GATE MA exam:gate PYQs & Answers — Page 3

Questions 21–30 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 3 of 65

Let

be a

real symmetric positive definite matrix. Which of the following statements is/are TRUE?

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

is positive definite for all nonzero

is positive semidefinite for all

is positive definite if

is nonsingular.

is not positive semidefinite for some

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Let

be a function defined as follows:

Which of the following statements is/are TRUE?

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

is continuous at

For any

, the directional derivative of

in the direction of

exists.

is differentiable at

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Let

be the ring of integers modulo 11. Let

be the ring of all polynomials with coefficients in

. Which of the following statements is/are TRUE?

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

The polynomial

is irreducible over

is a field.

The ideal

is maximal.

The ideal

is not a prime ideal.

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Consider

with the topology

Which of the following statements is/are TRUE?

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

is a Hausdorff space.

Any finite subset of

is closed.

is compact.

is connected.

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Consider the following partial differential equation:

where

and

are distinct positive real numbers. The combination(s) of the values of the real parameters

and

for which

is a solution of the given partial differential equation, is/are

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

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Consider the following assignment problem where

are tasks,

are agents and the cost matrix is given by

Which of the following statements is/are TRUE for an optimal assignment?

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

The cost is 9.

Agent P is assigned to task Y.

Agent Q is assigned to task X.

Agent R is assigned to task Y.

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Consider the following differential equation:

Which of the following statements is/are TRUE?

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

The point

is not a singular point.

The point

is a singular point.

The point

is a regular singular point.

The point

is not a regular singular point.

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Let

be the linear transformation which reflects every vector in

through a two-dimensional subspace of

. Let

be the matrix representation of

using the basis

. Then the value of

is equal to ________. (answer in integer)

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Let

, where

is the ring of all polynomials with coefficients in

. Then the degree of the field extension

is equal to ________. (answer in integer)

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Consider the differential equation

with the initial condition

. Use the modified Euler’s method, the second approximation to

, where

(step size), is equal to ________. (rounded off to TWO decimal places)

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GATE MA exam:gate PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30