GATE MA area:engineering-mathematics PYQs & Answers — Page 34

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Questions 331–340 of 403. Imported answers require independent review unless marked reviewed.

Topic practice 403 questionsPage 34 of 41

Consider the ordered square

, the set

with the dictionary order topology. Let the general element of

be denoted by

, where

. Then the closure of the subset

Your answerChoose one option.

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Let

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

(the set of real numbers). Let a linear transformation

be defined by

Consider the following statements.

I. The null space of

II. The range space of

is spanned by the set

III.

IV. If

is the matrix representation of

with respect to the standard basis

, then the trace of the matrix

is 3.

Which of the above statements are TRUE?

Your answerChoose one option.

I and II only

I, III and IV only

I, II and IV only

II and IV only

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Let

and

be two topologies defined on

(the set of all natural numbers), where

is the topology generated by

and

is the discrete topology on

. Consider the following statements:

I. In

, every infinite subset has a limit point.

II. The function

defined by

is a continuous function.

Which of the above statements is/are TRUE?

Your answerChoose one option.

Both I and II

I only

II only

Neither I nor II

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Let

. Consider the following statements:

II.

where

and

(

is the set of all real numbers)

Which of the above statements is/are TRUE?

Your answerChoose one option.

Both I and II

I only

II only

Neither I nor II

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Let

be the region in the

-plane bounded by the curves

and

Then the value of the integral

is equal to ______.

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Let

be the vector space of all

matrices with complex entries over the real field. If

then the dimension of

is equal to ______. (

denotes the conjugate transpose of

)

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The number of elements of order 15 in the additive group

is ______. (

denotes the group of integers modulo

, under the operation of addition modulo

, for any positive integer

)

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Let

be the ring of integers modulo 125 under the operations of addition modulo 125 and multiplication modulo 125. If

is the number of maximal ideals of

and

is the number of non-units of

, then

is equal to ______.

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Consider the inner product space

of all polynomials of degree at most 2 over the field of real numbers with the inner product

for

. Let

be an orthogonal set in

, where

and

are real constants. Then the value of

is equal to _____.

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The principal value of

Your answerChoose one option.

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GATE MA area:engineering-mathematics PYQs

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