Baixe 65879048 - Progressions - Qns e outras Exercícios em PDF para Matemática, somente na Docsity!
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
1. If
a b a b
n n n n
1 1 be the A.M. of a & b,
then n = (A) 1 (B) - 1 (C) 0 (D) None of these
2. The first term of an A.P. is 2 and common difference is 4. The sum of its 40 terms will be : (A) 3200 (B) 1600 (C) 200 (D) 2800 3. If the sum of the roots of the equation ax^2 + bx + c = 0 be equal to the sum of the reciprocals of their squares, then bc^2 , ca^2 , ab^2 will be in : (A) A.P. (B) G.P. (C) H.P. (D) None of these 4. If a & b are two different positive real numbers, then which of the following relations is true?
(A) (^2) a b > (a + b)
(B) 2 a b < (a + b)
(C) (^2) a b = (a + b) (D) None of these
5. If the 4th, 7th^ and 10th^ terms of a G.P. be a, b, c respectively, then the relation between a, b, c is :
(A) b =
a +c 2
(B) a^2 = bc
(C) b^2 = ac (D) c^2 = ab
6. If a1/x^ = b1/y^ = c1/z^ and a, b, c are in G.P. then x, y, z will be in : (A) A.P. (B) G.P.
(C) H.P. (D) None of these
7. If (p + q)th^ term of a G.P. be m and (p − q)th^ term be n, then the pth^ term will be :
(A)
m n
(B) mn
(C) (m n)3/2^ (D) None of these
8. If pth, qth, rth^ and sth^ terms of an A.P. be in G.P., then (p - q), (q - r), (r - s) will be in : (A) G.P. (B) A.P. (C) H.P. (D) None of these 9. If
to n terms to terms
then the value of n is : (A) 35 (B) 36 (C) 37 (D) 40
10. The sum of the first n terms of the
series
(A) 2 n^ - n - 1 (B) 1 - 2 -n (C) n + 2 - n^ - 1 (D) 2 n^ - 1
11. If the arithmetic, geometric & harmonic means between two distinct positive real numbers be A, G & H respectively, then the relation between them is : (A) A > G > H (B) A > G > H (C) H < G < A (D) G > A > H 12. If the arithmetic, geometric & harmonic means between two positive and real numbers be A, G and H, then : (A) A^2 = GH (B) H^2 = AG (C) G = AH (D) G^2 = AH
Progressions
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
13. If a 1 , a 2 , a 3 , ...... , an are in A.P., where ai > 0 for all i, then the value of 1 a 1 + a 2
a 2 + a 3
a (^) n − 1 + an
(A)
n a a (^) n
1
(B)
n a a (^) n
1
(C)
n a a (^) n
1
(D)
n a a (^) n
1
14. x = 1 + a + a^2 + ...... + ∞ (a < 1) y = 1 + b + b^2 + ...... + ∞ (b < 1) Then the value of 1 + ab + a^2 b^2 + ..... ∞ is :
(A)
x y x + y− 1
(B)
x y x + y+ 1
(C)
x y x − y− 1
(D)
x y x − y+ 1
15. If A 1 , A 2 ; G 1 , G 2 & H 1 , H 2 be two AM’s, GM’s & HM’s between two
quantities, then the value of
G G
H H
1 2 1 2
is
(A)
A A
H H
1 2 1 2
(B)
A A
H H
1 2 1 2
(C) A^ A
H H
1 2 1 2
(D) A^ A
H H
1 2 1 2
16. If the (m + 1)th, (n + 1)th^ and (r + 1)th terms of an A.P. are in G.P. & m, n, r are in H.P., then the value of the ratio of the common difference to the first term of the A.P. is :
(A) - 2
n
(B) 2
n
(C) - n 2
(D) n 2
17. Given ax^ = by^ = cz^ = du^ and a, b, c, d are in G.P., then x, y, z, u are in : (A) A.P. (B) G.P. (C) H.P. (D) None of these 18. The sum to n terms of the infinite series 1.3^2 + 2.5^2 + 3.7^2 + ...... ∞ is
(A)
n 6
(n + 1) (6n^2 + 14n + 7)
(B)
n 6
