$6.$Answer the following questions:

a$)$ Give an example of a string of length $6$ containing ab that is accepted by the FSA shown in figure $1.$

b$)$ Give an example of a string of length $5$ that is rejected by the FSA shown in figure $1.$

c$)$ Describe the language of this automaton in terms of a Regular Expression.

d$)$ Draw a FSA which accepts all binary strings which start with $0,$ the length of the string is even and it does not contain $001.$ For example, $0111,01$ should be accepted while $111$ and $0011$ should not.