Without explicitly determining the DFT X$[$r$]$X$[$r$]$X$[$r$]$ of the time$-$limited sequence

x$[$k$]=[6,8,5,4,16,22,7,8,9,44,2],$x$[$k$]=[6,8,-5,4,16,22,7,8,9,44,2],$x$[$k$]=[6,8,5,4,16,22,7,8,9,44,2],$

compute the following functions of the DFT X$[$r$]$X$[$r$]$X$[$r$]$:

$($i$)$ X$[0]$X$[0]$X$[0]$;

$($iv$)$r$=010$X$[$r$]\backslash$sum$\_\{$r$=0\}^\{10\}$ X$[$r$]$r$=010$X$[$r$]$;

$($v$)$r$=010$X$[$r$]2\backslash$sum$\_\{$r$=0\}^\{10\}|$X$[$r$]|^2$r$=010$X$[$r$]2.$