A positive point charge $q$ is brought near a neutral metal sphere.

Two small conductors $A$ and $B$ are given charges $q_1$ and $q_2$ respectively. Now they are placed inside a hollow metallic conductor ($C$) carrying a charge $Q.$ If all the three conductors $A, B$ and $C$ are connected by conducting wires as shown, the charges on $A, B$ and $C$ will be respectively:

If $g_E$ and $g_M$ are the accelerations due to gravity on the surfaces of the Earth and the Moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio $\frac{\text{electronic }\text{charge }\text{on }\text{the }\text{moon }}{\text{electronic }\text{charge }\text{on }\text{the }\text{earth }}$  to be

In the following figure, three paths of $\alpha$ particle crossing a nucleus $N$ are shown. The correct path is 

(a) 

(b) 

(c) 

A conducting sphere of radius $10 \mathrm{cm}$ is charged to $10 \mu \mathrm{C}$. Another uncharged sphere of radius $20 \mathrm{cm}$ is allowed to touch it for some time. After that, if the spheres are separated, then surface density of charges on the spheres will be in the ratio of