GATE PH year:2021 PYQs & Answers — Page 6

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

As shown in the figure, inverse magnetic susceptibility

is plotted as a function of temperature

for three different materials in paramagnetic states.

(Curie temperature of ferromagnetic material

Néel temperature of antiferromagnetic material

)

Choose the correct statement from the following

Your answerChoose one option.

Material 1 is antiferromagnetic (

), 2 is paramagnetic, and 3 is ferromagnetic (

Material 1 is paramagnetic, 2 is antiferromagnetic (

), and 3 is ferromagnetic (

Material 1 ferromagnetic (

), 2 is antiferromagnetic (

), and 3 is paramagnetic.

Material 1 is ferromagnetic (

), 2 is paramagnetic, and 3 is antiferromagnetic (

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A function

is defined only for

. The Laplace transform of

whereas the Fourier transform of

The correct statement(s) is(are)

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

The variable

is always real.

The variable

can be complex.

and

can never be made connected.

and

can be made connected.

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and

are two Hermitian matrices and there exists a matrix

, which diagonalizes both of them, such that

and

, where

and

are diagonal matrices. The correct statement(s) is(are)

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

All the elements of both matrices

and

are real.

The matrix

can have complex eigenvalues.

The matrix

can have complex eigenvalues.

The matrices

and

commute.

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A uniform block of mass

slides on a smooth horizontal bar. Another mass

is connected to it by an inextensible string of length

of negligible mass, and is constrained to oscillate in the X-Y plane only. Neglect the sizes of the masses. The number of degrees of freedom of the system is two and the generalized coordinates are chosen as

and

, as shown in the figure.

and

are the generalized momenta corresponding to

and

, respectively, then the correct option(s) is(are)

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

is conserved

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The Gell-Mann – Okuba mass formula defines the mass of baryons as

where

and

are constants,

represents the isospin and

represents the hypercharge. If the mass of

hyperons is same as that of

hyperons, then the correct option(s) is(are)

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

does not depend on

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The time derivative of a differentiable function

is added to a Lagrangian

such that

where

are the generalized coordinates, generalized velocities and time, respectively. Let

be the generalized momentum and

the Hamiltonian associated with

. If

and

are those associated with

, then the correct option(s) is(are)

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

Both

and

satisfy the Euler-Lagrange’s equations of motion

is conserved, then

is necessarily conserved

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A linear charged particle accelerator is driven by an alternating voltage source operating at 10 MHz. Assume that it is used to accelerate electrons. After a few drift-tubes, the electrons attain a velocity 2.9 × 10^8 m s⁻¹. The minimum length of each drift-tube, in m, to accelerate the electrons further (rounded off to one decimal place) is _____.

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The Coulomb energy component in the binding energy of a nucleus is 18.432 MeV. If the radius of the uniform and spherical charge distribution in the nucleus is 3 fm, the corresponding atomic number (rounded off to the nearest integer) is _____.

(Given:

MeV fm)

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For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices

for particles 1 and 2, respectively. The value of

(in integer) is _____.

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A contour integral is defined as

where

is a positive integer and

is the closed contour, as shown in the figure, consisting of the line from −100 to 100 and the semicircle traversed in the counter-clockwise sense.

The value of

(in integer) is _____.

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GATE PH year:2021 PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50