(C) For the expansion of $(x - \frac{1}{x})^{11}$,the index $n = 11$ is odd. Therefore,there are two middle terms given by the terms $T_{\frac{n+1}{2}

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(C) For the expansion of $(x - \frac{1}{x})^{11}$,the index $n = 11$ is odd. Therefore,there are two middle terms given by the terms $T_{\frac{n+1}{2}}$ and $T_{\frac{n+3}{2}}$,which are $T_6$ and $T_7$. The general term is $T_{r+1} = {^{11}C_r} (x)^{11-r} (-x^{-1})^r$. For $T_6$,$r = 5$: $T_6 = {^{11}C_5} (x)^6 (-x^{-1})^5 = 462 \cdot x^6 \cdot (-x^{-5}) = -462x$. For $T_7$,$r = 6$: $T_7 = {^{11}C_6} (x)^5 (-x^{-1})^6 = 462 \cdot x^5 \cdot (x^{-6}) = \frac{462}{x}$.

Class 11 Mathematics Binomial Theorem General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

Easy

The two middle terms in the expansion of ${\left( {x - \frac{1}{x}} \right)^{11}}$ are:

A
$231x$ and $\frac{231}{x}$
B
$462x$ and $\frac{462}{x}$
C
$-462x$ and $\frac{462}{x}$
D
None of these

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General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

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The two middle terms in the expansion of ${\left( {x - \frac{1}{x}} \right)^{11}}$ are:

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