GATE MA topic:calculus PYQs & Answers — Page 2

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topic:calculus

Questions 11–20 of 58. Imported answers require independent review unless marked reviewed.

Topic practice 58 questionsPage 2 of 6

Let

be the curve of intersection of the surfaces

and

. If

is a point on

at a minimum distance from the

-plane, then the distance of

from the origin is

Your answerChoose one option.

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Let

and

be a differentiable function such that

and

, for every

and

. The value of

is equal to ______ (answer in integer)

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Let

, where

. Let

be the inverse of

in a neighborhood of

. Then the determinant of the Jacobian matrix of

is equal to ______ (round off to TWO decimal places)

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The maximum of the function

subject to the constraints

is equal to ______ (round off to TWO decimal places)

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If the outward flux of

through the unit sphere

, then

is equal to ______ (round off to TWO decimal places)

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Let

be given by

. Let

be the

zero matrix. The space

may be identified with

in the usual manner. Which one of the following is correct?

Your answerChoose one option.

is a point of local minimum of

is a point of local maximum of

is a saddle point of

is not a critical point of

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Let

be a function such that

Which of the following is/are correct?

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

is continuous at

, but not differentiable at

is differentiable at

All the directional derivatives of

exist and they are equal to zero

Both the partial derivatives of

exist and they are equal to zero

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Let

be a continuously differentiable path from

and let

be defined by

. The line integral of

along

is equal to

(round off to TWO decimal places)

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The global maximum of

is equal to

(round off to TWO decimal places)

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Let

be defined by

and

for all

. Consider the following statements: P:

has a saddle point at

. Q:

has a saddle point at

. Then

Your answerChoose one option.

both P and Q are TRUE

P is FALSE but Q is TRUE

P is TRUE but Q is FALSE

both P and Q are FALSE

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GATE MA topic:calculus PYQs

Question 39

Question 26

Question 28

Question 34

Question 35

Question 39

Question 54

Question 61

Question 64

Question 11