GATE CSE topic:discrete-mathematics PYQs & Answers — Page 3

Questions 21–30 of 35. Imported answers require independent review unless marked reviewed.

Choose the correct choice(s) regarding the following propositional logic assertion

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

is neither a tautology nor a contradiction.

is a tautology.

is a contradiction.

The antecedent of

is logically equivalent to the consequent of

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In an undirected connected planar graph

, there are eight vertices and five faces. The number of edges in

is ________.

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There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

The fastest computer gets the toughest job and the slowest computer gets the easiest job.

Every computer gets at least one job. The number of ways in which this can be done is ________.

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Consider the string abccdeee. Each letter in the string must be assigned a binary code satisfying the following properties:

For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter.

For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter. Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string?

Your answerChoose one option.

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Let

be a group of order 6, and

be a subgroup of

such that

. Which one of the following options is correct?

Your answerChoose one option.

Both

and

are always cyclic.

may not be cyclic, but

is always cyclic.

is always cyclic, but

may not be cyclic.

Both

and

may not be cyclic.

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A relation

is said to be circular if

and

together imply

. Which of the following options is/are correct?

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

If a relation

is reflexive and symmetric, then

is an equivalence relation.

If a relation

is circular and symmetric, then

is an equivalence relation.

If a relation

is reflexive and circular, then

is an equivalence relation.

If a relation

is transitive and circular, then

is an equivalence relation.

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Let

be a set consisting of 10 elements. The number of tuples of the form

such that

and

are subsets of

, and

is ____________.

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Let

. Let

. Consider the following two statements on

. I.

II.

Which of the above statements is/are TRUE?

Your answerChoose one option.

Only I

Only II

Both I and II

Neither I nor II

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Let

be an arbitrary group. Consider the following relations on

if and only if

such that

if and only if

Which of the above is/are equivalence relation/relations?

Your answerChoose one option.

and

only

Neither

nor

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Consider the first order predicate formula

Here ‘

’ denotes that ‘

divides

’, where

and

are integers. Consider the following sets: S1.

S2. Set of all positive integers S3. Set of all integers Which of the above sets satisfy

Your answerChoose one option.

S1 and S2

S1 and S3

S2 and S3

S1, S2 and S3

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GATE CSE topic:discrete-mathematics PYQs

Question 15

Question 16

Question 19

Question 26

Question 34

Question 43

Question 50

Question 5

Question 10

Question 35