GATE PH format:msq PYQs & Answers — Page 9

Questions 81–88 of 88. Imported answers require independent review unless marked reviewed.

Among the term symbols

and

choose the option(s) possible in the

coupling notation.

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

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To sustain lasing action in a three-level laser as shown in the figure, necessary condition(s) is(are)

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

lifetime of the energy level 1 should be greater than that of energy level 2

population of the particles in level 1 should be greater than that of level 0

lifetime of the energy level 2 should be greater than that of energy level 0

population of the particles in level 2 should be greater than that of level 1

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is a solution of the differential equation

where

is an integer and the prime (

) denotes differentiation with respect to

, then acceptable plot(s) of

, is(are)

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

Diagram for Physics question 16 (figure 2)

Diagram for Physics question 16 (figure 3)

Diagram for Physics question 16 (figure 4)

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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)

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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)

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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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GATE PH format:msq PYQs

Question 14

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Question 16

Question 42

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Question 46