Class 11 Mathematics Sequences and Series MCQs Set E

Question. The sum to infinite term of the series 1+2/3 +6/3² +10/3³ + 14/3⁴ + … is
(a) 3
(b) 4
(c) 6
(d) 2
Answer: a

Question. A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then the common ratio is
(a) 5
(b) 1
(c) 4
(d) 3
Answer: c

Question. The sum of the series :
( b)² + 2(d)² + 3(6)² + … upto 10 terms is :
(a) 11300
(b) 11200
(c) 12100
(d) 12300
Answer: c

Question. Find the sum up to 16 terms of the series 1³/1 + 1³ + 2³/1+3 + 1³ + 2³ + 3³ /1+3+5+…
(a) 448
(b) 445
(c) 446
(d) None of these
Answer: c

Question. In a G.P. if (m + n)^th term is p and (m – n)^th term is q, then m^th term is:
(a) p/q
(b) q/p
(c) pq
(d) √pq
Answer: d

Question. If sum of the infinite G.P. is 4/3 and its first term is 3/4 then its common ratio is :
(a) 7/16
(b) 9/16
(c) 1/9
(d) 7/9
Answer: a

Question. If S₁,S₂ and S₃ denote the sum of first n₁, n₂ and n₃ terms respectively of an A.P., then value of s₁/n₁(n₂−n₃) +s₂/n₂(n₃−n₁) + s₃/n₃(n₁−n₂)is
(a) 1/2
(b) 0
(c) −1/2
(d) 3/2
Answer: b

Question. If the p^th, q^th and r^th terms of a G.P. are again in G.P., then which one of the following is correct?
(a) p, q, r are in A.P.
(b) p, q, r are in G.P.
(c) p, q, r are in H.P.
(d) p, q, r are neither in A.P. nor in G.P. nor in H.P.
Answer: a

Question. If the sum of the first ten terms of an arithmetic progression is four times the sum of the first five terms, then the ratio of the first term to the common difference is :
(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
Answer: a

Question. The series ( √2 +1),1,(√2 −1) … is in :
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
Answer: b

Question. If sixth term of a H. P. is 1/61 and its tenth term is 1/105 then the first term of that H.P. is
(a) 1/28
(b) 1/39
(c) 1/6
(d) 1/17
Answer: c

Question. In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is:
(a) 7
(b) 21
(c) 28
(d) 42
Answer: c

Question. The coefficient of x⁵⁰ in the binomial expansion of (1 + x)¹⁰⁰⁰ + x (1 + x)⁹⁹⁹ + x²(1 + x)⁹⁹⁸ + …. + x¹⁰⁰⁰ is:
(a) (1000)! / (50)!(950)!
(b) (1000)! / (49)!(951)!
(c) (1000)! / (51)!(950)!
(d) (1000)! / (50)!(951)!
Answer: d

Question. 5^1+x + 5^1–x, a/2 , 5^2x + 5^–2x are in A.P., then the value of a is:
(a) a < 12
(b) a ≤ 12
(c) a ≥ 12
(d) None of these
Answer: d

Question. If in a series S_n = an² + bn + c, where S_n denotes the sum of n terms, then
(a) The series is always arithmetic
(b) The series is arithmetic from the second term onwards
(c) The series may or may not be arithmetic
(d) The series cannot be arithmetic
Answer: b

Question. What is the sum of the first 50 terms of the series (1 × 3) + (3 × 5) + (5 × 7) + …. ?
(a) 1,71,650
(b) 26,600
(c) 26,650
(d) 26,900
Answer: a

Question. The first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms. then the sum of the series is
(a) 2
(b) 3
(c) 3/2
(d) 5/2
Answer: c

Question. The product of n positive numbers is unity, then their sum is :
(a) a positive integer
(b) divisible by n
(c) equal to n + 1/n
(d) never less than n
Answer: d

Question. The sum 1 + (1³+2³)/(1+2) + (1³+2³+3³)/(1+2+3) + …………… + (1³+2³+3³+….+15³)/(1+2+3+….+15 )− 1/2 (1+2+3+….+15) is equal to :
(a) 620
(b) 1240
(c) 1860
(d) 660
Answer: a

Question. The value of x + y + z is 15 if a, x, y, z, b are in A.P. while the value of 1/x+1/y+1/z is 5/3 if a, x, y, z, b are in H.P. Then the value of a and b are
(a) 2 and 8
(b) 1 and 9
(c) 3 and 7
(d) None of these
Answer: b