GATE EE area:engineering-mathematics PYQs & Answers — Page 8

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Questions 71–80 of 97. Imported answers require independent review unless marked reviewed.

Topic practice 97 questionsPage 8 of 10

and

, then

is __________.

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The probability of a resistor being defective is 0.02. There are 50 such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) 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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The value of the integral

in counter clockwise direction around a circle C of radius 1 with center at the point

Your answerChoose one option.

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Consider a non-singular 2×2 square matrix A. If trace(A)=4 and trace(

)=5, the determinant of the matrix A is ______ (up to 1 decimal place).

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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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is a circle

and

, then

Your answerChoose one option.

-1

-2

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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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GATE EE area:engineering-mathematics PYQs

Question 39

Question 40

Question 11

Question 12

Question 13

Question 17

Question 18

Question 35

Question 42

Question 43