Class 11 Mathematics Sequences and Series MCQs Set 06

Question. The sum of the 3rd and the 4th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7th term is :
(a) 7290
(b) 640
(c) 2430
(d) 320
Answer: d

Question. Three positive numbers form an increasing G. P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is:
(a) 2 – √3
(b) 2 + √3
(c) √2 + √3
(d) 3 + √2
Answer: b

Question. Let x be one A.M and g₁ and g₂ be two G.Ms between y and z. What is g₁³ + g₂³ equal to ?
(a) xyz
(b) xy²z
(c) xyz²
(d) 2 xyz
Answer: b

Question. Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4 ,then :
(a) a = 4/7, r = 3/7
(b) a = 2, r = 3/8 
(c) a = 3/2, r = 1/2 
(d) a = 3, r = 1/4
Answer: d

Question. The sum of first 9 terms of the series. 1³/1 + (1³+2³)/(1+3) + (1³+2³+3³)/(1+3+5) + ……
(a) 142
(b) 192
(c) 71
(d) 96
Answer: d

Question. The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by 10(1/2), then the number of terms in the A.P. is:
(a) 4
(b) 8
(c) 12
(d) 16
Answer: b

Question. Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of 1/a and 1/b. If 1/M : G is 4 : 5, then a : b can be:
(a) 1 : 4
(b) 1 : 2
(c) 2 : 3
(d) 3 : 4
Answer: a

Question. Let a, b, c, be in A.P. with a common difference d. Then e^{1/ c} , e^{b / ac} , e^{1/ a} are in :
(a) G.P. with common ratio e^d
(b) G.P with common ratio e^1/d
(c) G.P. with common ratio e^{d /(b2 − d2 )}
(d) A.P.
Answer: c

Question. If the sum of a certain number of terms of the A.P. 25, 22, 19, …….. is 116. then the last term is
(a) 0
(b) 2
(c) 4
(d) 6
Answer: c

Question. The product of first nine terms of a GP is, in general, equal to which one of the following?
(a) The 9th power of the 4th term
(b) The 4th power of the 9th term
(c) The 5th power of the 9th term
(d) The 9th power of the 5th term
Answer: d

Question. Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is
(a) 5
(b) 3/5
(c) 8/5
(d) 1/5
Answer: b

Question. If b², a², c² are in A.P., then 1/a + b, 1/b + c, 1/c + a will be in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
Answer: a

Question. If p, q, r are in A.P., a is G.M. between p & q and b is G.M. between q and r, then a², q², b² are in
(a) G.P.
(b) A.P.
(c) H.P
(d) None of these
Answer: b

Question. The sum of series 1/2! − 1/3! + 1/4! − ……….. upto infinity is
(a) e^½
(b) e^+½
(c) e^-2
(d) e^-1
Answer: d

Question. The value of 2^1/4 . 4^1/8 . 8^1/16 … ∞ is 
(a) 1
(b) 2
(c) 3/2
(d) 4
Answer: b

Question. The sum of the series 1/(1+√2) + 1/(√2+√3) + 1/(3√+√4) + …… upto 15 terms is
(a) 1
(b) 2
(c) 3
(d) 4
Answer: c

Question. The sum of the series 1 + 1/4.2! + 1/16.4! + 1/64.6! + …………… ad inf. is
(a) e-1 / √e
(b) e+1 / √e
(c) e-1 / 2√e
(d) e+1 / 2√e
Answer: d

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. If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then a + b / a – b is equal to :
(a) √6/2
(b) 3√2/4
(c) 7√3/12
(d) 5√6/12
Answer: d

Question. If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 13 + 14 + 18 +19 + … is (102)m, then m is equal to:
(a) 20
(b) 25
(c) 5
(d) 10
Answer: b

Question. The sum of the first 20 terms of the series 1 + 3/2 + 7/4 + 15/8 + 31/16 + …. is ?
(a) 38 + 1/2²⁰
(b) 39 + 1/2¹⁹
(c) 39 + 1/2²⁰
(d) 38 + 1/2¹⁹
Answer: d

