GATE MA topic:mathematical-sciences PYQs & Answers — Page 56

Home
GATE
Mathematics
Topics
topic:mathematical-sciences

Questions 551–560 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 56 of 65

Let

be the real vector space of all continuous real valued functions on

, and let

be the linear operator on

given by

Then the dimension of the range space of

equals ________.

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

Let

be such that the quadrature rule

is exact for all polynomials of degree less than or equal to 3. Then

________.

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

Let

and

have joint probability density function given by

denotes the marginal probability density function of

, then

________.

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

Let the cumulative distribution function of the random variable

be given by

Then

________.

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

Let

be a sequence of independent Bernoulli random variables with

and let

. Then

converges, in probability, 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 circle given by

, where

varies from 0 to

. Then

Your answerChoose one option.

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

The image of the half plane

under the map

is given by

Your answerChoose one option.

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

Let

denote the closed disc with center at the origin and radius 2. Then

Your answerChoose one option.

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

Consider the polynomial

in the ring

of polynomials in the variable

with coefficients in the field

of rational numbers. Then

Your answerChoose one option.

the set of zeros of

forms a group under multiplication

is reducible in the ring

the splitting field of

has degree 3 over

the splitting field of

has degree 4 over

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

Which one of the following statements is true?

Your answerChoose one option.

Every group of order 12 has a non-trivial proper normal subgroup

Some group of order 12 does not have a non-trivial proper normal subgroup

Every group of order 12 has a subgroup of order 6

Every group of order 12 has an element of order 12

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

GATE MA topic:mathematical-sciences PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30