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The coefficient of x^4 in (x//2-3//x^2) ...

The coefficient of `x^4` in `(x//2-3//x^2)` is

A

`(405)/(256)`

B

`(504)/(259)`

C

`(450)/(263)`

D

None of these

Text Solution

Verified by Experts

The general term in `((x)/(2)-(3)/(x^(2)))` is
`t_(r+1)=(-1)^(r).^(10)C_(r)((x)/(2))^(10-r)((3)/(x^(2)))^(r)=(-r)^(r).^(10)C_(r).(3^(r))/(2^(10-r)).x^(10-3r)`
For coefficient of `x^(4)`, we put `10-3r=4`
`implies3r=6`
`impliesr=2`
`therefore`coefficient of `x^(4)` in `((x)/(2)-(3)/(x^(2)))^(10)=(-1)^(2.).^(10)C_(2).(3^(2))/(2^(8))`
`=(45xx9)/(256)=(405)/(256)`
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