The two ends of a rod of length ' $x$ ' and uniform cross-sectional area ' A ' are kept at temperatures ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ ' respectively ( $\mathrm{T}_1>\mathrm{T}_2$ ). If the rate of heat transfer is ' $\mathrm{Q} / \mathrm{t}$ ', through the rod in steady state, then the coefficient of thermal conductivity ' K ' is

A particle of charge $q$ moves with a velocity $\overrightarrow{\mathrm{V}}=a \hat{\mathrm{i}}$ in a magnetic field $\overrightarrow{\mathrm{B}}=b \hat{\mathrm{j}}+c \hat{\mathrm{k}}$, where ' $a$ ', ' b ' and ' c ' are constants. The magnitude of force experienced by particle is

The graph given below represents I-V characteristics of zener diode. The part of the characteristics curve that is most relevant for its operation as a voltage regulator is

The excess pressure inside a soap bubble is 1.5 times the excess pressure inside a second soap bubble. The volume of the second bubble is ' $x$ ' times the volume of the first bubble. The value of ' x ' is