Which of the regular expression given below represent the following $$DFA?$$

Consider the following languages
$${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.} \right\}$$

Which one of the following statements is FALSE?

Consider the set of strings on $$\left\{ {0,1} \right\}$$ in which, every substring of $$3$$ symbols has at most two zeros. For example, $$001110$$ and $$011001$$ are in the language, but $$100010$$ is not. All strings of length less than $$3$$ are also in the language. A partially completed $$DFA$$ that accepts this language is shown below.

The missing arcs in the $$DFA$$ are

A deterministic finite automation $$(DFA)$$ $$D$$ with alphabet $$\sum { = \left\{ {a,b} \right\}} $$ is given below

Which of the following finite state machines is a valid minimal $$DFA$$ which accepts the same languages as $$D?$$