GATE CSE Engineering Mathematics PYQs & Answers — Page 4

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Questions 31–40 of 55. Imported answers require independent review unless marked reviewed.

Topic practice 55 questionsPage 4 of 6

Consider the following recurrence:

Then, which of the following statements is/are TRUE?

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

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Which of the properties hold for the adjacency matrix

of a simple undirected unweighted graph having

vertices?

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

The diagonal entries of

are the degrees of the vertices of the graph.

If the graph is connected, then none of the entries of

can be zero.

If the sum of all the elements of

is at most

, then the graph must be acyclic.

If there is at least a 1 in each of

's rows and columns, then the graph must be connected.

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Which of the following is/are the eigenvector(s) for the matrix given below?

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

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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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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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Which one of the following is a closed form expression for the generating function of the sequence

, where

for all

Your answerChoose one option.

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Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and Q. Assume that all 6 numbers on each die are equiprobable and that all trials are independent. The probability (rounded to 3 decimal places) that one of them wins on the third trial is ____.

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GATE CSE Engineering Mathematics PYQs

Question 51

Question 52

Question 53

Question 17

Question 18

Question 39

Question 42

Question 45

Question 1

Question 15