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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 9 of 23

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Q81.
Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(A | B) and P(B | A) respectively are

a.

1/4, 1/2

b.

1/2, 1/14

c.

1/2, 1

d.

1, 1/2

Discuss
Answer: (d).1, 1/2
Q82.
Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences, B and C are there such that (i) each is sorted in ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A?

a.

2

b.

30

c.

56

d.

256

Discuss
Answer: (c).56
Q83.
Let T(n) be the number of different binary search trees on n distinct elements. Then , where x is

a.

n-k+1

b.

n-k

c.

n-k-1

d.

n-k-2

Discuss
Answer: (b).n-k
Q84.
Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between

a.

k and n

b.

k - 1 and k + 1

c.

k - 1 and n - 1

d.

k + 1 and n - k

Discuss
Answer: (c).k - 1 and n - 1
Q85.
Which of the following is a valid first order formula ? (Here α and β are first order formulae with x as their only free variable)

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (d).D
Q86.
Consider the following formula a and its two interpretations I1 and I2. Which of the following statements is true?

a.

I1 satisfies α, I2 does not

b.

I2 satisfies α, I1 does not

c.

Neither I2 nor I2 satisfies α

d.

Both I1 and I2 satisfy α

Discuss
Answer: (d).Both I1 and I2 satisfy α
Q87.
m identical balls are to be placed in n distinct bags. You are given that m ≥ kn, where, k is a natural number ≥ 1. In how many ways can the balls be placed in the bags if each bag must contain at least k balls?

a.

A

b.

B

c.

C

d.

D

Discuss
Answer: (b).B
Q88.
Consider the following recurrence relation. The value of T(m^2) for m ≥ 1 is

a.

(m/6) (21m - 39) + 4

b.

(m/6) (4m^2 - 3m + 5)

c.

(m/2) (m^2.5 - 11m + 20) - 5

d.

(m/6) (5m^3 - 34m^2 + 137m - 104) + (5/6)

Discuss
Answer: (b).(m/6) (4m^2 - 3m + 5)
Q89.
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
Q90.
Consider the set {a, b, c} with binary operators + and × defined as follows :

+ a b c × a b c
a b a c a a b c
b a b c b b c a
c a c b c c c b

For example, a + c = c, c + a = a, c × b = c and b × c = a. Given the following set of equations :

(a × x) + (a × y) = c
(b × x) + (c × y) = c

The number of solution(s) (i.e., pair(s) (x, y)) that satisfy the equations is :

a.

0

b.

1

c.

2

d.

3

Discuss
Answer: (c).2
Page 9 of 23

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