(a) If maximum electron density of the ionosphere is $N_{\max}$ per $m^{3}$ then the critical frequency $f_{c}$ is given by $f_{c} = 9\left( N_{\max} \right)^{1/2}$
$\Rightarrow 10 \times 10^{6} = 9(N)^{1/2} \Rightarrow N = 1.2 \times 10^{12}m^{- 3}$