JEST 2019 Question Paper Physics

FOR JEST EXAM PREPARATION

JEST 2019
Question Paper ·
Physics
EXAM YEAR TYPE SUBJECT

JEST 2019 Question Paper Physics

Notes · Sample Papers · Previous Year Papers · Mock Tests

co m .
. e
em las

as fiziksag

PHYSICS
Joint Entrance Screening Test (JEST - 2019)

m
(Booklet Series-A)

om . co
.c e m
PLEASE READ THE INSTRUCTIONS CAREFULLY

e m l a s
s Part C contains multiple choice questions and only one of the four options
1. This paper contains three parts: Part A, Part B and Part C

l a a g
g question is correct. Questions in Part B has integers between 0 and 9999 as
2. Part A and
inaeach
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

m
answer. Part C contains 10 questions and each carries 3 (three marks). The answer to

c o
. must fill in 0000. If the zeros are not filled
these questions must be answered by integers of 4 digits each. Note that if the answer

m
enot be credited. There are NO NEGATIVE
a s
is, e.g. 5, you must fill in 0005. If it is 0, you

g l
MARKS for these questions. a
in (where required), the answer will

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
permitted inside the examination hall.

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 1
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 13

fiziks

Part-A: 1-Mark Questions

Q1. Let r be the position vector of a point on a closed contour C . What is the value of the line
 
integral  r  dr ?

1
(a) 0 (b) (c) 1 (d) 
2
Q2. A dc voltage of 80 Volt is switched on across a circuit containing a resistance of 5 in series
with an inductance of 20 H . What is the rate of change of current at the instant when the current
is 12 A ?
(a) 0 A / s (b) 1 A / s (c) 5 A / s (d) 80 A / s

Q3. Consider the function f  x, y   x  i y . In which domain of the complex plane is this function

analytic?
(a) First and second quadrants (b) Second and third quadrants
(c) Second and fourth quadrants (d) Nowhere
Q4. Consider the following transformation of the phase space coordinates  q, p    Q, P 

Q  q a cos bp P  q a sin bp
For what values of a and b will the transformation be canonical?
1 1 1 1
(a) 1,1 (b) , (c) 2, (d) ,2
2 2 2 2
Q5. What is the binding energy of an electron in the ground state of a He  ion?
(a) 6.8 eV (b) 13.6 eV (c) 27.2 eV (d) 54.4 eV
Q6. A collimated white light source illuminates the slits of a double slit interference setup and forms
the interference pattern on a screen. If one slit is covered with a blue filter, which one of the
following statements is correct?
(a) No interference pattern is observed after the slit is covered with the blue filter
(b) Interference pattern remains unchanged with and without the blue filter
(c) A blue interference pattern is observed
(d) The central maximum is blue with coloured higher order maxima

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 13
2

co m .
. e
em las

as fiziksag

Q7. Consider a system of N distinguishable particles with two energy levels for each particle, a
ground state with energy zero and an excited state with energy   0 . What is the average energy

m
per particle as the system temperature T   ?

om 2

. co
c m
(c)  (d) 
. e
(a) 0 (b)

e m a s
lzero.
a s g
Q8. Consider a diatomic molecule with an infinite number of equally spaced non-degenerate energy

g l a
Whatais the single particle partition function Z ?
levels. The spacing between any two adjacent levels is  and the ground state energy is

1 1
(a) Z  (b) Z 
 
1 1 e k BT
k BT


1

m1  
1 kBT

o
(c) Z  (d) Z 

.c k T
2

m
1 e k BT

s e of n turns per unit length carries a current which
B

l a
increases linearly with time, i  Kt .gWhat is the magnetic field inside the solenoid at a given
Q9. A very long solenoid (axis along z direction)

a
time t ?
(a) B  0 nKtzˆ (b) B  0 nKzˆ

(c) B  0 nKt  xˆ  yˆ  (d) B  0 cnKtzˆ
 
Q10. Suppose  A is a conservative vector, A is a non-conservative vector and  is non-zero scalar

m
m c. o
everywhere. Which one of the following is true?

