GATE CSE area:engineering-mathematics PYQs & Answers — Page 8

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Questions 71–80 of 109. Imported answers require independent review unless marked reviewed.

Topic practice 109 questionsPage 8 of 11

Consider the functions

II.

III.

Which of the above functions is/are increasing everywhere in [0,1]?

Your answerChoose one option.

III only

II only

II and III only

I and II only

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Let

be the set of all binary relations on the set . Suppose a relation is chosen from

at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is ________.

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Let

be a group of 35 elements. Then the largest possible size of a subgroup of

other than

itself is ________.

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Let

and

be two

matrices over real numbers. Let

and

denote the rank and determinant of a matrix

, respectively. Consider the following statements.

II.

III.

IV.

Which of the above statements are TRUE?

Your answerChoose one option.

I and II only

I and IV only

II and III only

III and IV only

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Which one of the following predicate formulae is NOT logically valid? Note that

is a predicate formula without any free occurrence of

Your answerChoose one option.

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The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ________.

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For

, let

be a non-zero vector. Suppose that

is chosen uniformly at random from

. Then, the probability that

is an odd number is ______.

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Let

be a square matrix. Consider the following two statements on

. I.

is invertible. II. Determinant of

is non-zero.

Which one of the following is TRUE?

Your answerChoose one option.

I implies II; II does not imply I.

II implies I; I does not imply II.

I does not imply II; II does not imply I.

I and II are equivalent statements.

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Compute

Your answerChoose one option.

Limit does not exist

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Two numbers are chosen independently and uniformly at random from the set {1, 2, ..., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ________.

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GATE CSE area:engineering-mathematics PYQs

Question 1

Question 17

Question 18

Question 27

Question 39

Question 42

Question 45

Question 9

Question 13

Question 22