A bulb is connected to an ideal battery of emf $10 \mathrm{V}$ so that the resulting current is $10 \mathrm{mA}.$ When the bulb is connected to $220 \mathrm{V}$ mains (ideal), the current is $50 \mathrm{mA}.$ Choose the correct alternative(s).

The cross section area and length of a cylindrical conductor are $A$ and $l$ respectively and it is connected with a voltage source $V_0$. The conductivity varies as$\mathrm{\sigma }={\mathrm{\sigma }}_0\frac{\mathit{l}}{\mathit{x}}$ where $\mathrm{x} (0 <\mathit{ }x\mathit{ }<\mathit{ }l)$ is the distance along the axis of the cylinder from one of its ends as shown in the figure. Choose the correct option.

In the circuit shown, the cell has $\text{emf}=10 \mathrm{V}$ and internal resistance$=1 \mathrm{\Omega }$.

In the network shown, points $A, B$ and $C$ are potentials of $70 \mathrm{V},$ zero and $10 \mathrm{V}$ respectively.

In the circuit shown in figure-

A battery of emf $E$ and internal resistance $r$ is connected across a resistance $R$. Resistance $R$ can be adjusted to any value greater than or equal to zero. A graph is plotted between the current $\left(\mathrm{i}\right)$ passing through the resistance and potential difference ($V$) across it. Select the correct alternative (s).