c. o   m
   
(a)   A  A  0 (b) A    0
s e
s em (c) A    0 (d)    A   A  0 gl
a
la
  

g a
a Q11. Consider two n  n matrices, A and B such that A  B is invertible. Define two matrices,

C  A  A  B  B and D  B  A  B  A . Which of the following relations always hold true?
1 1

(a) C  D (b) C 1  D (c) BCA  ADB (d) C  D

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

g 3
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 13

fiziks

Q12. The refractive index  n  of the entire environment around a double slit interference setup is

changed from n  1 to n  2 . Which one of the following statements is correct about the change
in the interference pattern?
(a) The fringe pattern disappears
(b) The central bright maximum turns dark, i.e. becomes a minimum
(c) Fringe width of the pattern increases by a factor 2
(d) Fringe width of the pattern decreases by a factor 2
Q13. A cyclotron can accelerate deuteron to 16 MeV . If the cyclotron is used to accelerate  -
particles, what will be their energy? Take the mass of deuteron to be twice the mass of proton
and mass of alpha particles to be four times the mass of protons.
(a) 8 MeV (b) 16 MeV (c) 32 MeV (d) 64 MeV
3 1
Q14. Consider a hypothetical world in which the electron has spin instead of . What will be the
2 2
electronic configuration for an element with atomic number Z  5 ?
(a) 1s 4 , 2s1 (b) 1s 4 , 2s 2 , 2 p1 (c) 1s 5 (d) 1s 3 , 2 s1 , 2 p1

Q15. Two objects of unit mass are thrown up vertically with a velocity of 1ms 1 at latitudes 450 N

and 450 S , respectively. The angular velocity of the rotation of Earth is given to be 7.29 105 s 1 .
In which direction will the objects deflect when they reach their highest point (due to Coriolis
force)? Assume zero air resistance.
(a) to the east in Northern hemisphere and west in Southern Hemisphere
(b) to the west in Northern hemisphere and east in Southern Hemisphere
(c) to the east in both hemispheres
(d) to the west in both hemispheres
Q16. Which one of the following vectors lie along the line of intersection of the two planes
x  3 y  z  5 and 2 x  2 y  4 z  3 ?

(a) 10 iˆ  2 ˆj  5kˆ (b) 10 iˆ  6 ˆj  8kˆ

(c) 10 iˆ  2 ˆj  5kˆ (d) 10 iˆ  2 ˆj  5kˆ

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 13
4

co m .
. e
em las

as fiziksag

What is the value of the integral  dx  x 2   2  cos x ?

Q17.


1 1
(a) 
m
(b)  (c)  (d) 0

co
2 
Q18.
.c om
Two joggers A and B are running at a steady pace around a circular track. A takes TA minutes
e m .
e m
whereas B takes TB   TA  minutes to complete one round. Assuming that they have started
l a s
l a s a g
a2g
together, what will be time taken by A to overtake B for the first time?
1
1 1 1  1 1 
(a) (b)  (c) (d)   
TA  TB TA TB TA  TB  TA TB 
Q19. The magnetic field (Gaussian units) in an empty space is described by
B  B0 exp  ax  sin  ky  t  zˆ

m
What is the y - component of the electric field?

c. oac B exp  ax  cos  ky  t 
em
ac
(a)  B0 sin  ky  t  (b) 

s (d) 0
 0

(c)  B0 sin  ky   t 
g l a
Q20. a
Let A be a hermitian matrix, and C and D be the unitary matrices. Which one of the following
matrices is unitary?
(a) C 1 AC (b) C 1 DC (c) C 1 AD (d) A1CD
 b2 x2 
Q21. The wave function   x   A exp    (for real constants A and b ) is a normalized eigen-
 2 

o m
m c
. is correct?
function of the Schrodinger equation for a particle of mass m and energy E in a one

c. o dimensional potential V  x  such that V  x   0 at x  0 . Which of thesfollowing
e m
em l aE   b
las b x b x b
a g
2 4 2 2 4 2 2 2 2 2

g
(a) V  (b) V  (c) E  (d)

a
m 2m 4m m

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

g 5
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 13

fiziks

Q22. A quantum particle of mass m is in a one dimensional potential of the form
1
 m x , if x  0
2 2
V  x   2
  if x  0

where  is a constant. Which one of the following represents the possible ground state wave
function of the particle?

