singular vs plural - "Each of them is" or "each of them are"?

Should I use the plural form of verb for each or the single form?

Example:

Each of them are used for different purposes.
Each of them is used for different purposes.

Answer

When you say "each of them", you're referring to each individual in a group (them), so you should use a singular verb. That leaves two possibilities:

Each of them is used for different purposes.

and

Each of them is used for a different purpose.

These two sentences have different meanings. The first means that each room is itself used for multiple different purposes. The second sentence means that each room is used for a purpose that is different than those of the other rooms.