# Principle of Mathematical Induction

This set of MCQs is about the chapter on the principle of mathematical induction which is frequently used in mathematics and is a key aspect of scientific reasoning, where collecting and analyzing data is the norm. In algebra or in another discipline of mathematics, there are certain results or statements that are formulated in terms of n, where n is a positive integer. To prove such statements the well-suited principle that is used–based on the specific technique, is known as the principle of mathematical induction.

Start Quiz

For principle of mathematical induction to be true, what type of number should ‘n’ be?

Whole number Natural number Rational number Any form of number

72n + 22n – 2 . 3n – 1 is divisible by 50 by principle of mathematical induction.

True False

By principle of mathematical induction, 24n-1 is divisible by which of the following?

8 3 5 7

If 103n + 24k + 1. 9 + k, is divisible by 11, then what is the least positive value of k?

7 6 8 10

P(n) = n(n2 – 1). Which of the following does not divide P(k+1)?

k k + 2 k + 3 k + 1

For any natural number n, 22n – 1 is divisible by

2 3 4 5

A student was asked to prove a statement P(n) by induction. He proved that P(k + 1) is true whenever P(k) is true for all k > 5 ∈ N and also that P(5) is true. Based on this, he could conclude that P(n) is true

for all n ∈ N for all n > 5 for all n ≥ 5 for all n < 5

If P (n): “49n + 16n + k is divisible by 64 for n ∈ N” is true, then the least negative integral value of k is

1 -2 -1 -3

For all n ∈ N, 3.52n+1 + 23n+1 is divisible by

19 17 23 25

Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

n(n+1)(n+2)/3 n(n+1)(n+2)/6 n(n+2)/6 (n+1)(n+2)/6

If n is an odd positive integer, then an + bn is divisible by :

a² + b² a + b a – b none of these

If xn – 1 is divisible by x – k, then the least positive integral value of k is,

1

2

3

4

The sum of the series 1² + 2² + 3² + ………..n² is,

n(n + 1)(2n + 1)

n(n + 1)(2n + 1)/2

n(n + 1)(2n + 1)/3

n(n + 1)(2n + 1)/6

1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)} equals to

n(n + 1)

n/(n + 1)

2n/(n + 1)

3n/(n + 1)

Quiz/Test Summary
Title: Principle of Mathematical Induction
Questions: 14
Contributed by: 