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Question
If the fifth term of the expansion \[\left( a^{2/3} + a^{- 1} \right)^n\] does not contain 'a'. Then n is equal to
Options
2
5
10
none of these
Solution
10
\[T_5 = T_{4 + 1} \]
\[ = ^{n}{}{C}_4 ( a^{2/3} )^{n - 4} ( a^{- 1} )^4 \]
\[ = ^{n}{}{C}_4 a^\left( \frac{2n - 8}{3} - 4 \right) \]
\[\text{ For this term to be independent of a, we must have} \]
\[\frac{2n - 8}{3} - 4 = 0\]
\[ \Rightarrow 2n - 20 = 0\]
\[ \Rightarrow n = 10\]
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