Explanation

(a)
Given
$\ ^{m}C_{0} + \ ^{m}C_{1} + \ ^{m}C_{2} = 46$
$\Rightarrow \ 2m + m(m - 1) = 90$
$\Rightarrow \ m^{2} + m - 90 = 0\ \Rightarrow \ m = 9\$as $m > 0$
Now, $(r + 1)$th term of $\left( x^{2} + \frac{1}{x} \right)^{m}$ is
$\ ^{m}C_{r}{(x^{2})}^{m - r}\left( \frac{1}{x} \right)^{r} = \ ^{m}C_{r}x^{2m - 3r}$
For this to be independent of $x$ put
$2m - 3r = 0 \Rightarrow r = 6$
$\therefore$ Coefficient of the term independent of $x$ is $\ ^{9}C_{6} = 84$