GATE 2022 Question Paper PH Physics

GATE 2022 General Aptitude
Q.1 – Q.5 Carry ONE mark each.

Q.1 You should _________ when to say _________.

(A) no / no

(B) no / know

(C) know / know

(D) know / no

Q.2 Two straight lines pass through the origin (𝑥 , 𝑦 ) = (0,0). One of them passes
through the point (𝑥 , 𝑦 ) = (1,3) and the other passes through the point
(𝑥 , 𝑦 ) = (1,2).

What is the area enclosed between the straight lines in the interval [0, 1] on
the 𝑥-axis?

(A) 0.5

(B) 1.0

(C) 1.5

(D) 2.0

Page 1 of 42

Q.3 If

𝑝∶𝑞=1∶2

𝑞∶𝑟=4∶3

𝑟∶𝑠=4∶5

and 𝑢 is 50% more than 𝑠, what is the ratio 𝑝 ∶ 𝑢?

(A) 2 ∶ 15

(B) 16 ∶ 15

(C) 1: 5

(D) 16: 45

Page 2 of 42

Q.4 Given the statements:

 P is the sister of Q.
 Q is the husband of R.
 R is the mother of S.
 T is the husband of P.

Based on the above information, T is ______ of S.

(A) the grandfather

(B) an uncle

(C) the father

(D) a brother

Page 3 of 42

Q.5 In the following diagram, the point R is the center of the circle. The lines PQ
and ZV are tangential to the circle. The relation among the areas of the squares,
PXWR, RUVZ and SPQT is

(A) Area of SPQT = Area of RUVZ = Area of PXWR

(B) Area of SPQT = Area of PXWR  Area of RUVZ

(C) Area of PXWR = Area of SPQT  Area of RUVZ

(D) Area of PXWR = Area of RUVZ  Area of SPQT

Page 4 of 42

Q. 6 – Q. 10 Carry TWO marks each.

Q.6 Healthy eating is a critical component of healthy aging. When should one start
eating healthy? It turns out that it is never too early. For example, babies who
start eating healthy in the first year are more likely to have better overall health
as they get older.

Which one of the following is the CORRECT logical inference based on the
information in the above passage?

(A) Healthy eating is important for those with good health conditions, but not for
others

(B) Eating healthy can be started at any age, earlier the better

(C) Eating healthy and better overall health are more correlated at a young age, but
not older age

(D) Healthy eating is more important for adults than kids

Page 5 of 42

Q.7 P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ 𝑥 per
month for 8 months of the year in a partnership business. The profit is shared in
proportion to the total investment made in that year.

If at the end of that investment year, Q receives of the total profit, what is the

value of 𝑥 (in ₹)?

(A) 2500

(B) 3000

(C) 4687

(D) 8437

Page 6 of 42

Q.8 16
14
14
12 11
10 9

Frequency
8 7
6
4
4 3
2
2
0
3 4 5 6 7 8 9
Marks

The above frequency chart shows the frequency distribution of marks obtained
by a set of students in an exam.

From the data presented above, which one of the following is CORRECT?

(A) mean > mode > median

(B) mode > median > mean

(C) mode > mean > median

(D) median > mode > mean

Q.9 In the square grid shown on the left, a person standing at P2 position is required
to move to P5 position.

Page 7 of 42

The only movement allowed for a step involves, “two moves along one
direction followed by one move in a perpendicular direction”. The permissible
directions for movement are shown as dotted arrows in the right.

For example, a person at a given position Y can move only to the positions
marked X on the right.

Without occupying any of the shaded squares at the end of each step, the
minimum number of steps required to go from P2 to P5 is

1 2 3 4 5

P

Q

R

S

T

Example: Allowed steps for a person at Y

(A) 4

(B) 5

(C) 6

(D) 7

Page 8 of 42

Q.10

Consider a cube made by folding a single sheet of paper of appropriate shape.
The interior faces of the cube are all blank. However, the exterior faces that are
not visible in the above view may not be blank.

Which one of the following represents a possible unfolding of the cube?