(n + 1) (2n + 1) (3n + 1)
(C) 4n^3 + 4n^2 + n (D) None of these
19. If a, b, c are in A.P., b, c, d are in G.P. & c, d, e are in H.P., then a, c, e are in : (A) No particular order (B) A.P. (C) G.P. (D) H.P. 20. If 2x, x + 8, 3x + 1 are in A.P., then the value of x will be : (A) 3 (B) 7 (C) 5 (D) - 2 21. The harmonic mean of two numbers is 4 and the arithmetic and geometric means satisfy the relation, 2A + G^2 = 27, the numbers are : (A) 6, 3 (B) 5, 4 (C) 5, - 2.5 (D) - 3, 1 22. If the sum of n terms of an A.P. is 2n^2 + 5n, then the nth^ term will be : (A) 4n + 3 (B) 4n + 5
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
(A) 12 (B) 13
(C) 14 (D) 15
34. The sum of infinite terms of a G.P. is x and on squaring the each term of it, the sum will be y, then the common ratio of this series is :
(A)
x y x y
2 2 2 2
(B)
x y x y
2 2 2 2
(C)
x y x y
2 2
(D)
x y x y
2 2
35. If 9 A.M.’s and H.M.’s are inserted between the 2 and 3 and if the harmonic mean H is corresponding to
arithmetic mean A, then A +
H
(A) 1 (B) 3
(C) 5 (D) 6
36. If the pth, qth^ and rth^ term of a G.P. and H.P. are a, b, c then, a (b − c) log a + b (c − a) log b + c (a − b) log c = (A) - 1 (B) 0 (C) 1 (D) Does not exist 37. The sum of n terms of the following series, 1 + (1 + x) + (1 + x + x^2 ) + ...... will be :
(A)
x x
n (B)
n ( x )
x
1 n 1
(C)
n ( x) x ( x )
x
1 1 n 1
(D) None of these
38. If log 3 2 , log 3 (2x^ - 5) and
log 3 2
x (^) − ^
^
are in A.P., then x is
equal to :
(A) 1,
(B) 1,
(C) 1,
(D) None of these
39. If the product of three terms of G.P. is 512. If 8 added to first and 6 added to second term, so that number may be in A.P., then the numbers are : (A) 2, 4, 8 (B) 4, 8, 16 (C) 3, 6, 12 (D) None of these 40. If the roots of the equation, x^3 - 12x^2 + 39x - 28 = 0 are in A.P., then their common difference will be (A) ± 1 (B) ± 2 (C) ± 3 (D) ± 4 41. Let n (> 1) be a positive integer, then the largest integer m such that (nm+1) divides (1 + n + n^2 + ...... + n^127 ), is (A) 32 (B) 63 (C) 64 (D) 127 42. If p, q, r are in A.P. and are positive, the roots of the quadratic equation, px^2 + qx + r = 0 are all real for :
(A) r p
− 7 ≥^4
(B) p
r
− 7 <^4
(C) All p & r (D) No p & r
43. Let an be the nth^ term of the G.P. of
positive numbers. Let n =
∑ 1
100 a2n = α and
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
n =
∑ 1
100 a2n - 1 = β , such that α ≠ β, then
the common ratio is :
(A)
α β
(B)
β α
(C)
α β
(D)
β α
44. Let Sn denotes the sum of n terms of
an A.P. If S2n = 3 Sn, then ratio
S
S
n n
(A) 4 (B) 6
(C) 8 (D) 10
45. If a, b, c are in G.P., then : (A) a^2 , b^2 , c^2 are in G.P. (B) a^2 (b + c), c^2 (a + b), b^2 (a + c) are in G.P.
(C)
a b + c
b c + a
c a + b
are in G.P.
(D) None of the above
ANSWERS
1. C 2. A 3. A 4. B 5. C 6. A
7. B 8. A 9. A 10. C 11. A 12.D
13. A 14. A 15. A 16. A 17. C 18.A
19. C 20. C 21. A 22. A 23. C 24.B
25. D 26. D 27. B 28. A 29. B 30.B
31. A 32. A 33. C 34. C 35. C 36.B
37. C 38. D 39. B 40. C 41. C 42.A
43. A 44. B 45. A
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