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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.

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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 2 of 23

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Q11.
Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:

S1: There is a subset of S that is larger than every other subset.
S2: There is a subset of S that is smaller than every other subset.

Which one of the following is CORRECT?

a.

Both S1 and S2 are true

b.

S1 is true and S2 is false

c.

S2 is true and S1 is false

d.

Neither S1 nor S2 is true

Discuss
Answer: (a).Both S1 and S2 are true
Q12.
Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L != G and that the size of L is at least 4. The size of L is __________.

a.

3

b.

5

c.

7

d.

9

Discuss
Answer: (b).5
Q13.
If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1 ∩ V2 is ______.

a.

1

b.

2

c.

3

d.

4

Discuss
Answer: (b).2
Q14.
There are two elements x, y in a group (G,∗) such that every element in the group can be written as a product of some number of x's and y's in some order. It is known that

x ∗ x = y ∗ y = x ∗ y ∗ x ∗ y = y ∗ x ∗ y ∗ x = e

where e is the identity element. The maximum number of elements in such a group is __________.

a.

2

b.

3

c.

4

d.

5

Discuss
Answer: (c).4
Q15.
Consider the set of all functions f: {0,1, … ,2014} → {0,1, … ,2014} such that f(f(i)) = i, for all 0 ≤ i ≤ 2014. Consider the following statements:

P. For each such function it must be the case that
for every i, f(i) = i.
Q. For each such function it must be the case that
for some i, f(i) = i.
R. Each such function must be onto.

Which one of the following is CORRECT?

a.

P, Q and R are true

b.

Only Q and R are true

c.

Only P and Q are true

d.

Only R is true

Discuss
Answer: (b).Only Q and R are true
Q16.
Let E, F and G be finite sets. Let X = (E ∩ F) - (F ∩ G) and Y = (E - (E ∩ G)) - (E - F). Which one of the following is true?

a.

X ⊂ Y

b.

X ⊃ Y

c.

X = Y

d.

X - Y ≠ φ and Y - X ≠ φ

Discuss
Answer: (c).X = Y
Q17.
Given a set of elements N = {1, 2, ..., n} and two arbitrary subsets A⊆N and B⊆N, how many of the n! permutations π from N to N satisfy min(π(A)) = min(π(B)), where min(S) is the smallest integer in the set of integers S, and π(S) is the set of integers obtained by applying permutation π to each element of S?

a.

(n - |A ∪ B|) |A| |B|

b.

(|A|^2+|B|^2)n^2

c.

n! |A∩B| / |A∪B|

d.

|A∩B|^2nC|A∪B|

Discuss
Answer: (c).n! |A∩B| / |A∪B|
Q18.
Let A, B and C be non-empty sets and let X = (A - B) - C and Y = (A - C) - (B - C). Which one of the following is TRUE?

a.

X = Y

b.

X ⊂ Y

c.

Y ⊂ X

d.

none of these

Discuss
Answer: (a).X = Y
Q19.
The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15. The inverses of 4 and 7 are respectively

a.

3 and 13

b.

2 and 11

c.

4 and 13

d.

8 and 14

Discuss
Answer: (c).4 and 13
Q20.
Let R and S be any two equivalence relations on a non-empty set A. Which one of the following statements is TRUE?

a.

R ∪ S, R ∩ S are both equivalence relations

b.

R ∪ S is an equivalence relation

c.

R ∩ S is an equivalence relation

d.

Neither R ∪ S nor R ∩ S is an equivalence relation

Discuss
Answer: (c).R ∩ S is an equivalence relation
Page 2 of 23

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