A Boolean function $$f\left( {A,B,C,D} \right) = \Pi \left( {1,5,12,15} \right)$$ is to be implemented using an $$8 \times 1$$ multiplexer ($$A$$ is $$MSB$$). The inputs $$ABC$$ are connected to the select inputs $${S_2}{S_1}{S_0}$$ of the multiplexer respectively.

Which one of the following options gives the correct inputs to pins $$0,1,2,3,4,5,6,7$$ in order?

In the following sequential circuit, the initial state (before the first clock pulse) of the circuit is $${Q_1}{Q_0}$$ $$=00.$$ The state $$\left( {{Q_1}{Q_0}} \right),$$ immediately after the $${333^{rd}}$$ clock pulse is

A series RL circuit is excited at t = 0 by closing a switch as shown in the figure. Assuming zero initial conditions, the value of $$\frac{\mathrm d^2\mathrm I}{\mathrm{dt}^2}$$ at t=0⁺ is

Find the transformer ratios a and b that the impedance (Z_in) is resistive and equal 2.5 Ω when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.