GATE PH format:msq PYQs & Answers — Page 8

Questions 71–80 of 88. Imported answers require independent review unless marked reviewed.

A parallel plate capacitor with spacing

and area of cross-section

is connected to a source of voltage

. If the plates are pulled apart quasistatically to a spacing of

, then which of the following statements are correct?

Your answerSelect all correct options. You can choose more than one.

The force between the plates at spacing

The work done in moving the plates is

The energy transferred to the voltage source is

The energy of the capacitor reduces by

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A system with time independent Hamiltonian

has two constants of motion

and

. Then which of the following Poisson brackets are always zero?

Your answerSelect all correct options. You can choose more than one.

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In the action-angle variables

, consider the Hamiltonian

and

. Let

. Which of the following are possible plots of the trajectories with different initial conditions in

plane?

Your answerSelect all correct options. You can choose more than one.

Diagram for Physics question 55 (figure 2)

Diagram for Physics question 55 (figure 3)

Diagram for Physics question 55 (figure 4)

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A particle of mass

in the

plane is confined in an infinite two-dimensional well with vertices at

. The eigenfunctions of this particle are

. If perturbation of the form

, where

is a real constant, is applied, then which of the following statements are correct for the first excited state?

Your answerSelect all correct options. You can choose more than one.

The unperturbed energy is

First order energy shift due to the applied perturbation is zero

The shift (

) in energy due to the applied perturbation is determined by an equation of the form

, where

and

are real, non-zero constants

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A junction is formed between a metal on the left and an

-type semiconductor on the right. Before forming the junction, the Fermi level

of the metal lies below that of the semiconductor. Then which of the following schematics are correct for the bands and the

characteristics of the junction?

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Diagram for Physics question 57 (figure 2)

Diagram for Physics question 57 (figure 3)

Diagram for Physics question 57 (figure 4)

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A plane polarized electromagnetic wave propagating in

plane is incident at the interface of two media at Brewster’s angle. Taking

as the boundary between the two media, the electric field of the reflected wave is given by

then which among the following statements are correct?

Your answerSelect all correct options. You can choose more than one.

The angle of refraction is

Ratio of permittivity of the medium of refraction (

) with respect to the medium on incidence (

The incident wave can have components of its electric field in

plane

The angle of reflection is

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A two-dimensional square lattice has lattice constant

represents the wavevector in reciprocal space. The coordinates

of reciprocal space where band gap(s) can occur, are

Your answerSelect all correct options. You can choose more than one.

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As shown in the figure, an electromagnetic wave with intensity

is incident at the interface of two media having refractive indices

and

. The wave is reflected with intensity

and transmitted with intensity

. Permeability of each medium is the same. (Reflection coefficient

and Transmission coefficient

.) Choose the correct statement(s).

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and polarization of incident light is parallel to the plane of incidence.

and polarization of incident light is perpendicular to the plane of incidence.

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A material is placed in a magnetic field intensity

. As a result, bound current density

is induced and magnetization of the material is

. The magnetic flux density is

. Choose the correct option(s) valid at the surface of the material.

Your answerSelect all correct options. You can choose more than one.

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For a finite system of Fermions where the density of states increases with energy, the chemical potential

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decreases with temperature

increases with temperature

does not vary with temperature

corresponds to the energy where the occupation probability is 0.5

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GATE PH format:msq PYQs

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 10

Question 11

Question 12

Question 13