GATE MA 2025 Paper 1 — page 8

Questions 22–24 of 65. Imported answers require review unless explicitly marked reviewed.

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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2025 · Paper 1

Question 22

Question 23

Question 24