A bar magnet is cut into two equal halves by a plane parallel to the magnetic axis. Of the following physical quantities the one which remains un-changed is

For a bar magnet the strength of the pole will be proportional to the area of the cross section. So when the bar magnet is cut into two equal halves by a plane parallel to the magnetic axis, the strength of the magnetic pole will be halved. 

Resulting in the change of magnetic moment.

$\text{ Final magnetic moment, }{\mathrm{M}}_{\mathrm{f}}=\frac{{\mathrm{ml}}_{\mathrm{ef}}}{2}$