Two D flip-flops are connected as a synchronous counter that goes through the following Q_B Q_A sequence $$00 \to 11 \to 01 \to 10 \to 00 \to ......$$

The output of a 3-stage Johnson (twisted-ring) counter is fed to a digital-to-analog (D/A) converter as shown in the figure below. Assume all the states of the counter to be unset initially. The waveform which represents the D/A converter output V_o is

Consider a closed surface S surrounding volume V. If $$\overrightarrow{\mathrm r}$$ is the position vector of a point inside S, with $$\widehat n$$ the unit normal on S, the value of the integral is

A transmission line of characteristic impedance 50 $$\Omega $$ is terminated by a 50 $$\Omega $$ load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm apart on the line is found to be $$\pi /4$$ radians. The phase velocity of the wave along the line is