 
1 1
(a) (b)
0 0
0 x  0 x 

1 1

 
1 1
(c) (d)
0 0
0 x  0 x 

1 1

 1 13 
Q23. Consider a 2  2 matrix A   27
 what is A ?
0 1 
 1 13   1 1327   1 27   1 351
(a)   (b)   (c)   (d)  
0 1  0 1  0 1  0 1 
Q24. Consider a grand ensemble of a system of one dimensional non-interacting classical harmonic
oscillators (each of frequency  ). Which one of the following equations is correct? Here the
angular bracket  indicate the ensemble average. N , E and T represent the number of particles,

energy and temperature, respectively. k B is the Boltzmann constant.

k BT k BT
(a) E  N (b) E  N
2 2
(c) E  Nk BT (d) E  N k BT

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 13
6

co m .
. e
em las

as fiziksag

Q25. A bullet with initial speed v0 is fired at a log of wood. The resistive force by wood on the bullet

is given by  v , where   1 . What is the time taken to stop the bullet inside the wood log?

m
co
m v0 1 m v0 1 m v01  v10

om .
(a) (b) (c) (d)

m
 1   1  1 m 1
.c s e
m a
e to go from town A to town B by taking either the route  R1  Rg2l with
s
PART- B: 3 Mark-Questions
Q1.
g a
l 1
A person plans
a
a 2 or the route  R1  R3 with probability 2 (see
probability
1
R2
1
figure). Further, there is a probability that R1 is blocked, a
3 R1
A B
1 1
probability that R 2 is blocked, and a probability that R3 is
3 3
R3
blocked. What is the probability that he/she would reach town B ?

m
8 1 4 2

c o
(a) (b) (c) (d)

. of the earth if its radius shrinks by 1% ?
9 3 9 3

m
ethe density is uniform.
s
Q2. What is the change in the kinetic energy of rotation
Assume that the mass remains the same a
g l (b) increases by 2%
and
(a) increases by 1% a
(c) decreases by 1% (d) decreases by 2%
Q3. Analysis the ideal op-amp circuit in the figure. Which one of the following statements is true
about the output voltage Vout , when terminal ‘ C ’ is connected to point ‘ A ’ and then to point
‘ B ’? R R

m
m c. o
c. o


e m
s


em la
Vin Vout

s ag
C

gla
a
A R B

(a) Vout  Vin and Vout  Vin when ‘ C ’ is connected to ‘ A ’ and ‘ B ’, respectively
(b) Vout  Vin and Vout  Vin when ‘ C ’ is connected to ‘ A ’ and ‘ B ’, respectively
(c) Vout  Vin when ‘ C ’ is connected to either ‘ A ’ or ‘ B ’
(d) Vout  Vin when ‘ C ’ is connected to either ‘ A ’ or ‘ B ’

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

g 7
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 13

fiziks

Q4. White light of intensity I 0 is incident normally on a filter plate of thickness d . The plate has a

 
wavelength    dependent absorption coefficient       0  1   per unit length. The band
 0 
pass edge of the filter is defined as the wavelength at which the intensity, after passig through the
I0
filter, is I  ,  0 , 0 and  are constants. The reflection coefficient of the plate may be

assumed to be independent of  . Which one of the following statements is true about the
bandwidth of the filter?
(a) The bandwidth is linear dependent on 0

(b) The bandwidth is independent of the plate thickness d
(c) The bandwidth is linearly dependent on  0

0
(d) The bandwidth is dependent on the ratio
d
Q5. Consider two concentric spherical metal shells of radii r1 and r2  r2  r1  . The outer shell has a

charge q and the inner shell is grounded. What is the charge on the inner shell?
r1 r1 r2
(a) q (b) q (c) 0 (d) q
r2 r2 r1
Q6. A wire with uniform line charge density  per unit length carries a current I as shown in the
figure. Take the permittivity and permeability of the medium to be  0  0  1 . A particle of

charge q is at a distance r and is travelling along a trajectory parallel to the wire. What is the
speed of the charge?

current  I
charge density   r V

   4
(a) (b) (c) (d)
I 2I 3I I

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 8 of 13
8

co m .
. e
em las

as fiziksag

Q7. Consider a non-relativistic two-dimensional gas of N electrons with the Fermi energy EF .

