If the sum offour numbers in GP is 60 and the arithmetic mean of

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 Multiple Choice QuestionsMultiple Choice Questions

141.

If a + b1 - ab, b + c1 - bc are in AP, then a, 1b and c are in

  • AP

  • GP

  • HP

  • None of these


142.

The number of terms in the series 105 + 103 + 101 + ... + 49 + 47 is

  • 28

  • 30

  • 25

  • 22


143.

The geometric mean of roots of the equation x2 - 18x + 81 = 0 is

  • 18

  • 6

  • 9

  • 3


144.

The sum of n terms of the series 1 + 5 + 12 + 22 + 35 + ... is

  • n2n + 18

  • n2n + 16

  • n2n + 12

  • None of these


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145.

If geometric mean and harmonic mean of two numbers a and b are 16 and 64/5 respectively, then the value of a : b is

  • 4 : 1

  • 3 : 2

  • 2 : 3

  • 1 : 4


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146.

If the sum offour numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18, then the numbers are

  • 3, 9, 27, 81

  • 4, 8, 16, 32

  • 2, 6, 18, 54

  • None of these


B.

4, 8, 16, 32

Let four terms mn a GP be ar3, ar, ar and ar3According to the given condition,ar3 + ar + ar + ar3 = 60    ...iand ar3 + ar32 = 18   ar3 + ar3 = 36            ...iiNow, from Eq (i), we havear + ar + ar3 + ar3 = 60     ar + 1r + 36 = 60    from Eq.(ii)              ar + 1r = 24      ...(iii)

On dividing Eq.(iii) by Eq.(ii), we getar3 + 1r3ar + 1r = 3624 r + 1rr2 + 1r2 - 1r + 1r = 32 2r2 + 112 - 1 = 3 2r4 + 1  -r2r2 = 3   2r4 + 2 - 2r2 = 3r2 2r4 - 5r2 + 2 = 0 2r4 - 4r2 - r2 + 2 = 0 2r2r2 - 2 - 1r2 - 2 = 0 r2 - 22r2 - 1 = 0 r2 = 2, 2r2 = 1 r = ± 2, r = ± 12

On putting r = 2 in Eq. (iii), we geta2 + 12 = 24  a2 + 12 = 24              3a = 24a2                a = 82 Senes becomes 8223, 822, 822and 8223 i.e., 32, 16, 8 and 4.If we take r = 12, we get the seris 4, 8, 16 and 32.


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147.

iF a,b and c are in HP, then for any n  N, which one of the following is true ?

  • an + cn < 2bn

  • an + cn > 2bn

  • an + cn = 2bn

  • None of the above


148.

The sum of the series 12 . 3 + 14 . 5 + 16 . 7 + ... is

  • loge2

  • log2e

  • e2

  • 2e


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149.

If an + 1 + bn + 1an + bn be the AM of a and b, then n is equal to

  • - 1

  • 0

  • 1

  • None of these


150.

x1/2 . x1/4 . x1/8 ...  equal to

  • 0

  • 1

  • x


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