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

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Questions
1 The first term of a GP is 1. The sum of the third term and fifth term is 90. The common ratio of GP is
A 1
B 2
C 3
D 4

Answer:3
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 10
B 12
C 11
D 13

Answer:11
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3 If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, c/b are in
A A.P.
B G.P.
C H.P.
D A.G.P.

Answer:H.P.
4 If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then
A a, b, c are in AP
B a², b², c² are in AP
C 1/1, 1/b, 1/c are in AP
D None of these

Answer:a², b², c² are in AP
5 The 35th partial sum of the arithmetic sequence with terms an = n/2 + 1
A 240
B 280
C 330
D 350

Answer:350
6 The sum of series 1/2! + 1/4! + 1/6! + ….. is
A e² – 1 / 2
B (e – 1)² /2 e
C e² – 1 / 2 e
D e² – 2 / e

Answer:(e – 1)² /2 e
7 If a, b, c are in G.P., then the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a, e/b, f/c are in
A AP
B GP
C HP
D none of these

Answer:AP
8 The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is
A n/(n+1)
B 1/(n+1)
C 1/n
D None of these

Answer:n/(n+1)
9 The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is
A 2
B 4
C 6
D 8

Answer:6
10 If 2/3, k, 5/8 are in AP then the value of k is
A 31/24
B 31/48
C 24/31
D 48/31

Answer:31/48
11 Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is
A 2 + √3
B 2 – √3
C 2 ± √3
D None of these

Answer:2 + √3
12 The sum of two numbers is 13/6 An even number of arithmetic means are being inserted between them and their sum exceeds their number by 1. Then the number of means inserted is
A 2
B 4
C 6
D 8

Answer:6
13 If a, b, c are in AP then
A b = a + c
B 2b = a + c
C b² = a + c
D 2b² = a + c

Answer:2b = a + c
14 If the third term of an A.P. is 7 and its 7 th term is 2 more than three times of its third term, then the sum of its first 20 terms is
A 228
B 74
C 740
D 1090

Answer:740
15 The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is
A n/(n+1)
B 1/(n+1)
C 1/n
D None of these

Answer:n/(n+1)
16 The third term of a geometric progression is 4. The product of the first five terms is
A 43
B 45
C 44
D none of these

Answer:45
17 Let Tr be the r th term of an A.P., for r = 1, 2, 3, … If for some positive integers m, n, we have Tm = 1/n and Tn = 1/m, then Tm n equals
A 1/m n
B 1/m + 1/n
C 1
D 0

Answer:1
18 If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then
A a, b, c are in AP
B a², b², c² are in AP
C 1/1, 1/b, 1/c are in AP
D None of these

Answer:a², b², c² are in AP
19 The sum of AP 2, 5, 8, …..up to 50 terms is
A 3557
B 3775
C 3757
D 3575

Answer:3775
20 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

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