Statement I: If a compass needle be kept at magneric north pole of the earth, the compass needle may stay in any direction.Statement II: Dip needle will stay vertical at the north pole of earth.

We know that at magnetic poles the horizontal component of earth's field is zero, only vertical component exists. So, as compass needle is free to rotate in horizontal plane and is thus affected by horizontal component only, as H = 0, hence, compass needle may stay in any direction. The dip needle rotates in a vertical plane and the angle of dip at poles is 90o. Hence, the dip needle will stand vertical at the north pole of earth.