(A)

(B)

(C)

(D)

END OF THE QUESTION PAPER

Page 9 of 42

Q.11 – Q.35 Carry ONE mark Each

Q.11 For the Op-Amp circuit shown below, choose the correct output waveform
corresponding to the input 𝑉 = 1.5 sin 20𝜋𝑡 (in Volts). The saturation voltage
for this circuit is 𝑉 = ±10 V.

(A)

(B)

Page 10 of 42

(C)

(D)

Page 11 of 42

Q.12 Match the order of 𝛽 – decays given in the left column to appropriate clause in the
right column. Here 𝑋(𝐼 ) and 𝑌(𝐼 ) are nuclei with intrinsic spin 𝐼 and parity 𝜋.

1. 𝑋 →𝑌 i) First forbidden 𝛽-decay

2. 𝑋 →𝑌 ii) Second forbidden 𝛽-decay

3. 𝑋(3 ) → 𝑌(0 ) iii) Third forbidden 𝛽-decay

4. 𝑋(4 ) → 𝑌(0 ) iv) Allowed 𝛽-decay

(A) 1 – i, 2 – ii, 3 – iii, 4 – iv

(B) 1 – iv, 2 – i, 3 – ii, 4 – iii

(C) 1 – i, 2 – iii, 3 – ii, 4 – iv

(D) 1 – iv, 2 – ii, 3 – iii, 4 – i

Q.13 What is the maximum number of free independent real parameters specifying an
𝑛-dimensional orthogonal matrix?

(A) 𝑛(𝑛 − 2)

(B) (𝑛 − 1)

(C) 𝑛(𝑛 − 1)
2

(D) 𝑛(𝑛 + 1)
2

Page 12 of 42

An excited state of Ca atom is [Mg]3p54s23d1. The spectroscopic terms corresponding to
Q.14 the total orbital angular momentum are

(A) S, P, and D

(B) P, D, and F

(C) P and D

(D) S and P

Q.15 On the surface of a spherical shell enclosing a charge free region, the electrostatic
potential values are as follows: One quarter of the area has potential 𝜙 , another
quarter has potential 2𝜙 and the rest has potential 4𝜙 . The potential at the
centre of the shell is

(You can use a property of the solution of Laplace’s equation.)

(A) 11
𝜙
4

(B) 11
𝜙
2

(C) 7
𝜙
3

(D) 7
𝜙
4

Page 13 of 42

Q.16 A point charge q is performing simple harmonic oscillations of amplitude 𝐴 at
angular frequency 𝜔. Using Larmor’s formula, the power radiated by the charge is
proportional to

(A) 𝑞𝜔 𝐴

(B) 𝑞𝜔 𝐴

(C) 𝑞 𝜔 𝐴

(D) 𝑞 𝜔 𝐴

Q.17 Which of the following relationship between the internal energy 𝑈 and the Helmholtz’s
free energy 𝐹 is true?

(A) 𝐹
𝜕 𝑇
𝑈 = −𝑇
𝜕𝑇

(B) 𝐹
𝜕 𝑇
𝑈 = +𝑇
𝜕𝑇

(C) 𝜕𝐹
𝑈 = +𝑇
𝜕𝑇

(D) 𝜕𝐹
𝑈 = −𝑇
𝜕𝑇

Page 14 of 42

Q.18 If nucleons in a nucleus are considered to be confined in a three-dimensional cubical box,
then the first four magic numbers are

(A) 2, 8, 20, 28

(B) 2, 8, 16, 24

(C) 2, 8, 14, 20

(D) 2, 10, 16, 28

Q.19 Consider the ordinary differential equation

𝑦 − 2𝑥𝑦 + 4𝑦 = 0

and its solution 𝑦(𝑥) = 𝑎 + 𝑏𝑥 + 𝑐𝑥 . Then

(A) 𝑎 = 0, 𝑐 = −2𝑏 ≠ 0

(B) 𝑐 = −2𝑎 ≠ 0, 𝑏 = 0

(C) 𝑏 = −2𝑎 ≠ 0, 𝑐 = 0

(D) 𝑐 = 2𝑎 ≠ 0, 𝑏 = 0

Page 15 of 42

Q.20 For an Op-Amp based negative feedback, non-inverting amplifier, which of the
following statements are true?

