JEE Mathematics Sequence and Series MCQs Set 03

Question.  If for an A.P., T₃ = 18 and T₇ = 30 then S₁₇ is equal to-
(a) 612
(b) 306
(c) 622
(d) None of these

Answer: A

Question. The first, second and middle terms of an AP are a, b, c respectively. Their sum is-
(a) 2 (c-a)/b-a
(b) 2c (b-a)/c-a
(c) 2b (c-a)/b-a
(d) None of these

Answer: A

Question. The sum of integers in between 1 and 100 which are divisible by 2 or 5 is-
(a) 3050
(b) 3100
(c) 3600
(d) 3500

Answer: A

Question. If 9th and 19th terms of an AP are 35 and 75 respectively, then 20th term is -
(a) 79
(b) 78
(c) 80
(d) 81

Answer: A

Question. If first term of an AP is 5, last term is 45 and the sum of the terms is 400, then the number of terms is-
(a) 16
(b) 8
(c) 10
(d) 20

Answer: A

Question. If the ratio of the sum of n terms of two AP’s is (3n + 1) : (2n + 3) then ratio of their 11th terms is
(a) 64 : 45
(b) 45 : 64
(c) 3 : 4
(d) 4 : 3

Answer: A

Question. If 4 AM’s are inserted between 1/2 and 3 then 3rd AM is-
(a) 2
(b) 1
(c) – 2
(d) – 1

Answer: A

Question. n AM’s are inserted between 2 and 38. If third AM is 14 then n is equal to -
(a) 8
(b) 9
(c) 7
(d) 10

Answer: A

Question. Four numbers are in A.P. If their sum is 20 and the sum of their square is 120, then the middle terms are -
(a) 4,6
(b) 8,10
(c) 2,4
(d) 6, 8

Answer: A

Question.  If b+c-a/a, c+a-b/b, a+b-c/c are in A.P. then which of the following is in A.P.?
(a) 1/a, 1/b, 1/c
(b) a,b,c
(c) a², b², c²
(d) None of these

Answer: A

Question.  If x , 2x + 2 and 3x + 3 are first three terms of a G.P., then its 4th term is-
(a) – 27/2
(b) 27
(c) – 27
(d) 27/2

Answer: A

Question. The nth term of a GP is 128 and the sum of its n terms is 255. If its common ratio is 2 then its first term is-
(a) 1
(b) 8
(c) 3
(d) None of these

Answer: A

Question. If first, second and eight terms of a G.P. are respectively n^–4, nⁿ, n⁵², then the value of n is-
(a) 4
(b) 1
(c) 10
(d) None of these

Answer: A

Question. Let a, b and c form a GP of common ratio r (0 < r < 1). If a, 2b and 3c form an AP, then r equals -
(a) 1/3
(b) None of these
(c) 1/2
(d) 2/3

Answer: A

Question. If the sum of an infinitely decreasing GP is 3, and the sum of the squares of its terms is 9/2, the sum of the cubes of the terms is-
(a) 108/13
(b) None of these
(c) 105/13
(d) 729/8

Answer: A

Question. If the sum of first two terms of an infinite GP is 1 and every term is twice the sum of all the successive terms, then its first term is-
(a) 3/4
(b) 2/3
(c) 1/3
(d) 1/4

Answer: A

Question. If ( x+ 1) , 3x and (4x + 2) are first three terms of an AP then its 5th term is-
(a) 24
(b) 14
(c) 19
(d) 28

Answer: A

Question. The sum of first ten terms of a A.P. is four times the sum of its first five terms, then ratio of first term and common difference is-
(a) 1/2
(b) 1/4
(c) 2
(d) 4

Answer: A

Question. The sum of all odd numbers of two digits is - (1) 2530 (2) 2475 (3) 4905 (4) less than 2500
(a) 2 and 4 are correct
(b) 1, 2 and 3 are correct
(c) 1 and 2 are correct
(d) 1 and 3 are correct

