Answer is (B).
We can decide whether G1 is connected or not, because if it is connected then at least one path cost must be 1 because in shortest path computed from v1 to some vertex not in G1, we must include an edge not in G1, and weight of that edge is 1.
If path cost is 0 for all vertices, that means all the edges included were of weight 0 i.e. of G1 only, hence G1 is not connected.