(A) Closed loop gain < Open loop gain

(B) Closed loop bandwidth < Open loop bandwidth

(C) Closed loop input impedance > Open loop input impedance

(D) Closed loop output impedance < Open loop output impedance

Q.21 From the pairs of operators given below, identify the ones which commute. Here 𝑙
and 𝑗 correspond to the orbital angular momentum and the total angular
momentum, respectively.

(A) 𝑙 ,𝑗

(B) 𝑗 ,𝑗

(C) 𝑗 ,𝑙

(D) 𝑙 ,𝑗

Page 16 of 42

Q.22 For normal Zeeman lines observed ∥ and ⊥ to the magnetic field applied to an
atom, which of the following statements are true?

(A) Only 𝜋-lines are observed ∥ to the field

(B) 𝜎-lines ⊥ to the field are plane polarized

(C) 𝜋-lines ⊥ to the field are plane polarized

(D) Only 𝜎-lines are observed ∥ to the field

Q.23 Pauli spin matrices satisfy

(A) 𝜎 𝜎 − 𝜎 𝜎 = 𝑖𝜖 𝜎

(B) 𝜎 𝜎 − 𝜎 𝜎 = 2𝑖𝜖 𝜎

(C) 𝜎 𝜎 +𝜎 𝜎 =𝜖 𝜎

(D) 𝜎 𝜎 + 𝜎 𝜎 = 2𝛿

Page 17 of 42

Q.24 For the refractive index 𝑛 = 𝑛 (𝜔) + 𝑖𝑛 (𝜔) of a material, which of the
following statements are correct?

(A) 𝑛 can be obtained from 𝑛 and vice versa

(B) 𝑛 could be zero

(C) 𝑛 is an analytic function in the upper half of the complex  plane

(D) 𝑛 is independent of 𝜔 for some materials

Q.25 Complex function 𝑓(𝑧) = 𝑧 + |𝑧 − 𝑎| (𝑎 is a real number) is

(A) continuous at (𝑎, 𝑎)

(B) complex-differentiable at (𝑎, 𝑎)

(C) complex-differentiable at (𝑎, 0)

(D) analytic at (𝑎, 0)

Page 18 of 42

Q.26 If 𝑔(𝑘) is the Fourier transform of 𝑓(𝑥), then which of the following are true?

(A) 𝑔(−𝑘) = +𝑔∗ (𝑘) implies 𝑓(𝑥) is real

(B) 𝑔(−𝑘) = −𝑔∗ (𝑘) implies 𝑓(𝑥) is purely imaginary

(C) 𝑔(−𝑘) = +𝑔∗ (𝑘) implies 𝑓(𝑥) is purely imaginary

(D) 𝑔(−𝑘) = −𝑔∗ (𝑘) implies 𝑓(𝑥) is real

Q.27 The ordinary differential equation

(1 − 𝑥 )𝑦′′ − 𝑥𝑦′ + 9𝑦 = 0

has a regular singularity at

(A) −1

(B) 0

(C) +1

(D) no finite value of 𝑥

Page 19 of 42

Q.28 For a bipolar junction transistor, which of the following statements are true?

(A) Doping concentration of emitter region is more than that in collector and base
region

(B) Only electrons participate in current conduction

(C) The current gain 𝛽 depends on temperature

(D) Collector current is less than the emitter current

Q.29 Potassium metal has electron concentration of 1.4 × 10 m3 and the
corresponding density of states at Fermi level is 6.2 × 10 Joule1 m3. If the
Pauli paramagnetic susceptibility of Potassium is 𝑛 × 10 in standard scientific
form, then the value of k (an integer) is __________ (Magnetic moment of
electron is 9. 3 × 10 Joule T1; permeability of free space is 4𝜋 × 10 T m
A1)

Q.30 A power supply has internal resistance 𝑅 and open load voltage 𝑉 = 5 V. When
a load resistance 𝑅 is connected to the power supply, a voltage drop of 𝑉 = 4 V
is measured across the load. The value of is __________ (Round off to the
nearest integer)

Page 20 of 42

Q.31 Electric field is measured along the axis of a uniformly charged disc of radius 25
cm. At a distance 𝑑 from the centre, the field differs by 10% from that of an
infinite plane having the same charge density. The value of 𝑑 is _______cm.
(Round off to one decimal place)

