Explanation

(a)
$rth\ term\ in\ the\ expansion\ of\ \left( 3x - \frac{2}{x^{2}} \right)^{15}is$
$T_{r} = \ ^{15}C_{r - 1}(3x)^{15 - r + 1}\left( \frac{- 2}{x^{2}} \right)^{r - 1}$
$= \ ^{15}C_{r - 1}(3)^{15 - r + 1}( - 2)^{r - 1}(x)^{15 - 3r + 3}$
For the term independent of $x,$ put
$15 - 3r + 3 = 0 \Longrightarrow r = 6$