Answer: A

Question. If roots of the equation x³ – 12x²+ 39 x – 28 = 0 are in AP, then its common difference is -
(1) more than – 4 (2) ± 2
(3) ± 3                  (4) ± 4
(a) 1 and 3 are correct
(b) 1 and 2 are correct
(c) 1, 2 and 3 are correct
(d) 2 and 4 are correct

Answer: A

Question. If A₁,A₂ be two AM’s and G₁, G₂ be two GM’s between two numbers a and b, then A₁+A₂/G₁+ G₂ is equal to -
(a) 1 and 3 are correct
(b) 1 and 2 are correct
(c) 1, 2 and 3 are correct
(d) 2 and 4 are correct

Answer: A

Question. There are two sets A and B each of which consists of three numbers in A.P. whose sum is 15 and their common differences are D and d such that D – d = 1. If p/q= 7/8,  where p and q are the product of the numbers in the sets respectively and d > 0, in the two sets.
Value of p is –
(a) 105
(b) 100
(c) 120
(d) 110

Answer: A

Question. There are two sets A and B each of which consists of three numbers in A.P. whose sum is 15 and their common differences are D and d such that D – d = 1. If p/q= 7/8,  where p and q are the product of the numbers in the sets respectively and d > 0, in the two sets.
Value of q is –
(a) 120
(b) 110
(c) 100
(d) 105

Answer: A

Question. There are two sets A and B each of which consists of three numbers in A.P. whose sum is 15 and their common differences are D and d such that D – d = 1. If p/q= 7/8,  where p and q are the product of the numbers in the sets respectively and d > 0, in the two sets.
Value of D + d is –
(a) 3
(b) 1
(c) 2
(d) 4

Answer: A

Question. Statement-1 : If one A.M. A and two G.M.'s p and q be inserted between any two numbers, then p³ + q³ = 2Apq.
Statement-2 : If x, y, z are in G.P., then y² = xz.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(b) Statement -1 is False, Statement-2 is True
(c) Statement -1 is True, Statement-2 is False.
(d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: A

Question. Statement-1 : If a₁, a₂, a₃, ....... are in A.P. such that a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 225 then a₁ + a₂ + a₃ + ........... + a₂₃ + a₂₄ = 900
Statement-2 : In any A.P. sum of the term equidistant from beginning and end is constant and is equal to sum of the first and the last term.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.

Answer: A

Question. If d, e, f are in G.P. and two quadratic equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root then, d/a, e/b, f/c are in-
(a) H.P.
(b) A.P.
(c) G.P.
(d) None of these

Answer: A

Question. If p^th term of a HP be q and q^th term be p, then its (p + q)^th term is-
(a) pq/p + q
(b) 1/p + q
(c) 1/p + 1/q
(d) p + q

Answer: A

Question.  If between 1 and 1/31 there are n H.M.’s and ratio of 7^th and (n – 1)^th harmonic means is 9 : 5, then value of n is -
(a) 14
(b) 13
(c) 12
(d) 5

Answer: A

Question. If a,b,c are in A.P. and a², b², c² are in H.P., then-
(a) a = b = c
(b) b = c + a
(c) a = b + c
(d) c = a + b

Answer: A

Question. Five numbers a, b, c, d, e are such that a, b, c, are in AP’ and b, c, d are in GP and c, d, e, are in HP. If a = 2, e = 18; then values of b, c, d are -
(a) 4, 6, 9
(b) – 2, – 6, 18
(c) 2, 6, 18
(d) 4, 6, 8

Answer: A

Question. If p^th, q^th and r^th terms of H.P.are u, v, w respectively, then the value of the expression (q – r) vw + (r – p) wu + (p – q) uv is-
(a) 0
(b) – 1
(c) 1
(d) – 2

Answer: A

Question. The sum of the series a – (a + d) + (a + 2d) – (a + 3d) + ...... upto (2n + 1) terms is-
(a) a + nd
(b) – nd
(c) a + 2 nd
(d) 2nd

