solution of the differential equation y  2 y  3 y  e u is given as C1e t  C2 e 2t  C3e 3t .

The values of the coefficients C1 , C2 and C3 are:

m
co
(a) C1 , C2 and C3 are arbitrary

o mand C  31 m .
. c
(b) C , C are arbitrary
se
m and C  1 a
1 3 2

s earbitrary g l
g la a
(c) C , C are

a
2 3 1
3
1
(d) C , C are arbitrary and C 
1 2 3
3
Q25. A free particle of energy E , characterized by a plane wave of wavelength  enters a
region of constant potential V (where E  V  0 ). Within the region of the potential, the
 V
wavelength of the particle is . The ratio is:

m
co
2 E
1
.
em
1
(a) (b) 3 (c) 3 (d)

s
3 3

g l a
a

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

m . c
c. o
s e m
m a
se l

g
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PART B: 3-Mark Questions
Q1. Consider a quantum particle of mass m moving in a potential
1
V  x, y    2
2 2 2
 
 m x  y , for x  0, y  0
 , otherwise

what is the degeneracy of the energy state 9 , where   0 measures the strength of the
potential?
(a) 4 (b) 2 (c) 10 (d) 5

Consider a particle with total energy E is oscillating in a potential U  x   A x
n
Q2. with

A  0 and n  0 in one dimension. Which one of the following gives the relation between
the time-period of oscillation T and the total energy E :
(a) T  E 1/ n 1/ 2 (b) T  E 0 (c) T  E n (d) T  E 1/ n
Q3. A classical gas of N particles is kept at a temperature T and is confined to move on a two-
dimensional surface ( xy -plane). If an external linear force field is applied along the x -axis,
then the partition function of the system will be proportional to
(a) T N (b) T 2 N (c) T N / 2 (d) T 3 N / 2
Q4. An electromagnetic field is given by
  1 q  
E r ,t      vt  r  r, B r,t   0
4 0 r 2

1 for x  0
where   x   
0 for x  0

The corresponding charge density  and current density J are given by
 q 
(a)   q 3  r   vt  r     vt  r  ; J 0
4 r 2
 
(b)   q 3  r   vt  r  ; J  0

q  qv
(c)     vt  r  ; J    vt  r  rˆ
4 r 2
4 r 2
 q  qv
(d)   q 3  r   vt  r     vt  r  ; J    vt  r  rˆ
4 r 2
4 r 2

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Q5. A particle of mass m is placed in a potential well U  x   cx n , where c is a positive

constant and n is an even positive integer. If the particle is in equilibrium at constant

m
temperature, which one of the following relations between average kinetic energy K and

om . co
.c e m
average potential energy U is correct?

e m (b) K  U l a s
s g
2 n

a
(a) K  U (c) K  (d) K  2 U
a
U
l
What isgthe charge stored on each capacitor C and C in the circuit shown in the given
n 2
Q6.
a 1 2

figure? 6 3
(a) 6 C , 6 C
2 F 1 F
(b) 6 C ,3 C
C1 C2
(c) 3 C , 6  C
m
. co 

em
(d) 3 C ,3 C 12V 3

l a s
g
Q7. A particle moving in two dimensions satisfies the equations of motion
a
x  t   x  t   y  t 

y  t   x  t   y  t 

x 
with x  0   0 . What is the ratio of ?
y 

m
1 1
(a) 1  (b) 1  2 1 2 1

c. o
(c) (d)

m
2 2

c. o s em
s em la
gla ag
a

m . c
c. o
s e m
m a
se l

g
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Q8. Analyse the common emitter transistor circuit given in the figure. If the current gain   

increases by 50% , the relative change in collector current  I C  is approximately
VCC

5k
400 k

IC
IB
  100

1k

(a) 5% (b) 15% (c) 20% (d) 25%
Q9. What is the value of the following contour integral I taken counterclockwise around the
circle z  2 ?

dz
I  z  z  4
C
3

i i i i
(a) (b) (c) (d)
2 32 16 4

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Q10. Consider a cube (see figure) of volume V containing N molecules each of mass m with
N
uniform density n  . Suppose this system is equivalent to a system of M non-
V
interacting gases such that molecules of the ith gas are N i  niV in number, each with an
o m
m . c
.co
identical y -component of velocity v . What is the pressure P on the surface  ABCD of
s e m
em a
i

area A ?
s
a nv g l
(a) P  ml
g
z
a
a
M 2
i 1 i i C

 nv
M 2 D
m i 1 i i
(b) P 
 n
M

i 1 i

y
 nv
M
m 2 B
i 1 i i

m
(c) P 

c. o
2 A
x

 nv
s em
M
(d) P  2m 2

l a
i 1 i i

ag to a spherically symmetric potential V  r  is
Q11. The wave function of a particle subjected

given by   r    x  y  2 z  f  r  . Which one of the following statements is true about

 r  ?

