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

You are given $n$ resistors each of resistance $r$. They are first connected to get the minimum possible resistance. In the second case,they are again connected differently to get the maximum possible resistance. Calculate the ratio between minimum and maximum values of resistance so obtained.

The power consumed when $10 \ V$ voltage is applied to a series combination of $10$ resistors of each $1 \ \Omega$ is $P_{s}$ and the power consumed when the same $10 \ V$ is applied to the parallel combination of these $10$ resistors is $P_p$. The value of $\frac{P_{s}}{P_{p}}$ is

You are given $10$ resistors each of resistance $1 \ \Omega$. First,they are connected to obtain the possible minimum resistance. Then,they are connected to obtain the possible maximum resistance. The ratio of minimum and maximum resistance is . . . . . . .

The effective resistance of two resistors in parallel is $\frac{12}{7} \ \Omega$. If one of the resistors is disconnected,the resistance becomes $4 \ \Omega$. The resistance of the other resistor is ............. $\Omega$.

The resistance of each wire between any two adjacent dots is $R$. Then the equivalent resistance between $A$ and $B$ as shown in the figure is: