JEST 2016 Question Paper Physics

FOR JEST EXAM PREPARATION

JEST 2016
Question Paper ·
Physics
EXAM YEAR TYPE SUBJECT

JEST 2016 Question Paper Physics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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JEST 2016
PART- A

m
⎛2 1⎞ ⎛πM ⎞

co
Q1. Given a matrix M = ⎜ ⎟ , which of the following represents cos ⎜ ⎟

om .
⎝1 2⎠ ⎝ 6 ⎠

.c (b) 3 ⎛ 1 −1⎞ e m
1 ⎛1 2⎞
e m
3 ⎛ 1 1⎞ 1⎛ 1 3⎞
l a s
s
⎜ ⎟
g
(a) ⎜ ⎟ ⎜ ⎟ (c) ⎜ ⎟ (d)

a
2 ⎜⎝ 3 1 ⎟⎠
a
4 ⎝ −1
l
2 ⎝2 1⎠ 1⎠ 4 ⎝ 1 1⎠

Q2.
a g
The wavefunction of a hydrogen atom is given by the following superposition of energy
eigen functions υ/ nlm ( r ) ( n, l , m are the usual quantum numbers):

2 3 1
υ/ ( r ) = υ/ 100 ( r ) − υ/ 210 ( r ) + υ/ 322 ( r )
7 14 14
The ratio of expectation value of the energy to the ground state energy and the
expectation value of L2 are, respectively:
o m 12
(b).
c
e m 504 and 7
229 12 2 101 2

s
(a) and

la (d) 229 and
504 7

(c)
101
504
and 2
a g 504
2

Q3. It is found that when the resistance R indicated in the figure below is changed from
1 kΩ to 10 kΩ the current flowing through the resistance R′ does not change. What is
10 kΩ
the value of the resistor R′ ?

m
1k Ω R 1kΩ

m c. o
c. o R′
s em
s em la
gla
10 kΩ
ag
a 5V
(a) 5 kΩ (b) 100 kΩ (c) 10 kΩ (d) 1 kΩ

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Q4. A hoop of radius a rotates with constant angular velocity ω about
the vertical axis as shown in the figure. A bead of mass m can slide
on the hoop without friction. If g < ω 2 a at what angle θ apart from
a
dθ d θ 2
0 and π is the bead stationary (i.e., = 2 = 0 )?
dt dt
θ
πg g
(a) tan θ = 2 (b) sin θ =
ω a ω 2a
g g
(c) cos θ = (d) tan θ =
ω a
2
πω 2 a
1
Q5. A spin- particle in a uniform external magnetic field has energy eigenstates 1 and 2 .
2

The system is prepared in ket-state
( 1 + 2 ) at time t = 0. It evolves to the state
2

described by the ket
( 1 − 2 ) in time T . The minimum energy difference between two
2
levels is:
h h h h
(a) (b) (c) (d)
6T 4T 2T T
Q6. You receive on avenge 5 emails per day during a 365 -days year. The number of days on
average on which you do not receive any emails in that year are:
(a) more than 5 (b) More than 2
(c) 1 (d) None of the above
Q7. The H 2 molecule has a reduced mass M = 8.35 × 10−28 kg and an equilibrium

internuclear distance R = 0.742 × 10−10 m . The rotational energy in terms of the rotational
quantum number J is
5
(a) Erot ( J ) = 7 J ( J − 1) meV (b) Erot ( J ) = J ( J + 1) meV
2
5
(c) Erot ( J ) = 7 J ( J + 1) meV (d) Erot ( J ) = J ( J − 1) meV
2

