Based on the definitions of O$,\backslash$Theta $,$ and $\backslash$Omega $,$ determine whether the following assertions are true or false.

$($a$)2$n$^2+5$n $+1$ in O$($n$2)$

$($b$)$ n $*$ n $*($n $+1)+7*$ n $*$ n in $\backslash$Theta $($n$^2)$

$($c$)2*$ n $*($n $1)$ in $\backslash$Omega $($n$*$log n$)$

$($d$)4*($n $*$ n $)+3*$ n in O$($n$2)$