GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Consider the following problems $\mathit{L}\left(\mathit{G}\right)$ denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M.
I. For an unrestricted grammar $\mathit{G}$ and a string $\mathit{w}$, where $\mathit{w}\in \mathit{L}\left(\mathit{G}\right)$.
II. Given a Turing Machine $\mathit{M}$, whether $\mathit{L}\left(\mathit{M}\right)$ is regular.
III. Given two grammars ${\mathit{G}}_1$ and ${\mathit{G}}_2$ whether $\mathit{L}\left({\mathit{G}}_1\right)=\mathit{L}\left({\mathit{G}}_2\right)$.
IV. Given an NFAN, whether there is a deterministic PDA P such that $\mathit{N}$ and $\mathit{P}$ accept the same language.
Which one of the following statements is correct?