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Q8. The maximum relativistic kinetic energy of β particles from a radioactive nucleus is
equal to the rest mass energy of the particle. A magnetic field is applied perpendicular to
the beam of β particles, which bends it to a circle of radius R . The field is given by:
m
3m0 c
om eR
2m0 c 3m0 c 3m0 c
. co
.c e m
(a) (b) (c) (d)

m s
eR eR 2eR

s e ( θ )
g l a
a
= +
a
Q9. The central force which results in the orbit r a 1 cos for a particle is proportional

g l
a
to:
2 −2
(a) r (b) r (c) r (d) None o the above
Q10. A gas of N molecules of mass m is confined in a cube of volume V = L3 at temperature
T . The box is in a uniform gravitational field − gzˆ . Assume that the potential energy of a

molecule is U = mgz where z ∈ [ 0, L ] is the vertical coordinate inside the box. The

pressure P ( z ) at height z is:
m
. co
em
⎛ ⎛ L⎞⎞ ⎛ ⎛ L⎞⎞
⎜ mg ⎜ z − 2 ⎟ ⎟
exp ⎜ − ⎝ ⎠⎟
l a s ⎜ mg ⎜ z − 2 ⎟ ⎟
exp ⎜ − ⎝ ⎠⎟

N mgL
⎜
⎜
⎝
k BT ⎟
⎟
⎠ a g N mgL
⎜
⎜
⎝
k BT ⎟
⎟
⎠
(a) P ( z ) = (b) P ( z ) =
V 2 ⎛ mgL ⎞ V 2 ⎛ mgL ⎞
sinh ⎜ ⎟ cosh ⎜ ⎟
⎝ 2 k BT ⎠ ⎝ 2 k BT ⎠
k BTN N
(c) P ( z ) = (d) P ( z ) = mgz
V V

m
Q11. A transistor in common base configuration has ratio of collector current to emitter current

m
β and ratio of collector to base current α . Which of the following is true?
c. o
c. o (a) β = α (α + 1)
s e m
em la
(b) β =

las (α + 1) α
ag
ag (c) β =
α
(d) β =
(α − 1)
(α − 1) α

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Q12. The energy of a particle is given by E = p + q where p and q are the generalized

momentum and coordinate, respectively. All the states with E ≤ E0 are equally probable

and states with E > E0 are inaccessible. The probability density of finding the particle at

coordinate q , with q > 0 is:

(a)
( E0 + q ) (b)
q
(c)
( E0 − q ) (d)
1
2
E0 E02 E 2
0 E0
Q13. Consider a quantum particle of mass m in one dimension in an infinite potential well, i.e.,
−a a a
V ( x ) = 0 for <x< and V ( x ) = ∞ for x≥ . A small perturbation,
2 2 2
2∈ x
V ′( x) = is added. The change in the ground state energy to O (∈) is:
a
∈ ∈
(a)
2π 2
π2 −4( ) (b)
2π 2
(
π2 +4 )
∈π 2 2 ∈π 2 2
(c)
2
(π + 4 ) (d)
2
(π − 4 )
Q14. The strength of magnetic field at the center of a regular hexagon with sides of length a
carrying a steady current I is:
μ0 I 6 μ0 I 3μ0 I 3μ 0 I
(a) (b) (c) (d)
3π a πa πa πa
Q15. An ideal gas with adiabatic exponent γ undergoes a process in which its pressure P is
related to its volume V by the relation P = P0 − αV , where P0 and α are positive
constants. The volume starts from being very close to zero and increases monotonically
P0
to . At what value of the volume during the process does the gas have maximum
α
entropy?
P0 γ P0 γ P0 P0
(a) (b) (c) (d)
α (1 + γ ) α (1 − γ ) α (1 + γ ) α (1 − γ )

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Q16. A point charge q of mass m is released from rest at a distance d from an infinite
grounded con ducting plane (ignore gravity). How long does it take for the charge to hit
the plane?
m
2π 3 ∈0 md 3
om
2π 3 ∈0 md
. co
.c e m
(a) (b)

m s
q q

s e g l a
qa
l a
π ∈0 md
3 3
π ∈0 md
3

ag
(c) (d)
q
N 1
Q17. A two dimensional box in a uniform magnetic field B contains localised spin-
2 2
N
particles with magnetic moment μ , and free spinless particles which do not interact
2
with each other. The average energy of the system at a temperature T is:

m N μ B tanh ⎜ k T ⎟
c. o 2
1 ⎛ μB ⎞ 1 ⎛ μB ⎞
(a) 3 NkT − N μ B sinh ⎜ ⎟ (b) NkT −

m
2 ⎝ k BT ⎠ ⎝ ⎠
e 3
B

⎛ μB ⎞
l a s (d) NkT + N μ B cosh ⎜ ⎟
⎛ μB ⎞
g
1 1 1
NkT − N μ B tanh ⎜
a
(c) ⎟
2 2 ⎝ k BT ⎠ 2 2 ⎝k T ⎠ B