Question. Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1² + 2.2² + 3² + 2.4² + 5² + 2.6² + …… If B – 2A = 100λ , then λ is equal to :
(a) 248
(b) 464
(c) 496
(d) 232
Answer: a

Question. The harmonic mean of a/1–ab and a/1+ab is :
(a) a
(b) a/1–a²b²
(c) 1/1–a²b²
(d) a/1+a²b²
Answer: a

Question. If a, b, c, d, e, f are in A.P., then e – c is equal to:
(a) 2(c – a)
(b) 2(d – c)
(c) 2(f – d)
(d) (d – c)
Answer: b

Question. Let Sn denote the sum of first n terms of an A.P. If S_2n = 3 S_n, then the ratio S_3n/ S_n is equal to :
(a) 4
(b) 6
(c) 8
(d) 10
Answer: b

Question. If the ratio of H.M. and G.M. between two numbers a and b is 4 : 5, then the ratio of the two numbers will be
(a) 1 : 2
(b) 2 : 1
(c) 4 : 1
(d) 1 : 4
Answer: c

Question. If (10)⁹ + 2(11)¹(10⁸) + 3(11)²(10)⁷ +….. +10(11)⁹ = K(10)⁹, then k is equal to:
(a) 100
(b) 110
(c) 121/10
(d) 441/100
Answer: a

Question. If the sum of the first n terms of the series √3 + √75 + √243 + v507 +…… is 435√3 , then n equals :
(a) 18
(b) 15
(c) 13
(d) 29
Answer: b

Question. If the nth term of an arithmetic progression is 3n + 7, then what is the sum of its first 50 terms?
(a) 3925
(b) 4100
(c) 4175
(d) 8200
Answer: c

Question. The A. M. between two positive numbers a and b is twice the G. M. between them. The ratio of the numbers is
(a) (√2 + 3) : (√2 – 3)
(b) (2 + √3 ) : (2 – √3 )
(c) (√3 + 1) : (√3 – 1)
(d) None of these
Answer: b

Question. If the sum of the first 2n terms of 2, 5, 8, ……. is equal to the sum of the first n terms of 57, 59, 61……., then n is equal to 
(a) 10
(b) 12
(c) 11
(d) 13
Answer: c

Question. The sum 3/1² + 5/1²+2² + 7/1²+2²+3² + ….. upto 11-terms is:
(a) 7/2
(b) 11/4
(c) 11/2
(d) 60/11
Answer: c

Question. Let x, y, be positive real numbers such that x + y + = 12 and x³y⁴z⁵ = (0.1) (600)³. Then x³ + y³ + z³ is equal to :
(a) 342
(b) 216
(c) 258
(d) 270
Answer: b

Question. The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 + ….. upto 11th term is:
(a) 915
(b) 946
(c) 945
(d) 916
Answer: b

Question. If the sum 3/1² + 5/1²+2² + 7/1²+2²+3² + …… + up to 20 terms is equal to k/21, then k is equal to:
(a) 120
(b) 180
(c) 240
(d) 60
Answer: a

Question. An infinite G.P has first term x and sum 5, then
(a) x < – 10
(b) – 10 < x < 0
(c) 0 < x < 10
(d) x > 10 C
(d) 4 : 1
Answer: a

Question. Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is:
(a) 2 – √3
(b) 2 + √3
(c) √3 – 2
(d) 3+ √2
Answer: b

Question. The sum of the series : 
1 + 1/1+2 + 1/1+2+3 + ……. upto 10 terms, is :
(a) 18/11
(b) 22/13
(c) 20/11
(d) 16/9
Answer: c

Question. What is the sum of terms equidistant from the beginning and end in an A.P. ?
(a) First term – Last term
(b) First term × Last term
(c) First term + Last term
(d) First term ÷ Last term
Answer: c

Question. Sum of n terms of series 1.3+3.5+5.7+………. is
(a) 1/3 n(n + 1)(2n + 1) − n
(b) 3/2 n(n + 1)(2n + 1) − n
(c) 4/5 n(n + 1)(2n + 1) − n
(d) 2/3 n(n + 1)(2n + 1) − n
Answer: d