1.

The coefficient of `x^4`in `(x//2-3//x^2)`is`(405)/(256)`b. `(504)/(259)`c. `(450)/(263)`d. none of theseA. `(405)/(256)`B. `(504)/(259)`C. `(450)/(263)`D. None of these

Answer» 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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