What is the value of resistance ' $R$ ' in circuit, so that the current through $4 \Omega$ resistance is zero?

The equivalent resistance between $A$ and $B$ in the situation shown is

In the situation shown, the currents through $3\mathrm{\Omega }$ and $2\mathrm{\Omega }$ resistances are in the ratio

The equivalent resistance between $A$ and $B$ in the following figure is

In the situation shown, resistances $R_1,R_2$ and $R_3$ are in the ratio $3: 2: 1$ then

In the situation shown, the potential difference across the cell of smaller $e.m.f.$ is

Figure shows mixed grouping of identical cells each of $e.m.f. 4V$  and internal resistance $1\mathrm{\Omega }.$ This combination can be replaced by an equivalent cell between $A$ and $B$ having e.m.f. $E$ and internal resistance $r,$ where

The situation shown in figure is equivalent to