$(16$ pts$)$ Construct regular expressions for the following languages:

$($a$)$ Construct a regular expression for the language, L$,$ that accepts all binary strings where the $5$th symbol from the right end is $0.$

$($b$)$ Construct a regular expression for the language, L $,$ that accepts all binary strings of length odd.

$($c$)$ Construct a regular expression for the language, L $,$ that accepts all binary strings where number of $0$ present is greater or equal to $2.$

$($d$)$ Construct a regular expression for the language, L$,$ that accepts all binary strings that consist of alternating $0$ s and $1$ s $.$