GATE PI topic: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 18. Imported answers require independent review unless marked reviewed.

Topic practice 18 questionsPage 1 of 2

Consider the line integral

where

is a semi-circle in the

plane with start point at

and end point at

The value of the line integral is _____ (in integer).

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and

are the orthogonal unit vectors in Cartesian x-y-z coordinate system, the curl of the vector

Your answerChoose one option.

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If i, j and k are the orthogonal unit vectors in Cartesian x-y-z coordinate system, the rate of change of the function

at point (1, 1, 1) in the direction of

is________. (Answer in integer)

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A vector field is given as

, where

and

are the unit vectors along the x and y axes in the Cartesian frame, respectively. Then the value of

where

is an elemental path taken over an anticlockwise circular contour

of radius

Diagram for Production and Industrial Engineering question 12

Your answerChoose one option.

−100π

−800π

−400π

400π

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, then

is ________ . (Answer in integer)

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Given,

, where

and

. All the variables are real. The total differential

Your answerChoose one option.

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The value of

is ____________. [round off to one decimal place]

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The minimum value of function

defined by

is ____________. [in integer]

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The divergence of the vector

Your answerChoose one option.

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The vector that is normal to the surface

at the point

Your answerChoose one option.

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GATE PI topic:calculus PYQs

How to practice topic:calculus

Question 34

Question 12

Question 44

Question 12

Question 32

Question 36

Question 45

Question 25

Question 1

Question 3