If the president doesn't want to deal with a bill and lets it sit for ten days while congress is in session, the bill: is sent back to congress is dead automatically becomes law is sent to the supreme court for judicial review

The correct answer is 'automatically becomes law'. This is known as a 'pocket veto'. The Constitution states that if Congress is in session and a President doesn't return a bill within 10 days, the bill automatically becomes law as if the President had signed their approval of it.