Cycle detection is graph is in $P$ as it can be done using a graph traversal $(O(V+E))$
Ref: http://www.geeksforgeeks.org/detect-cycle-undirected-graph/
If a problem is in $P$ then it is also in $NP$ as $P$ is a subset of $NP$. So, both 1 and 2 are TRUE.
Statement 3 is also true as $NP-Complete$ requires a problem to be in $NP$ and for any problem in $NP$, we have a non-deterministic polynomial time algorithm.
So, answer is A) - 1, 2 and 3 are TRUE.