Q18. If Yxy =
1
2
(Y22 − Y2,−2 ) where Yl ,m are spherical harmonics then which of the following is
true?
(a) Yxy is an eigenfunction of both L2 and Lz

m
c. o
(b) Yxy is an eigenfunction of L2 but not Lz

m
c. o e m
(c) Yxy is an eigenfunction both of Lz but not L2

em (d) Y is not an eigenfunction of either L and L la s
s ag
2

l a
xy z

ag Q19. The value of the integral ∫ ( x + 1) dx
ln x ∞

0 2

π2 π2
(a) (b) (c) π 2 (d) 0
4 2

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Q20.
⎛ 1 ⎞
A spin- 1 particle is in a state υ/ described by the colunm matrix ⎜ ⎟ 2,
⎝ 10 ⎠
{ 2, 2i }
in the S z basis. What is the probability that a measurement of operator S z will yield the

result h for the state S x υ/ ?

1 1 1 1
(a) (b) (c) (d)
2 3 4 6
Q21. Consider N non-interacting electrons ( N ∼ N A ) in a box of sides Lx , Ly , Lz Assuming

that the dispersion relation is ∈ ( k ) = Ck 4 where C is a constant, the ratio of the ground

state energy per particle to the Fermi energy is:
3 7 3 5
(a) (b) (c) (d)
7 3 5 7
Q22. The Hamiltonian of a quantum particle of mass in confined to a ring of unit radius is:

⎛ ∂
2
⎞
2
H= ⎜ −i −α ⎟
2m ⎝ ∂θ ⎠
where θ is the angular coordinate, α is a constant. The energy eigenvalues and
eigenfunctions of the particle are ( n is an integer):
einθ 2
(a) υ/ n (θ ) = (n −α )
2
and En =
2π 2m
sin ( nθ ) 2
(b) υ/ n (θ ) = (n −α )
2
and En =
2π 2m
cos ( nθ ) 2
(c) υ/ n (θ ) = (n −α )
2
and En =
2π 2m

einθ 2
(d) υ/ n (θ ) = (n +α )
2
and En =
2π 2m
1 1 1
Q23. The sum of the infinite series 1 − + − + ... is
3 5 7
π π
(a) 2π (b) π (c) (d)
2 4

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Q24. Light takes approximately 8 minutes to travel from the Sun to the Earth. Suppose in the
frame of the Sun an event occurs at t = 0 at the Sun and another event occurs on Earth at
t = 1 minute. The velocity of the inertial frame in which both these events are

m
mvector pointing from Earth to Sun . co
simultaneous is:

.c o e m
s
c

m a
(a) with the velocity

s e l
8

a a g
8 gl
c

a
(b) with the velocity vector pointing from Sun to Earth : -

(c) The events can never be simultaneous - no such frame exists
2
⎛1⎞
(d) c 1 − ⎜ ⎟ with velocity vector Pointing from to Earth
⎝8⎠
Q25. A spherical shell of radius R carries a constant surface charge density σ and is rotating

m
about one of its diameters with an angular velocity ω . The magnitude of the magnetic

c. o
m 4πσω R
moment of the shell is:

s e(c)
a
4πσω R 4 4
4πσω R 4
l
(a) 4πσω R 4
g
(b) (d)

a
3 15 9
Part-B: (1-Mark Questions)
d
Q26. The adjoint of a differential operator acting on a wavefunction υ/ ( x ) for a quantum
dx
mechanical system is:
d d d d
(a) (b) −i (c) − (d) i

m
dx dx dx dx

m c. o
c. o q = 6πη r ( v + v ) is moving upwards with a terminal velocity v due
Q27. In Millikan’s oil-drop experiment an oil drop of radius r , mass m and charge

e mto an applied
em l a s
s
1 2

la g
2

a The acceleration
E

ag electric field of magnitude E , where η is the coefficient of viscosity.
due to gravity is given
6πη rv1 3πη r v1 6πη r v2 3πη r v2
(a) g = (b) g = (c) g = (d) g =
m m m m

