Sequences and Series

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Question

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Question 1 :

If a, b, c are in G.P., then the equations ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a, e/b, f/c are in

1. AP
2. GP
3. HP
4. none of these
Answer
8128

Question 2 :

If a, b, c are in AP then

1. b = a + c
2. 2b = a + c
3. b² = a + c
4. 2b² = a + c
Answer
8129

Question 3 :

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in Ap. The common ratio of GP is

1. 2 + √3
2. 2 – √3
3. 2 ± √3
4. None of these
Answer
8130

Question 4 :

The sum of n terms of the series (1/1.2) + (1/2.3) + (1/3.4) + …… is

1. n/(n+1)
2. 1/(n+1)
3. 1/n
4. None of these
Answer
8131

Question 5 :

If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then

1. a, b, c are in AP
2. a², b², c² are in AP
3. 1/1, 1/b, 1/c are in AP
4. None of these
Answer
8132