GATE MA Calculus PYQs & Answers — Page 4

Questions 31–40 of 58. Imported answers require independent review unless marked reviewed.

Topic practice 58 questionsPage 4 of 6

Let

be a twice continuously differentiable scalar field such that

. Let

be the surface

and

be unit outward normal to

. Then the value of

Your answerChoose one option.

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

Let

be differentiable. Let

and

be the direction derivatives of

in the directions of the unit vectors

and

, respectively. If

and

, then

_____.

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

Let

denote the boundary of the square region

with vertices

and

oriented in the counter-clockwise direction. Then

__________.

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

Let

be given by

Consider the following statements: P:

is continuous at

but

is NOT differentiable at

. Q: The directional derivative

exists in the direction of every unit vector

. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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

Let

be the solid region in

bounded by the paraboloid

and the plane

. Then the value of

Your answerChoose one option.

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

Let

be given by

. Then

has

Your answerChoose one option.

a point of local maximum and a saddle point

a point of local minimum and a saddle point

a point of local maximum and a point of local minimum

two saddle points

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

The equation

can be solved in a neighborhood of the point

for some continuously differentiable function

. Then

Your answerChoose one option.

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

Let

. If the function

is defined by

then

Your answerChoose one option.

is continuous at

both the first order partial derivatives of

exist at

is finite

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

and

are critical points of the function

where

, then

Your answerChoose one option.

is a point of local maxima of

is a saddle point of

is a point of local minima of

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

Let

and let

be the surface of the tetrahedron bounded by the planes

is the unit outward normal to the tetrahedron, then the value of

is (rounded off to two decimal places)

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

GATE MA Calculus PYQs

Question 12

Question 15

Question 16

Question 37

Question 38

Question 39

Question 40

Question 2

Question 9

Question 50