GATE MA format:nat PYQs & Answers — Page 20

Questions 191–200 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 20 of 23

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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is the Laurent series of the function

for

, then

equals ______.

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Let

be the circle in

oriented positively. Then

equals ______.

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and

are the solutions of the system

and

with the initial conditions

and

, then

equals ______.

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Let

be a non-abelian group of order 125. Then the total number of elements in

equals ______.

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Let

and

be subfields of a finite field

consisting of

and

elements, respectively. Then the total number of elements in

equals ______.

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GATE MA format:nat PYQs

Question 53

Question 54

Question 55

Question 1

Question 2

Question 4

Question 6

Question 9

Question 11

Question 12