Ferro-magnetic materials used in transformer core must have:

high permeability and low hysteresis loss

The correct answer is Option (2) → high permeability and low hysteresis loss

Ferromagnetic material used in a transformer core must have high permeability because it allows the core to have a high magnetic induction value for a given field.

It must have low hysteresis loss in order to decrease the energy losses and the hysteresis curve of the core should have a small area.