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⎛ π⎞
Q28. The electric field E = E0 sin (ωt − kz ) xˆ + 2 E0 sin ⎜ ωt − kz + ⎟ yˆ represents:
⎝ 2⎠
(a) a linwearly polarized wave
(b) a right-hand circularly polarized wave
(c) a left-hand circularly polarized wave
(d) an elliptically polarized wave
CP
Q29. An ideal gas has a specific heat ratio = 2 . Starting at a temperature T1 the gas under
CV
goes an isothermal compression to increase its density by a factor of two. After this an
adiabatic compression increases its pressure by a factor of two. The temperature of the
gas at the end of the second process would be:
T1 T1
(a) (b) 2T1 (c) 2T1 (d)
2 2
Q30. Suppose yz plane forms the boundary between two linear dielectric media I and II
with dielectric constant ∈I = 3 and ∈II = 4 , respectively. If the electric field in region I at

the interface is given by EI = 4 xˆ + 3 yˆ + 5 zˆ , then the electric field EII at the interface in
region II is:
(a) 4 xˆ + 3 yˆ + 5 zˆ (b) 4 xˆ + 0.75 yˆ − 1.25 zˆ
(c) −3xˆ + 3 yˆ + 5 zˆ (d) 3xˆ + 3 yˆ + 5 zˆ
Q31. Given the condition ∇ φ = 0 , the solution of the equation ∇ 2ψ = k ∇φ .∇φ is given by
2

kφ 2 kφ ln φ kφ ln φ
(a) ψ = (b) ψ = kφ 2 (c) ψ = (d)ψ =
2 2 2
Q32. Circular fringes are obtained with a Michelson interferometer using 600 nm laser light.
What minimum displacement of one mirror will make the central fringe from bright to
dark?
o
(a) 600 nm (b) 300 nm (c) 150 nm (d) 120 A

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2π
Q33. If k is the wavevector of incident light ( k = , λ is the wavelength of light) and G is
λ
a reciprocal lattice vector, then the Bragg’s law can be written as:

m
co
(a) k + G = 0 (b) 2k .G + G 2 = 0
(c) 2k .G + k = 0
.c om (d) k .G = 0
e m .
s
2

e m
For the coupled system shown in the figure, the normal coordinates are x1 + x2 and
l a
s
Q34.

l a a g
ag
x1 − x2 corresponding to the normal frequencies ω0 and 3ω0 respectively.
x1 x2
k k k

m m

At t = 0 , the displacements are x1 = A , x2 = 0 , and the velocities are v1 = v2 = 0 . The

displacement of the second particle at time t is given by:

o m A ( cos (ω t ) − cos ( 3ω t ))
( ( 3ω t )) .c
A
(a) x2 ( t ) = cos (ω0t ) + cos (b) x2 ( t ) =

e m
0 0 0
2 2

( ( )) las A⎛ ⎞
( )
ag
A 1
(c) x2 ( t ) =
sin (ω0t ) − sin 3ω0t (d) x2 ( t ) = ⎜ sin (ω0t ) − sin 3ω0t ⎟
2 2⎝ 3 ⎠
Q35. How much force does light from a 1.8 W laser exe when it is totally absorbed by an
object?
(a) 6.0 ×10−9 N (b) 0.6 ×10−9 N (c) 0.6 × 10−8 N (d) 4.8 ×10−9 N
Q36. An electron confined within a thin layer of semiconductor may be treated as a free

m
particle inside an infinitely deep one-dimensional potential well. If the difference in

m c. o
energies between the first and the second energy levels is δ E , then the thickness of the

c. o layer is: s emπ
s em (a) 3 π la
la ag
2 2
2 π 2 2
π2 2 2 2

g
(b) (c) (d)
2mδ E 3mδ E 2mδ E mδ E
a

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Q37. The half-life of a radioactive nuclear source is 9 days. The fraction of nuclei which are
left under cayed after 3 days is:
7 1 5 1
(a) (b) (c) (d) 1
8 3 6 3
2
Q38. Self inductance per unit length of a long solenoid of radius R with n turns per unit
length is:
(a) μ0π R 2 n 2 (b) 2μ0π R 2 n

