If in the expansion of \(\Big(\text{x}^{4}-\frac{1}{\text{x}^{3}}\Big)^{15},\text{x}^{-17}\) occurs in r th…

If in the expansion of \(\Big(\text{x}^{4}-\frac{1}{\text{x}^{3}}\Big)^{15},\text{x}^{-17}\) occurs in rth term, then

  1. r = 11

  2. r = 13

  3. r = 10

  4. r = 12

Solution

Solution:

Here,

\(\text{T}^{\text{r}}={^\text{15}}\text{C}_{\text{r}-1}(\text{x}^{4})^{15-\text{r}+1}\Big(\frac{-1}{\text{x}^{3}}\Big)^{\text{r}-1}\)

\(=(-1)^{\text{r}}\times{^\text{15}}\text{C}_{\text{r}-1}\ \text{x}^{64-4\text{r}-3\text{r}+3}\)

For this term to contain x-17, we must have

\(67-7\text{r}=-17\)

\(\Rightarrow \text{r}=12 \)

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