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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)^10` is

A

`(405)/(256)`

B

`(504)/(259)`

C

`(450)/(263)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Suppose `x^{4}` occurs at the `(r+1)` th term in the given expansion.
Then, we have
`T_{r+1}=\ ^{10} C_{r}(frac{x}{2})^{10-r}(frac{-3}{2 x^{2}})^{r} `
`=(-1)^{r 10} C_{r} frac{3^{r}}{2^{10-r}} x^{10-r-2 r}`
...
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