GATE PH year:2021 PYQs & Answers — Page 5

Questions 41–50 of 65. Imported answers require independent review unless marked reviewed.

Consider two concentric conducting spherical shells as shown in the figure. The inner shell has a radius

and carries a charge +Q. The outer shell has a radius

and carries a charge

. The empty space between them is half-filled by a hemispherical shell of a dielectric having permittivity

. The remaining space between the shells is filled with air having the permittivity

The electric field at a radial distance

from the center and between the shells (

) is

Your answerChoose one option.

everywhere

on the air side and

on the dielectric side

on the air side and

on the dielectric side

everywhere

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For the given sets of energy levels of nuclei X and Y whose mass numbers are odd and even, respectively, choose the best suited interpretation.

Your answerChoose one option.

Set I: Rotational band of X Set II: Vibrational band of Y

Set I: Rotational band of Y Set II: Vibrational band of X

Set I: Vibrational band of X Set II: Rotational band of Y

Set I: Vibrational band of Y Set II: Rotational band of X

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Consider a system of three distinguishable particles, each having spin

such that

with corresponding magnetic moments

. When the system is placed in an external magnetic field

pointing along the z-axis, the total energy of the system is

. Let

be the state where the first spin has

. The probability of having the state

and the mean magnetic moment (in the +z direction) of the system in state

are

Your answerChoose one option.

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Consider a particle in a one-dimensional infinite potential well with its walls at

and

. The system is perturbed as shown in the figure.

The first order correction to the energy eigenvalue is

Your answerChoose one option.

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Consider a state described by

, where

and

are respectively the second and fourth normalized harmonic oscillator wave functions and

is the angular frequency of the harmonic oscillator. The wave function

will be orthogonal to

at time

equal to

Your answerChoose one option.

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Consider a single one-dimensional harmonic oscillator of angular frequency

, in equilibrium at temperature

. The states of the harmonic oscillator are all non-degenerate having energy

with equal probability, where

is the quantum number. The Helmholtz free energy of the oscillator is

Your answerChoose one option.

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A system of two atoms can be in three quantum states having energies

and

. The system is in equilibrium at temperature

. Match the following Statistics with the Partition function.

Statistics	Partition function
CD: Classical (distinguishable particles)	Z1:
CI: Classical (indistinguishable particles)	Z2:
FD: Fermi-Dirac	Z3:
BE: Bose-Einstein	Z4:

Your answerChoose one option.

CD: Z1, CI: Z2, FD: Z3, BE: Z4

CD: Z2, CI: Z3, FD: Z4, BE: Z1

CD: Z3, CI: Z4, FD: Z1, BE: Z2

CD: Z4, CI: Z1, FD: Z2, BE: Z3

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The free energy of a ferromagnet is given by

, where

, and

are positive constants,

is the magnetization,

is the temperature, and

is the Curie temperature. The relation between

and

is best depicted by

Your answerChoose one option.

Diagram for Physics question 38 (figure 2)

Diagram for Physics question 38 (figure 3)

Diagram for Physics question 38 (figure 4)

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Consider a spherical galaxy of total mass

and radius

, having a uniform matter distribution. In this idealized situation, the orbital speed

of a star of mass

(

) as a function of the distance

from the galactic centre is best described by

(

is the universal gravitational constant)

Your answerChoose one option.

Diagram for Physics question 39 (figure 2)

Diagram for Physics question 39 (figure 3)

Diagram for Physics question 39 (figure 4)

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Consider the potential

defined as

where

and

are real constants of appropriate dimensions. According to the first Born approximation, the elastic scattering amplitude calculated with

for a (wave-vector) momentum transfer

and

, is proportional to

(Useful integral:

)

Your answerChoose one option.

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GATE PH year:2021 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40