Which of the following languages are undecidable? Note that $\langle M \rangle$ indicates encoding of the Turing machine M. $L_1 = \{\langle M \rangle \mid L(M) = \emptyset\}$ $L_2 = \{\langle M, w, q \rangle \mid M \text{ on input } w \text{ reaches state } q \text{ in exactly 100 steps}\}$ $L_3 = \{\langle M \rangle \mid L(M) \text{ is not recursive}\}$ $L_4 = \{\langle M \rangle \mid L(M) \text{ contains at least 21 members}\}$

Which of the following languages are undecidable? Note that M indicates encoding of the Turing machine M. L1 = \ M L(M) = \ L2 = \ M, w, q M on input w reaches state q in exactly 100 steps\ L3 = \ M L(M) is not recursive\ L4 = \ M L(M) contains at least 21 members\

Topic-wise GATE CS PYQs with verified steps