(i) Mutual inductance decreases with the increase of distance between the coils. This is due to loose coupling between the coils.
(ii) With the decrease of the number of turns, the mutual inductance decreases. The coupling between two coils is proportional to np ns, where np and ns are the number of turns in primary and secondary coils respectively. Hence mutual inductance decreases with the decrease in number of turns of the two coils.
(iii) When a thin iron sheet is placed between the two coils the permeability of the medium is increased many times, which results in increase of mutual inductance between the coils.