靜電的簡單問題

Yes, they will attract one another.
Suppose the charged sphere (A) is +ve, when it is placed near a neutral conducting sphere (B), -ve charge will be induced on B at the side near to A and +ve charge on side far from A.
Since the -ve charge on B is closer to A than the +ve charge does, the attractive force between A and B will be gretaer than the repulsive force between them. As a result, the two spheres will attract.