Graph Equivalence and Planar Graphs, mostly Multiple Choice , PLZ Help

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Can somebody help me with these Questions pleaseeeeeee, it would be so much appreciated:

1 ) For the graph below, which choice best describes the path ABCDEFCA
http://i44.tinypic.com/33tnr7b.jpg ( please refer to this graph at the link provided )

a.Hamiltonian Circuit
b.Simple Path
c.Eulerian Circuit
d.Circuit, but not Hamiltonian and not Eulerian

2)For the graph below, which choice best describes the path BCDEFGAB
http://i44.tinypic.com/33tnr7b.jpg

a.Eulerian Circuit
b.Simple Path, but not a circuit
c.Circuit, but not Hamiltonian
d.Hamiltonian Circuit

3) A graph G (with no loops or multiple edges) has vertices of degree: 5, 4, 4, 4, 4, 3
Check the statement below that is true.

a.G must have a Hamiltonian circuit
b.G must have an Eulerian Circuit
c.G might have an Eulerian Circuit
d.G has neither an Eulerian nor a Hamiltonian Circuit

4) A simple connected graph G with no loops has 10 vertices. Each vertex of G has degree 6.
Which statement is true

a.G has only an Eulerian Circuit
b.G does not have a Hamiltonian circuit
c.G has an Eulerian circuit and a Hamiltonian circuit
d.G does not have an Eulerian Circuit

5) For the floor plan below, is it possible to start outside and walk through each doorway exactly once returning to the outside? Yes or NO ?
(Make a graph corresponding to the floor plan to help answer the question)
http://i40.tinypic.com/20st6p0.jpg

6) For the floor plan below, is it possible to start outside and pass through each room exactly once, returning to the outside? Yes or No
(Make a graph corresponding to the floor plan to help answer the question)
http://i40.tinypic.com/20st6p0.jpg

7) Suppose G is a simple graph with no loops and 14 vertices. If every vertex has maximum degree which of the following is true?
Answer
a.G definitely has an Eulerian Circuit.
b.G might have an Eulerian Circuit.
c.G definitely does not have an Eulerian Circuit

8) Suppose G is a simple connected graph with no loops.
If G has 12 vertices and 57 edges, which statement below is true?
Answer
a.G definitely has no Hamiltonian Circuit
b.G might not have a Hamiltonian Circuit
c.G must have a Hamiltonian Circuit
d.G might have a Hamiltonian Circuit

9) Is this a connected graph? ( Yes or No )
http://i42.tinypic.com/25stvgx.jpg

10) Suppose G is a graph with V=15 vertices.
What is the minimum number of edges that G can have in order to be a connected graph?

Thank You so Much