You use someone in affirmative clauses and anyone in negative and interrogative clauses. This is a question, so you should use anyone. See this link for more information.
When you ask this question, you are expecting each person to consider their own situation, rather than have somebody answering on behalf of the whole group. So, rather than saying "Does some of you..", you ask "Does anyone...".
Does anyone know the full name of our chemistry teacher?
Note that some is plural, so your question b should have been "Do some of you.."