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The number 51^(49)+51^(48)+51^(47)+........

The number `51^(49)+51^(48)+51^(47)+........+51+1` is divisible by a. `10` b. `20` c. `25` d. `50`

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The sum of 50 terms of the series 3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+........... is (a). (100)/(17) (b). (150)/(17) (c). (200)/(51) (d). (50)/(17)

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The value of .^(15)C_(0)^(2)-.^(15)C_(1)^(2)+.^(15)C_(2)^(2)-"...."-.^(15)C_(15)^(2) is a. 15 b. -15 c. 0 d. 51

Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then find the value of n.

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Simplify: (i^50+i^51+i^49)

If t_n denotes the nth term of the series 2+3+6+11+18+... then t_(50) a. 49^2-1 b. 49^2 c. 50^2+1 d. 49^2+2

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