A cube is made from 12 identical wires. Current enters one corner of the cube and it leaves the opposite comer. If the resistance of each wire is r, then equivalent resistance will be

Although this question is not going to be asked in any competitive examination, but students can directly remember the following results. 

$$\begin{gathered} {\mathrm{R}}_{\mathrm{ab}}=\frac{7\mathrm{r}}{12}, {\mathrm{R}}_{\mathrm{ac}}=\frac{9\mathrm{r}}{12}\mathrm{or}\frac{3\mathrm{r}}{4} \\ \mathrm{and} {\mathrm{R}}_{\mathrm{af}}=\frac{10\mathrm{r}}{12} \mathrm{or} \frac{5\mathrm{r}}{6} \end{gathered}$$