GATE MA topic:mathematical-sciences PYQs & Answers — Page 9

Questions 81–90 of 650. Imported answers require independent review unless marked reviewed.

Consider the system of ordinary differential equations

where

is a

skew-symmetric matrix with entries in

. Then, for this system, the origin is a stable critical point for

Your answerChoose one option.

any such matrix

only such matrices

whose rank is 2

only such matrices

whose rank is 4

only such matrices

whose rank is 6

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Let

with the norm

, where

is the space of all real-valued continuous functions on

. Let

with the norm

. Let

and

be the closed unit balls in

and

centred at the origin, respectively. Consider

and

given by

Consider the following statements:

S1:

is attained at a point of

S2:

is attained at a point of

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

be defined in

, where

is a continuously differentiable non-zero homogeneous function of degree 4. Then,

holds for

Your answerChoose one option.

all points

on the line given by

all points

in the region of

except on the line given by

all points

on the line given by

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The partial differential equation

Your answerChoose one option.

elliptic in the region

hyperbolic in the region

elliptic in the region

hyperbolic in the region

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Let

be the solution of the following initial-boundary value problem

Then, for each

, the value of

Your answerChoose one option.

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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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GATE MA topic:mathematical-sciences PYQs

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25