$1.(10$pts$)$: What is the simplified Big O notation of the expressions below:

a$.$ O$($n$/2+99)=$ O$($n$)$

b$.$ O$(($n$3+3)*($O$($n$)+5))=$ O$($n$4)$

c$.$ O$(12$n $+6$n$3+1000)=$ O$($n$3)$

d$.2$n$3+$ O$($n$2)=$ O$($n$3)$

e$.$ log$2$n $+2+$ log$5$n $=$ O$($logn$)$

$2.(20$pts$)$: What is the time complexity of the functions below $($express answer in simplified Big O notation$)?$