GATE MA year:2017 PYQs & Answers — Page 3

Questions 21–30 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 3 of 7

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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Let

(

) be a random sample from a

population, where

. The smallest

such that the length of the shortest 95% confidence interval for

will not exceed 10 is ______.

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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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and

are the null spaces of

and

, respectively, then the dimension of the subspace

equals ________.

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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

be a

matrix such that

for

and

, where

. Let

and

be the largest and the smallest eigenvalues of

, respectively. If

, then

equals ________.

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Let

be the simple, positively oriented circle of radius 2 centered at the origin in the complex plane. Then

equals ________.

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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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GATE MA year:2017 PYQs

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30