In the circuit shown below the value of R_L such that the power transferred to R_L is maximum

If the unit step response of a network is $$(1-e^{-\alpha t})$$, then its unit impulse response is

In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t=0. The current i(t) at a time t after the switch is closed is

In the circuit shown below, the network N is described by the following Y matrix: $$$Y\;=\;\begin{bmatrix}0.1S&-0.01S\\0.01S&0.1S\end{bmatrix}$$$ The voltage gain $$\frac{V_2}{V_1}$$ is