Why is it so that some of the paper pieces get stuck to it while others drop instantly when they stick? When we rub a comb on our head and held it near pieces of paper then they get attracted because of induced opposite charge. 
 A: Though there are many factors, the most dominant aspect playing the role here is that when a comb is charged by rubbing, the charge acquired on the comb is not the same at all places on the comb.
The comb gets charged because during rubbing, some electrons are transferred to (or from, depending upon material) the rubbing surface, rendering those atoms charged.
Thus, as a simple consequence of this, only those areas of the comb get charged which had been subjected to rubbing. And more effective the rubbing, more the charge acquired on those areas of the comb.
When you rub the comb, not all areas of the comb are equally rubbed. Some areas where the contact with the rubbing surface had been more effective, acquire higher charge. At the same time, there are also areas which were rubbed, but the contact wasn't that effective, so those areas of the comb are charged less.
The areas that acquired more charge attract the pieces of paper more strongly, while the regions with feeble charge attract weakly. When a paper piece is attracted by a stronger region, that one sticks, while those paper pieces which are attracted towards the feebly charged regions fall down (or dance up and down) because the attraction simply isn't enough.
