GATE AE Calculus PYQs & Answers — Page 2

Questions 11–20 of 34. Imported answers require independent review unless marked reviewed.

Topic practice 34 questionsPage 2 of 4

Given the function

, for

. What is the value of

at which the function has a minimum?

Your answerChoose one option.

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, what is the area bounded by

for the interval

on the

-axis?

Your answerChoose one option.

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The equation of the straight line representing the tangent to the curve

at the point

Your answerChoose one option.

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The arc length of the parametric curve:

from

is equal to ______ (round off to one decimal place).

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The height of a right circular cone of maximum volume that can be enclosed within a hollow sphere of radius

Your answerChoose one option.

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The real function

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

continuous for all

differentiable for all

not continuous at

not differentiable at

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is a vector field where

are the base vectors of a cartesian coordinate system.

Using the Gauss divergence theorem, the value of the outward flux of the vector field over the surface of a sphere of unit radius centered at the origin is ______ (rounded off to one decimal place).

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Consider the velocity field

. The field

Your answerChoose one option.

divergence-free and curl-free

curl-free but not divergence-free

divergence-free but not curl-free

neither divergence-free nor curl-free

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______ (round off to nearest integer).

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Which of the following statement(s) is/are true about the function defined as

for

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

Differentiable at

Continuous at

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GATE AE Calculus PYQs

Question 36

Question 3

Question 11

Question 31

Question 36

Question 43

Question 48

Question 3

Question 17

Question 31