Can police officers who suspect no wrongdoing randomly stop motorists to check drivers' licenses and vehicle registrations? When a prosecutor has a key witness hypnotized to jog his memory are the defendant's rights violated? Can a state pay unemployment compensation to strikers?

Can a man but not a woman be required to pay alimony? Can a state handicap women by giving civil-service preferences to veterans, regardless of comparative test scores? When a physician performing an abortion has good reason to believe the fetus "may be viable," can a state compel him to try to preserve its life?

When a cesarean section is being performed, can health officials bar the operating-room door to a husband who was invited in by his wife, her doctor and the hospital? Can a judge send a person to a mental hospital indefinitely - and possibly for life - without the need for such a commitment being proved beyond a reasonable doubt? Can a chiropractor's license be suspended for ads plugging drug-free "cures" - along with "Free Chicken"?

Such questions - variously profound, important, disturbing, provocative, tedious, funny, frivolous - illustrate the diversity of the cases percolating up from federal and state tribunals into Washington's marble catch basin of litigation: the Supreme Court of the United States.

There, promptly at 10 o'clock this morning - the traditional first Monday in October - Chief Justice Warren E. Burger and the eight associate justices will emerge from behind the maroon velvet drapes behind the bench to open the court's new term.

Moments later, Burger will release a list showing that the court, in a four-day closed conference last week, declined petitions for review of most of 982 cases - those that had accumulated mainly over the summer and were dispatched, 100 at a crack, to each justice wherever he was at the time.

The 982 cases were 36 fewer Chan the all-time record, which was set last year (in 1969, when Burger first presided over the opening of the court, the number was 696). By next summer's recess, the court will have disposed of an additional 3,000 or so cases while carrying over about 1,000 for a total caseload of about 5,000 (compared with, say, 2,000 30 years ago).

While throwing out the bulk of the cases without comment (the votes of at least four justices are required for review), the court probably will hear argument in about 175, including 5 that were accepted in the 1977 term and that will be heard starting today.

Most of the estimated 175 cases will be decided with full opinions. In addition, well over 100 cases will be decided without oral argument, if past records are a reliable guide.

Public interest in the new term in far below the level of a year ago, when the court was poised to hear argument in the case of Allan Bakke, the white turned away by a medical school that had set aside 16 of 100 slots for racial minorities.

In terms of major impacts on large numbers of people, however, at least one new case could turn out to be more important than Bakke. Indeed, it is in some ways an offshoot of the court's 5-to-4 Bakke decision, which upheld race-sensitive affirmative action by state universities while striking down the particular plan at the University of California Medical School at Davis and ordering the school to admit Bakke.

The new case arose in Gramercy. La. where Brian F. Weber and other whites, because of a quota for blacks agreed to by the Kaiser Aluminum and Chemical Corp. and the United Steelworkers of America, were denied admission to an in-plant training program for skilled crafts.

In a lawsuit, Weber charged that the program violated Title VII of the Civil Rights Act of 1964, because it was voluntary affirmative action that had not been shown to have been adopted to remedy past discrimination at the plant.

The 5th U.S. Circuit Court of Appeals agreed. Its ruling, so long as it stands, bars similar voluntary affirmative action programs in the states in its jurisdiction (Alabama, Florida, Georgia, Louisiana, Mississppi and Texas) and chills them elsewhere. All told, millions of workers could be affected.

Now the Supreme Court must decide whether to let the ruling remain in effect, nullify it and send it back to the court below (to put flesh on a bare-bones record, as urged by the federal government), or review it, as urged by the union. The company also recommends review, but is amenable to a remand.

In a related case involving Los Angeles County firefighters, the court agreed last spring to rule whether a judge can order an employer to use a hiring quota for blacks and Hispanics until their percentage among employes is the same as in the local population, even though there's no proof that the employer had intended to discriminate against minorities.

Obviously, it's impossible for a current survey to take into account the approximately 3,000 cases yet to be filed and considered by the junctions over the next nine months. Here, however are some of the questions comfronting the court, including these at the outset of this story. As anterisk denotes a case that has already been accepted for argument. After each question in the answer of the court below. DUE PROCESS

When police officers have no reson to suspect any improper activity, can they stop motorists at random to check operator's permits and vehicle registrations? Below: no.

When a prosecutor arranged for the hypnosis of a key identification witness, did he violate the defendant's rights? Below: no.

If a physician performing an abortion has sufficient reason to believe that the fetus may live outside the womb, even if with artifical aid, can he be required by the state to try to save its life? Below: no.

When a state hasn't proved beyond a reasonable doubt that an indefinite and possibly lifetime commitment to a mental hospital is nessary, can it order one? Below: yes.

Was it permissible for a 38-months delay to separate the government's seizure of eight canisters of bull semen from its filing of a complaint alleging smuggling? Below: yes.

If a mentally ill or retarded juvenile hasn't been given an opportunity for an adversary hearing, can his parents admit him to a state institution for custody and treatment? Below: no.

If a motorist isn't allowed to have a prior hearing, can his operator's permit be suspended for refusing to take a test designed to determine if he was drunk. Below: no.

