An n$-$channel MOS transistor has its substrate at ground potential, its source is $2$V$,$ drain at $4$V and

gate at $5$V$.$ Given that $$ms $=-1$V$,$ Qox $=2$x$108$ coulamb$/$cm$2,$ tox $=1000$A and NA $=2$x$1015/$cm$3.$

Determine the following:

$($i$)$ Flat$-$band voltage

$($ii$)$ Threshold voltage at the source end

$($iii$)$ Threshold voltage at the drain end

$($iv$)$ Whether the transistor is in the linear region or saturation regi