Consider the $$DFA$$ $$A$$ given below.

Which of the following are FALSE?
$$1.$$ Complement of $$L(A)$$ is context - free.
$$2.$$ $$L(A)$$ $$ = \left( {{{11}^ * }0 + 0} \right)\left( {0 + 1} \right){}^ * {0^ * }\left. {{1^ * }} \right)$$
$$3.$$ For the language accepted by $$A, A$$ is the minimal $$DFA.$$
$$4.$$ $$A$$ accepts all strings over $$\left\{ {0,1} \right\}$$ of length at least $$2.$$

Consider the languages $${L_1}$$, $${L_2}$$ and $${L_3}$$ are given below. $$$\eqalign{ & {L_1} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.} \right\} \cr & {L_2} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.\,\,and\,\,p = q} \right\}\,\,and \cr & {L_3} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r\, \in N\,\,\,and\,\,\,p = q = r} \right.} \right\}. \cr} $$$

Which of the following statements is not TRUE?

Consider the languages $$$\eqalign{ & {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \left\{ {{0^i}{1^j}\,\left| {i = j} \right.} \right\}, \cr & {L_3} = \left\{ {{0^i}{1^j}\,\left| {i = 2j + 1} \right.} \right\}, \cr & {L_4} = \left\{ {{0^i}{1^j}\,\left| {i \ne 2j} \right.} \right\}, \cr} $$$

Which of the following statements are true?
$$1.$$ Every left-recursive grammar can be converted to a right-recursive grammar and vice-versa
$$2.$$ All ε-productions can be removed from any context-free grammar by suitable transformations
$$3.$$ The language generated by a context-free grammar all of whose productions are of the form $$X \to w$$ or $$X \to wY$$ (where, $$w$$ is a string of terminals and $$Y$$ is a non terminal), is always regular
$$4.$$ The derivation trees of strings generated by a context-free grammar in Chomsky Normal Form are always binary trees