The time required to raise the temperature 3 litre of water from $0^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ by a heater operated under 200 V having resistance of $50 \Omega$ is [specific heat capacity of water is $4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ ] [density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ ]

The current density in a circular wire is given by $J(r)=\left(1 \times 10^5 \mathrm{~A} / \mathrm{m}^3\right) r$, where $r$ is the radial distance and the wire's radius is 2 mm . If the potential applied across the wire is 70 V , then the energy consumed by the wire in 1000 s is

Statement I Specific resistance depends on nature of material and independent of temperature of the material. Statement II A wire of resistance $6 \Omega$ is drawn out, so that its new length is four times its original length. The resistance of the new wire is $48 \Omega$.

Statement III Drift velocity is the average constant velocity acquired by free electrons inside a metal by the application of an electric field which results in current. Which of the following is correct?

Find the mobility of electron in a wire, if its average collision time is $9.1 \times 10^{-15} \mathrm{~s}$. (Charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ and mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ )