GATE MA format:nat PYQs & Answers — Page 22

Questions 211–220 of 222. Imported answers require independent review unless marked reviewed.

Topic practice 222 questionsPage 22 of 23

Let

be the group of all permutations of the set

. Then the total number of elements of

that commute with

equals ________.

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Let

be the ring of polynomials over

. Then the total number of maximal ideals in the quotient ring

equals ________.

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Let

be the polynomial of degree at most 2 that interpolates the data

and

. If

is a polynomial of degree at most 3 such that

interpolates the data

and

, then

equals ________.

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Let

be the solution of

satisfying the condition

on the circle

. Then

equals ________.

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Let

be a random variable with probability mass function

for

. Then

equals ________.

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Let

and

be independent and identically distributed random variables with probability mass function

. Then

equals (rounded to 2 decimal places) ________.

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Let

be a sequence of independent and identically distributed Poisson random variables with mean 4. Then

equals ________.

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Let

and

be independent and identically distributed exponential random variables with probability density function

Then

equals (rounded to 2 decimal places) ________.

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Let

and

be any two events with

and

. Then

equals (rounded to 2 decimal places) ________.

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Let

be a random sample from a

population. For testing

against

, the most powerful test rejects

, where

is to be chosen such that the level of significance is 0.1. Then the power of this test equals ________.

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GATE MA format:nat PYQs

Question 37

Question 38

Question 41

Question 43

Question 46

Question 47

Question 48

Question 49

Question 50

Question 52