GATE MA year:2025 PYQs & Answers — Page 3

Questions 21–30 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 3 of 7

Consider the function

given by

Then, for the function

, the inverse function theorem is

Your answerChoose one option.

applicable at all points of

not applicable at exactly one point of

not applicable at exactly two points of

not applicable at exactly three points of

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Let the functions

and

be given by

Consider the following statements:

S1: For every compact subset

is compact.

S2: For every compact subset

is compact.

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Let

denote the characteristic polynomial of a square matrix

. Then, for which of the following invertible matrices

, the polynomial

is constant?

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

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Consider the balanced transportation problem with three sources

, and four destinations

, for minimizing the total transportation cost whose cost matrix is as follows:

					Supply
	2	6	20	11
	12	7	4	10
	8	14	16	11	5
Demand		10

where

. If the associated cost to the starting basic feasible solution obtained by using the North-West corner rule is 290, then which of the following is/are correct?

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

The optimal cost of the transportation problem is 260

The optimal cost of the transportation problem is 290

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Consider the following regions:

Then, which of the following is/are TRUE?

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

The maximum value of

is 3 on the region

The maximum value of

is 5 on the region

The maximum value of

is 3 on the region

The maximum value of

is 4 on the region

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Let

be a function defined by

Consider the following three statements:

S1:

exists.

S2:

exists.

S3:

exists.

Then, which of the following is/are correct?

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

S2 and S3 are TRUE and S1 is FALSE

S1 and S2 are TRUE and S3 is FALSE

S1 and S3 are TRUE and S2 is FALSE

S1, S2 and S3 all are TRUE

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Let

be a

matrix with entries in

and having the characteristic polynomial

Let

, where

is the

identity matrix. If

is the minimal polynomial of

, then

is equal to _____ (in integer)

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Let

be the unique polynomial of degree

satisfying the Legendre differential equation

Then, the value of

is equal to _____ (in integer)

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Let

be a unit vector parallel to the tangent at the point

to the curve of intersection of the surfaces

and

. Then, the absolute value of the directional derivative of

in the direction of

is _____ (in integer)

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The volume of the region bounded by the cylinders

and

is _____ (rounded off to TWO decimal places)

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GATE MA year:2025 PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30