GATE PH topic:vector-calculus PYQs & Answers

Home
GATE
Physics
Topics
topic:vector-calculus

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–8 of 8. Imported answers require independent review unless marked reviewed.

Topic practice 8 questionsPage 1 of 1

For a scalar field

and a vector field

is equivalent to the expression

Your answerChoose one option.

Null vector

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Sketch of a two-dimensional vector field

is shown below. Here, length and arrow head of the arrows denote magnitude and direction of the vector field, respectively. Which of the following statements is correct for

Your answerChoose one option.

It is zero everywhere in the two-dimensional space.

Its magnitude is non-zero and its direction is out of the two-dimensional plane.

Its magnitude is non-zero and its direction is into the two-dimensional plane.

It points in opposite directions above and below the x-axis.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

For which of the following functions does the Laplacian vanish?

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The function

of complex variable

given below,

has singular points at

Your answerChoose one option.

1 and

and

1 and

only

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the function

of a complex variable

. The residues of the function at

and

, respectively, are

Your answerChoose one option.

and

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

In coordinates

, a contravariant second rank tensor

has non-zero diagonal components

and

, with all other components vanishing, and

being real constants. Here,

is time and

is space coordinate. Consider a Lorentz transformation

to another frame that moves with relative speed

in the

direction, so that

. If

and

are the diagonal components of

, then setting the speed of light

, and with

, which of the following option(s) is/are correct?

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the integral

where

is a complex variable and

are positive real numbers. The integral is taken over a unit circle with center at the origin. Which of the following option(s) is/are correct?

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

when

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the set

. An orthonormal basis in

is formed from these three terms, where the normalization of a function

is defined via

. If the orthonormal basis set is

, then the value of

(in integer) is ______

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE PH topic:vector-calculus PYQs

How to practice topic:vector-calculus

Question 14

Question 22

Question 27

Question 36

Question 21

Question 50

Question 55

Question 61