$A$ $12 \text{ HP}$ motor has to be operated $8 \text{ hours/day}$. How much will it cost at the rate of $50 \text{ paisa/kWh}$ in $10$ days? (in $Rs.$)

$A$ 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.

In the figure shown,the power generated in $y$ is maximum when $y = 5\,\Omega$. Then $R$ is

$A$ railway compartment is lit up by thirteen lamps,each taking $2.1\,A$ at $15\,V$. The heat generated per second in each lamp will be ............ $cal$.

An electric heater of resistance $6 \, \Omega$ is run for $10 \, \text{minutes}$ on a $120 \, \text{V}$ line. The energy liberated in this period of time is:

What is the ratio of heat generated in resistors $R$ and $2R$ connected in parallel as shown in the figure?