Is it necessary to mention the distance between the coils? This is a question in a competitive exam, and I am asking it here to know whether there is a mistake in this question or not.

It is not necessary to mention the distance between the coils.

Magnetic moment is given by m=nIA. 

Magnetic moment depends only on number of turns of the coil 'n'. current flowing through the coil 'I' and area of cross-section of the coil 'A'.

Magnetic moment due to one coil is least affected by the presence of other coil.

Hence, net magnetic moment of the entire system is always obtained by adding magnetic moment of individual coil.