GATE CSE area:engineering-mathematics PYQs & Answers — Page 2

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Questions 11–20 of 109. Imported answers require independent review unless marked reviewed.

Topic practice 109 questionsPage 2 of 11

Consider the function

defined as follows:

where

is continuous at

, then

. (answer in integer)

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Let

be defined as follows:

Which of the following statements is/are true?

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

has a local maximum

has a local minimum

is continuous over

is not differentiable over

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Let

be a random variable which takes values in the set

. Further,

and

. The expected value of

, denoted by

, is equal to __________. (rounded off to two decimal places)

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The determinant of a 4 × 4 matrix A is 3. The value of the determinant of 2A is __________. (answer in integer)

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Suppose an unbiased coin is tossed 6 times. Each coin toss is independent of all previous coin tosses. Let E_1 be the event that among the second, fourth, and sixth coin tosses, there are at least two heads. Let E_2 be the event that among the first, second, third, and fifth coin tosses, there are equal number of heads and tails.

The conditional probability P(E_1|E_2) is equal to __________. (rounded off to one decimal place)

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Consider a function

defined as follows.

For a real number

if the second digit after the decimal point in

is one of the four digits 2, 3, 6 and 7. Otherwise,

is equal to 0.

The number of points in (0,1) at which

is discontinuous is __________. (answer in integer)

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A fair six-faced dice, with the faces labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, is rolled thrice. What is the probability of rolling ‘6’ exactly once?

Your answerChoose one option.

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, then which ONE of the following is

Your answerChoose one option.

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The value of

such that

, satisfying the equation

Your answerChoose one option.

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Let

, and

be non-singular matrices of order 3 satisfying the equations

and

. Which ONE of the following is the value of the determinant of

Your answerChoose one option.

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GATE CSE area:engineering-mathematics PYQs

Question 32

Question 46

Question 58

Question 62

Question 63

Question 64

Question 8

Question 11

Question 12

Question 14