Class 11 Mathematics Sequences and Series MCQs Set 07

Question. The sum of the first n terms of the series 1² + 2.2² + 3² + 2.4² + 5² + 2.6² + …. is n(n+1)² / 2 when n is even. When n is odd the sum is
(a) [ n(n+1) / 2 ]²
(b) n²(n+1) / 2
(c) n(n+1)² / 4
(d) 3n(n+1) / 2
Answer: b

Question. Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation
(a) x² -18x -16 = 0
(b) x² -18x +16 = 0
(c) x² +18x -16 =0
(d) x² +18x +16 = 0
Answer: b

Question. 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 and c/b are in
(a) Arithmetic – Geometric Progression
(b) Arithmetic Progression
(c) Geometric Progression
(d) Harmonic Progression.
Answer: d

Question. There are four arithmetic means between 2 and –18. The means are
(a) –4, –7, –10, –13
(b) 1, –4, –7, –10
(c) –2, –5, –9, –13
(d) –2, –6, –10, –14
Answer: d

Question. If the ^jth term and kth term of an A.P. are k and j respectively, the ( k + j) th term is
(a) 0
(b) 1
(c) k + j + 1
(d) k + j –1
Answer: a

Question. In an AP. the pth term is q and the (p + q)th term is 0. Then the qth term is
(a) – p
(b) p
(c) p + q
(d) p – q
Answer: b

Question. If a, b, c are in A.P. and a, b, d in G.P., then a, a – b, d – c will be in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
Answer: b

Question. The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,….., is
(a) 7/81 (179 − 10⁻²⁰)
(b) 7/99 (99 − 10⁻²⁰)
(c) 7/81 (179 − 10⁻²⁰)
(d) 7/9 (99 − 10⁻²⁰)
Answer: c

Question. If a₁, a₂, ………., an are in H.P., then the expression a₁a₂ + a₂a₃ + ………. + a_n–1a_n is equal to
(a) n(a₁ – a_n )
(b) (n -1)(a₁ – a_n )
(c) na₁a_n
(d) (n -1)a₁a_n
Answer: d

Question. If 1, x, y, z, 16 are in geometric progression, then what is the value of x + y + z ?
(a) 8
(b) 12
(c) 14
(d) 16
Answer: c

Question. The sum of the series 1² + 2.2² + 3² + 2.4² + 5² + 2.6² + …. + 2(2m)² is
(a) m(2m + 1)²
(b) m2(m + 2)
(c) m2(2m + 1)
(d) m(m + 2)²
Answer: c

Question. The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is
(a) –4
(b) –12
(c) 12
(d) 4
Answer: b

Question. If 5 (3^{a – 1} + 1), (6^{2a – 3} +2) and 7(5^{a – 2} + 5) are in AP, then what is the value of a?
(a) 7
(b) 6
(c) 5
(d) None of these
Answer: d

Question. 1³ – 2³ + 3³ – 4³ + … + 9₃ =
(a) 425
(b) –425
(c) 475
(d) –475
Answer: a

Question. If 1 + (1 – 2² · 1) + (1 – 4² · 3) + (1 – 6² · 5) + . . . . . . . + (1 – 20² × 19) = α – 220β, then an ordered pair (α, β) is equal to :
(a) (10, 97)
(b) (11, 103)
(c) (10, 103)
(d) (11, 97)
Answer: b

Question. The value of l² + 3² + 5² + …………………..+ 25² is :
(a) 2925
(b) 1469
(c) 1728
(d) 1456
Answer: a

Question. If the sum of the series 1² + 2.2² + 3² + 2.4² + 5² + … 2.6² +… upto n terms, when n is even, is n(n+1)² / 2 , then the sum of the series, when n is odd, is
(a) n²(n + 1)
(b) n²(n − 1)/2
(c) n²(n + 1)/2
(d) n²(n − 1)
Answer: c

 Question. If 1/b–a + 1/b–c = 1/a + 1/c then a, b, c are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) In G.P. and H.P. both
Answer: c

Question. Sum of the first n terms of the series 1/2 + 3/4 + 7/8 + 15/16 + ……… is equal to :
(a) 2ⁿ – n – 1
(b) 1 – 2^–n
(c) n + 2^–n – 1
(d) 2ⁿ + 1
Answer: c

Question. Let Tr be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m,n, m ≠ n, T_m = 1/n and T_n = 1/m, then a – d equals
(a) 1/m + 1/n 
(b) 1
(c) 1/mn
(d) 0
Answer: d

Question. Third term of the sequence whose nth term is a_n = 2ⁿ, is
(a) 2
(b) 4
(c) 8
(d) 3
Answer: c

Question. The sum of series 1/2! + 1/4! + 1/6! + …….. is
(a) (e² – 2)/e
(b) (e – 1)²/2e
(c) (e² – 1)/2e
(d) (e² – 1)/2
Answer: b

Question. Let a₁, a₂ , a_3.……….. be terms of an A.P. If a₁ + a₂ +……..a_p / a₁ + a₂ +……..a_q = p²/q², p ≠ q , then equals a₆/a₂₁
(a) 41/11
(b) 7/2
(c) 2/7
(d) 11/41
Answer: d

Question. If the 7^th term of a H.P. is 1/10 and the 12^th term is 1/25, then the 20^th term is
(a) 1/37
(b) 1/41
(c) 1/45
(d) 1/49
Answer: d

Question. The first and eight terms of a G.P. are x^–4 and x⁵² respectively. If the second term is x^t, then t is equal to:
(a) –13
(b) 4
(c) 5/2
(d) 3
Answer: b

Question. If A > 0, B > 0 and A + B = π/6 , then the minimum value of tanA + tanB is :
(a) √3 – √2
(b) 4 – 2√3
(c) 2/√3
(d) 2 – √3
Answer: b

Question. If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4^th A.M. is equal to 2^nd G.M., then m is equal to ___________.
Answer: 39