Solve the given Problem $($Students$)$

$(1)-RE,$ that start with $"0"$ and $|w|=$ EVEN

$(2)-RE,$ that start with $"1"$ and $|w|=$ EVEN

$(3)$ RE$,$ that start with $"0"$ and $|w|=$ ODD

$(4)-$ RE$,$ that start with $"1"$ and $|w|=$ ODD

$(5)-$ RE$,$ that must include $2$a$\text{'}$s OR $2$b$\text{'}$s

$(6)*$ RE$,$ that

IF start with $"$a$"$ THEN ends on $"$b$"$

OR

IF start with $"$b$"$ THEN ends on $"$a$"$