GATE CSE Discrete Mathematics PYQs & Answers

Questions 1–10 of 35. Imported answers require independent review unless marked reviewed.

The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?

Note: The figure shown is representative.

Diagram for Computer Science and Information Technology question 10

Your answerChoose one option.

Bridges on P, Q, and T

Bridges on P, Q, S, and T

Bridges on Q, R, T, and V

Bridges on P, Q, S, U, and V

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Let

be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?

Your answerChoose one option.

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is a function from

, and their composition defined as

is a mapping from

and

are onto (surjective) functions, which ONE of the following is TRUE about the function

Your answerChoose one option.

must be an onto (surjective) function.

must be a one-to-one (injective) function.

must be a bijective function, that is, both one-to-one and onto.

is not required to be a one-to-one or onto function.

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Let

be the set of all ternary strings defined over the alphabet

. Consider all strings in

that contain at least one occurrence of two consecutive symbols, that is, “aa”, “bb” or “cc”. The number of such strings of length 5 that are possible is ______. (Answer in integer)

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Let

be the set of all functions from

. Define the binary relation

as follows:

if and only if

, where

Which of the following statement(s) is/are TRUE?

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

is a symmetric relation

is a partial order

is a lattice

is an equivalence relation

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Which of the following predicate logic formula/formula is/are CORRECT representation(s) of the statement: “Everyone has exactly one mother”? The means of the predicates used are:

is the mother of

and

are not equal

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

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is the set of non-negative integers. Let F be the set of functions from A to itself. For any two functions,

, we define

for every number

in A. Which of the following is/are CORRECT about the mathematical structure

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

is an Abelian group.

is an Abelian monoid.

is a non-Abelian group.

is a non-Abelian monoid.

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A quadratic polynomial

over complex numbers is said to be square invariant if

. Suppose from the set of all square invariant quadratic polynomials we choose one at random.

The probability that the roots of the chosen polynomial are equal is __________. (rounded off to one decimal place)

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Let

and

be the following propositions:

: Fail grade can be given.

: Student scores more than 50% marks.

Consider the statement: “Fail grade cannot be given when student scores more than 50% marks.”

Which one of the following is the CORRECT representation of the above statement in propositional logic?

Your answerChoose one option.

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Consider a permutation sampled uniformly at random from the set of all permutations of

for some

. Let

be the event that 1 occurs before 2 in the permutation, and

the event that 3 occurs before 4. Which one of the following statements is TRUE?

Your answerChoose one option.

The events

and

are mutually exclusive

The events

and

are independent

Either event

must occur

Event

is more likely than event

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GATE CSE Discrete Mathematics PYQs

How to practice Discrete Mathematics

Question 10

Question 15

Question 17

Question 30

Question 42

Question 48

Question 49

Question 64

Question 12

Question 14