Design a deterministic finite automaton to recognise the following language

$L=\{0^{2m}+1^{3n}+\frac{2^k}{m}>0,n>0,k>2\},$ where $=\{0,1,2,+\}.$

Write regular expression for each of the following languages over the alphabet ${\displaystyle \underset{?}{\overset{?}{}}}=\{a,b\}.$

i$.$ The set of strings containing $ab$ as a substring.

ii$.$ The set of strings having at most one pair of consecutive $a^{\text{'}}s$ and at most one pair of

consecutive $b\text{'}$s$.$

iii. The set of strings whose length is divisible by $6.$