What is the equivalent resistance between $A$ and $B$?

The resistance of the series combination of two identical resistors is $S$. When they are joined in parallel,the total resistance is $P$. If $S = nP$,then the minimum possible value of $n$ is

$A$ wire of resistance $R$ is bent into a circle of radius $r$. What is the equivalent resistance between points $X$ and $Y$?

Some bulbs are connected in series to a $220\, V$ supply. If one bulb gets fused and the remaining bulbs are reconnected in series to the same supply,the brightness in the room will:

$A$ wire of resistance $R$ is bent into a circular ring of radius $r$. The equivalent resistance between two points $X$ and $Y$ on its circumference,where the central angle $XOY$ is $\alpha$ (in radians),is given by:

$A$ $100\, W$ bulb $B_1$ and two $60\, W$ bulbs $B_2$ and $B_3$ are connected to a $220\, V$ source,as shown in the figure. If $P_1, P_2$,and $P_3$ are the output powers of the bulbs $B_1, B_2$,and $B_3$ respectively,then: