GATE CSE area:engineering-mathematics PYQs & Answers — Page 11

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Questions 101–109 of 109. Imported answers require independent review unless marked reviewed.

Topic practice 109 questionsPage 11 of 11

P and Q are considering to apply for a job. The probability that P applies for the job is

, the probability that P applies for the job given that Q applies for the job is

, and the probability that Q applies for the job given that P applies for the job is

. Then the probability that P does not apply for the job given that Q does not apply for the job is

Your answerChoose one option.

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The value of

Your answerChoose one option.

is 0

is -1

is 1

does not exist

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Let

and

be two vectors in

whose Euclidean norms satisfy

. What is the value of

such that

bisects the angle between

and

Your answerChoose one option.

1/2

−1/2

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Let

be an

real valued square symmetric matrix of rank 2 with

. Consider the following statements.

(I) One eigenvalue must be in

(II) The eigenvalue with the largest magnitude must be strictly greater than 5

Which of the above statements about eigenvalues of

is/are necessarily CORRECT?

Your answerChoose one option.

Both (I) and (II)

(I) only

(II) only

Neither (I) nor (II)

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For any discrete random variable

, with probability mass function

, and

, define the polynomial function

. For a certain discrete random variable

, there exists a scalar

such that

. The expectation of

Your answerChoose one option.

Not expressible in terms of

and

alone

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If the ordinary generating function of a sequence

, then

is equal to __________.

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If a random variable

has a Poisson distribution with mean 5, then the expectation

equals __________.

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If the characteristic polynomial of a

matrix

over

(the set of real numbers) is

, and one eigenvalue of

is 2, then the largest among the absolute values of the eigenvalues of

is __________.

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The number of roots of

in the range

Your answerChoose one option.

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GATE CSE area:engineering-mathematics PYQs

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Question 64