The frequency of $AC$ mains in India is ....... $Hz$.

An $AC$ source rated $220\, V, 50\, Hz$ is connected to a resistor. The time taken by the current to change from its maximum value to the $rms$ value is:

In an $A.C.$ circuit,the instantaneous current and $E.M.F.$ are represented as $i = i_0 \sin(\omega t - \frac{\pi}{6})$ and $E = E_0 \sin(\omega t + \frac{\pi}{3})$ respectively. The voltage leads the current by

The instantaneous voltages at three terminals marked $X, Y$ and $Z$ are given by
$V_x = V_0 \sin \omega t$
$V_y = V_0 \sin \left(\omega t + \frac{2 \pi}{3}\right)$
$V_z = V_0 \sin \left(\omega t + \frac{4 \pi}{3}\right)$
An ideal voltmeter is configured to read the $rms$ value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z$. The reading$(s)$ of the voltmeter will be:
$[A]$ $V_{XY}^{rms} = V_0 \sqrt{\frac{3}{2}}$
$[B]$ $V_{YZ}^{rms} = V_0 \sqrt{\frac{1}{2}}$
$[C]$ $V_{XY}^{rms} = V_0$
$[D]$ independent of the choice of the two terminals

The $r.m.s.$ value of an $AC$ of $50 \ Hz$ is $10 \ A$. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be:

The variation of $EMF$ with time for four types of generators is shown in the figures. Which amongst them can be called $AC$?