GATE MA year:2021 PYQs & Answers — Page 5

Questions 41–50 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 5 of 7

The initial value problem

where

, is solved by the following Euler method

with step-size

. Then

, provided

Your answerChoose one option.

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Consider the Linear Programming Problem

subject to

where

and

are real numbers (

Let

be a feasible solution of

such that

and let all feasible solutions

satisfy

. Then, which one of the following statements is NOT true?

Your answerChoose one option.

has an optimal solution

The feasible region of

is a bounded set

is a feasible solution of the dual of

, then

The dual of

has at least one feasible solution

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Let

be the Hilbert space of real valued square integrable functions on

equipped with the norm

. Consider the subspace

. For

, define

. Then

Your answerChoose one option.

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Let

be the Banach space of real valued continuous functions on

equipped with the supremum norm. Define

Let

denote the range space of

. Consider the following statements: P:

is a bounded linear operator. Q:

exists and is bounded. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be the sequence space equipped with the norm

. Consider the subspace

and the linear transformation

given by

for

. Then

Your answerChoose one option.

is closed but NOT bounded

is bounded

is neither closed nor bounded

exists and is an open map

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Let

be given by

for

. Consider the following statements: P:

is equicontinuous on

. Q:

does NOT converge uniformly on

. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be given by

Consider the following statements: P:

is continuous at

but

is NOT differentiable at

. Q: The directional derivative

exists in the direction of every unit vector

. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be the solid region in

bounded by the paraboloid

and the plane

. Then the value of

Your answerChoose one option.

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Let

be given by

. Then

has

Your answerChoose one option.

a point of local maximum and a saddle point

a point of local minimum and a saddle point

a point of local maximum and a point of local minimum

two saddle points

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The equation

can be solved in a neighborhood of the point

for some continuously differentiable function

. Then

Your answerChoose one option.

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GATE MA year:2021 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40