The net resistance between $X$ and $Y$ is ............... $\Omega$.

In the given figure,switches $S_{1}$ and $S_{2}$ are initially open. What is the equivalent resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed? (in $\Omega$)

First,a set of $n$ equal resistors of $R$ each are connected in series to a battery of $emf$ $E$ and internal resistance $R$. $A$ current $I$ is observed to flow. Then,the $n$ resistors are connected in parallel to the same battery. It is observed that the current increases $10$ times. What is $n$?

$A$ regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the centre by wires of the same resistance. If the current enters at one corner and leaves at the opposite corner,the equivalent resistance of the hexagon between the two opposite corners will be:

Three resistances of $4\,\Omega$ each are connected in the form of an equilateral triangle. The effective resistance between any two corners is:

The equivalent resistance between $A$ and $B$ is $:-$