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Coefficient of x^25 in the expansion of ...

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

A

`""^50C_25`

B

`-""^50C_24`

C

`-""^50C_25`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`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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