Welcome to the Induction and Recursion MCQs Page

Dive deep into the fascinating world of Induction and Recursion with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Induction and Recursion, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Induction and Recursion, 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 Discrete Mathematics.

Check out the MCQs below to embark on an enriching journey through Induction and Recursion. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Induction and Recursion. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Induction and Recursion MCQs | Page 1 of 3

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Q1.

By induction hypothesis, the series 1² + 2² + 3² + … + p² can be proved equivalent to ____________

Discuss

Answer: (b).b

Q2.

What is the base case for the inequality 7ⁿ > n³, where n = 3?

652 > 189

42 < 132

343 > 27

42 <= 431

Discuss

Answer: (c).343 > 27

Q3.

In the principle of mathematical induction, which of the following steps is mandatory?

induction hypothesis

inductive reference

induction set assumption

minimal set representation

Discuss

Answer: (a).induction hypothesis

Q4.

For m = 1, 2, …, 4m+2 is a multiple of ________

Discuss

Answer: (d).2

Q5.

For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________

m²+3

m+1

mᵐ

3m²+4

Discuss

Answer: (a).m²+3

Q6.

For every natural number k, which of the following is true?

(mn)ᵏ = mᵏnᵏ

m*k = n + 1

(m+n)ᵏ = k + 1

mᵏn = mnᵏ

Discuss

Answer: (a).(mn)ᵏ = mᵏnᵏ

Q7.

For any positive integer m ______ is divisible by 4.

5m² + 2

3m + 1

m² + 3

m³ + 3m

Discuss

Answer: (d).m³ + 3m

Q8.

According to principle of mathematical induction, if P(k+1) = m⁽ᵏ⁺¹⁾ + 5 is true then _____ must be true.

P(k) = 3m⁽ᵏ⁾

P(k) = m⁽ᵏ⁾ + 5

P(k) = m⁽ᵏ⁺²⁾ + 5

P(k) = m⁽ᵏ⁾

Discuss

Answer: (b).P(k) = m⁽ᵏ⁾ + 5

Q9.

Which of the following is the base case for 4ⁿ⁺¹ > (n+1)² where n = 2?

64 > 9

16 > 2

27 < 91

54 > 8

Discuss

Answer: (a).64 > 9

Q10.

What is the induction hypothesis assumption for the inequality m ! > 2ᵐ where m>=4?

for m=k, k+1!>2ᵏ holds

for m=k, k!>2ᵏ holds

for m=k, k!>3ᵏ holds

for m=k, k!>2ᵏ⁺¹ holds

Discuss

Answer: (b).for m=k, k!>2ᵏ holds

Page 1 of 3

Welcome to the Induction and Recursion MCQs Page

Induction and Recursion MCQs | Page 1 of 3

Explore more Topics under Discrete Mathematics

Logics and Proofs

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Counting Theory

Discrete Probability

Relations

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

Group Theory

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