**MCQs Questions for Class 11 Maths Chapter 4 Principle of Mathematical Induction**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns. In most of the competitive examinations, only MCQ Questions are asked.

In future, if you want to prepare for competitive examination, then you should focus on the MCQs questions. Thus, let’s solve these MCQs questions to make our foundation strong.

In this post, you will find **15** **MCQs questions for class 11 maths chapter 4 principle of mathematical induction**.

**MCQs Questions for Class 11
Maths Chapter 4 Principle of Mathematical Induction**

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

(a) Whole number

(b) Natural number

(c) Rational number

(d) Any form of number

**Answer: a**

**2. **The sum of the series 1³ + 2³ + 3³ + ……….. + n³ is

(a) {(n + 1)/2}²

(b) {n/2}²

(c) n(n + 1)/2

(d) {n(n + 1)/2}²

**Answer: d**

## 3. For any natural
number n, 7ⁿ – 2ⁿ is divisible by

(a) 3

(b) 4

(c) 5

(d) 7

**Answer: c**

**4. ** By the principle of mathematical induction, 2^{4n – 1} is divisible by which of the following?

(a) 8

(b) 3

(c) 5

(d) 7

**Answer: a**

**5. **1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)} is
equal to

(a) n(n + 1)

(b) n/(n + 1)

(c) 2n/(n + 1)

(d) 3n/(n + 1)

**Answer: b**

## 6. 1 ∙ 2 + 2 ∙ 3 + 3
∙ 4 + ….. + n(n + 1) is equal to

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

(b) {n(n + 1)(n + 2)}/2

(c) {n(n + 1)(n + 2)}/3

(d) {n(n + 1)(n + 2)}/4

**Answer: c**

**7. **If 10^{3n} + 2^{4k + 1}. 9 + k, is divisible by 11, then what is the
least positive value of k?

(a) 7

(b) 6

(c) 8

(d) 10

**Answer: d**

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

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

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

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

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

**Answer: d**

## 9. n(n + 1) (n +
5) is a multiple of *……… *for all n ∈ N.

(a) 2

(b) 3

(c) 5

(d) 7

**Answer: b**

**10. **If
P(n) = n(n^{2} – 1), then which
of the following does not divide P(k + 1)?

(a) k

(b) k + 2

(c) k + 3

(d) k + 1

**Answer: c**

## 11. For all positive integers n, the number n(n² − 1) is divisible by:

(a) 36

(b) 24

(c) 6

(d) 16

**Answer: c**

**12. **n^{2} + 3n is always divisible
by which number, provided n is an integer?

(a) 2

(b) 3

(c) 4

(d) 5

**Answer: a**

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

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

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

(c) n(n + 2)/6

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

**Answer: b**

**14. **What will be P(k + 1) for P(n) = n^{3} (n + 1)?

(a) (k + 1)^{4}

(b) k^{4} + 5k^{3} + 9k^{2} + 7k + 2

(c) k^{4} + 6k^{3} + 9k^{2} + 7k + 2

(d) k^{4} + 3k^{3} + 9k^{2} + 6k + 2

**Answer: b**

**15. **For all n ∈ N,
7^{2n} − 48n − 1 is divisible by:

(a) 25

(b) 2304

(c) 1234

(d) 26

**Answer: b**