# NCERT Solutions For Class 11 Maths Chapter 4: Principle Of Mathematical Induction

These NCERT Solutions For Class 11 Maths Chapter 4 are most important for your upcoming examinations including JEE Main & JEE Advanced. These NCERT Solutions For Class 11 Maths Chapter 4 will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## NCERT Solutions For Class 11 Maths Chapter 4

1. 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

2. (1 + x)n ≥ ____ for all n ∈ N,where x > -1

(A) 1 + nx

(B) 1 – nx

(C) 1 + nx/2

(D) 1 – nx/2

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

(A) 3

(B) 4

(C) 5

(D) 7

4. The nth terms of the series 3 + 7 + 13 + 21 +………. is

(A) 4n – 1

(B) n² + n + 1

(C) none of these

(D) n + 2

Answer: n² + n + 1

5. (n² + n) is ____ for all n ∈ N.

(A) Even

(B) odd

(C) Either even or odd

(D) None of these

6. for any natural number n, 7n – 2n is divisible by

(A) 3

(B) 4

(C) 5

(D) 7

7. 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

8. (n² + n) is ____ for all n ∈ N.

(A) Even

(B) odd

(C) Either even or odd

(D) None of these

9. The sum of n terms of the series 12 + 32 + 52 +……… is

(A) n(4n2 – 1)/3

(B) n2(2n2+1)/6

(C) none of these.

(D) n2(n2+1)/3

10. (1 + x)n ≥ ____ for all n ∈ N,where x > – 1

(A) 1 + nx

(B) 1 – nx

(C) 1 + nx/2

(D) 1 – nx/2

11. (12 + 22 + …… + n2 ) _____ for all values of n ∈ N

(A) = n3 /3

(B) < n3 /3

(C) > n3 /3

(D) None of these

12. The nth term of the series 1 + 4 + 10 + 22 + ….. is

(A) 2n2+2

(B) 3*2n-1 – 2

(C) 2n2+2n

(D) 5n-1

13. n < 2n for all

(A) n ∈ R

(B) n ∈ N

(C) n may be any number

(D) None of these

14. 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

15. (2 ∙ 7N + 3 ∙ 5N – 5) is Divisible by ___ for all N ∈ N

(A) 6

(B) 12

(C) 18

(D) 24

16. The nth term of the series 1 + 4 + 10 + 22 + ….. is

(A) 2n2+2

(B) 3*2n-1 – 2

(C) 2n2+2n

(D) 5n-1

17. A + AR + AR2 + ……. + ARN – 1 = (ARN – 1)/(R – 1) for

(A) r ≥ 1 and n ∈ N

(B) r ≤ 1 and n ∈ N

(C) r > 1 and n ∈ N

(D) r < 1 and n ∈ N

Answer: r > 1 and n ∈ N

18. The sum of n terms of the series 1+ 3+ 5+……… is

(A) n(4n2 – 1)/3

(B) n2(2n2+1)/6

(C) none of these.

(D) n2(n2+1)/3

19. For all n∈N, 52n − 1 is divisible by :

(A) 26

(B) 24

(C) 11

(D) 25

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

(A) 652 > 189

(B) 42 < 132

(C) 343 > 27

(D) 42 <= 431