Q.32 In a solid, a Raman line observed at 300 cm1 has intensity of Stokes line four
times that of the anti-Stokes line. The temperature of the sample is _______K.
(Round off to the nearest integer) (1 cm1 ≡ 1.44 K)

Q.33 An electromagnetic pulse has a pulse width of 103 s. The uncertainty in the
momentum of the corresponding photon is of the order of 10 kg m s1, where 𝑁
is an integer. The value of 𝑁 is ____________ (speed of light = 3 × 10 m s1,
ℎ = 6.6 × 10 J s)

Q.34 The wavefunction of a particle in a one-dimensional infinite well of size 2𝑎 at a
certain time is 𝜓(𝑥) = √2sin + √3cos + cos . Probability of
√
finding the particle in n = 2 state at that time is ______% (Round off to the nearest
integer)

Page 21 of 42

Q.35 A spectrometer is used to detect plasma oscillations in a sample. The spectrometer
can work in the range of 3 × 10 rad s1 to 30 × 10 rad s1. The minimum
carrier concentration that can be detected by using this spectrometer is 𝑛 × 10
m. The value of 𝑛 is _____________ (Round off to two decimal places)

(Charge of an electron = −1.6 × 10 C, mass of an electron = 9.1 × 10 kg
and 𝜖 = 8.85 × 10 C2 N1 m2)

Q.36 – Q.65 Carry TWO marks Each

Q.36 Consider a non-interacting gas of spin 1 particles, each with magnetic moment 𝜇,
placed in a weak magnetic field 𝐵, such that ≪ 1. The average magnetic
moment of a particle is

(A) 2𝜇 𝜇 𝐵
3 𝑘 𝑇

(B) 𝜇 𝜇𝐵
2 𝑘 𝑇

(C) 𝜇 𝜇𝐵
3 𝑘 𝑇

(D) 3𝜇 𝜇 𝐵
4 𝑘 𝑇

Page 22 of 42

Q.37 Water at 300 K can be brought to 320 K using one of the following processes.

Process 1: Water is brought in equilibrium with a reservoir at 320 K directly.

Process 2: Water is first brought in equilibrium with a reservoir at 310 K and then
with the reservoir at 320 K.

Process 3: Water is first brought in equilibrium with a reservoir at 350 K and then
with the reservoir at 320 K.

The corresponding changes in the entropy of the universe for these processes are
∆𝑆 , ∆𝑆 and ∆𝑆 , respectively. Then

(A) ∆𝑆 > ∆𝑆 > ∆𝑆

(B) ∆𝑆 > ∆𝑆 > ∆𝑆

(C) ∆𝑆 > ∆𝑆 > ∆𝑆

(D) ∆𝑆 > ∆𝑆 > ∆𝑆

Page 23 of 42

Q.38 A student sets up Young’s double slit experiment with electrons of momentum 𝑝
incident normally on the slits of width w separated by distance 𝑑. In order to
observe interference fringes on a screen at a distance 𝐷 from the slits, which of the
following conditions should be satisfied?

(A) ℏ 𝐷𝑤
>
𝑝 𝑑

(B) ℏ 𝑑𝑤
>
𝑝 𝐷

(C) ℏ 𝑑
>
𝑝 𝐷

(D) ℏ 𝑑
>
𝑝 √𝐷𝑤

Page 24 of 42

Q.39 Consider a particle in three different boxes of width 𝐿. The potential inside the
ℏ
boxes vary as shown in figures (i), (ii) and (iii) with 𝑉 ≪ . The
corresponding ground-state energies of the particle are 𝐸 , 𝐸 and 𝐸 ,
respectively. Then

(A) 𝐸 >𝐸 >𝐸

(B) 𝐸 >𝐸 >𝐸

(C) 𝐸 >𝐸 >𝐸

(D) 𝐸 >𝐸 >𝐸

Page 25 of 42

Q.40 In cylindrical coordinates (𝑠, 𝜑, 𝑧), which of the following is a Hermitian
operator?

