The coefficient of x -3 in the expansion of \(\Big(\text{x}-\frac{\text{m}}{\text{x}}\Big)^{11}\) is:

The coefficient of x-3 in the expansion of \(\Big(\text{x}-\frac{\text{m}}{\text{x}}\Big)^{11}\) is:

  1. -792m5

  2. -330m7

  3. -924m7
  4. -792m6

Solution

Solution:

Let x-3 occur at (r + 1)th term in the given expansion.

Then, we have

\(\text{T}_{r+1}={^\text{11}}\text{C}_{\text{r}}\ \text{x}^{11-\text{r}}\ \Big(\frac{-\text{m}}{\text{x}}\Big)^{\text{r}}\)

\(=(-1)^{\text{r}}\times{^\text{11}}\text{C}_{\text{r}}\ \text{m}^{\text{r}}\ \text{x}^{11-\text{r}-\text{r}}\)

For this term to contain x-3, we must have

\(=11-2\text{r}=-3\)

\(\Rightarrow \text{r}=7\)

Required coefficient \(=(-1)^{7}\ {^\text{11}}\text{C}_{\text{7}}\ \text{m}^{7}\)

\(=-\frac{11\times10\times9\times8}{4\times3\times2}\ \text{m}^{7}\)

\(=-330\text{m}^{7}\)

Asked in: School

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