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Xercise: Multiple Correct (Objective Questions)

The document provides 8 multiple choice questions related to arithmetic progressions (AP), geometric progressions (GP), and harmonic progressions (HP). The questions test concepts such as determining the common difference or ratio that defines a sequence, evaluating infinite series, and relating properties of sequences that have the same first and last terms but follow different patterns of progression.

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Priyanshu Raj
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106 views1 page

Xercise: Multiple Correct (Objective Questions)

The document provides 8 multiple choice questions related to arithmetic progressions (AP), geometric progressions (GP), and harmonic progressions (HP). The questions test concepts such as determining the common difference or ratio that defines a sequence, evaluating infinite series, and relating properties of sequences that have the same first and last terms but follow different patterns of progression.

Uploaded by

Priyanshu Raj
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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SEQUENCE & SERIES Page # 37

EXERCISE – II MULTIPLE CORRECT (OBJECTIVE QUESTIONS)


n
1. For the A.P. given by a1, a2,...............an,..........., 1
the equations satisfied are 7. The value of 
r 1 a  rx  a  (r  1)x
is
(A) a1 +2a2 + a3 = 0 (B) a1 – 2a2 + a3 = 0
(C) a1 + 3a2 – 3a2 – a4 = 0
n n
(A) (B)
(D) a1 – 4a2 + 6a3 – 4a4 + a5 = 0 a  a  nx a  a  nx

a  nx  a a  a  nx
(C) (D)
1 1 1 9 x x
2. If sum of the infinite G.P., p,1, , 2 , 3 ,...... is ,
p p p 2
8. Let a, x, b be in A.P; a, y, b be in G.P. and a, z, b be
the value of p is in H.P. If x = y + 2 and a = 5z then
(A) y2 = xz (B) x > y > z
2 3 1
(A) 3 (B) (C) (D) (C) a =9, b = 1 (D) a = 1/4, b = 9/4
3 2 3

2 2 2
3. If positive numbers a, b, c are in A.P. and a , b , c
are in H.P., then
(A) a = b = c (B) 2b = a + c

2 ac
(C) b = (D) None of these
8

4. If the arithmetic mean of two positive numbers


a & b (a > b) is twice their geometric mean, then a : b is

(A) 2 + 3 :2– 3 (B) 7 + 4 3 :1

(C) 1 : 7 – 4 3 (D) 2 : 3

n
4 3 2
5. If 
r 1
r (r+1) (2r+3)=an +bn +cn +dn+e, then

(A) a + c = b + d (B) e = 0
(C) a, b –2/3, c – 1 are in A.P. (D) c/a is an integer

6. If b1, b2, b3 (bi > 0) are three successive terms of


a G.P. with common ratio r, the value of r for which
the inequality b3 > 4b2 – 3b1, holds is given by
(A) r > 3 (B) 0 < r < 1 (C) r = 3.5 (D) r = 5.2

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