(A) 1𝜕
𝑖 𝜕𝑠

(B) 1 𝜕 1
+
𝑖 𝜕𝑠 𝑠

(C) 1 𝜕 1
+
𝑖 𝜕𝑠 2𝑠

(D) 𝜕 1
+
𝜕𝑠 𝑠

Q.41 A particle of mass 1 kg is released from a height of 1 m above the ground. When
it reaches the ground, what is the value of Hamilton’s action for this motion in J s?
(𝑔 is the acceleration due to gravity; take gravitation potential to be zero on the
ground)

(A) 2
− 2𝑔
3

(B) 5
2𝑔
3

(C) 3 2𝑔

(D) 1
− 2𝑔
3

Page 26 of 42

Q.42 If (𝑥̇ 𝑦̇ + 𝛼𝑥𝑦) is a constant of motion of a two-dimensional isotropic harmonic
oscillator with Lagrangian

𝑚(𝑥̇ + 𝑦̇ ) 𝑘(𝑥 + 𝑦 )
𝐿= −
2 2
then 𝛼 is

(A) 𝑘
+
𝑚

(B) 𝑘
−
𝑚

(C) 2𝑘
−
𝑚

(D) 0

Q.43 In a two-dimensional square lattice, frequency 𝜔 of phonons in the long
wavelength limit changes linearly with the wave vector k. Then the density of
states of phonons is proportional to

(A) 𝜔

(B) 𝜔

(C) √𝜔

(D) 1
√𝜔

Page 27 of 42

Q.44 At T = 0 K, which of the following diagram represents the occupation probability
𝑃(𝐸) of energy states of electrons in a BCS type superconductor?

(A) P(E)

1

EF E

(B) P(E)

1

EF E

(C) P(E)

1

EF E

(D) P(E)

1

EF E

Page 28 of 42

Q.45 For a one-dimensional harmonic oscillator, the creation operator (𝑎 ) acting on the
nth state |𝜓 ⟩, where 𝑛 = 0, 1, 2, …, gives 𝑎 |𝜓 ⟩ = √𝑛 + 1|𝜓 ⟩. The matrix
ℏ
representation of the position operator 𝑥 = (𝑎 + 𝑎 ) for the first three rows
and columns is

(A) 1 0 0
ℏ
0 √2 0
2𝑚𝜔
0 0 √3

(B) 0 1 0
ℏ
1 0 1
2𝑚𝜔
0 1 0

(C) 0 1 0
ℏ
1 0 √2
2𝑚𝜔
0 √2 0

(D) 1 0 √3
ℏ
0 0 0
2𝑚𝜔
√3 0 1

Page 29 of 42

Q.46 A piston of mass m is fitted to an airtight horizontal cylindrical jar. The cylinder
and piston have identical unit area of cross-section. The gas inside the jar has
volume V and is held at pressure 𝑃 = 𝑃 . The piston is pushed inside the
jar very slowly over a small distance. On releasing, the piston performs an
undamped simple harmonic motion of low frequency. Assuming that the gas is
ideal and no heat is exchanged with the atmosphere, the frequency of the small
oscillations is proportional to

(A)
𝑃
𝛾𝑚𝑉

(B)
𝑃𝛾
𝑉𝑚

(C)
𝑃
𝑚𝑉

(D)
𝛾𝑃
𝑚𝑉

Page 30 of 42

Q.47 A paramagnetic salt of mass m is held at temperature T in a magnetic field H. If S
is the entropy of the salt and M is its magnetization, then 𝑑𝐺 = −𝑆𝑑𝑇 − 𝑀𝑑𝐻,
where G is the Gibbs free energy. If the magnetic field is changed adiabatically by
Δ𝐻 → 0 and the corresponding infinitesimal changes in entropy and temperature
are ΔS and Δ𝑇, then which of the following statements are correct

(A) 1 𝜕𝐺
Δ𝑆 = − Δ𝑇
𝑇 𝜕𝑇

(B) Δ𝑆 = 0

(C) 𝜕𝑀
𝜕𝑇
Δ𝑇 = − Δ𝐻
𝜕𝑆
𝜕𝑇

(D) Δ𝑇 = 0

Page 31 of 42

Q.48 A particle of mass m is moving inside a hollow spherical shell of radius 𝑎 so that
the potential is

0 for 𝑟 < 𝑎
𝑉(𝑟) =
∞ for 𝑟 ≥ 𝑎

The ground state energy and wavefunction of the particle are 𝐸 and 𝑅(𝑟),
respectively. Then which of the following options are correct?