Answer: A

Question. 1+ 2.2 + 3.2² + 4.2³ + ....+ 100.2⁹⁹ equals-
(a) 1 + 99.2¹⁰⁰
(b) 99.2¹⁰⁰
(c) 100.2¹⁰⁰
(d) None of these

Answer: A

Question. a,b,c are first three terms of a GP. If HM of a and b is 12 and that of b and c is 36, then a equals-
(a) 8
(b) 1/3
(c) 24
(d) 72

Answer: A

Question. If x, 1, z are in A.P. x, 2,z are in G.P. then x, 4, z are in-
(a) HP
(b) AP
(c) GP
(d) None of these

Answer: A

Question. If a,b,c are in H.P., then a/b+c, b/c+a, c/a+b will be in-
(a) H.P.
(b) A.P.
(c) G.P
(d) None of these

Answer: A

Question. If the (m + 1)^th, (n + 1)^th, (r + 1)^th terms of an A.P. are in G.P. and m,n,r are in H.P. then the ratio of common difference to the first terms in the A.P. is-
(a) – 2/n
(b) 2/n
(c) n/2
(d) – n/2

Answer: A

Question. If a, x, y, z, b are in AP, then x + y + z = 15 and if a, x, y, z, b are in HP, then 1/x + 1/y +1/z = 5/3 Numbers a,b are -
(a) 9, 1
(b) 8, 2
(c) 11, 3
(d) None of these

Answer: A

Question. If r^th term of a series is (2r + 1) 2^–r, then sum of its infinite terms is-
(a) 5
(b) 10
(c) 8
(d) 0

Answer: A

Question. aⁿ⁺¹ + bⁿ⁺¹ / aⁿ+bⁿ is AM/GM/HM, between a and b if n is equal
(a) 0, –1/2, – 1
(b) -1, –1/2, 0
(c) Both
(d) None of these

Answer: A

Question. Let A₁, G₁, H₁ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For n≥2, let A_n–1 and H_n–1 have arithmetic, geometric and harmonic means as A_n, G_n, H_n respectively.
Which one of the following statements is correct ?
(a) G₁ = G₂ = G₃ = ...
(b) G₁ < G₃ < G₅ < ... and G₂ > G₄ > G₆ > ....
(c) G₁ < G₂ < G₃ < ...
(d) None of these

Answer: A

Question. Let A₁, G₁, H₁ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For n≥2, let A_n–1 and H_n–1 have arithmetic, geometric and harmonic means as A_n, G_n, H_n respectively.
Which one of the following statements is correct ?
(a) A₁ > A₂ > A₃ > ...
(b) A₁ < A₂ < A₃ < ...
(c) A₁ > A₃ > A₅ > ... and A₂ < A₄ < A₆ < ...
(d) None of these

Answer: A

Question. Let A₁, G₁, H₁ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For n≥2, let A_n–1 and H_n–1 have arithmetic, geometric and harmonic means as A_n, G_n, H_n respectively.
Which one of the following statements is correct ?
(a) H₁ < H₂ < H₃ < ...
(b) H₁ > H₃ > H₅ > ... and H₂ < H₄ < H₆ < ...
(c) H₁ > H₂ > H₀ > ...
(d) None of these

Answer: A

Question. Let a, b, c and d be distinct positive real numbers in H.P. Statement-1 : a + d > b + c Statement-2 : 1/a + 1/d = 1/b + 1/c
(a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.

Answer: A

Question. Suppose four distinct positive numbers a₁, a₂, a₃, a₄ are in G.P. Let b₁ = a₁, b₂ = b₁ + a₂, b₃ = b₂ + a₃ and b₄ = b₃ + a₄.
Statement-1 : The numbers b₁, b₂, b₃, b₄ are neither in A.P. nor in G.P.
Statement-2 : The numbers b₁, b₂, b₃, b₄ are in H.P.
(a) Statement-1 is True, Statement-2 is False.
(b) Statement-1 is False, Statement-2 is True.
(c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Answer: A