GATE ECE topic:vector-calculus PYQs & Answers

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topic:vector-calculus

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Questions 1–10 of 14. Imported answers require independent review unless marked reviewed.

Topic practice 14 questionsPage 1 of 2

A surface is given by

and

are unit normal vectors to the surface at the point

. Which of the following vectors can be

, where

and

are the unit vectors along x, y and z axes, respectively?

Your answerChoose one option.

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Let

and

represent density and velocity, respectively, at a point

and time

. Assume

is continuous. Let V be an arbitrary volume in space enclosed by the closed surface S and

be the outward unit normal of S. Which of the following equations is/are equivalent to

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

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Let

, and

be functions of

. Suppose that for every given pair of points

and

in space, the line integral

evaluates to the same value along any path

that starts at

and ends at

. Then which of the following is/are true?

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

For every closed path

, we have

There exists a differentiable scalar function

such that

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The rate of increase, of a scalar field

, in the direction

at a point

Your answerChoose one option.

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The value of the line integral

along the straight line joining the points

and

Your answerChoose one option.

-5

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Consider the two-dimensional vector field

, where

and

denote the unit vectors along the

-axis and the

-axis, respectively. A contour

in the

plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral

is ________.

Diagram for Electronics and Communication Engineering question 11

Your answerChoose one option.

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The vector function

is defined over a circular arc

shown in the figure.

Diagram for Electronics and Communication Engineering question 1

The line integral of

Your answerChoose one option.

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Consider the vector field

in a rectangular coordinate system

with unit vectors

and

. If the field

is irrotational (conservative), then the constant

(in integer) is __________.

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For a vector field

in a cylindrical coordinate system

with unit vectors

and

, the net flux of

leaving the closed surface of the cylinder

(rounded off to two decimal places) is ________.

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For a vector field

, which one of the following is FALSE?

Your answerChoose one option.

is solenoidal if

is another vector field.

is irrotational if

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GATE ECE topic:vector-calculus PYQs

How to practice topic:vector-calculus

Question 12

Question 25

Question 54

Question 12

Question 37

Question 11

Question 1

Question 17

Question 37

Question 2