GATE MA area:engineering-mathematics PYQs & Answers — Page 26

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Questions 251–260 of 403. Imported answers require independent review unless marked reviewed.

Topic practice 403 questionsPage 26 of 41

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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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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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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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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Suppose that

and

are topologies on

induced by metrics

and

, respectively, such that

. Then which of the following statements is TRUE?

Your answerChoose one option.

If a sequence converges in

then it converges in

If a sequence converges in

then it converges in

Every open ball in

is an open ball in

The map

from

is continuous

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Let

. If the function

is defined by

then

Your answerChoose one option.

is continuous at

both the first order partial derivatives of

exist at

is finite

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Consider the following statements:

is harmonic on

II:

has a harmonic conjugate on

Then

Your answerChoose one option.

both I and II are true

I is true but II is false

I is false but II is true

both I and II are false

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Let

and

be defined by

Suppose

and

are analytic functions. Consider the following statements:

is independent of paths

joining

and

II:

is independent of paths

joining

and

Then

Your answerChoose one option.

both I and II are true

I is true but II is false

I is false but II is true

both I and II are false

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Let

and let, for

If for a subset

denotes the closure of

, then

Your answerChoose one option.

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GATE MA area:engineering-mathematics PYQs

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