= Solution
{c}
For a <tiny object> $A$, the exponential <functor> $E_A=(-)^A$ has a <right adjoint>, say $R_A$. The defining exponential adjunction gives the natural isomorphism
$$
E_{A\times B}\cong E_AE_B,
$$
since $(X^B)^A\cong X^{A\times B}$. If $A,B$ are <tiny objects>, the composite on the right is a <left adjoint> with right adjoint $R_BR_A$. Thus $A\times B$ is tiny. The <terminal object> is tiny because exponentiation by it is naturally the identity, which is its own right adjoint. Induction, including this empty-product case, proves <tiny objects are closed under finite products>:
$$
\boxed{A_1,\ldots,A_n\text{ tiny}\ \Longrightarrow\ \prod_{i=1}^nA_i\text{ tiny}.}
$$
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