Which of the following contains a grammatical error?
a. The train is usually on time, but it was late three times this week.
b. Each of the project leaders are in charge of developing one new project design.
c. Trevor had done five somersaults in a row before becoming dizzy.
The answer to your question would be B, which should read,
Each of the project leaders is in charge of developing one new project design.
The word "each" is both a pronoun and a determiner. In this case, it determines, or singles out, nouns separately. The definition given by Webster states that the determiner "each" is used to
refer to every one of two or more people or things, regarded and identified separately
That being said, when this pronoun is used, it is assumed that the nouns that will be included in the sentence or premise will be addressed individually or independently. The word "each" would be followed by the verb "is" and not "are."
Just as an addition, the first sentence in the question is correct in its use of subject/verb agreement, as well as in the use of the comma. The latter is used in sentence A to separate two independent clauses.
The third sentence is also correct because it does not need commas (it cannot be divided into two independent clauses), and because the past tense (past perfect) employed there may not be the most widely used, but it is correct. The reason "had done" is correct is because you can still use it if the sentence reflects any of the following:
- a clarification that something took place as a cause of something else (in this case, the five somersaults)
- for reported speech
- for if/then sentences
The cause of the dizziness was the somersaults. If he had not done those he would have not become dizzy.