GATE XE 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 28. Imported answers require independent review unless marked reviewed.

Topic practice 28 questionsPage 1 of 3

Let

be the lamina of the form

, with density

. Then, the mass of

(in integer) is __________

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Match each entry of List-1 with a suitable entry in List-2 and choose the correct option.

List-1	List-2
P. The sum of the series is equal to	I.
Q. is equal to	II.
R. Let be the Fourier series expansion of the function , . Then, is equal to	III.

Your answerChoose one option.

I, Q

III, R

III, Q

II, R

III, Q

I, R

II, Q

I, R

III

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Consider the infinite series

Then which one of the following statements is correct?

Your answerChoose one option.

Series

and

both converge

Series

converges and series

diverges

Series

and

both diverge

Series

diverges and series

converges

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Consider the function

Then which one of the following statements is correct?

Your answerChoose one option.

is a point of local maxima of

is a point of local minima of

is a point of local maxima of

is a saddle point of

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For positive non-zero real variables

and

, if

then, the value of

Your answerChoose one option.

1/2

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Let

with

. If

represents the Fourier series of

, then the value of

Your answerChoose one option.

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Assume that

is continuous on

and differentiable on

such that

for some

. If

, and

is expressed in terms of

and

, then the value of

Your answerChoose one option.

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then the value (in integer) of

is _____

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Which one of the given figures P, Q, R and S represents the graph of the following function?

Diagram for Engineering Sciences question 9

Your answerChoose one option.

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Let

be a function defined by

Then which one of the following statement is TRUE?

Your answerChoose one option.

is NOT continuous at

, and

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GATE XE Calculus PYQs

How to practice Calculus

Question 16

Question 18

Question 13

Question 19

Question 4

Question 11

Question 14

Question 20

Question 9

Question 12