Figure shows the output characteristics of two different Bipolar Junction

Transistors (BJT), BJT 1 with magnitude of Early voltage $\left|V_{A 1}\right|$, and BJT 2 with magnitude of Early voltage $\left|V_{A 2}\right|$.

Which of the following options is/are correct regarding the Early voltages?

Consider an LED based on a direct bandgap semiconductor material with energy bandgap 1.3 eV .

Given: Plank's constant, $h=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}$ and speed of light in free space is $3 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$.

In which of the following wavelength ranges the LED will NOT emit?

Consider that the concentration of electrons in a semiconductor bar varies linearly from $2 \times 10^{17} \mathrm{~cm}^{-3}$ at $x=1 \mu \mathrm{~m}$ to $1 \times 10^{16} \mathrm{~cm}^{-3}$ at $x=4 \mu \mathrm{~m}$ along the $x$-direction. Assume that the concentration of electrons is not varying along other directions (that is along $y$ and $z$-directions).

[Given: the mobility of electron is $1400 \mathrm{~cm}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$, thermal voltage is 25 mV and electronic charge is $1.6 \times 10^{-19}$ Coulomb.]

The density of electron diffusion current (in $\mathrm{A} / \mathrm{mm}^2$ ) is $\_\_\_\_$ .

(rounded off to two decimal places)

Consider the differential equation $\dot{\vec{w}}=A \vec{w}$, with $\vec{w}(t=0)=\left[\begin{array}{l}1 \\ 1\end{array}\right]$.

If $\vec{w}(t)=e^t \vec{u}_x+e^{-2 t} \vec{u}_y$ be the solution to the equation where $\vec{u}_x$ and $\vec{u}_y$ are unit vectors along the positive x and y axes respectively, then which of the following options is the correct matrix representing $A$ ?