$L_2$ is finite, so regular.
$L_1$ is non-regular.
(It seems CFL to me as I think it can be implement with the help of PDA , as stack can ensure $(m=n \vee n = p)$ and we can also ensure $(m+n+p \geq 10)$ with minimum states changes along with transitions).
$L_2$ is actually {$c^p$ | $p \leq 10$} $\cup$ {$abc^p$ | $p \leq 8$} $\cup$ {$a^2b^2c^p$ | $p \leq 6$}$\cup$ {$a^3b^3c^p$ | $p \leq 4$} $\cup${$a^4b^4c^p$ | $p \leq 2 $} $\cup${$a^5b^5$}$\cup$ {$a^p$ | $p\leq 10$} $\cup$ {$a^pbc$ | $p\leq 8$} $\cup$ {$a^pb^2c^2$ | $p\leq 6$} $\cup$ {$a^pb^3c^3$ | $p\leq 4$} $\cup$ {$a^pb^4c^4$ | $p\leq 2$} $\cup$ {$b^5c^5$ | $p\leq 10$}
Correct Answer: $D$