$512$ identical drops of mercury are charged to a potential of $2 \ V$ each. The drops are joined to form a single drop. The potential of this drop is ......... $V.$

Minimum number of $2\,\mu F$ and $250\, V$ capacitors required to make a combination of $12\,\mu F$ and $500\, V$ is:

$A$ radioactive substance in the form of a metallic sphere of diameter $10^{-3} \ m$ emits particles at a constant rate of $6.25 \times 10^{10}$ particles per second. If the sphere is electrically isolated,how long will it take for its potential to increase by $1.0 \ V$? Assume that $80\%$ of the emitted particles escape from the surface. The time taken is $... \mu s$.

Two identical capacitors are joined in parallel,charged to potential $V$,separated and then connected in series,$i.e.$,the positive plate of one is connected to the negative plate of the other. Then

$A$ positive point charge of $10^{-8} \ C$ is kept at a distance of $20 \ cm$ from the center of a neutral conducting sphere of radius $10 \ cm$. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of $10 \ cm$ further away from the center of the sphere along the radial direction. Taking $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \ N \cdot m^2 / C^2$ (where $\epsilon_0$ is the permittivity of free space),which of the following statements is/are correct:
$(A)$ Before the grounding,the electrostatic potential of the sphere is $450 \ V$.
$(B)$ Charge flowing from the sphere to the ground because of grounding is $5 \times 10^{-9} \ C$.
$(C)$ After the grounding is removed,the charge on the sphere is $-5 \times 10^{-9} \ C$.
$(D)$ The final electrostatic potential of the sphere is $300 \ V$.

The charge on any one of the $2\,\mu F$ capacitors and the $1\,\mu F$ capacitor will be given respectively (in $\mu C$) as