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
(a) 2
(b) 5
(c) 10
(d) none of these
Solution:
(c) 10
$T_{5}=T_{4+1}$
$={ }^{n} C_{4}\left(a^{2 / 3}\right)^{n-4}\left(a^{-1}\right)^{4}$
$={ }^{n} C_{4} a^{\left(\frac{2 n-8}{3}-4\right)}$
For this term to be independent of a, we must have
$\frac{2 n-8}{3}-4=0$
$\Rightarrow 2 n-20=0$
$\Rightarrow n=10$
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