Combination of Resistors question from JEE Main 2023 (30 Jan, Shift 2)

Answer: (b)

1. The left vertical wire makes both left corners one node (A); the right vertical wire makes both right corners one node (B). Every branch then runs from A to B.
2. Branches: top $1.5 + 0.5 = 2$, $12$, diagonal $8 + 6 = 14$, diagonal $2 + 4 = 6$, $6$, bottom $1 + 1 = 2\ \Omega$, all in parallel.
3. $\dfrac{1}{R} = \dfrac12 + \dfrac1{12} + \dfrac1{14} + \dfrac16 + \dfrac16 + \dfrac12 = \dfrac{125}{84} \Rightarrow R \approx 0.67\ \Omega$
4. This is closest to (b) $\dfrac{2}{3}\ \Omega$.