Explanation

(a)
$Genaral\ term\ T_{r + 1} = \ ^{10}C_{r}\left( \frac{1}{3}x^{1/2} \right)^{10 - r}(x^{- 1/4})^{r}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ ^{10}C_{r}\frac{1}{3^{10 - r}}x^{5 - 3r/4}$
For the coefficient of $x^{2}$ put
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5 - \frac{3r}{4} = 2$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r = 4$
$\therefore Coefficient\ of\ x^{2} = \ ^{10}C_{4}\frac{1}{3^{10 - 4}} = \frac{70}{243}$