(A) ℏ 𝜋
𝐸 =
2𝑚𝑎

(B) ℏ 1 𝑑 𝑑𝑅
− 𝑟 =𝐸 𝑅 (𝑟 < 𝑎)
2𝑚 𝑟 𝑑𝑟 𝑑𝑟

(C) ℏ 1𝑑 𝑅
− =𝐸 𝑅 (𝑟 < 𝑎)
2𝑚 𝑟 𝑑𝑟

(D) 1 𝜋𝑟
𝑅(𝑟) = sin (𝑟 < 𝑎)
𝑟 𝑎

Page 32 of 42

Q.49 A particle of unit mass moves in a potential 𝑉(𝑟) = −𝑉 𝑒 . If the angular
momentum of the particle is 𝐿 = 0.5 𝑉 , then which of the following statements
are true?

(A) There are two equilibrium points along the radial coordinate

(B) There is one stable equilibrium point at 𝑟 and one unstable equilibrium point at
𝑟 >𝑟

(C) There are two stable equilibrium points along the radial coordinate

(D) There is only one equilibrium point along the radial coordinate

Q.50 In a diatomic molecule of mass 𝑀, electronic, rotational and vibrational energy
scales are of magnitude 𝐸 , 𝐸 and 𝐸 , respectively. The spring constant for the
vibrational energy is determined by 𝐸 . If the electron mass is m then

(A) 𝑚
𝐸 ~ 𝐸
𝑀

(B) 𝑚
𝐸 ~ 𝐸
𝑀

(C) 𝑚
𝐸 ~ 𝐸
𝑀

(D) 𝑚 ⁄
𝐸 ~ 𝐸
𝑀

Page 33 of 42

Q.51 Electronic specific heat of a solid at temperature 𝑇 is 𝐶 = 𝛾𝑇, where 𝛾 is a
constant related to the thermal effective mass 𝑚 of the electrons. Then which
of the following statements are correct?

(A) 𝛾 ∝ 𝑚

(B) 𝑚 is greater than free electron mass for all solids

(C) Temperature dependence of 𝐶 depends on the dimensionality of the solid

(D) The linear temperature dependence of 𝐶 is observed at 𝑇 ≪ Debye temperature

Q.52 In a Hall effect experiment on an intrinsic semiconductor, which of the following
statements are correct?

(A) Hall voltage is always zero

(B) Hall voltage is negative if the effective mass of holes is larger than those of
electrons

(C) Hall coefficient can be used to estimate the carrier concentration in the
semiconductor

(D) Hall voltage depends on the mobility of the carriers

Page 34 of 42

Q.53 A parallel plate capacitor with spacing 𝑑 and area of cross-section 𝐴 is connected
to a source of voltage 𝑉. If the plates are pulled apart quasistatically to a spacing
of 2𝑑, then which of the following statements are correct?

(A) The force between the plates at spacing 2𝑑 is

(B) The work done in moving the plates is

(C) The energy transferred to the voltage source is

(D) The energy of the capacitor reduces by

Q.54 A system with time independent Hamiltonian 𝐻(𝑞, 𝑝) has two constants of motion
𝑓(𝑞, 𝑝) and 𝑔(𝑞, 𝑝). Then which of the following Poisson brackets are always
zero?

(A) {𝐻, 𝑓 + 𝑔}

(B) 𝐻, {𝑓, 𝑔}

(C) {𝐻 + 𝑓, 𝑔}

(D) {𝐻, 𝐻 + 𝑓𝑔}

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Q.55 In the action-angle variables (𝐼 , 𝐼 , 𝜃 , 𝜃 ), consider the Hamiltonian 𝐻 = 4𝐼 𝐼
and 0 ≤ 𝜃 , 𝜃 < 2𝜋. Let = . Which of the following are possible plots of the
trajectories with different initial conditions in 𝜃 -𝜃 plane?

(A)

(B)

(C)

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(D)

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Q.56 A particle of mass 𝑚 in the x-y plane is confined in an infinite two-dimensional
well with vertices at (0, 0), (0, L), (L, L), (L, 0). The eigenfunctions of this particle
are 𝜓 , = sin sin . If perturbation of the form 𝑉 = 𝐶𝑥𝑦, where
𝐶 is a real constant, is applied, then which of the following statements are correct
for the first excited state?