(c) 2μ0π R 2 n 2 (d) μ0π R 2 n
Q39. A gas contains particles of type A with fraction 0.8 , and particles of type B with
fraction 0.2 . The probability that among 3 randomly chosen particles at least one is of
type A is:
(a) 0.8 (b) 0.25 (c) 0.33 (d) 0.992
Q40. The number of different Bravais lattices possible in two dimensions is:
(a) 2 (b) 3 (c) 5 (d) 6
Q41. The output intensity I of radiation from a single mode of resonant cavity obeys
d ω
I =− 0 I
dt Q
where Q is the quality factor of the cavity ω0 is the resonant frequency. The form of the
frequency spectrum of the output is:
(a) Delta function (b) Gaussian (c) Lorentzian (d) Exponential
⎛ 1⎞
Q42. For a quantum mechanical harmonic oscillator with energies, En = ⎜ n + ⎟ ω , where
⎝ 2⎠
n = 0,1, 2... , the partition function is:
ω ω
k BT ω ω 2 k BT
e e
(a) ω
(b) e 2 kBT − 1 (c) e 2 kBT + 1 (d) ω

e 2 kBT −1 e kBT −1

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Q43. If the direction with respect to a right-handed cartesian coordinate system of the ket
vector z , + is (0. u. I), then the direction of the ket vector obtained by application of

m
⎛ π⎞ ⎛ π⎞

co
rotations: exp ⎜ −iσ z ⎟ exp ⎜ iσ y ⎟ , on the ket z , + is ( σ y , σ z are the Pauli matrices):

om .
⎝ 2⎠ ⎝ 4⎠

.c e m
s
(a) ( 0, 1, 0 ) (b) (1, 0, 0 )

(1, 1, s0 )e m l a
l2a ( ) 1, 1, 1
a g
g
Q44. In theaground state of hydrogen atom, the most probable distance of the electron from the
(c) (d)
3

nucleus, in units of Bohr radius a0 is:

1 3
(a) (b) 1 (c) 2 (d)
2 2
Q45. For operators P and Q , the commutator ⎡⎣ P, Q −1 ⎤⎦ is

m
(a) Q −1 [ P, Q ] Q −1
c. o
(b) −Q −1 [ P, Q ] Q −1 (c) Q −1 [ P, Q ] Q (d) −Q [ P, Q ] Q −1

e m x
a s
Q46. The mean value of random variable with probability density

g l
a
1 ⎡ ( x + μ x) ⎤ 2

p ( x) = .exp ⎢ − ⎥ is:
σ 2π ⎢ ( 2σ ) ⎥
⎣
2
⎦
μ −μ
(a) 0 (b) (c) (d) σ
2 2

Q47. A spin
1
particle is in a state
( ↑ + ↓ ) where ↑ and ↓ are the eigenstates of S
m
z
2 2

m c. o
c. o direction is: m
operator. The expectation value of the spin angular momentum measured along x

s e
s em (a) g l a
la a 2
(b) −
g
(c) 0 (d)

a Q48. A semicircular piece of paper is folded to make a cone with the centre of the semicircle
as the apex. The half-angle of the resulting cone would be:
(a) 90o (b) 60o (c) 45o (d) 30o

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Q49. If the Rydberg constant of an atom of finite nuclear mass is α R∞ , where R∞ the Rydberg
constant corresponding to an infinite nuclear mass, the ratio of the electronic to nuclear
mass of the atom is:-

(a)
(1 − α ) (b)
(α − 1) (c) (1 − α ) (d)
1
α α α
Q50. A cylindrical shell of mass in has an outer radius b and an inner radius a . The moment
of inertia of the shell about the axis of the cylinder is:

(a)
1
2
(
m b2 − a 2 ) (b)
1
2
(
m b2 + a 2 ) (
(c) m b 2 + a 2 ) (
(d) m b 2 − a 2 )

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