GATE MA area:engineering-mathematics PYQs & Answers — Page 3

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Questions 21–30 of 403. Imported answers require independent review unless marked reviewed.

Topic practice 403 questionsPage 3 of 41

For

, the power series

converges at

and diverges at

. Then the radius of convergence of this power series is equal to ________. (answer in integer)

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Let

. Define an inner product on

with respect to

. Consider the subspace

. Which one of the following sets is an orthonormal basis of

with respect to

Your answerChoose one option.

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The value of the contour integral

, where

, oriented in the counter-clockwise direction, is equal to

Your answerChoose one option.

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Let

. On which one of the following domains, does

represent an analytic function?

Your answerChoose one option.

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Which one of the following statements is TRUE?

Your answerChoose one option.

The set of all

real matrices under usual matrix addition and multiplication is a Unique Factorization Domain.

The set of all real valued functions under usual function addition and multiplication is a Unique Factorization Domain.

The set of all polynomials with coefficients in

under usual polynomial addition and multiplication is a Unique Factorization Domain.

The set of Riemann integrable functions in

under usual function addition and multiplication is a Unique Factorization Domain.

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Let

with the supremum norm. Let

be given by

. Which one of the following is TRUE?

Your answerChoose one option.

is bounded but not one-to-one.

is one-to-one but not bounded.

is bounded and the inverse (from the range of

) exists but not bounded.

is bounded and the inverse (from the range of

) is bounded.

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Let

satisfy the wave equation

, with

and

. By using D’Alembert’s formula, the maximum value of

for

Your answerChoose one option.

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Consider the Laplace equation

, with the boundary conditions

. Then the value of

is equal to

Your answerChoose one option.

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Let

and

be subsets of a normed linear space

, and

. Which one of the following is NOT TRUE?

Your answerChoose one option.

If either of

is open, then

is open.

and

are convex, then

is convex.

and

are closed, then

is closed.

and

are connected, then

is connected.

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Let

and

be topological spaces and

be a continuous and bijective mapping. Which one of the following statements is TRUE?

Your answerChoose one option.

is a homeomorphism if

and

are compact.

is a homeomorphism if

is Hausdorff and

is compact.

is a homeomorphism if

is compact and

is Hausdorff.

is a homeomorphism if

and

are Hausdorff.

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GATE MA area:engineering-mathematics PYQs

Question 35

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Question 45

Question 47