$P_{1}:$ {$<M>|M $ is a TM that accepts atleast $2$ strings of different length} $P_{2}:$ {$<M>|M $ is a TM and there exists an input whose length less than $100,$ on which $M$ halts } The number of problem which is $RE$ but not $REC$ _____________

How many number of $DFA$ states(minimal DFA) required which accepts the language $L=\left \{ a^{n}:n=\text{3 or n>= 2m for all m>= 1} \right \}$ ___________ Answer will be $3$ or $6?$

Consider $\left \langle M \right \rangle$ be the encoding of a turing machine as a string over alphabet $\Sigma =\left \{ 0,1 \right \}$. Consider $D=${$\left \langle M \right \rangle$ $M$ ... Recursive $(B)$ Non-Recursive $(C)$ Recursively enumerable $(D)$ Not Recursively enumerable My question is Is it not a Halting Problem they are asking for?