a
(a) Resistance between \(P\) and \(Q\) \({R_{PQ}} = R||\left( {\frac{R}{3} + \frac{R}{2}} \right)\)\( = \frac{{R \times \frac{5}{6}R}}{{R + \frac{5}{6}R}}\)\( = \frac{5}{{11}}R\)Resistance between \(Q\) and \(R\) \({R_{QR}} = \frac{R}{2}||\left( {R + \frac{R}{3}} \right)\)\( = \frac{{\frac{R}{2} \times \frac{{4R}}{3}}}{{\frac{R}{2} + \frac{{4R}}{3}}}\)\( = \frac{4}{{11}}R\)Resistance between \(P\) and \(R\) \({R_{PR}} = \frac{R}{3}||\left( {\frac{R}{2} + R} \right)\)\( = \frac{{\frac{R}{3} \times \frac{{3R}}{2}}}{{\frac{R}{3} + \frac{{3R}}{2}}}\)\( = \frac{3}{{11}}R\) Hence it is clear that \({P_{PQ}}\) is maximum.