Stanford University's general tuition will increase to $11,208 from $10,476 for graduate and undergraduate students, a 7% hike for 1986-87, the school's Board of Trustees announced. Tuition at Stanford's professional schools will rise between 6.8% in the School of Law and 9% in the School of Medicine and the Graduate School of Business. Law School tuition will go up to $11,508 from $10,776. The increase at the business school will be to $12,102 from $11,100, and medical students will pay $13,440, up from $12,330. Basic room and board will rise 6.4%, to $4,700 from $4,417, as the school anticipates construction of several hundred units of additional housing for graduate students. The university will continue its policy of need-based undergraduate admissions, meeting financial need through a combination of scholarships, grants, loans and jobs, officials said. More than 60% of all Stanford undergraduates now receive need-based aid.