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Q.

Let $p(n)$ be the number of digits when $8^{n}$ is written is base 6, and let $q(n)$ be the number of digits when $6^{n}$ is written in base 4. For example, $8^{2}$ in base 6 is 144, hence $p(2) = 3$. Then $lim_{n \rightarrow \infty}$ ${p(n)q(n) \over n^2}$ equals :

(A) 1

(B) $\frac{4}{3}$

(C) $\frac{3}{2}$

(D) 2