GATE MA topic:mathematical-sciences PYQs & Answers — Page 39

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topic:mathematical-sciences

Questions 381–390 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 39 of 65

Let

and

be the positively oriented boundary of

. Then the value of the integral

is __________.

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Let

and

be the function defined by

for

, then

__________.

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The number of zeroes (counting multiplicity) of

in the annular region

is __________.

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Let

be a square matrix such that

, where

denotes the determinant of a square matrix

. If

, then the geometric multiplicity of the eigenvalue

is __________.

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(

) is the power series solution of the differential equation

, then

__________.

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solves the following initial boundary value problem

then

__________.

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Let

be the vector space of all polynomials of degree at most 2 over the real field

. Let

be the linear operator given by

Then the sum of the eigenvalues of

is __________.

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The quadrature formula

is exact for all polynomials of degree

. Then

__________.

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For each

, consider the decimal representation

. Define

is rational and

is irrational, where

is the number of zeroes immediately after the decimal point up to the first nonzero digit in the decimal representation of

. Then the Lebesgue integral

__________.

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Let

be an optimal solution of the following Linear Programming Problem

subject to

is an optimal solution of the dual of

, then

__________ (round off to two decimal places).

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GATE MA topic:mathematical-sciences PYQs

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