GATE MA 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 58. Imported answers require independent review unless marked reviewed.

Topic practice 58 questionsPage 1 of 6

Let

be the integral defined as follows:

If the order of the integration is changed, then which one of the following is the correct expression for

Your answerChoose one option.

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Let

be defined as

Which one of the following is TRUE?

Your answerChoose one option.

is one-to-one.

The Jacobian of

is negative.

is locally invertible.

is invertible on

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Let

be a function defined as follows:

Which of the following statements is/are TRUE?

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

is continuous at

For any

, the directional derivative of

in the direction of

exists.

is differentiable at

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Let

, where

and

is the sphere with centre at

and radius 9. Here,

is the unit normal drawn outward and

are unit vectors. Then the value of

is equal to ________. (answer in integer)

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Let

and let

denote the smallest integer greater than or equal to

. Then the value of the integral

is ________. (answer in integer)

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Let

be defined in

, where

is a continuously differentiable non-zero homogeneous function of degree 4. Then,

holds for

Your answerChoose one option.

all points

on the line given by

all points

in the region of

except on the line given by

all points

on the line given by

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Let

be a function defined by

Consider the following three statements:

S1:

exists.

S2:

exists.

S3:

exists.

Then, which of the following is/are correct?

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

S2 and S3 are TRUE and S1 is FALSE

S1 and S2 are TRUE and S3 is FALSE

S1 and S3 are TRUE and S2 is FALSE

S1, S2 and S3 all are TRUE

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Let

be a unit vector parallel to the tangent at the point

to the curve of intersection of the surfaces

and

. Then, the absolute value of the directional derivative of

in the direction of

is _____ (in integer)

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The volume of the region bounded by the cylinders

and

is _____ (rounded off to TWO decimal places)

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Let

be a vector field, and let

be the surface

. If

denotes the unit outward normal vector to

, then the value of

is equal to _____ (in integer)

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GATE MA Calculus PYQs

How to practice Calculus

Question 12

Question 16

Question 22

Question 56

Question 64

Question 18

Question 26

Question 29

Question 30

Question 32