For hydrogen atom, ' $\lambda_1$ ' and ' $\lambda_2$ ' are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ' $\lambda_1$ ' and ' $\lambda_2$ ' is $\frac{x}{32}$. The value of ' $x$ ' is

A metallic sphere ' A ' isolated from ground is charged to $+50 \mu \mathrm{C}$. This sphere is brought in contact with other isolated metallic sphere ' $B$ ' of half the radius of sphere ' $A$ '. Then the charge on the two isolated spheres A \& B are in the ratio

For a photosensitive material, work function is ' $\mathrm{W}_0$ ' and stopping potential is ' V '. The wavelength of incident radiation is ( $\mathrm{h}=$ Planck's constant, $c=$ velocity of light, $e=$ electronic charge)