$A$ diode detector is used to detect an amplitude modulated wave of $60\%$ modulation by using a condenser of capacity $250\, pF$ in parallel with a load resistance $100\, k\Omega$. Find the maximum modulated frequency which could be detected by it.

The output in the circuit shown in the figure is taken across a capacitor. The input signal is as shown in the figure.

Statement-$I$: To get a steady $DC$ output from the pulsating voltage received from a full wave rectifier,we can connect a capacitor across the output parallel to the load $R_L$.
Statement-$II$: To get a steady $DC$ output from the pulsating voltage received from a full wave rectifier,we can connect an inductor in series with $R_L$.
In the light of the above statements,choose the most appropriate answer from the options given below:

In the half-wave rectifier circuit shown,which of the following waveforms is true for $V_{CD}$,the output across $C$ and $D$?

If the frequency of the input voltage is $50 \,Hz$, applied to a $(a)$ half-wave rectifier and $(b)$ full-wave rectifier, what is the output frequency in both cases, respectively?

The frequency of a given $AC$ signal is $N \ Hz$. When it is connected to a half-wave rectifier,the number of output pulses given by the rectifier in $1 \ s$ is: