a
(a) Suppose temperature difference between \(A\) and \(B\) is \(100°C\) and \(\theta_A > \theta_B\)

Heat current will flow from \(A\) to \(B\) via path \(ACB\) and \(ADB\) . Since all the rod are identical so

(\(\Delta \theta_{AC} > \Delta \theta_{AD}\) (Because heat current \(H = \frac{{\Delta \theta }}{R};\)here \(R =\) same for all.)

==> \({\theta _A} - {\theta _C} = {\theta _A} - {\theta _D}\)

==> \({\theta _C} = {\theta _D}\) i.e. temperature difference between \(C\) and \(D\) will be zero.