$2\mathrm{.}1.$ In each part below, draw an FA accepting the indicated language over $(a,b).$

a$.$ The language of all strings containing exactly two $a\text{'}$s$.$

b$.$ The language of all strings containing at least two $a\text{'}$s$.$

c$.$ The language of all strings that do not end with $ab.$

d$.$ The language of all strings that begin or end with $aa$ or $bb.$

e$.$ The language of all strings not containing the substring $aa.$

f$.$ The language of all strings in which the number of $a^{\text{'}}\text{'}$s is even.

g$.$ The language of all strings in which both the number of $a^{\text{'}}s$ and the number of $b^{\text{'}}s$ are even.

h$.$ The language of all strings containing no more than one occurrence of the string $da.($The string aaa contains two occurrences of $aa.)$

i$.$ The language of all strings in which every $a($if there are any$)$ is followed immediately by $bb.$

j$.$ The language of all strings containing both $bb$ and aba as substrings.

k$.$ The language of all strings containing both aba and bab as substrings.