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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 3 of 23

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Q21.
Let f: B → C and g: A → B be two functions and let h = f o g. Given that h is an onto function. Which one of the following is TRUE?

a.

f and g should both be onto functions

b.

f should be onto but g need not be onto

c.

g should be onto but f need not be onto

d.

both f and g need not be onto

Discuss
Answer: (b).f should be onto but g need not be onto
Q22.
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs (a, b) and (c, d) in the chosen set such that "a ≡ c mod 3" and "b ≡ d mod 5" .

a.

4

b.

6

c.

16

d.

24

Discuss
Answer: (c).16
Q23.
Consider the binary relation:

S = {(x, y) | y = x+1 and x, y ∈ {0, 1, 2, ...}}

The reflexive transitive closure of S is

a.

{(x, y) | y > x and x, y ∈ {0, 1, 2, ... }}

b.

{(x, y) | y ≥ x and x, y ∈ {0, 1, 2, ... }}

c.

{(x, y) | y < x and x, y ∈ {0, 1, 2, ... }}

d.

{(x, y) | y ≤ x and x, y ∈ {0, 1, 2, ... }}

Discuss
Answer: (b).{(x, y) | y ≥ x and x, y ∈ {0, 1, 2, ... }}
Q24.
The following is the incomplete operation table a 4-element group.
 *  e  a  b  c
 e  e  a  b  c
 a  a  b  c  e
 b
 c
The last row of the table is

a.

c a e b

b.

c b a e

c.

c b e a

d.

c e a b

Discuss
Answer: (d).c e a b
Q25.
The inclusion of which of the following sets into

S = {{1, 2}, {1, 2, 3}, {1, 3, 5}, (1, 2, 4), (1, 2, 3, 4, 5}}

is necessary and sufficient to make S a complete lattice under the partial order defined by set containment ?

a.

{1}

b.

{1}, {2, 3}

c.

{1}, {1, 3}

d.

{1}, {1, 3}, (1, 2, 3, 4}, {1, 2, 3, 5)

Discuss
Answer: (a).{1}
Q26.
Consider the set ∑* of all strings over the alphabet ∑ = {0, 1}. ∑* with the concatenation operator for strings

a.

does not form a group

b.

forms a non-commutative group

c.

does not have a right identity element

d.

forms a group if the empty string is removed from ∑*

Discuss
Answer: (a).does not form a group
Q27.
Let (5, ≤) be a partial order with two minimal elements a and b, and a maximum element c.

Let P : S → {True, False} be a predicate defined on S.
Suppose that P(a) = True, P(b) = False and
P(x) ⇒ P(y) for all x, y ∈ S satisfying x ≤ y,
where ⇒ stands for logical implication.

Which of the following statements CANNOT be true ?

a.

P(x) = True for all x ∈ S such that x ≠ b

b.

P(x) = False for all x ∈ S such that x ≠ a and x ≠ c

c.

P(x) = False for all x ∈ S such that b ≤ x and x ≠ c

d.

P(x) = False for all x ∈ S such that a ≤ x and b ≤ x

Discuss
Answer: (d).P(x) = False for all x ∈ S such that a ≤ x and b ≤ x
Q28.
Let f : A → B be an injective (one-to-one) function.

Define g : 2^A → 2^B as :
g(C) = {f(x) | x ∈ C}, for all subsets C of A.
Define h : 2^B → 2^A as :
h(D) = {x | x ∈ A, f(x) ∈ D}, for all subsets D of B.

Which of the following statements is always true ?

a.

g(h(D)) ⊆ D

b.

g(h(D)) ⊇ D

c.

g(h(D)) ∩ D = ф

d.

g(h(D)) ∩ (B - D) ≠ ф

Discuss
Answer: (a).g(h(D)) ⊆ D
Q29.
Which of the following is true?

a.

The set of all rational negative numbers forms a group under multiplication

b.

The set of all non-singular matrices forms a group under multiplication

c.

The set of all matrices forms a group under multiplication

d.

Both (2) and (3) are true

Discuss
Answer: (b).The set of all non-singular matrices forms a group under multiplication
Q30.
The binary relation S = ф (empty set) on set A = {1, 2, 3} is :

a.

Neither reflexive nor symmetric

b.

Symmetric and reflexive

c.

Transitive and reflexive

d.

Transitive and symmetric

Discuss
Answer: (d).Transitive and symmetric
Page 3 of 23

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