GATE IN 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 19. Imported answers require independent review unless marked reviewed.

Topic practice 19 questionsPage 1 of 2

Which one among the following statements is true for the function

Your answerChoose one option.

is discontinuous but not differentiable at

is discontinuous and differentiable at

is continuous but not differentiable at

is continuous and differentiable at

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

Given

The complete contour of the equation

is described by the option(s) __.

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

A line,

A circle with radius 1

An ellipse with length of major axis equal to 1

A line,

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

Let

Then

_____ (rounded off to one decimal place)

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

for all real values of

, which one of the following statements is true?

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

The value of the surface integral

over the sphere

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

The value of the integral

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 the closed curve in the

-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at

. The value of the line integral

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

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

Diagram for Instrumentation Engineering question 9

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

What is

, where

Your answerChoose one option.

Limit does not exist

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

Consider the real-valued function

, where

. The minimum value attained by

is ______ (rounded off to one decimal place).

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

GATE IN Calculus PYQs

How to practice Calculus

Question 12

Question 53

Question 57

Question 3

Question 36

Question 38

Question 46

Question 9

Question 23

Question 57