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 10 of 23

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Q91.

A graph G = (V, E) satisfies |E| ≤ 3 |V| - 6. The min-degree of G is defined as follows. Therefore, min-degree of G cannot be

Discuss

Answer: (d).6

Q92.

Consider the following system of linear equations Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of a, does this system of equations have infinitely many solutions?

infinitely many

Discuss

Answer: (b).1

Q93.

A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn to scale). If we use the Newton-Raphson method to find the roots of f(x) = 0 using x0, x1 and x2 respectively as initial guesses, the roots obtained would be

1.3, 0.6, and 0.6 respectively

0.6, 0.6, and 1.3 respectively

1.3, 1.3, and 0.6 respectively

1.3, 0.6, and 1.3 respectively

Discuss

Answer: (d).1.3, 0.6, and 1.3 respectively

Q94.

Consider two languages L1 and L2 each on the alphabet ∑. Let f : ∑ → ∑ be a polynomial time computable bijection such that (∀ x) [x ∈ L1 iff f(x) ∈ L2]. Further, let f^-1 be also polynomial time computable. Which of the following CANNOT be true?

L1 ∈ P and L2 is finite

L1 ∈ NP and L2 ∈ P

L1 is undecidable and L2 is decidable

L1 is recursively enumerable and L2 is recursive

Discuss

Answer: (c).L1 is undecidable and L2 is decidable

Q95.

In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of 1.....n ?

n(n - 1)/2

n(n - 1)/4

n(n + 1)/4

2n[log2 n]

Discuss

Answer: (b).n(n - 1)/4

Q96.

In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?

Θ (n^2)

Θ (n log n)

Θ (n^1.5)

Θ (n)

Discuss

Answer: (d).Θ (n)

Q97.

The cube root of a natural number n is defined as the largest natural number m such that m^3 ≤ n. The complexity of computing the cube root of n (n is represented in binary notation) is:

O(n) but not O(n^0.5)

O(n^0.5) but not O((log n)^k) for any constant k > 0

O((log n)^k) for some constant k > 0, but not O ((log log n)^m) for any constant m > 0

O((log log n)^m) for some constant k > 0.5, but not O((log log n)^0.5)

Discuss

Answer: (c).O((log n)^k) for some constant k > 0, but not O ((log log n)^m) for any constant m > 0

Q98.

Let G = (V, E) be an undirected graph with a subgraph G1 = (V1, El). Weights are assigned to edges of G as follows :
A single-source shortest path algorithm is executed on the weighted graph (V, E, w) with an arbitrary vertex ν1 of V1 as the source. Which of the following can always be inferred from the path costs computed?

The number of edges in the shortest paths from ν1 to all vertices of G

G1 is connected

V1 forms a clique in G

G1 is a tree

Discuss

Answer: (b).G1 is connected

Q99.

Consider the following logic program P A(x) <- B(x, y), C(y) <- B(x,x) Which of the following first order sentences is equivalent to P?

Discuss

Answer: (c).C

Q100.

The following resolution rule is used in logic programming:

Derive clause (P v Q) from clauses (P v R), (Q v ¬ R)

Which of the following statements related to this rule is FALSE?

((P v R) ^ (Q v ¬ R)) (P v Q) is logically valid

(P v Q) ⇒ ((P v R) ^ (Q v ¬ R)) is logically valid

(P v Q) is satisfiable if and only if (P v R) ^ (Q v ¬ R) is satisfiable

(P v Q) ⇒ FALSE if and only if both P and Q are unsatisfiable

Discuss

Answer: (b).(P v Q) ⇒ ((P v R) ^ (Q v ¬ R)) is logically valid

Page 10 of 23

Welcome to the Engineering Mathematics MCQs Page

Engineering Mathematics MCQs | Page 10 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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