The sequence loga, loga2b, loga3b2, ... 

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 Multiple Choice QuestionsShort Answer Type

81.

The harmonic mean of two numbers is 4. Their arithmetic mean A and geometric mean G satisfy the relation 2A +G2 = 27. Find the numbers.


 Multiple Choice QuestionsMultiple Choice Questions

82.

The sum of the series 11 . 2 - 12 . 3 + 13 . 4 - ... 

  • 2loge2 + 1

  • 2loge2

  • 2loge2 - 1

  • loge2 - 1


83.

If C4n, C5n and C6n are in AP, then n is

  • 7 or 14

  • 7

  • 14

  • 14 or 21


84.

If w  1 is a cube root of unity, then the sum of the series S = 1 + 2w + 3w2 + ... + 3nw3n -1 is

  • 3nw - 1

  • 3n(w - 1)

  • w - 13n

  • 0


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85.

If log3x + log3y = 2 + log32 and log3x + y = 2, then

  • x = 1, y = 8

  • x = 8, y = 1

  • x = 3, y = 6

  • x = 9, y = 3


86.

If log72 = λ, then the value of log4928 is

  • 2λ + 1

  • 2λ + 3

  • 122λ + 1

  • 22λ + 1


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87.

The sequence loga, loga2b, loga3b2, ... is

  • a GP

  • an AP

  • a HP

  • both a GP and a HP


B.

an AP

Let S = loga, loga2b, loga3b2, ...

loga,2loga - logb, 3loga - 2logb, ...

Now,        T2 - T1 = loga - logband T3 - T2 = loga - logb

Hence, it is an AP


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88.

If in a ABC. ABC, sin(A), sin(B), sin(C) are in AP, then

  • the altitudes are in AP

  • the altitudes are in HP

  • the angles are in AP

  • the angles are in HP


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89.

The value of 23! +45! + 67! + ...

  • e12

  • e- 1

  • e

  • e- 13


90.

If sum of an infinite geometric series is 4/3 and its Ist term is 3/4, then its common ratio is

  • 7/16

  • 9/16

  • 1/9

  • 7/9


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