Question $1$: Design PDA for the given language descriptions $($preferred with minimum states$).$

$[2$ marks$]$

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

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

Question $2$: Write CFGs for the following language descriptions in normalized form. $[2$ marks$]$

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

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

Question $3$: Using the second version of Pumping lemma to prove that the given language is not

context free.

$[1$ mark$]$

L$=$ww; w belongs to $(a+b)*$