GATE MA format:mcq PYQs & Answers — Page 35

Questions 341–350 of 366. Imported answers require independent review unless marked reviewed.

Topic practice 366 questionsPage 35 of 37

Let

be the distribution function of a random variable

. Consider the functions:

Which of the above functions are distribution functions?

Your answerChoose one option.

Neither

nor

Only

Both

and

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Let

(

) be independent and identically distributed random variables with finite variance

and let

. Then the covariance between

and

Your answerChoose one option.

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Consider the linear programming problem (LP): Maximize

Subject to

is unrestricted in sign. Then the LP has

Your answerChoose one option.

no optimal solution

only one basic feasible solution and that is optimal

more than one basic feasible solution and a unique optimal solution

infinitely many optimal solutions

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For a linear programming problem (LP) and its dual, which one of the following is NOT TRUE?

Your answerChoose one option.

The dual of the dual is primal

If the primal LPP has an unbounded objective function, then the dual LPP is infeasible

If the primal LPP is infeasible, then the dual LPP must have unbounded objective function

If the primal LPP has a finite optimal solution, then the dual LPP also has a finite optimal solution

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Given two

matrices

and

with entries in

, consider the following statements: (P): If

and

have the same minimal polynomial, then

is similar to

. (Q): If

has

distinct eigenvalues, then there exists

such that

are linearly independent. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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Let

and

, respectively, denote the real part and the imaginary part of a complex number

. Let

be the bilinear transformation such that

and

. Then, the image of

under the mapping

Your answerChoose one option.

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Let

and

be two sequences in a complete metric space

such that

and

for all

. Then

Your answerChoose one option.

both

and

converge

converges but

need NOT converge

converges but

need NOT converge

neither

nor

converges

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Let

be defined by

Then, at

Your answerChoose one option.

is continuous and the directional derivative of

does NOT exist in some direction

is NOT continuous and the directional derivatives of

exist in all directions

is NOT differentiable and the directional derivatives of

exist in all directions

is differentiable

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Let

and

for

. Consider the following statements: (P):

and

are linearly independent solutions of

. (Q): The Wronskian

for all

. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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Let

be an orthonormal basis of a Hilbert space

. Let

be given by

. For each

, define

. Then

Your answerChoose one option.

but for each

for each

but the sequence

is unbounded

there exist

such that

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GATE MA format:mcq PYQs

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Question 33

Question 35

Question 39