If S1, S2 and S3 are the sums of n, 2n and 3n terms of an arithme

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 Multiple Choice QuestionsMultiple Choice Questions

131.

If a1, a2, a3 ..., an are in AP, where ai > 0 for all i. Find the sum of series 1a1 + a2 + 1a2 + a3 + 1a3 + a4 + ... + 1an - 1 + an

  • n + 1a1 + an

  • n - 1a1 - an

  • n + 1a1 + an

  • n - 1a1 + an


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132.

If S1, S2 and S3 are the sums of n, 2n and 3n terms of an arithmetic progression respectively, then

  • S2 = 3S3 - 2S1

  • S3 = 4(S1 + S2)

  • S3 = 3(S2 - S1)

  • S3 = 2(S2 + S1)


C.

S3 = 3(S2 - S1)

Let the first term and common difference of an AP be a and d respectively

   S1 = n22a + n - 1d       S2 = 2n22a + 2n - 1dand S3 = 3n22a + 3n - 1dNow,  S2 - S1 = n22a + 3n - 1d = S33 3S2 - S1 = S3


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133.

C01 + C23 + C45 + C67 + ... is equal to

  • 2n - 1n - 1

  • 2n + 1n + 3

  • 2nn + 1

  • 2n - 2n


134.

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in AP. The commonratio of the GP will be

  • 2 - 3

  • 2 ± 3

  • 32

  • 2 + 3


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135.

If in an AP, 3rd term is 18 and 7th term is 30, the sum of its 17 terms is

  • 600

  • 612

  • 624

  • None of these


136.

The sum of the digitsin the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is

  • 432

  • 108

  • 36

  • 18


137.

If a, b, c are in HP, then the value of b +ab - a + b + cb - c is

  • 0

  • 1

  • 2

  • 3


138.

If the sides of a ABC are in AP and a is the smallest side, then cos(A) equals

  • 3c - 4b2c

  • 3c - 4b2b

  • 4c - 3b2c

  • 4c - 3b2b


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139.

If logxa, ax2 and logbx are in GP, then x is equal to

  • logblogab

  • logloga

  • logloga + loglogb

  • logalogba


140.

At the foot of a mountain the elevation of its summit is 45°. After ascending 2 km towards the mountain up an incline of 30°, the elevation changes to 60°. The height ofmountain will be

  • 3 - 1

  • 1 - 3

  • 1 + 3

  • 3


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