A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It
A) will stay in north- south direction only
B) will stay in east- west direction only
C) will become rigid showing no movement
D) will stay in any position

Hint: We will use the concept of Earth's magnetism which is also known as geomagnetic field. The north pole of a compass needle, is attracted to the geomagnetic north pole. This Earth's north pole is magnetic south pole whereas its geomagnetic south pole is a magnetic north pole. Magnetic field becomes zero at the geomagnetic pole.

Complete step by step solution:
Earth's magnetic field is also known as the geomagnetic field which extends from the Earth's interior to its outskirts.
Now we know that, the horizontal component of earth magnetic field is given by
${B_H} = B\cos \delta $
Where $\delta $ is the angle of dip.
The angle of Dip with the horizontal component of the Earth’s magnetic field becomes zero, at the geomagnetic pole. That is
${B_H} = 0$
So, the magnetic field no more acts on it.
Hence, the compass needle will move in any direction as there will be no influence of earth’s magnetic-field on the compass needle at geomagnetic pole.

Therefore, option(D) is correct.

Additional information:
Geomagnetic field is the magnetic field that extends from the earth's interior to outer space. Magnetic reversals of the Earth's have changed the polarities of the geomagnetic poles a lot of times.
The geomagnetic poles are close to the geographical North and South poles, and to the Earth's magnetic poles.
The vertical component of earth’s magnetic field is
${B_v} = B\sin \delta $

Note:
All elements help us to connect all principles of earth’s magnetic field so that we can provide detailed study on earth’s magnetism. Earth is largely protected from the solar wind, which is a stream of energetic charged particles.