Your relative clause is
who/whom the committee believes is best qualified for the position.
You rewrite the relative clause putting a blank (_____) in where the relative pronoun goes:
the committee believes ______ is best qualified for the position.
You substitute the relative clause into the blank: either who or whom. If you are unsure which one is correct, then substitute either she or her. If she is correct use who; if her is correct, use whom.
(The correct answer here is who, since she and not her is correct.)
Note I've written this "easy and quick" answer because the original poster still did not know the answer after looking at the possible duplicated question(s), which, by the way, contain a morass of information– much of it confusing and some of it bad.