A) 10
B) 9
C) 8
D) 12
Correct Answer: B
Solution :
[b] Given \[\frac{{{T}_{7}}}{{{T}_{n-7+2}}}=\frac{1}{6}\Rightarrow \frac{{{T}_{7}}}{{{T}_{n-s}}}=\frac{1}{6}\] \[\Rightarrow \frac{^{n}{{C}_{6}}{{\left( \sqrt[3]{2} \right)}^{n-6}}{{\left( \frac{1}{\sqrt[3]{3}} \right)}^{6}}}{^{n}{{C}_{n-6}}{{\left( \sqrt[3]{2} \right)}^{6}}{{\left( \frac{1}{\sqrt[3]{3}} \right)}^{n-6}}}=\frac{1}{6}\] \[\Rightarrow {{2}^{\frac{n-12}{3}}}.\,{{3}^{\frac{n-12}{3}}}=\frac{1}{6}\Rightarrow {{6}^{\frac{n-12}{3}}}={{6}^{-1}}\] \[\therefore \frac{n-12}{3}=-1\Rightarrow n=9\]
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