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

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

In the given circuit,all resistances are of value $R \ \Omega$ each. The equivalent resistance between $A$ and $B$ is:

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? ............. $\Omega$

Three unequal resistances are connected in parallel. Two of these resistances are in the ratio $1:2$. The equivalent resistance of these three resistors connected in parallel is $1 \Omega$. What is the highest resistance value among these three resistances if no resistance is fractional (in $\Omega$)?

$A$ wire has resistance $12\,\Omega$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to ................ $\Omega$.