GATE EE Calculus PYQs & Answers — Page 3

Questions 21–30 of 31. Imported answers require independent review unless marked reviewed.

Topic practice 31 questionsPage 3 of 4

and

, then

is __________.

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Let f be a real-valued function of a real variable defined as

for

, and

for

. Which one of the following statements is true?

Your answerChoose one option.

f(x) is discontinuous at x = 0.

f(x) is continuous but not differentiable at x = 0.

f(x) is differentiable but its first derivative is not continuous at x = 0.

f(x) is differentiable but its first derivative is not differentiable at x = 0.

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The value of the directional derivative of the function

at the point (2, −1, 1) in the direction of the vector

Your answerChoose one option.

0.95

0.93

0.9

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Let f be a real-valued function of a real variable defined as

, where [x] denotes the largest integer less than or equal to x. The value of

is ______ (up to 2 decimal places).

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As shown in the figure,

is the arc from the point

to the point

on the circle

. The value of the integral

is ______ (up to 2 decimal places).

Diagram for Electrical Engineering question 42

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Let

. The maximum value of

over the interval

is ______ (up to 1 decimal place).

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Let

, where

is the region shown in the figure and

. The value of

equals ________. (Give the answer up to two decimal places.)

Diagram for Electrical Engineering question 17

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Consider a function

given by

The partial derivative of this function with respect to

at the point,

and

is _________.

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Let

and

. The value of

equals ________. (Give the answer up to three decimal places)

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A function

is defined as

, where

. Which one of the following statements is TRUE?

Your answerChoose one option.

is NOT differentiable at

for any values of

and $b.

is differentiable at

for the unique values of

and $b.

is differentiable at

for all values of

and

such that

is differentiable at

for all values of

and

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GATE EE Calculus PYQs

Question 39

Question 11

Question 12

Question 18

Question 42

Question 43

Question 17

Question 18

Question 20

Question 26