Consider a software project with the following information domain characteristics for calculation of function point metric.

Number of external inputs $$\left( {\rm I} \right) = 30$$
Number of external outputs $$\left( O \right) = 60$$
Number of external inquiries $$\left( E \right) = 23$$
Number of files $$(F) = 08$$
Number of external interfaces $$(N) = 02$$

It is given that the complexity weighting factors for $$I, O, E, F$$ and $$N$$ are $$4, 5, 4, 10$$ and $$7,$$ respectively. It is also given that, out of fourteen value adjustment factors that influence the development effort, four factors are not applicable, each of the other four factors have value $$3,$$ and each of the remaining factors have value $$4.$ The computed value of function point metric is _____________.

Let $$L$$ be the language represented by the regular expression $$\sum {^ * 0011\sum {^ * } } $$ where $$\sum { = \left\{ {0,1} \right\}} .$$ What is the minimum number of states in a $$DFA$$ that recognizes $$\overline L $$ (complement of $$L$$)?

Language $${L_1}$$ is polynomial time reducible to language $${L_2}$$ . Language $${L_3}$$ is polynomial time reducible to $${L_2}$$ , which in turn is polynomial time reducible to language $${L_4}$$ . Which of the following is/are true?

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_2} \in P$$
$$\,\,\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P$$ or $$\,\,\,{L_3} \in P,$$ then $$\,\,\,{L_2} \in P$$
$$\,\,\,\,\,\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,$$ if $$\,\,\,{L_1} \in P,$$ and only $$\,\,\,{L_3} \in P$$
$$\,\,\,\,\,\,\,\,\,\,{\rm I}V.\,\,\,\,$$ if $$\,\,\,{L_4} \in P,$$ then $$\,\,\,{L_1} \in P$$ and $$\,\,\,{L_3} \in P$$

Which of the following languages are context-free? $$$\eqalign{ & {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1} \right\} \cr & {L_2} = \left\{ {{a^m}{b^n}{a^m}{b^n}|m,n \ge 1} \right\} \cr & {L_3} = \left\{ {{a^m}{b^n}|m = 2n + 1} \right\} \cr} $$$