The Supreme Court, adding to a list of church-state cases on its docket, yesterday agreed to hear the appeal of a blind student denied state financial aid because he was studying to be a minister.

The Washington state Supreme Court ruled in October that the "principal or primary effect of the aid . . . would be to advance religion and would thus violate the establishment clause of the First Amendment."

The case, to be argued in the next term, asks the U.S. high court again to balance the constitutional prohibition against aiding religion with the prohibition against restricting religious expression and belief.

In other action yesterday, the court:

* Without comment, left standing a lower court ruling that Texas A&M University improperly denied campus recognition to a homosexual students' group.

* Agreed to hear appeals by Japanese television manufacturers about alleged dumping of underpriced sets in the United States.

* Declined to hear an appeal involving a ban by North Carolina State University on religious solicitations in campus dormitories.

The court also issued signed opinions in two cases, both written by Justice Thurgood Marshall.

But in two other cases, the court, again showing the effect of Justice Lewis F. Powell Jr.'s 10-week absence, issued 4-to-4 votes.

Such ties automatically mean that lower court rulings in a car-search case (Oklahoma v. Castleberry) and a criminal-extradition case (Ramirez v. Indiana) will stand but have no effect beyond those states.

Yesterday's action brings the number of tie cases this year to seven, the most in 45 years.

Powell, who underwent prostate surgery in early January, missed hearing arguments in 56 cases in January, February and the first half of March.

Seventeen of them have been acted upon, with seven dismissed on ties and six decided without Powell's participation.

Four others, including a case yesterday, have been ordered reargued this year, presumably because the court was evenly divided and wanted Powell's vote. No records on rearguments were available yesterday, but knowledgeable observers said it is highly unusual for the court to order reargument in so many cases without at least asking new questions.

The case, City of Cleburne v. Cleburne Living Center, tests the legal standard that governments must meet in order to justify laws that in effect discriminate against the mentally retarded.

Over the years, the high court has established tests for determining the constitutionality of laws affecting the rights of aliens, racial and religious minorities and other groups.

In those cases, the court decided that governments must show varying types of special justifications for passing certain laws. The question presented by the case to be reargued is whether retarded persons as a group are entitled to some form of enhanced judicial protection.

In the blind student's case, the state of Washington's Commission for the Blind denied vocational rehabilitation funding in 1980 to Larry Witters, who wanted to study for the ministry.

The state Supreme Court upheld the decision, saying aid to him would violate the First Amendment's prohibition against establishment of religion by the state.

Witters appealed, saying denial of funds violated his right to practice religion freely and to equal protection of the law.

Witters noted that programs such as the GI Bill provide funding for students attending theological seminaries and said the state court incorrectly concluded that aiding Witters' studies would have the "primary effect" of advancing religion.

"The primary effect" of the aid, Witters argued, was to "train him for suitable employment consistent with his medical condition . . . . There is no question that the primary effect of the program is to aid blind people in finding and holding employment." The case is Witters v. Washington Commission for the Blind.

In Texas A&M v. Gay Student Services, the 5th U.S. Circuit Court of Appeals said last year that the school violated the First Amendment in withholding recognition of the group based on the "homosexual content" of the group's ideas.

The group said it wanted to provide a forum for speakers and discussion of issues involving homosexuality and to provide information about homosexuals to the general public. The group, which has been meeting off-campus, claims membership of between 30 and 70 students in a campus of about 35,000 students.

Campus recognition would entitle the group to use meeting space on campus and to have access to some campus facilities.

In one of the two signed opinions issued yesterday, the court, siding with the Justice Department, upheld the conviction of James Rual Miller, who was indicted on multiple counts of fraud but convicted only of lying to his insurer about the value of his loss from a burglary.

Miller argued that the Fifth Amendment right to a grand jury does not allow such sweeping indictments that result in conviction on a lesser charge.

Marshall, writing for a unanimous eight-member court, disagreed, saying the indictment clearly set out the offense for which Miller was convicted. Powell did not participate in the case, U.S. v. Miller.

In the second case, with Powell participating and dissenting, Marshall wrote for a five-member majority in upholding forfeiture of unpatented mining claims if patent holders do not comply with annual filing requirements. The case is U.S. v. Locke.