(a) It is an eigenfunction of L2 with l  0


m
(b) It is an eigenfunction of L2 with l  1

m c. o


c. o
(c) It is an eigenfunction of L2 with l  2

e m
s


em a
(d) It is not an eigenfunction of L2

s p  gql
la Q12. The Hamiltonian for a particle of mass m is given by H   a2m  , where  is a non-

2

ag
zero constant. Which one of the following equations is correct?
(a) p  mq (b)  p  q
1
(c) q  0 (d) L  mq 2   qq
2

m . c
c. o
s e m
m a
se l

g
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Q13. A continuous He  Ne laser beam    632.8 nm  is ‘chopped’, using a spinning aperture

into 1  s square pulses. The order-of-magnitude estimate of the spectral width  of the
emerging ‘pulsed’ light is
(a) 10 9 m (b) 10 12 m (c) 10 15 m (d) 10 18 m

p 2 kq 2
Q14. The Hamiltonian of a classical particle is given by H  p, q    . Given
2m 2

k
F  p, q, t   ln  p  im q   it is a constant of motion (where   ). What is the
m
value of  ?
(a) 2 (b) 0 (c) 1 (d) 
Q15. Three polarizers are stacked, normal to a central axis, along which is incident a beam of
unpolarized light of intensity I 0 . The first and the third polarizers are perpendicular to each

other and the middle polarizer is rotated at an angular frequency  about the central axis
(light beam). The time dependent intensity of light emerging after the third polarizer will be
given by
I  I 
(a) I  t    0  1  cos  4t  (b) I  t    0  1  cos  2t 
 16  8
I  I 
(c) I  t    0  1  2 cos t (d) I  t    0  cos 2 t
4 2

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PART C: 3- Mark Numerical Questions
Q1. A thin film of water having refractive index n  1.333 floats on the surface of a beaker of
silicone oil having refractive index ns  1.40 . The arrangement is illuminated by 600 nm
m
m . co
c. o thickness of the film (in nm)?
light incident normally from top and a large region of the film appears bright red. What is

e m
emof the following integral? s
the minimum possible

s g l a
la I  100 2 x  2sin x  2  dx a
Q2. What is the value

a g  
 /2

0

Q3. Two compartments in a cylinder with uniform cross section and total length 102 cm are
separated by a sliding partition which can move but does not allow heat to pass across it.
No molecules are present in either of the compartments. The radiation inside each
compartment is in thermal equilibrium with its walls. The walls at the two ends of the

o m
c
cylinder are maintained at temperatures 2000 K and 4000 K , respectively. The sides are

m . measured from the left end of the
e
perfectly insulated. Find the location of the partition,

l a s
Insulator
g
container.

a
2000 K

1000 K

Insulator
102 cm

m
Q4. A laser has output power of 150 mW with beam diameter of 2 mm at a wavelength 630 nm .

m c. o
c. o 1  9 10 Nm C
What is the value of the electric field in units of V / m is? Use Coulomb’s constant,

e m
em a s
2

l
9 2

s
 
g
 

la Q5. A two-state quantum system has energy eigenvalues   corresponding
4

a
0

ag to normalised
  
states   . At time t  0 the system is in the quantum state  
. Find the 10000 
2
h
probability that the system will be in the same state at time t  , where h is the
 6 
Planck’s constant.

m . c
c. o
s e m
m a
se l

g
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13

fiziks

Q6. A small insect of mass m is sitting on the rim of a uniform circular horizontal disk of
radius R and mass M . The system is rotating at a constant angular velocity i about a
frictionless vertical axis passing through the center of the disk. The insect started to crawl
M
towards the center of the disk. Assume  10 , and let the final angular velocity of the
m
100 f
system, when the insect reaches the centre of the disk be  f . What is the value of ?
i
Q7. A particle is moving on a one-dimensional discrete lattice with lattice spacing unity. It can
move from a site to its nearest neighbour site every 1/ 5 seconds with p being the

probability to move right and q  1  p  being the probability to move left. Consider that

3
the particle starts at origin, x  0 at time t  0 . Taking p  , calculate the variance
4

x  x 
2
at time t  5 10 4 seconds, where x is the average position.

Q8. Analyse the op-amp circuit shown in the figure below. What is the output voltage V0  in

millivolts if V1  2.5 and V2  2.25V ?

10V
V2 

 5 k
10V 5 k

5 k 10V

500  V0

5 k 10V
10V 5 k
5 k


V1 
10V

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14

co m .
. e
em las

as fiziks ag

Q9. Some bacteria are added to a bucket at time 10 am. The number of bacteria doubles every
minute and reaches a number 16 1015 at 10 :18 am. How many seconds after 10 am were
there 25 1013 bacteria?

o m
m . c
A cleaning machine presses a circular mop of radius R  30 cm vertically down on a floor
with a total force Fco
Q10.

. e m
s
 25 N and rotates it with a constant angular speed about the vertical

s em the centre of mop. If the force is distributed uniformly over the mop g l a
and if thelacoefficient of friction between the mop and the floor is   0.25 , what isathe
axis passing through

ag
value of torque in N - cm applied by the machine on the mop?

m
. co
s em
g l a
a

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

m . c
c. o
s e m
m a
se l

g
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15