A) (a) \[\frac{16486}{{{x}^{8}}}\]
B) (b) \[\frac{13486}{{{x}^{8}}}\]
C) (c) \[\frac{17010}{{{x}^{8}}}\]
D) (d) \[\frac{16010}{{{x}^{8}}}\]
Correct Answer: C
Solution :
[c] 5th term from the end of expansion \[\left( 3x-\frac{1}{{{x}^{2}}} \right)\] \[{{=}^{10}}{{C}_{4}}.{{\left( \frac{-1}{{{x}^{2}}} \right)}^{6}}.{{(3x)}^{4}}=\frac{10}{4.6}\times \frac{{{(3)}^{4}}}{{{x}^{8}}}\]\[=\frac{10\times 9\times 8\times 7}{4\times 3\times 2}\times \frac{81}{{{x}^{8}}}=\frac{10\times 7\times 3\times 81}{{{x}^{8}}}=\frac{17010}{{{x}^{8}}}\]Hence, option [c] is correct.
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