GATE PH Mathematical Physics PYQs & Answers — Page 2

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Questions 11–20 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 2 of 5

Consider the vector field

consisting of the velocities of points on a thin horizontal disc of radius

, moving anticlockwise with uniform angular speed

about an axis passing through its center. If

, then which of the following options is(are) CORRECT? (In the options,

and

are unit vectors corresponding to the plane polar coordinates

and

You may use the fact that in cylindrical coordinates

(

is the distance from the

-axis), the gradient, divergence, curl and Laplacian operators are:

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

, where

is a unit vector perpendicular to the

plane

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What is the maximum number of free independent real parameters specifying an

-dimensional orthogonal matrix?

Your answerChoose one option.

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Consider the ordinary differential equation

and its solution

. Then

Your answerChoose one option.

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Complex function

(

is a real number) is

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

continuous at

complex-differentiable at

analytic at

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is the Fourier transform of

, then which of the following are true?

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

implies

is real

implies

is purely imaginary

implies

is purely imaginary

implies

is real

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The ordinary differential equation

has a regular singularity at

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

no finite value of

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In cylindrical coordinates

, which of the following is a Hermitian operator?

Your answerChoose one option.

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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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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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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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GATE PH Mathematical Physics PYQs

Question 57

Question 13

Question 19

Question 25

Question 26

Question 27

Question 40

Question 16

Question 25

Question 42