NCERT Solutions for class 11 Maths | Chapter 9 - Sequences and Series

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Questions
1 The lengths of three unequal edges of a rectangular solid block are in G.P. If the volume of the block is 216 cm3 and the total surface area is 252 cm2, then the length of the longest edge is
A 12 cm
B 6 cm
C 18 cm
D 3 cm

Answer:12 cm
2 If the sum of the first 2n terms of the A.P. 2, 5, 8, ….., is equal to the sum of the first n terms of the A.P. 57, 59, 61, ….., then n equals
A 492 – 1
B 492
C 502+l
D 492 +2

Answer:492 +2
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3 The minimum value of 4x+41-x, x€ R is
A 2
B 4
C 1
D 0

Answer:4
4 Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
A 4
B 6
C 8
D 10

Answer:6
5 If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the AP, then Sq equals
A q3/2
B mnq
C q3
D (m+n)q2

Answer:q3
6 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
7 If the third term of G.P. is 4, then the product of its first 5 terms is
A 43
B 44
C 45
D none of these

Answer:45
8 If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is
A 3
B 2
C 6
D 4

Answer:4
9 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 274
B 273
C 272
D 27

Answer:27
10 log45 , log20 5, log1005 are in
A A.P.
B G.P.
C H.P.
D None of these

Answer:A.P.
11 Let a, b and c be positive real numbers such that a + b + c = 6. Then range of ab2c3 is
A (0, ¥)
B (0, 1)
C (0, 108]
D (6, 108]

Answer:(0, 108]
12 Let p, q, r Î R+ and 27pqr ³ ( p + q + r)3 and 3p + 4q + 5r = 12 then p3 + q4 + r5 is equal to
A 3
B 6
C 2
D None of these

Answer:3
13 If the sum Sn of n terms of a progression is a cubic polynomial in n, then the progression whose sum of n terms is Sn – Sn-1 is
A An A. P.
B A G. P.
C A H.P.
D An A. G. P.

Answer:An A. P.
14 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
15 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.
16 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
17 If = 0 and a + c −b ¹ 0, then a, b, c are in
A A.P.
B G.P.
C H.P.
D None of these

Answer:H.P.
18 If a, b, c are in A.P., then a3 + c3 − 8b3 is equal to
A 2abc
B 6abc
C 4abc
D None of these

Answer:None of these
19 If the roots of the equation a(b − c)x2+ 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.
20 If b + c, c + a, a + b are in H.P., then a2, b2, c2 will be in
A G.P.
B H.P.
C A.P.
D None of these

Answer:A.P.

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