What can be said about a regular language $$L$$ over $$\left\{ a \right\}$$ whose minimal finite state automation has two states?

Let $$L$$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimum state deterministic finite-state automaton accepting $$L$$ is

Which one of the following regular expressions over $$\left\{ {0,\,\,1} \right\}$$ denotes the set of all strings not containing $$100$$ as substring?

Which of the following definitions below generates the same language as $$L$$
Where $$L = {\left\{ x \right.^n}{y^n}\left| {n \ge \left. 1 \right\}} \right.$$
i) $$\,\,E \to xEy\left| {xy} \right.$$
ii) $$\,\,xy\left| {\left( {{x^ + }xy{y^ + }} \right)} \right.$$
iii) $${\,\,{x^ + }{y^ + }}$$
$$L = \left\{ {xn\,{y^n}\left| {n \ge 1} \right.} \right\} - $$ generates string where equal no. of $$x$$ and equal no. of $$y's.$$
$$E \to XBy\left| {xy\,abo} \right.$$ generators tips same.