GATE PH year:2025 PYQs & Answers — Page 4

Questions 31–40 of 65. Imported answers require independent review unless marked reviewed.

A linear dielectric sphere of radius

has a uniform frozen-in polarization along the

-axis. The center of the sphere initially coincides with the origin, about which the electric dipole moment is

. When the sphere is shifted to the point

, the corresponding dipole moment with respect to the origin is

. The value of

(in integer) is ______

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The effective magnetic moment (in units of Bohr magneton) for the ground state of an isolated

ion with 6 unpaired electrons in the

shell according to Hund’s rules is (in integer) _____

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Powder X-ray diffraction pattern of a cubic solid with lattice constant

has the (111) diffraction peak at

. If the lattice expands such that the lattice constant becomes

, the angle (in degrees) corresponding to the (111) peak changes to

. The value of

(rounded off to one decimal place) is _____

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Consider a monatomic chain of length 30 cm. The phonon density of states is

s. Assuming the Debye model, the velocity of sound in m/s (rounded off to one decimal place) is _____

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The

baryon with spin

, at rest, decays to a proton and a pion (

). The

has positive intrinsic parity and

has negative intrinsic parity. The orbital angular momentum of the proton-pion system (in integer) is _____

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The screened nuclear charge of neutral Helium atom is given as

, where

is the magnitude of the electronic charge. Assuming the Bohr model of the atom for which the energy levels are

atomic units (

is the atomic number), the first ionization potential of Helium in atomic units is

Your answerChoose one option.

0.89

1.78

0.94

3.16

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The wire loop shown in the figure carries a steady current

. Each straight section of the loop has length

. A part of the loop lies in

plane and the other part is tilted at

with respect to the

plane. The magnitude of the magnetic dipole moment of the loop (in appropriate units) is

Your answerChoose one option.

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The figure shows a system of two equal masses

and three massless horizontal springs with spring constants

. Ignore gravity. The masses can move only in the horizontal direction and there is no dissipation. If

and

(all in appropriate units), the frequencies of the normal modes of the system in the same system of units are

Your answerChoose one option.

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Two projectile protons

and

both with spin up (along the +

direction) are scattered from another fixed target proton

with spin up at rest in the

plane, as shown in the figure. They scatter one at a time. The nuclear interaction potential between both the projectiles and the target proton is

, where

is the orbital angular momentum of the system with respect to the target,

is the spin angular momentum of the system and

is a negative constant in appropriate units. Which one of the following is correct?

Your answerChoose one option.

will be scattered in the +

direction (upward) and

will be scattered in the −

direction (downward)

will be scattered in the +

direction (upward) and

will be scattered in the +

direction (upward)

will be scattered in the −

direction (downward) and

will be scattered in the +

direction (upward)

will be scattered in the −

direction (downward) and

will be scattered in the −

direction (downward)

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A thin circular ring of radius

lies in the

plane with its centre coinciding with the origin. The ring carries a uniform line charge density

. The quadrupole contribution to the electrostatic potential at the point

, where

, is

Your answerChoose one option.

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GATE PH year:2025 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40