The vector function $F(r) = -x \hat{i} + y \hat{j}$ is defined over a circular arc C shown in the figure,

The line integral of $\int\limits_{C} \mathbf{F(r)} \cdot d\mathbf{r}$ is

A silicon $P-N$ junction is shown in the figure. The doping in the $P$ region is $5 \times 10^{16} \mathrm{~cm}^3$ and doping in the $N$ region is $10 \times 10^{-16} \mathrm{~cm}^{-3}$. The parameters given are

Built-in voltage $\left(\phi_{b i}\right)=0.8 \mathrm{~V}$

Electro charge $(q)=1.6 \times 10^{-19} \mathrm{C}$

Vacuum permittivity of silicon $\left(\varepsilon_{s i}\right)=12$

The magnitude of reverse bias voltage that would completely deplete one of the two regions ( $P$ or $N$ ) prior to the other (rounded off to one decimal place) is $\_\_\_\_$ V.

A bar of silicon is doped with boron concentration of $10^{16} \mathrm{cm}^{-3}$ and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of $10^{20} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}$. If the recombination lifetime is $100 \mu \mathrm{~s}$, intrinsic carrier concentration of silicon is $10^{10} \mathrm{~cm}^{-3}$ and assuming $100 \%$ ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is