Welcome to the Engineering Mathematics MCQs Page

Dive deep into the fascinating world of Engineering Mathematics with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Engineering Mathematics, a crucial aspect of GATE CSE Exam. In this section, you will encounter a diverse range of MCQs that cover various aspects of Engineering Mathematics, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within GATE CSE Exam.

Check out the MCQs below to embark on an enriching journey through Engineering Mathematics. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of GATE CSE Exam.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Engineering Mathematics. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Engineering Mathematics MCQs | Page 5 of 23

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Q41.

Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a ∈ A. Which of the following statements is always true for all such functions f and g?

g is onto => h is onto

h is onto => f is onto

h is onto => g is onto

h is onto => f and g are onto

Discuss

Answer: (c).h is onto => g is onto

Q42.

Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets S1 and S2 in C, either S1 ⊂ S2 or S2⊂ S1. What is the maximum cardinality of C?

n + 1

2n-1 + 1

Discuss

Answer: (b).n + 1

Q43.

A binary relation R on N x N is defined as follows:

(a, b) R (c, d) if a <= c or b <= d.

Consider the following propositions:
P: R is reflexive
Q: R is transitive

Which one of the following statements is TRUE?

Both P and Q are true

P is true and Q is false

P is false and Q is true

Both P and Q are false

Discuss

Answer: (b).P is true and Q is false

Q44.

For the set N of natural numbers and a binary operation f : N x N → N, an element z ∊ N is called an identity for f, if f (a, z) = a = f(z, a), for all a ∊ N. Which of the following binary operations have an identity?

1. f (x, y) = x + y - 3
2. f (x, y) = max(x, y)
3. f (x, y) = x^y

I and II only

II and III only

I and III only

None of these

Discuss

Answer: (a).I and II only

Q45.

Given a boolean function f (x1, x2, ..., xn), which of the following equations is NOT true

f (x1, x2, ..., xn) = x1'f(x1, x2, ..., xn) + x1f(x1, x2, ..., xn)

f (x1, x2, ..., xn) = x2f(x1, x2, …, xn) + x2'f(x1, x2, …,xn)

f (x1, x2, ..., xn) = xn'f(x1, x2, …, 0) + xnf(x1, x2, …,1)

f (x1, x2, ..., xn) = f(0, x2, …, xn) + f(1, x2, .., xn)

Discuss

Answer: (d).f (x1, x2, ..., xn) = f(0, x2, …, xn) + f(1, x2, .., xn)

Q46.

Consider the following first order logic formula in which R is a binary relation symbol. ∀x∀y (R(x, y) => R(y, x)) The formula is

satisfiable and valid

satisfiable and so is its negation

unsatisfiable but its negation is valid

satisfiable but its negation is unsatisfiable

Discuss

Answer: (b).satisfiable and so is its negation

Q47.

Let P, Q and R be sets let Δ denote the symmetric difference operator defined as PΔQ = (P U Q) - (P ∩ Q). Using Venn diagrams, determine which of the following is/are TRUE? PΔ (Q ∩ R) = (P Δ Q) ∩ (P Δ R) P ∩ (Q ∩ R) = (P ∩ Q) Δ (P Δ R)

I only

II only

Neither I nor II

Both I and II

Discuss

Answer: (c).Neither I nor II

Q48.

What is the cardinality of the set of integers X defined below? X = {n | 1 ≤ n ≤ 123, n is not divisible by either 2, 3 or 5} ?

Discuss

Answer: (b).33

Q49.

Let A = {a, b, c, d }, B = { p, q, r, s } denote sets. R : A –> B, R is a function from A to B. Then which of the following relations are not functions ?

(i) { (a, p) (b, q) (c, r) }
(ii) { (a, p) (b, q) (c, s) (d, r) }
(iii) { (a, p) (b, s) (b, r) (c, q) }

(i) and (ii) only

(ii) and (iii) only

(i) and (iii) only

None of these

Discuss

Answer: (c).(i) and (iii) only

Q50.

Let A = { 1,2,3,4,…….∞ } and a binary operation ‘+’ is defined by a + b = ab ∀ a,b ∈ A. Which of the following is true ?

( A, + ) is a semi group but not monoid

( A, + ) is a monoid but not group

( A, + ) is a group

( A, + ) is not a semi group

Discuss

Answer: (b).( A, + ) is a monoid but not group

Page 5 of 23

Welcome to the Engineering Mathematics MCQs Page

Engineering Mathematics MCQs | Page 5 of 23

Explore more Topics under GATE CSE Exam

Networking

Operating System

Data Structures and Algorithms

Computer Architecture

DBMS

Compiler Design

Theory of Computation(TOC)

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