$(6$pts$)$ For ${\displaystyle \underset{?}{\overset{?}{}}}=\{a,b\},$ construct DFA's that accept the sets consisting of all strings with no more than two a$\text{'}$s$.$

$(6$pts$)$ For ${\displaystyle \underset{?}{\overset{?}{}}}=\{a,b\},$ construct DFA's that accept the sets consisting of all strings of length greater than $5$

$(4$pts$)$ In the below figure, find ${}^{**}(q_0,a)$ and ${}^{**}(q_1,).$

$(4$pts$)$ For the NFA in the below Figure, find ${}^{**}(q_0,1010)$ and ${}^{**}(q_1,00)$