If a, b, c be in arithmetic progression, then the value of (a + 2

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 Multiple Choice QuestionsMultiple Choice Questions

101.

The value of 1log312 + 1log412 is

  • 0

  • 12

  • 1

  • 2


102.

If x = logabc, y = logbca, z = logcab,  then the value of 11 + x + 11 + y + 11 + z will be

  • x + y + z

  • 1

  • ab + bc + ca

  • abc


 Multiple Choice QuestionsShort Answer Type

103.

Find the sum of the first n terms of the series 0.2 + 0.22 + 0.222 + ...


 Multiple Choice QuestionsMultiple Choice Questions

104.

If the mth term and the nth term of an AP are respectively 1n and 1m, then the mnth term of the AP is

  • 1mn

  • mn

  • 1

  • nm


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105.

-  π2π2sin9xcos5xdx equals

  • 120

  • 20

  • 0

  • 1330


106.

The sum of the series (1 + 2) + (1 + 2 + 22) + (1 + 2 + 22 + 23) + ...upto n terms is

  • 2n + 2 - n - 4

  • 2(2n - 1) - n

  • 2n + 1 - n

  • 2n + 1 - 1


107.

The 5th term of the series 109, 13203, 23, ... is

  • 13

  • 1

  • 25

  • 23


108.

The sum of the infinite series

132 + 13134 + 15136 + ... is

  • 14loge2

  • 12loge2

  • 16loge2

  • 14loge32


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109.

If a, b, c be in arithmetic progression, then the value of (a + 2b - c)(2b + c - a)(a + 2b + c) is

  • 16abc

  • 4abc

  • 8abc

  • 3abc


A.

16abc

Since, a, b, care in AP.

 2b = a + c

Now, (a + 2b - c)(2b + c - a)(a + 2b + c)

= (a + a + c - c)(a + c + c - a)(2b + 2b)

= 2a . 2c . 4b

= 16abc


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110.

If three real numbers a, b, c are in harmonic progression, then which of the following is true ?

  • 1a, b, 1c are in AP

  • 1bc, 1ca, 1ab are in HP

  • ab, bc, ca are in HP

  • ab, bc, ca are in HP


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