Two isolated metallic spheres of radii $R$ and $2R$ are charged such that both have the same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the larger sphere is $\sigma_1$. The ratio $\sigma_1$ to $\sigma$ is

A parallel plate capacitor with air between the plate has a capacitance of $15$ pF. The separation between the plates becomes twice and the space between them is filled with a medium of dielectric constant $3.5$. Then the capacitance becomes $x/4$ pF.
The value of $x$ is

Resistances are joint as shown in the figure. In the balanced condition, the current $I$ drawn from the battery is

In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf $1.5$ V is found to be $60$ cm. If this cell is replaced by another cell of emf $E$, the length of null point increases by $40$ cm. The value of $E$ is $x/10$ V.
The value of $x$ is