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JEE frequently features non-standard circuit topologies:

Cube of resistors: 12 equal resistors along edges. Between opposite corners: $R_{\text{eq}} = 5R/6$ (by symmetry, identify three groups of parallel paths: 3, 6, 3 resistors). Between adjacent corners: $R_{\text{eq}} = 7R/12$. Between face-diagonal corners: $R_{\text{eq}} = 3R/4$.

Infinite ladder networks: Self-similar structure where adding one more section doesn't change the total. Set up equation $R_{\text{eq}} = R_1 + R_2 \| R_{\text{eq}}$ and solve the quadratic.

Symmetric circuits: Identify points at equal potential (by symmetry) and short them — zero current flows between equipotential points. This dramatically simplifies the circuit.

Star-delta transformation: Convert a Y-network ($R_1, R_2, R_3$) to delta ($R_{12}, R_{23}, R_{31}$) where $R_{12} = R_1R_2/R_3 + R_1 + R_2$ (and cyclic). For balanced networks: $R_\Delta = 3R_Y$.

Wire bent into shapes: A wire of total resistance $R$ bent into a circle gives $R_{\text{eq}} = R/4$ between diametrically opposite points (two $R/2$ halves in parallel). Between adjacent points at angle $\theta$: $R_{\text{eq}} = R\theta(2\pi - \theta)/(4\pi^2)$.