GATE XE purpose:exam-prep PYQs & Answers — Page 109

Questions 1081–1090 of 1772. Imported answers require independent review unless marked reviewed.

Topic practice 1772 questionsPage 109 of 178

For a matrix

, the diagonal elements are all zero and

. The minimum number of elements required to fully specify the matrix is _____.

Your answerChoose one option.

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The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 - 2018 is _____.

Diagram for Engineering Sciences question 10

Your answerChoose one option.

15 : 17

16 : 17

17 : 15

17 : 16

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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 the solution of the initial value problem

If the plane curve parameterized by

having

-coordinate

and

-coordinate

is closed, then necessarily

Your answerChoose one option.

is a non-zero rational number.

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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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GATE XE purpose:exam-prep PYQs

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