GATE PH year:2021 PYQs & Answers — Page 4

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

Three non-interacting bosonic particles of mass

each, are in a one-dimensional infinite potential well of width

. The energy of the third excited state of the system is

. The value of

(in integer) is ______.

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The spacing between two consecutive S-branch lines of the rotational Raman spectra of hydrogen gas is 243.2 cm

. After excitation with a laser of wavelength 514.5 nm, the Stoke’s line appeared at 1761.1 cm

for a particular energy level. The wavenumber (rounded off to the nearest integer), in cm

, at which Stoke’s line will appear for the next higher energy level is ______.

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The transition line, as shown in the figure, arises between

and

states without any external magnetic field. The number of lines that will appear in the presence of a weak magnetic field (in integer) is ______.

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Consider the atomic system as shown in the figure, where the Einstein A coefficients for spontaneous emission for the levels are

and

. If

atoms/cm

are excited from level 0 to level 2 and a steady state population in level 2 is achieved, then the steady state population at level 1 will be

. The value of

(in integer) is ______.

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and

are constant vectors,

and

are generalized positions and conjugate momenta, respectively, then for the transformation

and

to be canonical, the value of

(in integer) is ______.

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The above combination of logic gates represents the operation

Your answerChoose one option.

NAND

AND

NOR

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In a semiconductor, the ratio of the effective mass of hole to electron is 2:11 and the ratio of average relaxation time for hole to electron is 1:2. The ratio of the mobility of the hole to electron is

Your answerChoose one option.

4:9

4:11

9:4

11:4

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Consider a spin

particle in the state

. The probability that a measurement finds the state with

Your answerChoose one option.

5/18

11/18

15/18

17/18

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An electromagnetic wave having electric field

is incident at

(normal incidence) on a square slab from vacuum (with refractive index

) as shown in the figure. The slab is composed of two different materials with refractive indices

and

. Assume that the permeability of each medium is the same. After passing through the slab for the first time, the electric field amplitude, in

, of the electromagnetic wave, which emerges from the slab in region 2, is closest to

Your answerChoose one option.

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Consider a point charge

of mass

suspended by a mass, inextensible string of length

in free space (permittivity

) as shown in the figure. It is placed at a height

(

) over an infinitely large, grounded conducting plane. The gravitational potential energy is assumed to be zero at the position of the conducting plane and is positive above the plane. If

represents the angular position and

its corresponding canonical momentum, then the correct Hamiltonian of the system is

Your answerChoose one option.

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GATE PH year:2021 PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30