pronouns - "One of them" vs. "One of which"

Which one is grammatically correct or better?

I have two assignments, One of them is done.

I have two assignments, One of which is done.

I watched a video tutorial that the teacher said the second one is correct and the first one is wrong. But I can not understand why the first one is wrong. He said if you have a quantifier in an adjective clause, You can not use them and should use whom for people and which for objects.

Answer

You don't need to capitalize the o in the word "one" if it is not the first word of a sentence. The tutorial you watched is correct. The reason the first sentence is ungrammatical is because it is a run-on sentence, which is a very common grammar error. A run-on sentence has two or more parts (clauses), each of which can be a stand-alone sentence. (See how my sentence is similar to the sentences are you asking about?) To avoid making run-on sentences, you need to connect these clauses with conjunctions, such as "and", "or", "but".

So the problem with the first sentence is that "them" is not a relative pronoun and the clause is an independent clause. You need a conjunction to connect the two clauses if you want them both in one sentence.

I have two assignments, and one of them is done.

Or alternatively you need to make them two separate sentences, which means you need to replace the comma with a period.

I have two assignments. One of them is done.

The second sentence reads fine as long as you follow the correct sentence case and change "One" to "one".

I have two assignments, one of which is done.