GATE MA year:2019 PYQs & Answers — Page 6

Questions 51–60 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 6 of 7

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the differential equation

is the Laplace transform of

, then the value of

is ______ (round off to 2 places of decimal). (Here, the inverse trigonometric functions assume principal values only)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be the region in the

-plane bounded by the curves

and

Then the value of the integral

is equal to ______.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the following cost matrix of assigning four jobs to four persons:

Persons / Jobs	J₁	J₂	J₃	J₄
P₁	5	8	6	10
P₂	2	5	4	8
P₃	6	7	6	9
P₄	6	9	8	10

Then the minimum cost of the assignment problem subject to the constraint that job J₄ is assigned to person P₂, is ______.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

with

satisfy the Legendre differential equation

Then the value of

is equal to ______ (round off to 2 places of decimal).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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 ______.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE MA year:2019 PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50