Which of the following decision problems are undecidable? I. Given NFAs $N_1$ and $N_2$, is $L(N_1) \cap L(N_2) = \Phi$? II. Given a CFG $G = (N, \Sigma, P, S)$ and a string $x \in \Sigma^*$, does $x \in L(G)$? III. Given CFGs $G_1$ and $G_2$, is $L(G_1) = L(G_2)$? IV. Given a TM $M$, is $L(M) = \Phi$?

Let us analyze the decidability of each decision problem:

1. Problem I (Emptiness of Intersection for Regular Languages): Regular languages are closed under intersection. We can construct a product automaton for $N_1$ and $N_2$ and test whether any final state is reachable from the start state using standard graph search (BFS/DFS). Hence, this problem is decidable.

2. Problem II (Membership for CFG): Given a CFG $G$ and string $x$, we can check if $x \in L(G)$ using parsing algorithms such as the CYK algorithm in $O(|x|^3)$ time. Hence, this problem is decidable.

3. Problem III (Equivalence of CFGs): Determining whether two context-free grammars generate the same language ($L(G_1) = L(G_2)$) is a well-known undecidable problem (closely related to the undecidability of $L(G) = \Sigma^*$).

4. Problem IV (Emptiness for TM): Testing whether $L(M) = \Phi$ for a Turing machine is a non-trivial property of the language recognized by the TM, which is undecidable by Rice's theorem.

Therefore, problems III and IV are undecidable, making (C) the correct option.