'$$\mathrm{F}$$' is the force between the two identical charged particles placed at a distance '$$\mathrm{Y}$$' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes

A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is changing) so that their centres coincide. ( $$R > r$$ ). If both coplanar, then the mutual inductance between them is proportional to

'$$\lambda_1$$' is the wavelength of series limit of Lyman series, '$$\lambda_2$$' is the wavelength of the first line line of Lyman series and '$$\lambda_3$$' is the series limit of the Balmer series. Then the relation between $$\lambda_1, \lambda_2$$ and $$\lambda_3$$ is

The velocity of a small ball of mass '$$M$$' and density '$$\mathrm{d}_1$$' when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is '$$\mathrm{d}_2$$', the viscous force acting on the ball is ( $$\mathrm{g}=$$ acceleration due to gravity)