An ideal MOS capacitor has boron doping concentration of 10¹⁵ cm^-3 in the substrate. When a gate voltage is applied, a depletion region of width 0.5 $$\mu m$$ is formed with a surface (channel) potential of 0.2V. Given that $${\varepsilon _0} = 80854 \times {10^{ - 14}}F/cm$$ and the relative permittivities of silicon and silicon dioxide are 12 and 4, respectively, the peak electric field (in V/ $$\mu m$$ ) in the oxide region is ______

For the MOSFET M₁ shown in the figure, assume W/L =2, V_DD = 2.0 V, $$\mu n$$ C_OX = 100$$\mu {\rm A}/{V^2}$$ and V_TH =0.5 V. The transistor M₁ switches from saturation region to linear regionm when V_in(in Volts) is _____

Which one of the following statements is NOT true for a square matrix $$A$$?

The maximum value of the function $$\,f\left( x \right) = \ln \left( {1 + x} \right) - x$$ (where $$x > - 1$$ ) occurs at $$x=$$________.