Two radioactive materials $A$ and $B$ having decay constant ' $7 \lambda$ ' and ' $\lambda$ ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is

A centigrade and Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit temperature observed is $140^{\circ} \mathrm{F}$. At that time the temperature registered by the centigrade thermometer is

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light rays $\left(v_1>v_2\right)$. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of $1: \mathrm{k}$, then the threshold frequency of metallic surface is

The electric charges ' $+2 q$ ', ' $+2 q$ ', ' $-2 q$ ' and ' $-2 q$ ' are placed at the corners of square of side ' 2 L ' as shown in figure. The electric potential at point 'A', midway between the two charges ' $+2 q$ ' and ' $+2 q$ ' is

( $\varepsilon_0=$ permittivity of free space)