Two wires of same material and same length have their resistances in the ratio$5: 7$, the ratio of the masses of the wires is

In a conductor, if the number of conduction electrons per unit volume is $8.5\times {10}^{28}{\mathrm{m}}^{-3}$ and mean free time is $25f\mathrm{s}$ (femtosecond), its approximate resistivity is: $\left({\mathrm{m}}_{\mathrm{e}}=9.1\times {10}^{-31}\mathrm{k}\mathrm{g}\right)$

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $a$ and a concentric thin cylindrical shell of radius $b$ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R$, the maximum Joule heating in $R$ will take place for :

If the last band on the carbon resistor is absent, then the tolerance is