(1)Planar Graph:-A graph G is planar if it can be drawn in the plane in such a way that no two edges meet each other except at a vertex to which they are incident.
This graph is a planar graph.Here no edges cross each other.
(2)Eulerian Graph:- A connected graph G is Eulerian if there is a closed trail which includes every edge of G, such a trail is called an Eulerian trail.
If every vertex of G has even degree, then G is Eulerian.
In Given Graph every vertex has even degree.Hence it is Eulerian.
(3)Hamiltonian Graph:-A connected graph G is Hamiltonian if there is a cycle which includes every vertex of G; such a cycle is called a Hamiltonian cycle.
There is no Hamilton cycle present in the graph.So given graph is not Hamiltonian graph.
Option(C)1 and 3 should be the correct choice.
Reference:http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/planarity.htm
http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/eulerGraph.htm