A) \[^{18}{{C}_{9}}\]
B) \[\,{{-}^{18}}{{C}_{9}}\]
C) \[^{18}{{C}_{10}}\]
D) \[{{-}^{18}}{{C}_{10}}\]
Correct Answer: B
Solution :
The general term in the expansion \[{{\left( x-\frac{1}{x} \right)}^{18}}\] is given by \[{{T}_{r+1}}={{\,}^{18}}{{C}_{r}}{{(x)}^{18-r}}{{\left( -\frac{1}{x} \right)}^{r}}\] Here, \[n=18\] \[\therefore \] The middle term is \[{{T}_{9+1}},\] where \[r=9\] \[\therefore \] \[{{T}_{9+1}}={{\,}^{18}}{{C}_{9}}\,{{(-1)}^{9}}{{x}^{18-2r}}\] \[={{-}^{18}}{{C}_{9}}{{x}^{18-18}}={{-}^{18}}{{C}_{9}}\]
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