A) \[\frac{1}{512{{x}^{9}}}\]
B) \[\frac{-1}{512{{x}^{9}}}\]
C) \[\frac{-1}{256.{{x}^{8}}}\]
D) \[\frac{1}{256.{{x}^{8}}}\]
Correct Answer: D
Solution :
The general term of the expansion \[{{(x+a)}^{n}}\] is \[{{T}_{r+1}}{{=}^{n}}{{C}_{r}}{{x}^{n-r}}{{a}^{r}}\]. We have \[{{\left( 3x-\frac{1}{2x} \right)}^{8}}\] Here, \[r=8,\] \[x=3x,\] \[a=\left( -\frac{1}{2x} \right),n=8\] \[\therefore \] Nineth term \[{{T}_{9}}{{=}^{8}}{{C}_{8}}{{(3x)}^{\mathbf{8}-8}}{{\left( \frac{-1}{2x} \right)}^{8}}\] \[=\frac{1}{256.{{x}^{8}}}\]
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