GATE CSE area:engineering-mathematics PYQs & Answers — Page 4

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Questions 31–40 of 109. Imported answers require independent review unless marked reviewed.

Topic practice 109 questionsPage 4 of 11

Let

be a continuous function from

such that

Which one of the following options is the CORRECT value of

Your answerChoose one option.

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When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is

Your answerChoose one option.

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Let

and

be two events in a probability space with

, and

. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The two events

and

are independent

, where

is the complement of the event

, where

and

are the complements of the events

and

, respectively

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Let

and

be random variables, not necessarily independent, that take real values in the interval

. Let

and let the mean values of

, respectively. Which one of the following statements is TRUE?

Your answerChoose one option.

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Let

be an

matrix over the set of all real numbers

. Let

be a matrix obtained from

by swapping two rows. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

The determinant of

is the negative of the determinant of

is invertible, then

is also invertible

is symmetric, then

is also symmetric

If the trace of

is zero, then the trace of

is also zero

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Let

be any

matrix, where

. Which of the following statements is/are TRUE about the system of linear equations

Your answerSelect all correct options. You can choose more than one.

There exist at least

linearly independent solutions to this system

There exist

linearly independent vectors such that every solution is a linear combination of these vectors

There exists a non-zero solution in which at least

variables are 0

There exists a solution in which at least

variables are non-zero

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A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decimal places) that both balls drawn are red is ________.

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The Lucas sequence

is defined by the recurrence relation:

with

and

Which one of the options given is TRUE?

Your answerChoose one option.

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Let

and

Let

and

denote the determinants of the matrices

and

, respectively.

Which one of the options given below is TRUE?

Your answerChoose one option.

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Geetha has a conjecture about integers, which is of the form

where

is a statement about integers, and

is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha’s conjecture?

Your answerSelect all correct options. You can choose more than one.

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GATE CSE area:engineering-mathematics PYQs

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