Explanation

(a)
$Sum\ of\ coefficients\ of\ the\ expansion\ \left( \frac{1}{x} + 2x \right)^{n} = \ 6561$
$\therefore\ (1 + 2)^{n} = 3^{8}\ \Longrightarrow 3^{n} = 3^{8} \Longrightarrow n = 8$
$Now,\ T_{r + 1} = \ ^{8}C_{r}2^{8 - r}x^{- 8 + 2r}$
Since, this term is independent of $x$, then
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - 8 + 2r = 0 \Longrightarrow r = 4$
$\therefore$ Coefficient of independent term, $T_{5} = \ ^{8}C_{4} \bullet 2^{4} = 16 \bullet \ ^{8}C_{4}$