How many $60 \,W$ bulbs may be safely run on $220 \,V$ using a $5 \,A$ fuse?

Two conductors made of the same material are connected across a common potential difference. Conductor $A$ has twice the diameter and twice the length of conductor $B$. The power delivered to the two conductors $P_A$ and $P_B$ respectively is such that $P_A/P_B$ equals to

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

The current flowing through a lamp marked as $50\, W$ and $250\, V$ is ............. $amp$.

Two wires $A$ and $B$ of the same material and mass have their lengths in the ratio $1 : 2$. On connecting them to the same source, the rate of heat dissipation in $B$ is found to be $5\,W$. The rate of heat dissipation in $A$ is............ $W$

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature,$100 \ W$,$60 \ W$ and $40 \ W$ bulbs have filament resistances $R_{100}$,$R_{60}$ and $R_{40}$,respectively,the relation between these resistances is