(A) The unperturbed energy is
ℏ

(B) The unperturbed energy is
ℏ

(C) First order energy shift due to the applied perturbation is zero

(D) The shift () in energy due to the applied perturbation is determined by an
𝑎−𝛿 𝑏
equation of the form = 0, where a and b are real, non-zero
𝑏 𝑎−𝛿
constants

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Q.57 A junction is formed between a metal on the left and an 𝑛-type semiconductor on
the right. Before forming the junction, the Fermi level EF of the metal lies below
that of the semiconductor. Then which of the following schematics are correct for
the bands and the I-V characteristics of the junction?

(A)
Conduction Band
EF
EF
Metal n-type semiconductor

Valence Band

(B) Conduction Band

EF EF
Metal n-type semiconductor

Valence Band

(C) I

-V0
V

(D) I

-V0
V

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Q.58 A plane polarized electromagnetic wave propagating in 𝑦-𝑧 plane is incident at the
interface of two media at Brewster’s angle. Taking 𝑧 = 0 as the boundary
between the two media, the electric field of the reflected wave is given by

√3 1
𝐸⃗ = 𝐴 cos 𝑘 𝑦 − 𝑧 − 𝜔𝑡 𝑥
2 2

then which among the following statements are correct?

(A) The angle of refraction is

(B) Ratio of permittivity of the medium of refraction (𝜖 ) with respect to the medium
on incidence (𝜖 ), =3

(C) The incident wave can have components of its electric field in 𝑦-𝑧 plane

(D) The angle of reflection is

Q.59 The minimum number of two-input NAND gates required to implement the
following Boolean expression is ________________

𝑌 = [𝐴𝐵 (𝐶 + 𝐵𝐷) + 𝐴̅𝐵 ]𝐶

Q.60 In a nucleus, the interaction 𝑉 𝑙⃗ ⋅ 𝑠⃗ is responsible for creating spin-orbit doublets.
ℏ
The energy difference between 𝑝 / and 𝑝 / states in units of 𝑉 is
____________ (Round off to the nearest integer)

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Q.61 Two identical particles of rest mass 𝑚 approach each other with equal and
opposite velocity 𝑣 = 0.5𝑐, where 𝑐 is the speed of light. The total energy of one
particle as measured in the rest frame of the other is 𝐸 = 𝛼𝑚 𝑐 . The value of 𝛼
is _______________ (Round off to two decimal places)

Q.62 In an X-Ray diffraction experiment on a solid with FCC structure, five diffraction
peaks corresponding to (111), (200), (220), (311) and (222) planes are observed
using 1.54 Å X-rays. On using 3 Å X-rays on the same solid, the number of
observed peaks will be ________________

Q.63 For 1 mole of Nitrogen gas, the ratio of entropy change of the gas in
processes (I) and (II) mentioned below is ______________ (Round off to one
decimal place)

(I) The gas is held at 1 atm and is cooled from 300 K to 77 K.

(II) The gas is liquified at 77 K.

(Take Cp = 7.0 cal mol1 K1, Latent heat L = 1293.6 cal mol1)

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Q.64 Frequency bandwidth ∆𝜈 of a gas laser of frequency 𝜈 Hz is

2𝜈 𝛼
Δ𝜈 =
𝑐 𝐴

where 𝛼 = 3.44 × 106 m2 s2 at room temperature and 𝐴 is the atomic mass of the
lasing atom. For 4He - 20Ne laser (wavelength = 633 nm), Δ𝜈 = 𝑛 × 10 Hz. The
value of 𝑛 is ________ (Round off to one decimal place)

Q.65 A current of 1 A is flowing through a very long solenoid made of winding density
3000 turns/m. As shown in the figure, a parallel plate capacitor, with plates
oriented parallel to the solenoid axis and carrying surface charge density
6𝜖 C m2, is placed at the middle of the solenoid. The momentum density of the
electromagnetic field at the midpoint X of the capacitor is 𝑛 × 10 N s m3. The
value of 𝑛 is ______________ (Round off to the nearest integer)

(speed of light 𝑐 = 3 × 10 m s1)

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