List of top Theory of Computation Questions on Turing machines and undecidability asked in GATE CS

Which one of the following statements is equivalent to the following assertion?
Turing machine \(M\) decides the language \(L \subseteq \{0,1\}^*\)

Consider the following two statements about regular languages:
\(S_1:\) Every infinite regular language contains an undecidable language as a subset.
\(S_2:\) Every finite language is regular.
Which one of the following choices is correct?

For a Turing machine \(M\), \(\langle M \rangle\) denotes an encoding of \(M\). Consider the following two languages: \[ L_1 = \{\langle M \rangle \mid M \text{ takes more than } 2021 \text{ steps on all inputs}\} \] \[ L_2 = \{\langle M \rangle \mid M \text{ takes more than } 2021 \text{ steps on some input}\} \] Which one of the following options is correct?