Option A: Any regular language
Every regular language is accepted by a deterministic finite automaton (DFA). A DFA can be viewed as a DPDA that never uses its stack (or uses it trivially). Hence, every regular language is a deterministic context-free language (DCFL) and is accepted by a DPDA.
Option B: Any context-free language
Not all context-free languages are deterministic. A classic counterexample is
$$
L = \{ w w^R \mid w \in \{a,b\}^* \},
$$
the set of even-length palindromes. Any DPDA would need to know the exact middle of the input to switch from pushing to popping, but without a marker, it cannot do so deterministically. Thus, $ L \in \text{CFL} \setminus \text{DCFL} $. Not accepted by any DPDA.
Option C: Any language accepted by a non-deterministic PDA
Languages accepted by NPDAs are exactly the CFLs. As shown above, some CFLs are not DCFLs. Hence, this class strictly contains languages not accepted by any DPDA.
Incorrect.
Option D: Any decidable language
Decidable languages include languages that are not even context-free. For example,
$$
L = \{ a^n b^n c^n \mid n \geq 0 \}
$$
is decidable (a Turing machine can count and compare), but it is not context-free, so no PDA deterministic or not can accept it. Since DPDAs accept only DCFLs ⊂ CFL ⊂ Decidable, this is false.
Not accepted by a DPDA.
Only regular languages are guaranteed to be accepted by a DPDA among the given options.
$$
\color{skyblue} \boxed{\text{Answer: A}}
$$
