The battery of a mobile phone is rated as $4.2 \ V, 5800 \ mAh$. How much energy is stored in it when fully charged (in $kJ$)?

$A$ circular wire has a current density $J = (2 \times 10^{10} \text{ A/m}^2) r^2$, where $r$ is the radial distance from the center and the wire radius is $2 \text{ mm}$. The potential difference applied across the wire is $50 \text{ V}$. How much energy (in Joules) is converted to thermal energy in $100 \text{ s}$ (in $\pi$)?

The maximum current that flows through a fuse wire before it blows out varies with its radius as

$A$ wire of resistance $R$ is connected across a cell of emf $\varepsilon$ and internal resistance $r$. The current through the circuit is $I$. In time $t$,the work done by the battery to establish the current $I$ is

The number of electrons flowing per second in the filament of a $110 \,W$ bulb operating at $220 \,V$ is : (Given $e=1.6 \times 10^{-19} \,C$ )

$A$ student in a town in India,where the price per unit $(1 \text{ unit} = 1 \,kWh)$ of electricity is $₹ 5.00$,purchases a $1 \,kVA$ $UPS$ (uninterrupted power supply) battery. $A$ day before the exam,$10$ friends arrive at the student's home with their laptops and all connect their laptops to the $UPS$. Assume that each laptop has a constant power requirement of $90 \,W$. Consider the following statements.
$I.$ All the $10$ laptops can be powered by the $UPS$,if connected directly.
$II.$ All the $10$ laptops can be powered,if connected using an extension box with a $3 \,A$ fuse.
$III.$ If all the $10$ friends use the laptop for $5 \,h$,then the cost of the consumed electricity is about $₹ 22.50$.
Select the correct option with the true statements.