The sum of the infinite series 1 + 13 +&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

71.

The remainder obtained when 1! + 2! + ... + 95! is divided by 15 is

  • 14

  • 3

  • 1

  • 0


72.

If a, b and c are in arithmetic progression, then the roots of the equation ax - 2bx + c = 0 are

  • 1 and ca

  • - 1a and - c

  • - 1 and - ca

  • - 2 and - c2a


73.

Let the coefficients of powers of x in the 2nd, 3rd and 4th terms in the expansion of (1 + x)n, where n is a positive integer, be in arithmetic progression. Then, the sum of the coefficients of odd powers of x in the expansion is

  • 32

  • 64

  • 128

  • 256


74.

The sum 1 x 1! + 2 x 2! + ... + 50 x 50! equals

  • 51!

  • 51! + 1

  • 51! + 1

  • × 51!


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75.

Six numbers are in AP such that their sum is 3. The first term is 4 times the third term. Then, the fifth term is

  • - 15

  • - 3

  • 9

  • - 4


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76.

The sum of the infinite series 1 +13 + 1 . 33 . 6 +1 . 3 . 53 . 6 . 9 + 1 . 3 . 5 . 73 . 6 . 9 . 12 + ... is equal to

  • 2

  • 3

  • 32

  • 13


B.

3

Given series,

1 +13 + 1 . 33 . 6 +1 . 3 . 53 . 6 . 9 + 1 . 3 . 5 . 73 . 6 . 9 . 12 + ... = 1 +13 + 2 . 21 . 2232 +2 . 2 . 21 . 2 . 3233 + ... = 1 + 12 . 23 +1212 +12!232 + 1212 +112 + 23!233 ... = 1 - 23- 12= 312= 3


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77.

If 64, 27, 36 are the Pth Qth and Rth terms of a GP, then P + 2Q is equal to

  • R

  • 2R

  • 3R

  • 4R


78.

The coefficient of x10 in the expansion of 1 + (1 + x) + ... + (1 + x)20

  • C919

  • C1020

  • C1121

  • C1222


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79.

Let a, b, c, p, q and r be positive real numbers such that a, band c are in GP and ap = bq = cr . Then,

  • p, q, r are in GP

  • p, q, r are in AP

  • p, q, r are in HP

  • p2, q2, r2 are in AP


80.

Let Sk be the sum of an infinite GP series whose first term is k and common ratio is kk + 1(k > 0). Then, the value of k = 1 - 1Sk is equal to

  • loge4

  • loge2 - 1

  • 1 - loge2

  • 1 - loge4


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