Can a retirement plan make women pay more than men for equal pension benefits Does a teacher's admission that he's homosexual warrant his dismissal for "immorality" Can unemployment compensation be paid to night students but denied to day students?

Can police forcibly enter an office where a dentist is raping an unconscious patient Can a judge be sued for ordering the sterilization of a 15-year-old girl who'd been told she has having an appendectomy Can a Methodist church force the resignation of its organist/choir director for converting from the Methodist to the Anglican faith?

Can neighborhood on street parking be restricted to the people who live there Can a state bar sales of inexpensive life insurance to nonresidents Must work on a nearly finished $127.5 million dam be halted because completion would endanger a fish species called the snail darter?

Over the summer, the nine justices of the Supreme Court, at their vacation sites and hometown offices, regularly received mail bags full of cases that raised such questions under the Constitution and the laws.

Last week, in five day-long secret conferences presided over by Chief Justice Warren E. Burger, the justices sifted through a record list of 1.028 cases, mostly appeals and petitions for review of decisions by lower federal and state courts.

The disposition of an uncertain number of the cases will be disclosed shortly after 10 a.m. Monday, when the Supreme Court opens its nine month term with the crier. Alfred Wong, chanting the traditional "Oyez! Oyez! Oyez! All persons having business before the Honorable, the Supreme Court of the United States are admonished to draw near and give their attention, for the Court is now sitting. God save the United States and this Honorable Court."

The court probably has set a few of the 1.028 cases for oral argument: this requires the approval of at least four justices. But for a great many more cases the court almost certainly has decreed sudden death, meaning that, with no explanation by the justices, rulings by courts below will be left standing. For yet other cases, the justices, again inscrutably, doubtless have chosen to take no action for the time being.

Meanwhile, the inflow of cases continues unabated. By the end of the term in mid-1978, the court probably will have disposed of about 4,000 a large portion of which the justices quickly recognize as undeserving of serious notice.

Later Monday morning, the justices will listen to lawyers argue four of the 88 cases they have accepted during the first half of this year.

Most everyone has heard about one of these cases, because of continuing heavy press coverage, and because - depending on how it ultimately is decided - it could produce the most important court ruling since the school desegregation case of 1954.

The case in point is of course that of Allan Bakke, who challenged the constitutionality of the so-called "reverse discrimination" special-admissions program that reserved 16 of 100 slots for black, Hispanic and Asian-American applicants to the Medical School of the University of California at Davis.

Last year, the California Supreme Court ruled 6 to 1 that the special admissions program denied Bakke, who is white, the equal protection of the laws guaranteed by the 14th Amendment.

Fifty-eight friend-of-the-court briefs that attack or defend the ruling have been offered to the high court. Counsel for the university and for Bakke have an hour on Oct. 12 to argue and to answer the justices' questions.

The justices have yet to act on a government request for extra time to argue the hotly disputed assertion in its friend-of-the-court brief that the only question to be resolved is "whether a state university admissions program may take race into account to remedy the effects of societal discrimination."

Important as is the Bakke case the justices have to deal with a penoramic array of questions posed by the 87 other cases awaiting argument and decision, the 1.028 cases they took up in conference last week and the additional cases that may number around 3,000 by July.

Here are some of those questions, each with the answer given by a court below. An asterisk denotes a case the Supreme Court already has accepted for argument. HOMOSEXUALS

Does homosexuality constitute "immorality" for which a teacher may be fired? Below yes.

Do out-of-school activities in behalf of the "gay" cause permit school authorities to order 2 teacher to take a psychiatricesam? Below: Yes. SEX DISCRIMINATION

Can a retirement plan charge women more than men for identical pension benefits (or charge the same for lesser benefits)." Below: no.

Does a veterans' preference in state civil service hiring discriminate against women? Below: yes.

"Can a company that pays wages to employees disabled by non occupational illness or accident withhold them from employees disabled by normal pregnancies? Below: no.

Can an Indian tribe refuse to enroll children of mixed marriages because the parent who is a tribe member is female? Below: no. EQUAL PROTECTION

Can a state that pays unemployment compensation to night students deny to day student? Below: no.

Can a state (Virginia) provide financial tuition aid sufficient to educate affluent but not poor handicapped deny to day students? Below: no.

Can a felony conviction bar issuance but not retention of a license to drive a taxi? Below: no. PRIVACY

Was a search warrant needed by police who buttered down a door to catch a dentist raping a drugged patient Below: yes.

Does the Constitution forbid warrantless, surpirise safety and health inspections of business premises by government agencies? Below: yes.

*Can evidence from an illegal search be used in a federal prosecution for perjury committed after the search? Below: no. PERSONAL LIABILITY OF PUBLIC OFFICIALS

Does judicial immunity bar a damage suit against a judge for ordering the sterilization of a 15-year-old girl who was not consuled and was told her appendix was being removed? Below: no.