What is the average energy per particle at temperature T  0 ?

o m
3 2 1

m . c
(a) EF (b) EF (c) EF (d) EF

co is fed by a sinusoidal voltage V  V sin t . Assume that the cut-in
5 5 2

. e m
m is 0.7 volts and V is a positive dc voltage smaller than V . Which one s
a of
Q8. The circuit given below
ediode l
in 0

s
la statements is true about V ?
voltage of the
a g
g
1 0

a
the following out

R1
Vin Vout

V1
R1

m
c. o
R2

e m voltage of 0.7  R V
l a s
(a) Positive part of V is restricted to a maximum 2

g
R R
out 1

a
1 2

R
(b) Negative part of V is restricted to a maximum voltage of 0.7  V 2
R1  R2
out 1

R1
(c) Positive part of Vout is restricted to a maximum voltage of 0.7  V1
R1  R2
R1
(d) Negative part of Vout is restricted to a maximum voltage of 0.7  V1

m
R1  R2

m c. o
c. o circumference as shown in the figure. The acceleration due to gravity gseism
Q9. A hoop of diameter D is pivoted at the topmost point on the

s em acting downwards. What is the time period of small oscillationsglina the
la a
D g

ag plane of the hoop?

D 5D
(a) 2 (b) 2
2g 6g

D 2D
(c) 2 (d) 2
2g g

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

g 9
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 9 of 13

fiziks

1
Q10. For a spin particle placed in a magnetic field B , the Hamiltonian is H   BS y   S y ,
2
where S y is the y -component of the spin operator. The state of the system at time t  0 is


  t  0    , where S z     . At a later time t , if S z measured then what is the
2

probability to get a value  ?
2
 t 
(a) cos 2 t  (b) sin 2 t  (c) 0 (d) sin 2  
 2 
Q11. In a fixed target elastic scattering experiment, a projectile of mass m , having initial velocity v0 ,

and impact parameter b , approaches the scatterer. It experiences a central repulsive force
k
f r    k  0  . What is the distance of the closest approach d ?
r2
1 1
 k 2  k 2
(a) d   b 2  2  (b) d   b 2  2 
 mv0   mv0 

k
(c) d  b (d) d 
mv02

Q12. Consider a quantum particle in a one-dimensional box of length L . The coordinates of the
leftmost wall of the box is at x  0 and that of the rightmost wall is at x  L . The particle is in
the ground state at t  0 . At t  0 , we suddenly change the length of the box to 3L by moving
the right wall. What is the probability that the particle is in the ground state of the new system
immediately after the change?
9 81 0.5
(a) 0.36 (b) (c) (d) L
8 64 2 

Consider a function f  x   Pk  x  e
  in the domain x  ,  , where P is any
 
 x4  2 x2
Q13. k

polynomial of degree k . What is the maximum possible number of extrema of the function?
(a) k  3 (b) k  3 (c) k  2 (d) k  1

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 13
10

co m .
. e
em las

as fiziksag

Q14. The energy spectrum of a particle consists of four states with energies 0,, 2 ,3  . Let

Z B T  , Z F T  and Z C T  denote the canonical partition functions for four non-interacting

o m
c
particles at temperature T . The subscripts B, F and C corresponds to bosons, fermions and

m .
.co particles, respectively. Let y  exp   k T  . Which one of stheem
  

m a
distinguishable classical

s e g l
la
B

g
is true about Z T  , Z T  and Z T  ? a
a are polynomials in y of degree 12, 6 and 12 , respectively.
following statements B F C

