1.

Coefficient of x^25 in the expansion of the expression sum_(r = 0)^50 ""^50C_r (2x - 3)^r (2-x)^(n-r)is :

Answer»

`""^50C_25`
`-""^50C_24`
`-""^50C_25`
None of these

Solution :`sum_(R =0)^50 ""^50C_r (2x - 3)^r (2-x)^(N-r)`
`= ""^50C_0 (2x - 3)^0 . (2-x)^n + ""^50C_1 (2x - 3)^1 (2-x)^(n-1) + ""^50C_2(2x - 3)^2 (2-x)^(n-2) + ……""^50C_50(2x - 3)^n`
` = (x - 1)^50 = ""^50C_0 x^50 - ""^50C_1 x^49 + …….`
COEFFICIENT of `x^25` is`-""^50C_25` .


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