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 1^{3} + 2^{3} + 3^{3} + ………..n^{3} 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 1^{2} + 3^{2} + 5^{2} +……… is

(A) n(4n^{2} – 1)/3

(B) n^{2}(2n^{2}+1)/6

(C) none of these.

(D) n^{2}(n^{2}+1)/3

**Answer:** n(4n^{2} – 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. (1^{2} + 2^{2} + …… + n^{2} ) _____ for all values of n ∈ N

(A) = n^{3} /3

(B) < n^{3} /3

(C) > n^{3} /3

(D) None of these

**Answer:** > n^{3} /3

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

(A) 2n^{2}+2

(B) 3*2^{n-1} – 2

(C) 2n^{2}+2n

(D) 5n-1

**Answer:** 3*2^{n-1} – 2

13. n < 2^{n} 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 ∙ 7^{N} + 3 ∙ 5^{N} – 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) 2n^{2}+2

(B) 3*2^{n-1} – 2

(C) 2n^{2}+2n

(D) 5n-1

**Answer:** 3*2^{n-1} – 2

17. A + AR + AR^{2} + ……. + AR^{N – 1} = (AR^{N – 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^{2 }+ 3^{2 }+ 5^{2 }+……… is

(A) n(4n^{2} – 1)/3

(B) n^{2}(2n^{2}+1)/6

(C) none of these.

(D) n^{2}(n^{2}+1)/3

**Answer:** n(4n^{2} – 1)/3

19. For all n∈N, 5^{2n} − 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