In a half-wave rectifier, an $AC$ input source of frequency $50 \,Hz$ is used. The fundamental frequency of the output is: (in $\,Hz$)

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(a)$ Rectifier	$(i)$ Used for stepping up or stepping down the $\text{A.C.}$ voltage
$(b)$ Stabilizer	$(ii)$ Used to convert $\text{A.C.}$ voltage into $\text{D.C.}$ voltage
$(c)$ Transformer	$(iii)$ Used to remove any ripple in the rectified output voltage
$(d)$ Filter	$(iv)$ Used for constant output voltage

In a full-wave rectifier,the input $AC$ current has a frequency '$v$'. The output frequency of the current is

If a centre-tap transformer is used with two $p-n$ junction diodes for full-wave rectification,then the output voltage of the rectifier with respect to each diode is (secondary voltage of transformer $= V_s$)

$A$ 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.

As shown in the figure,the input is applied between $A$ and $C$,and the output is taken between $B$ and $D$. What should the output be?