In a federal criminal case, can the judge suppress otherwise admisible evidence because the government fails to comply fully with a federal regulation that neither the Constitution nor the law requires? Below: yes.

Is an independent public authority immune from a lawsuit attacking its blanket refusal to hire any former heroin addict who has successfully completed a methadone maintenance program? Below: no.

In a state that automatically exempts women, solely because of their sex, from trial juries if they elect not to serve, was a murder defendant constitutionally convicted by a jury composed of 12 men? Below: yes.

When an under-18 female is capable of giving "informed consent" to an abortion, can a state require her physician to obtain parental or judicial consent to perform one, unless she is married, widowed or divorced? Below: no.

Can victims of an alleged violation of federal law (opening, reading and copying of their mail) file individual suits for money damages against present and former government officials (including former CIA directors William E. Colby and Richard M. Helms) in a U.S. District Court anywhere in the nation? Below: Yes EQUAL PROTECTION OF THE LAWS

Can a state allow alimony to be awarded only to women? Below: yes.

Can a state give civil-service proferences to veterans - mostly man with test scores inferior to woman rivals? Below: No.

Can diplomats be forced to retire at 60 when Civil Service employes don't have to retire until they're 70? Below: No.

Can a private citizen - here, a woman denied admission to a medical school - sue to enforce the law prohibiting sex discrimination by educational institutions receiving federal funds? Below: No.

Can a state imprison a defendant who, as a condition of probation, agrees to a fine but then, because of poverty, can't pay it? Below: Yes.

Can a state exempt publicly financed libraries, museums and schools from obscenity laws? Below: Yes. FREEDOM OF SPEECH

Can a state suspend the license of a chiropractor for advertising drug-free "cures" along with "Free Chicken / Free Refreshments / Free Spinal X-Ray"? Below: Yes.

Is a public employe who is protected when "blowing the whistle" in public also protected when blowing it in private to a superior? Below: No.

Can the Federal Communications require cable-television systems to provide, on unused channels, access to the public, educational authorities, local governments and paying lessors? Below: No. FREEDOM OF RELIGION

Does the National Labor Relations Board have jurisdiction over teachers of religious and secular subjects in Roman Catholic secondary schools? Below: No.

Is the General Council on Finance and Administration, said by a trial judge to control the purse strings of the United Methodist Church, immunized from being a co-defendant in a $366 million lawsuit arising from the financial failure of a California not-for-profit corporation that operates 14 care facilities for the aged? Below: No. FREEDOM OF THE PRESS

"Can a public figure compel journalists he is suing for libel to disclose how they formulated judgments on what to air (or print) and what to omit? Below: no. FAIR TRIAL

Did a state deny a fair trial to a defendant who, accused of an offense for which he could have been (but wasn't) imprisoned, came before a judge without counsel, went to trial at once because he misunderstood a question, and, without seeing a copy of the complaint, was convicted and fined? Below: no.

In a federal criminal case, was a defendant denied a fair trial when he was convicted by a jury 11 of whose members, after holding out two days for acquitted, yielded to the 12th jurer - a woman admittedly infatuated with the prosecutor? Below: no.

Can a defendant be convicted by a 5-to-1 vote of a six-person jury? Below: yes.

FREE PRESS/FAIR TRIAL

"Can a pretrial criminal preceeding be closed to press and public on the basis of an untested defense claim that the proceeding would expess penalty prejudicial evidence? Below: you. PRIVACY

When a woman undergoing a cesarean section, her doctor and the hospital welcome her husband to the operating room, can health authorities for him? Below: you. HOUSING

"Can homeowner and manicipolitics see real-estate firms for "steering" prospective home buyers on the basis of race? Below: yes.

Can a state suspended the license of a real estate saleman for alleged "steering"? Below: yes. "MIRANDA" RIGHTS"

*Can an intoxicated suspect "knowingly and intelligently" waive his right not to incriminate himself? Below: no. PENSIONS

*Do the anti-fraud provisions of the securities laws apply to pension plans that employers pay for and that enroll employes - millions of them - automatically? Below: yes. SAFETY AND HEALTH

Is residential aluminum electrical wiring subject to regulation by the Consumer Product Safety Commission? Below: yes.

Can the Labor Department prohibit retaliation against workers who reject particular assignments in the reasonable belief that they present an immediate danger to life or limb?Below: no.

Can the Food and Drug Administration require on all packaged cosmetics labels that list the ingredients? Below: yes. FREEDOM OF INFORMATION

*When a federal contractor supplies the government with data claimed to be confidential and exempt from mandatory disclosure under the Freedom of Information Act, can a government agency disclose the materials? Below: yes. FREEDOM OF INFORMATION

*When a federal contractor supplies the government with data claimed to be confidential and exempt from mandatory disclosure under the Freedom of Information Act, can a government agency disclose the materials? Below: yes. UNEMPLOYMENT "COMP"

*Can a state pay unemployment compensation benefits - which employers finance - to strikers? Below: yes.

Can a state that denies such benefits to strikers pay them to locked-out employes?Below: yes.

A story on business-related cases before the Supreme Court appears on page 00000.