(a) They
(b) They are polynomials in y of degree 16,10 and 16 , respectively
(c) They are polynomials in y of degree 9, 6 and 12 , respectively.
(d) They are polynomials in y of degree 12,10 and 16 , respectively.

m
Q15. Consider a quantum particle of mass m and a charge e moving in a two dimensional potential
given as:
. c o
V  x, y    x  y  em
s
k
a
k  x  y
2 2

2
g l
The particle is also subject to an a

external electric field E    iˆ  ˆj  , where  is a constant iˆ

and ĵ corresponds to unit vectors along x and y directions, respectively. Let E1 and E0 be the

energies of the first excited state and ground state, respectively. What is the value of E1  E0 ?

2k 2k
(a)  (b)   e 2

m
m m

m c. o
c. o m
2k 2k

e
(c) 3 (d) 3  e 2

em la s
m m

las ag
ag

o m . c
m
c
. www.physicsbyfiziks.com | Email: [email protected]
s e
m a
se l
Website:


11 For more Question Papers, Sample Papers, Notes & Syllabus visit
g
Page 11 of 13

fiziks

PART C: 3-Mark Numerical Questions
Q1. A thin uniform steel chain is 10 m long with a linear mass density of 2 kg m 1 . The chain hangs
vertically with one end attached to a horizontal axle, having a negligibly small radius compared
to its length. What is the work done (in N  m ) to slowly wind up the chain on to the axle? The
acceleration due to gravity is g  9.81 ms 1 .
Q2. A one-dimensional harmonic oscillator is in the state

1
  n
n 0 n!
 1
where n is the normalized energy eigenstate with eigenvalue  n    . Let the expectation
 2
1
value of the Hamiltonian in the state  be expressed as   . What is the value of  ?
2
Q3. The Euler polynomials are defined by

2e xs xn
  n   n!
e x  1 n 0
E s

What is the value of E5  2   E5  3 ?

Q4. What is the angle (in degrees) between the surfaces y 2  z 2  2 and y 2  x 2  0 at the point

1, 1,1
Q5. Consider a system of 15 non-interacting spin-polarized electrons. They are trapped in a two

dimensional isotropic harmonic oscillator potential V  x, y  
1
2
 
m 2 x 2  y 2 . The angular

frequency  is such that   1 in some chosen unit. What is the ground state energy of the
system in the same units?
Q6. Consider the motion of a particle in two dimensions given by the Lagrangian

L
m 2
2
 4

x  y 2   x  y 
2

where   0 . The initial conditions are given as y  0   0, x  0   42 meters, x  0   y  0   0 .

What is the value of x  t   y  t  at t  25 seconds in meters?

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 12 of 13
12

co m .
. e
em las

as fiziksag

Q7. A diatomic ideal gas at room temperature, is expanded at a constant pressure P0 . If the heat

absorbed by the gas is Q  14 Joules, what is the maximum work in Joules that can be extracted

o m
from the system?

m . c
.co e m
0

s
Q8. An optical line of wavelength 5000 A in the spectrum of light from a star is found to be red-

m of 2 A . Let v be the velocity at which the star is receding. Ignoring
shifted by aneamount l a
s
laeffects, what is the value of c ? g
0

g a
a
relativistic
v
Q9. In the Young’s double slit experiment (screen distance D  50 cm and d  0.1 cm ), a thin mica
sheet of refractive index n  1.5 is introduced in the path of one of the beams. If the central
fringe gets shifted by 0.2 , what is the thickness (in micrometer) of the mica sheet?
Q10. A circular metal loop of radius a  1 m spins with a constant angular velocity 

o m
c
  20 rad/s in a magnetic field B  3 Tesla, as shown in the figure. The
resistance of the loop is 10 Ohms. Let P be. the power dissipated in one
m
B

P se
complete cycle. What is the value of lain Watts?
a

ag
3

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

o m . c
m
c
. www.physicsbyfiziks.com | Email: [email protected]
s e
m a
se l
Website:


13 For more Question Papers, Sample Papers, Notes & Syllabus visit
g
Page 13 of 13