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

Answer: n(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

Answer: 1 + nx


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

(A) 3

(B) 4

(C) 5

(D) 7

Answer: 5


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

Answer: Even


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

(A) 3

(B) 4

(C) 5

(D) 7

Answer: 5


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

Answer: {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

Answer: Even


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

Answer: n(4n2 – 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

Answer: 1 + nx


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

(A) = n3 /3

(B) < n3 /3

(C) > n3 /3

(D) None of these

Answer: > n3 /3


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

Answer: 3*2n-1 – 2


13. n < 2n for all

(A) n ∈ R

(B) n ∈ N

(C) n may be any number

(D) None of these

Answer: n ∈ N


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

Answer: n(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

Answer: 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

Answer: 3*2n-1 – 2


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

Answer: n(4n2 – 1)/3


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

(A) 26

(B) 24

(C) 11

(D) 25

Answer: 24


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

Answer: 343 > 27


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