GATE MT topic:vector-calculus PYQs & Answers

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 1–10 of 15. Imported answers require independent review unless marked reviewed.

Topic practice 15 questionsPage 1 of 2

Value of scalar triple product

is (answer in integer) ____________.

Here,

and

are mutually orthogonal unit vectors.

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Given a scalar field

Magnitude of a vector in the direction of the most rapid increase of

at a point P (3,4,1), rounded off to two decimal places, is __________

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For a two-dimensional field described by

, the magnitude of its gradient at the point

is _____ (rounded off to two decimal places).

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The divergence of the vector field

at the point

is ________. (Round off to the nearest integer)

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A fluid flow field is given by the velocity vector

. The curl of velocity at (1, 2, 3) is

Your answerChoose one option.

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Given,

. S is a surface bounded by the planes

, and

. If

is the unit vector normal to S, then

Your answerChoose one option.

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Given that

is a closed volume in space bounded by the surface

with unit normal

. If

is any non-zero vector and

is the gradient operator, then the volume integral

is equal to the surface integral

by value of __________

Your answerChoose one option.

Stokes Curl theorem

Reynolds transport theorem

Buckingham Pi theorem

Gauss divergence theorem

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The divergence of a vector field

, where its three components

are functions of

, is:

Your answerChoose one option.

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The work done by a force

along a straight line from point (0, 0) to (1, 2) is: ________ (round off to nearest integer).

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Given the three vectors

and

, which one of the following statements is TRUE?

Your answerChoose one option.

and

are mutually perpendicular.

and

are coplanar.

makes an angle of 30° with the normal to the plane containing

and

makes an angle of 60° with the normal to the plane containing

and

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GATE MT topic:vector-calculus PYQs

How to practice topic:vector-calculus

Question 32

Question 65

Question 48

Question 31

Question 40

Question 41

Question 23

Question 3

Question 38

Question 13