GATE ECE area:engineering-mathematics PYQs & Answers — Page 2

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Questions 11–20 of 100. Imported answers require independent review unless marked reviewed.

Topic practice 100 questionsPage 2 of 10

The function

satisfies

where

and

denote the first and second derivatives of

, respectively.

Given

and

, the maximum value of

over

is _____ (rounded off to two decimal places).

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Consider a non-negative function

which is continuous and bounded over the interval

. Let

and

denote, respectively, the maximum and the minimum values of

over the interval.

Among the combinations of

and

given below, choose the one(s) for which the inequality

is guaranteed to hold.

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

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Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle

in the complex plane is/are TRUE?

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

, when

is an even integer

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Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable

denote the sum of the outcomes obtained.

The expectation of

is ______ (rounded off to two decimal places).

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Consider the vectors

For real-valued scalar variable

, the value of

is __________ (rounded off to two decimal places).

denotes the Euclidean norm, i.e., for

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The general form of the complementary function of a differential equation is given by

, where A and B are real constants determined by the initial condition. The corresponding differential equation is _____.

Your answerChoose one option.

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Let

and

represent density and velocity, respectively, at a point

and time

. Assume

is continuous. Let V be an arbitrary volume in space enclosed by the closed surface S and

be the outward unit normal of S. Which of the following equations is/are equivalent to

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

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Let

and

denote the set of real numbers and the three dimensional vector space over it, respectively. The value of

for which the set of vectors

does not form a basis of

is ______.

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Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that X ≥ Y is ______ .

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Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the 60°N latitude circle, that contains the north pole in its interior is ______.

Your answerChoose one option.

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GATE ECE area:engineering-mathematics PYQs

Question 32

Question 51

Question 52

Question 58

Question 59

Question 11

Question 25

Question 30

Question 33

Question 36