@lalitver10 For option A, we use BFS for single source shortest path.

Just to add few more points for option D:

→ If there are two back edges then it will imply that there are at least two cycles in the graph. So, one edge removal may or may not destroy all cycles and that one edge can never be back edge.

You cannot find single source shortest path using general DFS on any weighted graph. But there is some modifications which can find SSSP but it takes Quadratic complexity. (Refer: https://stackoverflow.com/a/54199609/14777974)

Topological sorting can be done on Directed Acyclic Graph using DFS.

@lalitver10 They told if it is possible or not. Even if the graph is cyclic you can find out using DFS that it is not possible to topologically sort that graph (i.e. finding if your graph a DAG or not).