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 ...... $\Omega$.

Three resistances of $1\, \Omega$ each are connected in parallel. Such a connection is then connected in series with a $\frac{2}{3}\, \Omega$ resistor. The resultant resistance will be ........... $\Omega$.

The effective resistance of a parallel connection that consists of four wires of equal length,equal area of cross-section,and same material is $0.25\, \Omega$. What will be the effective resistance if they are connected in series? (In $\Omega$)

The equivalent resistance between the points $A$ and $D$ is ................ $\Omega$.

In the given star circuit,find the equivalent resistance between $A$ and $H$. (in $r$)