GATE XE area:engineering-mathematics PYQs & Answers — Page 7

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Questions 61–70 of 102. Imported answers require independent review unless marked reviewed.

Topic practice 102 questionsPage 7 of 11

Let

be the line segment from

, and let

be the arc of the circle

from

. If

where

, then the value of

is ________ (round off to two decimal places).

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Let

be a

non-zero matrix and let

be a

column vector. Then

has

Your answerChoose one option.

a solution for every

no solution for some

a solution only when

a solution if

and the columns of

form a linearly independent set.

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Let

be the sequence generated by the Newton-Raphson method applied to the function

with

. Then the sequence

Your answerChoose one option.

converges to 0.

becomes unbounded.

converges to a root of

does not converge.

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Let

be a complex number. Then the series

Your answerChoose one option.

converges for all

converges for

and diverges for

converges for

and diverges for any

converges for

and diverges for

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Let

be a vector field whose curl is zero. Then necessarily

Your answerChoose one option.

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Let

be a continuous function on the real line such that for any

. Then

is _____.

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The number of points at which the function

has local minima is _____.

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Let

be a real-valued differentiable function on

such that

and

for

. Then the series

Your answerChoose one option.

converges but not absolutely.

is unbounded.

converges absolutely.

is bounded but does not converge.

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Let

be a random variable with probability density function

Let

. Then the probability

depends only on

Your answerChoose one option.

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Let

be a

matrix such that

. Then it is necessary that

Your answerChoose one option.

is the identity matrix or the zero matrix.

the determinant of

is either 0 or 1.

the rank of

is 3.

has one imaginary eigenvalue.

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GATE XE area:engineering-mathematics PYQs

Question 11

Question 1

Question 2

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10