GATE PH 2021 Paper 1 — page 18

Questions 52–54 of 65. Imported answers require review unless explicitly marked reviewed.

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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2021 · Paper 1

Question 42

Question 43

Question 44