GATE MA year:2023 PYQs & Answers — Page 4

Questions 31–40 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 4 of 7

Let

be the portion of the plane

which lies inside the cylinder

. If the surface area of

, then the value of

is equal to __________.

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Let

and the norm

for

. Let

be defined by

denotes the norm of the linear functional

, then

is equal to _________.

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Let

be the solution of the initial value problem

, then the value of

is ______ (rounded off to 2 decimal places).

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Consider

with the inner product

, for

and

. Let

and

denote the orthogonal complement of

. The dimension of

is equal to ______.

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Let

and

. If

for some

, then the value of

is equal to __________.

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Let

denote the group of

invertible complex matrices with usual matrix multiplication. For

denotes the subgroup generated by

and

. Let

and

be three subgroups of

given by

Let

denote the center of

for

. Which of the following statements is correct?

Your answerChoose one option.

is isomorphic to

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Let

. For a sequence

, define

. Let

and

be defined by

Then

Your answerChoose one option.

is a compact linear map and

is NOT a compact linear map

is NOT a compact linear map and

is a compact linear map

both

and

are compact linear maps

NEITHER

NOR

is a compact linear map

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Let

. For

, let

. Define

for all

. Then

Your answerChoose one option.

is continuous but

is NOT continuous

is NOT continuous but

is continuous

both

and

are continuous

NEITHER

NOR

is continuous

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Consider the Cauchy problem

on the initial curve

. Consider the following statements:

: If

, then there exists a unique solution to the Cauchy problem in a neighborhood of

: If

, then there exist infinitely many solutions to the Cauchy problem in a neighborhood of

Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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Consider the linear system

, where

and

. Suppose

, where

and

are lower triangular and upper triangular square matrices, respectively. Consider the following statements:

: If each element of the main diagonal of

is 1, then

: For any choice of the initial vector

, the Jacobi iterates

converge to the unique solution of the linear system

Then

Your answerChoose one option.

both

and

are TRUE

is FALSE and

is TRUE

is TRUE and

is FALSE

both

and

are FALSE

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GATE MA year:2023 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40