Consider above graph,
S1)
Now suppose shortest path from S to A was S-B and then B-A. shortest path length = SB + BA = 5+5 =10
Now if we increase weight of each edge by 1, then new shortest path will be
shortest path length = min (SB + BA, SA)= min(6+6,11) =11
that means shortest path has changed. So S1 is wrong
S2)
Now even if we double the edge weight shortest path remains the same
shortest path length = min(SB + BA, SA) = min(10+10,20) = 20
that means shortest path is still S-B and then B-A
So S2 is correct
Hence answer should be C)