In the following star circuit diagram,the equivalent resistance between the points $A$ and $H$ will be ..............$r$.

The total resistance between $x$ and $y$ is ...... $\Omega$.

The equivalent resistance between the terminals $A$ and $B$ is ............. $\Omega$.

Consider the ladder network shown in the figure. What should be the value of resistance $R$ so that the effective resistance between $A$ and $B$ becomes independent of the number of elements in the combination? ............. $\Omega$

The equivalent resistance between $A$ and $B$ as shown in the figure is $........\,k\Omega$.

Write the equation for the equivalent resistance of $n$ resistors connected in series and the equation for the equivalent resistance of $n$ resistors connected in parallel.