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

Consider the following series:

(i) $\sum\limits_{n=1}^{\infty} \frac{1}{\sqrt{n}}$

(ii) $ \sum\limits_{n=1}^{\infty} \frac{1}{n(n+1)}$

(iii) $\sum\limits_{n=1}^{\infty} \frac{1}{n!}$

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.

What is the probability that the two balls drawn have different colours?