A one-sided abrupt $p n$ junction diode has a depletion capacitance $C_D$ of 50 pF at a reverse bias 0.2 V . The plot of $\frac{1}{C_D^2}$ versus the applied voltage $V$ for this diode is a straight line as shown in the figure below. The slope of the plot is $\_\_\_\_$ $\times 10^{20} \mathrm{~F}^{-2} \mathrm{~V}^{-1}$.

The band diagram of $p$-type semiconductor with a bandgap of the 1 eV is shown. Using this semiconductor, a MOS capacitor having $V_{T H}$ of $-0.16 \mathrm{~V}, C_{o x}^{\prime}$ of $100 \mathrm{nF} / \mathrm{cm}^2$ and metal work function of 3.87 eV is fabricated. There is no charge within the oxide. If the voltage across the capacitor is $V_{T H}$, the magnitude of depletion charge per unit area (in $\mathrm{C} / \mathrm{cm}^2$ ) is

If $\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}} \ldots \mathbf{v}_{\mathbf{6}}$ are six vectors in $\mathbb{R}^4$, which one of the statements is FALSE?

The two sides of a fair coin are labelled as 0 and 1 . The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X=\min (M, N)$, the expected value $E[X]$ (rounded off to two decimal places) is $\_\_\_\_$ .