GATE MA branch:ma PYQs & Answers — Page 59

Questions 581–590 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 59 of 65

For

, let

. Then

_________.

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Let

be independent exponential random variables with mean

, respectively. Then

has exponential distribution with mean equal to _________.

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Let

be the number of heads in 4 tosses of a fair coin by Person 1 and let

be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosses are independent. Then the value of

correct up to three decimal places is _________.

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Let

and

be independent geometric random variables with the same probability mass function given by

. Then the value of

correct up to three decimal places is _________.

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A certain commodity is produced by the manufacturing plants

and

whose capacities are 6 and 5 units, respectively. The commodity is shipped to markets

and

whose requirements are 1, 2, 3 and 5 units, respectively. The transportation cost per unit from plant

to market

is as follows:

					Supply
	1	3	5	8	6
	2	5	6	7	5
Demand	1	2	3	5

Then the optimal cost of transportation is _________.

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Consider the vector space

of polynomials of degree at most 2. Let

be a linear functional such that

and

. Then

equals ______.

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Let

be a

matrix such that

, where

is the identity matrix. If

has two distinct eigenvalues and each eigenvalue has geometric multiplicity 3, then the total number of nonzero entries in the Jordan canonical form of

equals ______.

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Let

and

for

. Then, in the complex plane

Your answerChoose one option.

is analytic and

is NOT analytic

is NOT analytic and

is analytic

neither

nor

is analytic

both

and

are analytic

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is the Laurent series of the function

for

, then

equals ______.

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Let

be given by

. Then the sequence

Your answerChoose one option.

converges uniformly on

does NOT converge uniformly on

but has a subsequence that converges uniformly on

does NOT converge pointwise on

converges pointwise on

but does NOT have a subsequence that converges uniformly on

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GATE MA branch:ma PYQs

Question 51

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Question 53

Question 54

Question 55

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Question 5