*Are federal officials absolutely immune from suits for damages based upon how they performed official enforcement duties? Below: no.

[TEXT OMITTED FROM SOURCE] munize federal legislators from damage suits based on unconstitutional conduct? Below: no.

Can citizens collect reasonable damages from public officials who violate their civil rights? Below: yes. FREEDOM OF RELIGION

Can a congregation force its organist to resign because he converts from its faith to another Fellow: yes.

Can a state grant scholarship and tuition aid to students at church-related colleges? Below: yes.

Can a school bar a student Bible study club's on-campus activities during school hours? Below: yes.

Can a state bar the election of a minister to the legislature Below: yes. FREEDOM OF SPEECH

Is a nonprofit group's lawyer denied free speech by judicial disciplining for "solicitation" of a client: telling a woman who accepted sterilization rather than lose Medicaid that she might sue? Below: no.

*Is a corporation's right to contribute money in an election campaign interior to a natural person's? Below: yes. ENVIRONMENTAL

Does the Endangered Species Act require stopping construction of a Tennessee Valley Authority dam that would destroy the only know habitat of the snail darter, a three-inch species of perch? Below: yes.

New York City implement the clean-air plan it helped to devise, even though its officials say the plan's drastic restrictions on the movement and parking of motor vehicles and freight deliveries, along with the tolls it would impose on 11 free bridges, would jeopardize Mahattan's existence as a commerical center? Below: yes. NUCLEAR POWER

Could victims of a possible reactor accident collect - for all deaths injuries and property damage - a grand total of no more than $560 million, the liability limit set by Congress as an incentive to the industry? Below: no.

*Did the Nuclear Regulatory Commission try to circumvent its own procedures under the National Environmental Policy Act to allow introduction of highly controversial technology to recover plutonium from other radioactive wastes and recycle it as reactor fuel? Below: yes. FREEDOM OF THE PRESS

*Can the press criminally prosecuted for carrying truthful information about a public official's performance of his duties? Below: yes.

Can an official who runs a public institution such as a jail deny the press greater access than the general public? Below: no.

Can a newspaper, as a defendant in a civil suit, be compelled to disclose confidential sources? Below: yes.

Can police who got a search warrant rather than a subpoena for specific items, rummage through newsroom desks and files in a hunt for photos of possible law violators? Below:

Can a judge seek to assure a fair trial of a public figure by ordering all participants to shun the press, suppressing names of veniremen, banning sketches or photos of jurors, and prohibiting interviews of witnesses? Below: yes. OTHER TOPICS

CONGRESS VS EXECUTIVE

Can Congress permit either the House or Senate to veto or modify authority delegated by law to the executive? Below: yes. RICHARD NIXON

*Can tapes of Nixon's White House conversations that were played at the Watergate cover-up trial of his top aides be copied for sale to the public? Below: yes.

Does the former President have a privilege of confidentiality that allows him to withhold tapes from litigants in a class action against other involved in mass arrests on the Capitol steps in 1971? Below: no. RESIDENTS VS NONRESIDENTS

Can a community restrict neighborhood street parking to residents? Below: no.

Can low-cost life policies be denied residents of a state other than the seller's.Below: yes.

*Can a state hunting license fee be 75 times higher for a resident than a nonresident? Below: yes. AGE DISCRIMINATION

Was it legal to ground, at age 52, a test pilot who was maneuvering F-4 Phantom jets at up to 1,400 miles per hour over populated areas? Below: yes. TAXATION

Was congressional consent needed by states that set up the Multistate Tax Compact, which prescribes uniform procedures for taxing multistate firms? Below: no. ANTITRUST/BUSINESS Can a state (Maryland) bar ownership of service stations by petroleum producers and refiners? Below: yes.

Can the Federal Communications Commission prohibit formation of any new daily newspaper/broadcast combination in a community while "grandfathering" about 90 per cent of the existing combinations? Below: no.

Does the National Society of Professional Engineers' comprehensive ban on competitive price bidding for engineering services violate the Sherman Act? Below: yes. JUDICIARY

Does a criminal trial with a five member jury satisfy the constitutional guarantee of a jury trial? Below: yes. PUNISHMENT

Does the constitutional-ban on cruel and unusual punishment permit police to use deadly force solely to arrest a fleeing suspect in a crime against property who has not engaged in violence? Below: yes. DUE PROCESS

Can a state - in advance of a hearing - suspend the driver's license of a drunk-driving suspect because he refuses to take a breath-analysis test? Below: no.

Can a state let parents voluntarily admit a child to mental hospital for an indefinite stay? Below: no. CIVIL RIGHTS

Can the government allow lawyers' fees for successful civil rights plain-tiffs but disallow them for successful defendants? Below: yes. UNIONS

Can unions threaten or inflict punishment on supervisor/members who cross strike picket lines? Below: yes said one court, no said another.