GATE MA kind:question PYQs & Answers — Page 50

Questions 491–500 of 650. Imported answers require independent review unless marked reviewed.

For the linear programming problem (LPP):

(

is the set of all real numbers)

consider the following statements:

I. The LPP always has a finite optimal value for any

II. The dual of the LPP may be infeasible for some

III. If for some

, the point

is feasible to the dual of the LPP, then

, for any feasible solution

of the LPP.

IV. If for some

and

are the basic variables in the optimal table of the LPP with

, then the optimal value of dual of the LPP is 10.

Then which of the above statements are TRUE?

Your answerChoose one option.

I and III only

I, III and IV only

II and IV only

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Let

be defined by

Consider the following statements:

I. The partial derivatives

exist at

but are unbounded in any neighbourhood of

II.

is continuous but not differentiable at

III.

is not continuous at

IV.

is differentiable at

(

is the set of all real numbers and

)

Which of the above statements is/are TRUE?

Your answerChoose one option.

I and II only

I and IV only

IV only

III only

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Let

be an infinite matrix over

(the set of all complex numbers) such that

(i) for each

(the set of all natural numbers), the

row

is in

and

(ii) for every

is summable for all

, and

, where

Let the set of all rows of

be denoted by

. Consider the following statements:

is a bounded set in

is a dense set in

Which of the above statements is/are TRUE?

Your answerChoose one option.

Both P and Q

P only

Q only

Neither P nor Q

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Consider the following heat conduction problem for a finite rod

with the boundary conditions

and the initial condition

. If

, then which one of the following is CORRECT?

Your answerChoose one option.

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Let

be non-zero and analytic at all points in

. If

for

, then the residue of

is _____.

(

is the set of all complex numbers,

is the set of all integers and

denotes the set of all complex numbers excluding integers)

Your answerChoose one option.

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The general integral of the partial differential equation

is given by

, where

is a continuously differentiable function.

(

is the set of all real numbers and

)

Then which one of the following is TRUE?

Your answerChoose one option.

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Consider the following statements:

I. If

denotes the additive group of rational numbers and

is a non-trivial homomorphism, then

is an isomorphism.

II. Any quotient group of a cyclic group is cyclic.

III. If every subgroup of a group

is a normal subgroup, then

is abelian.

IV. Every group of order 33 is cyclic.

Which of the above statements are TRUE?

Your answerChoose one option.

II and IV only

II and III only

I, II and IV only

I, III and IV only

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A solution of the Dirichlet problem

is given by

Your answerChoose one option.

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Consider the subspace

of the normed linear space

. If

is a bounded linear functional on

, defined by

, then which one of the following sets is equal to

(

is the set of all complex numbers,

and

)

Your answerChoose one option.

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Consider the following statements:

I. The ring

is a unique factorization domain.

II. The ring

is a principal ideal domain.

III. In the polynomial ring

, the ideal generated by

is a maximal ideal.

IV. In the polynomial ring

, the ideal generated by

is a prime ideal.

(

denotes the set of all integers,

denotes the set of all integers modulo

, for any positive integer

)

Which of the above statements are TRUE?

Your answerChoose one option.

I, II and III only

I and II only

I, II and IV only

II and III only

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GATE MA kind:question PYQs

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