Explanation

(a)
Mean of $1^{2},2^{2},3^{2}\ ,\ldots.n^{2}\ is$
$\frac{1^{2} + 2^{2} + 3^{3} + \ldots n^{2}}{n} = \frac{\Sigma n^{2}}{n}$
$\frac{46n}{11} = \frac{n(n + 1)(2n + 1)}{6n}$
$\Rightarrow 22n^{2} + 33n + 11 - 276n = 0$
$\Rightarrow \ \ \ \ (n - 11)(22n - 1) = 0$
$\Rightarrow n = 11\ \ and\ n \neq \frac{1}{22}$