Which of the following languages are undecidable? Note that $$\langle M\rangle $$ indicates encoding of the Turing machine M.

L₁ = $$\left\{ {\langle M\rangle |L\left( M \right) = \phi } \right\}$$
L₂ = $$\{ \langle M,w,q\rangle |$$ M on input w reaches state q in exactly 100 steps }
L₃ = { $$\langle M\rangle |$$ L(M) is not recursive }
L₄ = { $$\langle M\rangle |$$ L(M) contains at least 21 members }

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 one of the following problems is un-decidable?

Which of the following is/are undecidable?
$$1.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \Phi ?$$
$$2.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \sum {{}^ * } ?$$
$$3.$$ $$M$$ is a Turing Machine. Is $$L(M)$$ regular?
$$4.$$ $$A$$ is a $$DFA$$ and $$N$$ is an $$NFA.$$
Is $$L(A)=L(N)?$$