Question $1$: Design a Turing machine for the given language descriptions. $[2$ marks$]$

$1.L=a^n{b}^{3n}$;$n>0.$

$2.L=a^{n+1}{b}^{n+3}$;$n0$

Question $2$: Design a Turing machine for $2^p$ where $P$ is the prime number. Also explain the procedure like the $a^{n{b}^n}$ examples in the slides $[1\mathrm{.}5$ marks$]$

Question $3$: Consider the following language over $|),(minN$ and $m$ is a multiple of $n$ marks