The coefficient of `x^(-17)` in the expansion of `(x^4-1/x^3)^(15)` is

Options

A. `1365`
B. `-1365`
C. `3003`
D. `-3003`

Answer

B

Explanation

Suppose the `(r+1)` th term in the given expansion contains the coefficient of `x^{-17}`.

Then, we have :

`T_{r+1}=\ ^{15} C_{r}(x^{4})^{15-r}(frac{-1}{x^{3}})^{r} `

`=(-1)^{r 15} C_{r} x^{60-4 r-3 r}`

For this term to contain `x^{-17}`, we must have :

`60-7 r=-17 `

`Rightarrow 7 r=77 `

`Rightarrow r=11`

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