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

The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by $25 \%$ by keeping tension same then frequency change of second harmonic is