A) 1
B) \[{{\log }_{e}}10\]
C) 10
D) x does not exist
Correct Answer: C
Solution :
[c] It is given that \[{{6}^{th}}\]term in the expansion of \[{{\left( \frac{1}{{{x}^{8/3}}}+{{x}^{2}}{{\log }_{10}}x \right)}^{8}}\] \[^{8}{{C}_{5}}{{({{x}^{2}}lo{{g}_{10}}x)}^{5}}{{\left( \frac{1}{{{x}^{8/3}}} \right)}^{3}}=5600\] Or \[56{{x}^{10}}{{(lo{{g}_{10}}x)}^{5}}\frac{1}{{{x}^{8}}}=5600\] Or \[{{x}^{2}}{{(lo{{g}_{10}}x)}^{5}}=100\] Or \[{{x}^{2}}{{(lo{{g}_{10}}x)}^{5}}={{10}^{2}}{{(lo{{g}_{10}}10)}^{5}}\] Or \[x=10\]
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