JEE Mathematics Sequence and Series MCQs Set C

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: 612

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: 2 (c-a)/b-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: 3050

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

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: 79

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: 16

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: 64 : 45

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: 2

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: 8

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: 4,6

Question:

• a) 53261
• b) None of these
• c) 55216
• d) 55215

Answer: 53261

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: 1/a, 1/b, 1/c

Question: Sum of n term of series 1.3 + 3.5 + 5.7 + ... is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

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: – 27/2

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: 1

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: 4

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: 1/3

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: 108/13

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: 3/4

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: 24

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: 1/2

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: 2 and 4 are correct

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: 1 and 3 are correct

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: 1 and 3 are correct

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: 105

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: 120

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: 3

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: Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

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: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement-1 : If three positive numbers in G.P. represent sides of a triangle then common ratio of G.P. must lie between

Statement-2 : Three positive real numbers can be length of a triangle if sum of any 2 is greater than third.

• 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: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

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: H.P.

Question:

• a) HP
• b) AP
• c) GP
• d) None of these

Answer: HP

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: pq/p + q

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: 14

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 = b = c

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: 4, 6, 9

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: 0

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 + nd

Question:

• a) n²
• b) n (1 + 1/n)²
• c) n (n + 1)
• d) None of these

Answer: n²

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: 1 + 99.2¹⁰⁰

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: 8

Question:

• a) 44/9
• b) 33/4
• c) 11/4
• d) 44/8

Answer: 44/9

Question: 

• a) 9
• b) 1
• c) 5
• d) None of these

Answer: 9

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: HP

Question:

• a) Both
• b)

  

• c)

  

• d) None of these

Answer: Both

Question:

• a) 2n
• b) 0
• c) n
• d) 1

Answer: 2n

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: H.P.

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: – 2/n

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: 9, 1

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: 5

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: 0, –1/2, – 1

Question:

• 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: 1 and 3 are correct

Question:  If (m+1)^th,(n +1)^th and (r +1)^th terms of an A.P. are in G.P. and m, n, r are in H.P., then the ratio of the first term of the A.P. to its common difference is

• 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: 1 and 3 are correct

Question: For the series

(1) 7th term is 16
(2) 7th term is 18
(3) sum of first 10 terms is 505/4
(4) sum of first 10 terms is 405/ 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: 1 and 3 are correct

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: G₁ = G₂ = G₃ = ...

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: A₁ > A₂ > A₃ > ...

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: H₁ < H₂ < H₃ < ...

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: Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

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.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Answer: Statement-1 is True, Statement-2 is False.

Question:

• 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: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.