We can get minimal DFA for both A and B, as minimal DFAs for both of them are just single state DFAs,
And we know minimal DFA for any regular language is always unique. So they should be isomorphic to $DFA_{min}(\phi)$ and $DFA_{min}(\sum^{*})$ respectively.
It’s easy to check if $DFA_{min}$ for A is isomorphic to $DFA_{min}(\phi)$ as there’s only 1 state, if they are isomorphic we say ‘Yes’, otherwise we say ‘No’.
Same procedure can be applied to check if $DFA_{min}$ for B = $DFA_{min}(\sum^{*}).$
Another algorithm to prove both cases can be found here. (reference)
Hence both (A) and (B) are decidable.
For every PDA we can covert it into a CFG, minimize the CFG (removing all useless symbols and productions), if Start symbol is useless then we can say ‘Yes’, otherwise we can say ‘No’. Hence (C) is decidable.
Only option left is (D). It is undecidable, There’s no way to determine if a CFG can generate everything or not. Proof (not meant for GATE) is given here.
Final ans is D.