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

Questions 11–20 of 87. Imported answers require independent review unless marked reviewed.

Topic practice 87 questionsPage 2 of 9

denotes the Laplace transform of some function

, then the Laplace transform of

, where

is a real constant, is

Your answerChoose one option.

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Which one of the following equations is a linear differential equation?

Your answerChoose one option.

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A bag contains 5 red, 7 green and 3 blue balls. Two balls are drawn at random from the bag one-by-one. The probability of the second drawn ball being red is

Your answerChoose one option.

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The solution of the linear differential equation

when

, is

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Which one of the following functions is analytic, given

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The value of the integral

obtained by using Simpson’s 1/3 rule with 4 subintervals is equal to

. The value of n is ________. (Answer in integer)

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If i, j and k are the orthogonal unit vectors in Cartesian x-y-z coordinate system, the rate of change of the function

at point (1, 1, 1) in the direction of

is________. (Answer in integer)

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The annual profit of a company depends on its annual marketing expenditure. The information of preceding 3 years’ annual profit and marketing expenditure is given in the table. Based on linear regression, the estimated profit (in units) of the 4

year at a marketing expenditure of 5 units is ________. (Rounded off to two decimal places)

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In the Taylor series expansion of

around

, the coefficient of the term

Your answerChoose one option.

1/3

−1/6

−1/3

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A vector field is given as

, where

and

are the unit vectors along the x and y axes in the Cartesian frame, respectively. Then the value of

where

is an elemental path taken over an anticlockwise circular contour

of radius

Diagram for Production and Industrial Engineering question 12

Your answerChoose one option.

−100π

−800π

−400π

400π

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GATE PI area:engineering-mathematics PYQs

Question 13

Question 14

Question 15

Question 36

Question 37

Question 43

Question 44

Question 58

Question 11

Question 12