GATE XE area:engineering-mathematics PYQs & Answers — Page 9

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Questions 81–90 of 102. Imported answers require independent review unless marked reviewed.

Topic practice 102 questionsPage 9 of 11

Let

, where

and

is the circle

oriented counter clockwise. Then, the value of

rounded off to one decimal place is ________ .

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Box-S has 2 white and 4 black balls and box-T has 5 white and 3 black balls. A ball is drawn at random from the box-S and put in box-T. Subsequently, the probability of drawing a white ball from box-T is _____. (round off to 2 decimal places)

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Let

be a three times continuously differentiable real valued function on

such that its third derivative

for all

. If

is a polynomial of degree

such that

and

then

equals ____________

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For real numbers

and

, if the formula

is exact for all polynomials of degree

then

equals ______________

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Raju has four fair coins and one fair dice. At first Raju tosses a coin. If the coin shows head then he rolls the dice and the number that dice shows is taken as his score. If the coin shows tail then he tosses three more coins and the total number of tails shown (including the first one) is taken as his score. If Raju tells that his score is 2 then the probability that he rolled the dice is (up to two decimal places) ______________

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Let

be a continuously differentiable real valued function defined by

Then the value of

is ______________

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A rectangular box without top cover having a square base is to be made from a sheet of 108 square meters. Then the largest possible volume of the box in cubic meters is ______________

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Let

. Then the trace of

equals

Your answerChoose one option.

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Let

denote the set of complex numbers and

. Let

be the simple positively oriented circle

and

. If

is analytic in

and is given by

then the value of the contour integral

Your answerChoose one option.

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Let

denote the three dimensional Euclidean space and

for all

. If

is the curve described by the parametric equation

, then the value of the line integral

is ______________

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GATE XE area:engineering-mathematics PYQs

Question 11

Question 17

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10