GATE MA kind:question PYQs & Answers — Page 2

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Questions 11–20 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 2 of 65

Let

be the vector space of all

real matrices over

under usual matrix addition and scalar multiplication. Let

be the set of all

real upper triangular matrices. Which one of the following is TRUE?

Your answerChoose one option.

The quotient space

is isomorphic to the vector space of all

real skew symmetric matrices over

under usual matrix addition and scalar multiplication.

The quotient space

is isomorphic to the vector space of all

real symmetric matrices over

under usual matrix addition and scalar multiplication.

The quotient space

is isomorphic to the vector space of all

real lower triangular matrices over

under usual matrix addition and scalar multiplication.

The quotient space

is isomorphic to the vector space of all

real matrices with trace zero over

under usual matrix addition and scalar multiplication.

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Let

be the integral defined as follows:

If the order of the integration is changed, then which one of the following is the correct expression for

Your answerChoose one option.

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Let

denote the Cantor set and

be defined as follows:

The value of the Lebesgue integral of

over the interval

is equal to

Your answerChoose one option.

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Let

be a group of order 595. Which one of the following is TRUE?

Your answerChoose one option.

cannot have a proper normal subgroup.

must have a proper normal subgroup.

cannot have an element of order 17.

The number of Sylow 5-subgroups is 17.

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Let

be the solution of the initial value problem for the heat equation on the real line:

with the initial condition

is the Fourier transform of

with respect to

, then

is equal to

Your answerChoose one option.

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Let

be defined as

Which one of the following is TRUE?

Your answerChoose one option.

is one-to-one.

The Jacobian of

is negative.

is locally invertible.

is invertible on

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Let

be defined by

. Which one of the following is TRUE?

Your answerChoose one option.

is differentiable at

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Let

denote the unit disc in the complex plane

. Let

be an analytic function which satisfies

. Then which one of the following is a possible value of

Your answerChoose one option.

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Let

be the space of all continuously differentiable real valued functions on

. Define the following norms on

and

. Which one of the following is TRUE?

Your answerChoose one option.

is a Banach space.

is not a Banach space.

is a Banach space.

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Let

be a set with at least two elements. Let

and

be metrics on

. Which one of the following is NOT a metric on

Your answerChoose one option.

for all

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GATE MA kind:question PYQs

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20