A MOSFET $($Metal$-$Oxide$-$Silicon FieldEffect Transistor$)$ with a channel length $($L$)$ of $200$ nm and a channel width $($W$)$ of $\backslash (200\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash )$ was fabricated and the transfer characteristics was measured as in the below figure. $($Q$)$ Calculate the maximum field effect mobility $(\backslash (\backslash$mu $\backslash )$ eff$)$ of this transistor in linear region. Assume that the maximum transconductance of $48$ mS $,$ Vth $\backslash (=-4\backslash$mathrm$\{$~V$\}\backslash ),$ and $\backslash (\backslash$mathrm$\{$Cox$\}=2\mathrm{.}5\backslash$mathrm$\{$uF$\}/\backslash$mathrm$\{$cm$\}2\backslash ).$ Write the value only considering the unit as cm$2/$Vs$.(10$ pts$)$