If the two ends of a p-n junction are joined by a wire:

The correct answer is Option (3) → there will not be a steady current in the circuit

A p-n junction has a built-in junction (barrier) potential, but it is an internal potential difference across the depletion region, not a source of emf. Inside the junction the diffusion current of the majority carriers is exactly balanced by the drift current of the minority carriers, so the net current is zero.

Joining the two ends with a wire does not change this: the potential differences at the two metal-semiconductor contacts together cancel the junction potential, so the net emf around the closed loop is zero. A steady current would also deliver energy continuously (for example as heat in the wire) with no source of energy to supply it, which conservation of energy forbids.

Hence there is no steady current in either direction.