GATE MA format:msq PYQs & Answers — Page 2

Questions 11–20 of 62. Imported answers require independent review unless marked reviewed.

Topic practice 62 questionsPage 2 of 7

Let

and

be the roots of the indicial equation obtained in the method of finding Frobenius series solution to the differential equation:

Which of the following statements is/are TRUE?

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

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Let

be the ring of all polynomials with coefficients in

under the usual polynomial addition and multiplication. Let

be defined by

Which of the following statements is/are TRUE?

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

is a ring homomorphism.

is one-to-one.

is onto.

is a ring isomorphism.

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Let

be any normed linear space and

be the dual space of

. Which of the following statements is/are TRUE?

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

is separable and

is non-separable, then

must be reflexive.

is separable and

is non-separable, then

cannot be reflexive.

is reflexive, then

is reflexive.

is separable, then

is separable.

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Let

be the group of integers modulo

. Let

be the external direct product of

and

. Then which of the following statements is/are TRUE?

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

is not a cyclic group.

The order of the element

is 98.

The order of the element

is 60.

There is an element in

of order 360.

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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?

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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?

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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 the vector space (over

) of all

matrices with entries in

. Consider the linear transformation

defined by

, where

and

. If

is the matrix representation of

with respect to the standard basis of

, then which of the following is/are TRUE?

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

is an invertible matrix

The trace of

is 25

The rank of

is 4, where

is the

identity matrix

The nullity of

is 0, where

is the

identity matrix

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Consider the linear programming problem (LPP):

Maximize

Subject to

Given that

forms the optimal basis of the LPP with basis matrix

and respective

. If

is the optimal solution of the dual of the LPP, then which of the following is/are TRUE?

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

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GATE MA format:msq PYQs

Question 51

Question 52

Question 53

Question 54

Question 23

Question 24

Question 25

Question 26

Question 48

Question 49