Explanation

(a)
For greatest term in $(x + a)^{a}$is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{n - r + 1}{r}\left| \frac{a}{x} \right| \geq 1$
$\Longrightarrow \ \ \ \frac{54 - r + 1}{r}\left| \frac{3x}{1} \right| \geq 1$
$\Longrightarrow 55 - r \geq r \Longrightarrow r = 27\ \ \ \ \left\lbrack \because x = \frac{1}{3} \right\rbrack$
$\therefore$ Greatest term in the expansion of $(1 + 3x)^{54}$ is $T_{28}.$