In which direction does a free hanging magnet get stabilized? Explain.

(N/A) freely suspended magnet always comes to rest in the $North-South$ direction.
This happens because the Earth acts like a giant magnetic dipole.
The magnetic North pole of the Earth is located near the geographic South pole,and the magnetic South pole of the Earth is located near the geographic North pole.
When a magnet is suspended freely,its North pole is attracted by the Earth's magnetic South pole (near the geographic North),and its South pole is attracted by the Earth's magnetic North pole (near the geographic South).
Thus,the magnet aligns itself along the Earth's magnetic field lines,which run approximately in the $North-South$ direction.