In an extrinsic semiconductor, the hole concentration is given to be 1.5$$n_i$$ where $$n_i$$ is the intrinsic carrier concentration of 1 $$\times$$ 10$$^{10}$$ $$cm^{-3}$$. The ratio of electron to hole mobility for equal hole and electron drift current is given as ___________ (rounded off to two decimal places).

In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at T = 300 K is 1 $$\times$$ 10$$^{19}$$ cm$$^{-3}$$. The thermal equilibrium hole concentration in silicon at 400 K is _____________ $$\times$$ 10$$^{13}$$ cm$$^{-3}$$ (rounded off to two decimal places).

Given kT at 300 K is 0.026 eV.

In the circuit below, the voltage V$$_{\mathrm{L}}$$ is _____________ V (rounded off to two decimal places).

Let $${v_1} = \left[ {\matrix{ 1 \cr 2 \cr 0 \cr } } \right]$$ and $${v_2} = \left[ {\matrix{ 2 \cr 1 \cr 3 \cr } } \right]$$ be two vectors. The value of the coefficient $$\alpha$$ in the expression $${v_1} = \alpha {v_2} + e$$, which minimizes the length of the error vector e, is