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Find the coefficient of x^(25) in expans...

Find the coefficient of `x^(25)` in expansion of expression `sum_(r=0)^(50)^(50)C_r(2x-3)^r(2-x)^(50-r)` .

A

`""^(50)C_(25)`

B

`-""^(50)C_(24)`

C

`-""^(50)C_(25)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`sum_(r=0)^(50)""^(50)C_(r )(2x-3)^(r )(2-x)^(n-r)`
`=""^(50C_(0)(2x-3)^(o).(2-x)^(n)+""^(50)C_(1)(2x-3)^(1)(2-x)^(n-1)+""^(50)C_(2)(2x-3)^(2)(2-x)^(n-2)+`…….`""^(50)C_(50)(2x-3)^(n)`
`=(x-1)^(50)=""^(50)C_(0)x^(50)-""^(50)C_(1)x^(49)+`……..
coeffocoent of `x^(25)` is - `""^(50)C_(25)`
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