These Sequences And Series Class 11 NCERT Question and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Sequences And Series Class 11 NCERT Question and Answers 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.

## Sequences And Series Class 11 NCERT Question and Answers

1. If a is the A.M. of b and c and G1 and G2 are two GM between them then the sum of their cubes is

(A) abc

(B) 2abc

(C) 3abc

(D) 4abc

**Answer:** 2abc

2. Let S_{n} denote the sum of the first n terms of an A.P. If S_{2n} = 3S_{n}, then S3_{n} : S_{n} is equal to

(A) 4

(B) 6

(C) 8

(D) 10

**Answer:** 6

3. If a, b, c are in A.P., then a^{3} + c^{3} − 8b^{3} is equal to

(A) 2abc

(B) 6abc

(C) 4abc

(D) None of these

**Answer:** None of these

4. If the roots of the equation a(b − c)x^{2}+ b(c − a)x + c(a − b) = 0 are equal, then a, b, c are in

(A) A.P.

(B) .G.P.

(C) H.P.

(D) None of these

**Answer:** H.P.

5. If b + c, c + a, a + b are in H.P., then a^{2}, b^{2}, c^{2 }will be in

(A) G.P.

(B) H.P.

(C) A.P.

(D) None of these

**Answer:** A.P.

6. If in an A.P., S_{n} = qn^{2} and S_{m} = qm^{2}, where S_{r} denotes the sum of r terms of the AP, then S_{q} equals

(A) q^{3}/2

(B) mnq

(C) q^{3}

(D) (m+n)q^{2}

**Answer:** q^{3}

7. If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is

(A) 0

(B) 22

(C) 198

(D) 220

**Answer:** 0

8. If the third term of G.P. is 4, then the product of its first 5 terms is

(A) 4^{3}

(B) 4^{4}

(C) 4^{5}

(D) none of these

**Answer:** 4^{5}

9. If the sum of n terms of an A.P. is given by S_{n} = 3n + 2n^{2}, then the common difference of the A.P. is

(A) 3

(B) 2

(C) 6

(D) 4

**Answer:** 4

10. If the product of three positive real numbers say a, b, c be 27, then the minimum value of ab + bc + ca is equal to

(A) 27^{4}

(B) 27^{3}

(C) 27^{2}

(D) 27

**Answer:** 27

11. log_{4}5 , log_{20} 5, log_{100}5 are in

(A) A.P.

(B) G.P.

(C) H.P.

(D) None of these

**Answer:** A.P.

12. Let a, b and c be positive real numbers such that a + b + c = 6. Then range of ab^{2}c^{3} is

(A) (0, ¥)

(B) (0, 1)

(C) (0, 108]

(D) (6, 108]

**Answer:** (0, 108]

13. Let p, q, r Î R^{+} and 27pqr ³ ( p + q + r)^{3} and 3p + 4q + 5r = 12 then p^{3} + q^{4} + r^{5} is equal to

(A) 3

(B) 6

(C) 2

(D) None of these

**Answer:** 3

14. If the sum S_{n} of n terms of a progression is a cubic polynomial in n, then the progression whose sum of n terms is S_{n} – S_{n-1} is

(A) An A. P.

(B) A G. P.

(C) A H.P.

(D) An A. G. P.

**Answer:** An A. P.

15. If a, b, c are in H.P. and a > c > 0 , then 1/b-c – 1/a-b

(A) Is positive

(B) Is zero

(C) Is negative

(D) Has no fixed sign.

**Answer:** Is positive

16. Let the positive numbers a, b, c, d be in A.P. then abc, abd, acd, bcd are

(A) Not in A.P./G.P./H.P.

(B) In A.P.

(C) In G.P.

(D) In H.P.

**Answer:** In H.P.

17. Three non-zero numbers a, b and c are in A.P.. Increasing a by 1 or increasing c by 2 the number become in G.P., then ‘b’ equals to

(A) 10

(B) 12

(C) 14

(D) 16

**Answer:** 12