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 4 of 23

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Q31.

Consider the following relations:

R1(a,b) iff (a+b) is even over the set of integers
R2(a,b) iff (a+b) is odd over the set of integers
R3(a,b) iff a.b > 0 over the set of non-zero rational numbers
R4(a,b) iff |a - b| <= 2 over the set of natural numbers

Which of the following statements is correct?

R1 and R2 are equivalence relations, R3 and R4 are not

R1 and R3 are equivalence relations, R2 and R4 are not

R1 and R4 are equivalence relations, R2 and R3 are not

R1, R2, R3 and R4 are all equivalence relations

Discuss

Answer: (b).R1 and R3 are equivalence relations, R2 and R4 are not

Q32.

Consider the following statements:

S1: There exists infinite sets A, B, C such that
A ∩ (B ∪ C) is finite.
S2: There exists two irrational numbers x and y such
that (x+y) is rational.

Which of the following is true about S1 and S2?

Only S1 is correct

Only S2 is correct

Both S1 and S2 are correct

None of S1 and S2 is correct

Discuss

Answer: (c).Both S1 and S2 are correct

Q33.

A relation R is defined on the set of integers as xRy if f(x + y) is even. Which of the following statement is true?

R is not an equivalence relation

R is an equivalence relation having 1 equivalence class

R is an equivalence relation having 2 equivalence classes

R is an equivalence relation having 3 equivalence classes

Discuss

Answer: (c).R is an equivalence relation having 2 equivalence classes

Q34.

Let R be the relation on the set of positive integers such that aRb if and only if a and b are distinct and have a common divisor other than 1. Which one of the following statements about R is True?

R is symmetric and reflexive but not transitive

R is reflexive but not symmetric and not transitive

R is transitive but not reflexive and not symmetric

R is symmetric but not reflexive and not transitive

Discuss

Answer: (d).R is symmetric but not reflexive and not transitive

Q35.

The cardinality of the power set of {0, 1, 2 . . ., 10} is _________.

1024

1023

2048

2043

Discuss

Answer: (c).2048

Q36.

Consider two relations R1(A, B) with the tuples (1, 5), (3, 7) and R1(A, C) = (1, 7), (4, 9). Assume that R(A,B,C) is the full natural outer join of R1 and R2. Consider the following tuples of the form (A,B,C)

a = (1, 5, null),
b = (1, null, 7),
c = (3, null, 9),
d = (4, 7, null),
e = (1, 5, 7),
f = (3, 7, null),
g = (4, null, 9).

Which one of the following statements is correct?

R contains a, b, e, f, g but not c, d

R contains a, b, c, d, e, f, g

R contains e, f, g but not a, b

R contains e but not f, g

Discuss

Answer: (c).R contains e, f, g but not a, b

Q37.

The number of onto functions (surjective functions) from set X = {1, 2, 3, 4} to set Y = {a, b, c} is ________________

Discuss

Answer: (a).36

Q38.

Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible functions defined from X and Y. Let f be randomly chosen from F. The probability of f being one-to-one is _________.

0.95

0.80

0.75

0.70

Discuss

Answer: (a).0.95

Q39.

Let R be a relation on the set of ordered pairs of positive integers such that ((p, q), (r, s)) ∈ R if and only if p–s = q–r. Which one of the following is true about R?

Both reflexive and symmetric

Reflexive but not symmetric

Not reflexive but symmetric

Neither reflexive nor symmetric

Discuss

Answer: (c).Not reflexive but symmetric

Q40.

Let R1 be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R2 be another relation from B to C = {1, 2, 3, 4} as defined below:

1. An element x in A is related to an element y in B (under R1) if x + y is divisible by 3.
2. An element x in B is related to an element y in C (under R2) if x + y is even but not divisible by 3.

Which is the composite relation R1R2 from A to C?

R1R2 = {(1, 2), (1, 4), (3, 3), (5, 4), (7, 3)}

R1R2 = {(1, 2), (1, 3), (3, 2), (5, 2), (7, 3)}

R1R2 = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)}

R1R2 = {(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)}

Discuss

Answer: (c).R1R2 = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)}

Page 4 of 23

Welcome to the Engineering Mathematics MCQs Page

Engineering Mathematics MCQs | Page 4 of 23

Explore more Topics under GATE CSE Exam

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Data Structures and Algorithms

Computer Architecture

DBMS

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Theory of Computation(TOC)

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