GATE MA discipline:mathematics-and-statistics PYQs & Answers — Page 6

Home
GATE
Mathematics
Topics
discipline:mathematics-and-statistics

Questions 51–60 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 6 of 65

Let

and

be the roots of the indicial equation obtained in the method of finding Frobenius series solution to the differential equation:

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

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 all polynomials with coefficients in

under the usual polynomial addition and multiplication. Let

be defined by

Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is a ring homomorphism.

is one-to-one.

is onto.

is a ring isomorphism.

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

Let

be any normed linear space and

be the dual space of

. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is separable and

is non-separable, then

must be reflexive.

is separable and

is non-separable, then

cannot be reflexive.

is reflexive, then

is reflexive.

is separable, then

is separable.

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

Let

be the group of integers modulo

. Let

be the external direct product of

and

. Then which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is not a cyclic group.

The order of the element

is 98.

The order of the element

is 60.

There is an element in

of order 360.

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

Let

. Then the geometric multiplicity of the eigenvalue 2 of

is equal to ________. (answer in integer)

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

Let

, where

and

is the sphere with centre at

and radius 9. Here,

is the unit normal drawn outward and

are unit vectors. Then the value of

is equal to ________. (answer in integer)

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

Consider the problem of maximizing

subject to

Then the maximum value of

is ________. (answer in integer)

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 polynomials of degree at most three with the real coefficients under usual polynomial addition and scalar multiplication. Let

be the linear transformation defined as

for all

, where

is the derivative of

. Then the nullity of

is equal to ________. (answer in integer)

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

The number of zeros of the complex polynomial

in the annulus

is equal to ________. (answer in integer)

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

Let

denote the space of all real valued Lebesgue square integrable functions on

. Let

be defined as follows:

Then the value of

is equal to ________. (answer in integer)

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

GATE MA discipline:mathematics-and-statistics PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60