Two electric bulbs $A$ and $B$ are rated as $60\, W$ and $100\, W$. They are connected in parallel to the same source. Then,

$A$ 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.

$A$ $10\, \Omega$ electric heater operates on a $110\, V$ line. Calculate the rate at which it develops heat in $watts$.

An electric lamp is marked $60\, W$, $230\, V$. The cost of $1\, kWh$ of power is Rs. $1.25$. The cost of using this lamp for $8$ hours is Rs. ................

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?
$(A)$ The temperature distribution over the filament is uniform
$(B)$ The resistance over small sections of the filament decreases with time
$(C)$ The filament emits more light at higher band of frequencies before it breaks up
$(D)$ The filament consumes less electrical power towards the end of the life of the bulb

$A$ constant potential difference is applied to the ends of a graphite rod, whose resistance decreases with a rise in temperature. The rod can be $(1)$ covered with asbestos or $(2)$ left open to the atmosphere. Answer for the steady state.