The intrinsic carrier concentration of a semiconductor is $2.5 \times 10^{16} / \mathrm{m}^3$ at 300 K . If the electron and hole mobilities are $0.15 \mathrm{~m}^2 / \mathrm{Vs}$ and $0.05 \mathrm{~m}^2 / \mathrm{Vs}$, respectively, then the intrinsic resistivity of the semiconductor (in $\mathrm{k} \Omega . \mathrm{m}$ ) at 300 K is _________ (Charge of an electron $e=1.6 \times 10^{-19} \mathrm{C}$.)

The electron mobility $\mu_n$ in a non-degenerate germanium semiconductor at 300 K is $0.38 \mathrm{~m}^2 / \mathrm{Vs}$.

The electron diffusivity $D_n$ at 300 K (in $\mathrm{cm}^2 / \mathrm{s}$, rounded off to the nearest integer) is ____________

(Consider the Boltzmann constant $k_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$ and the charge of an electron $e=1.6 \times 10^{-19} \mathrm{C}$.)

An ideal p-n junction germanium diode has a reverse saturation current of $10 \mu \mathrm{~A}$ at 300 K . The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias current of 100 mA at 300 K is __________. (Consider the Boltzmann constant $k_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$ and the charge of an electron $e=1.6 \times 10^{-19} \mathrm{C}$.)

Consider the matrix $A$ below:

$$ A=\left[\begin{array}{llll} 2 & 3 & 4 & 5 \\ 0 & 6 & 7 & 8 \\ 0 & 0 & \alpha & \beta \\ 0 & 0 & 0 & \gamma \end{array}\right] $$

For which of the following combinations of $\alpha, \beta$ and $\gamma$, is the rank of $A$ at least three?

(i) $\alpha=0$ and $\beta=\gamma \neq 0$

(ii) $\alpha=\beta=\gamma=0$

(iii) $\beta=\gamma=0$ and $\alpha \neq 0$

(iv) $\alpha=\beta=\gamma \neq 0$