GATE Electronics and Communications (EC) 2016 Shift 2 Solved Paper

A voltage ${\mathrm{V}}_{\mathrm{G}}$ is applied across a MOS capacitor with metal gate and p-type silicon substrate at $\mathrm{T}=300\mathrm{K}$. The inversion carrier density (in number of carriers per unit area) for ${\mathrm{V}}_{\mathrm{G}}=0.8\mathrm{V}$ is $2\times {10}^{11}{\mathrm{cm}}^{-2}$. For ${\mathrm{V}}_{\mathrm{G}}=1.3\mathrm{V}$, the inversion carrier density is $4\times {10}^{11}{\mathrm{cm}}^{-2}$. What is the value of the inversion carrier density for ${\mathrm{V}}_{\mathrm{G}}=1.8\mathrm{V}$ ?