Let $x$ : An object

$p(x)$: $x$ is a paper

$n(x)$: $x$ is a pen and

$h(x)$: $x$ is handmade

No paper is pen.$\equiv$ There does not exist an $x$ such that $x$ is a paper and it is a pen $\equiv\ \sim \exists x ( p(x) \wedge n(x)) \equiv \forall x$$(\sim p(x)\ \vee \sim n(x) )$

Also from $\forall x (\sim p(x)\ \vee \sim n(x) )$ we can conclude $\exists x (\sim p(x)\ \vee \sim n(x) ) \equiv \exists x ( p(x) \rightarrow \sim n(x)) $

Some paper are handmade$\equiv$ There exists some $x$ such that $x$ is a paper and it is handmade $\equiv \exists x(p(x) \wedge h(x))$

Using the above two equations

$\exists x ( p(x) \rightarrow \sim n(x)) $

$\underline{\exists x(p(x) \wedge h(x))}$

$\exists x( \sim n(x) \wedge h(x))$

- All paper are handmade. $\equiv \forall x$( if $x$ is a paper then it is handmade) $\equiv \forall x ( p(x) \rightarrow h(x)) \equiv \forall x (\sim p(x)\ \vee h(x))$
- Some handmade are pen$\equiv$ There exists some $x$ such that $x$ is a handmade and it is a pen $\equiv \exists x(h(x) \wedge n(x))$
- Some handmade are not pen$\equiv$ There exists some $x$ such that $x$ is a handmade and it is not a pen $\equiv \exists x(h(x) \wedge \sim n(x))$
- All handmade are paper $\equiv \forall x$( if $x$ is a handmade then it is a paper) $\equiv \forall x ( r(x) \rightarrow f(x)) \equiv \forall x (\sim h(x)\ \vee p(x))$

$\therefore$ Option $C.$ is correct