The Supreme Court heard arguments yesterday in the much-publicized Bakke case about whether a state university can take race into account in an admissions program in order to try to overcome the effects of past racial discrimination in American society.

The arguments centered on Allan P. Bakke, whose applications for admission to the University of California Medical School at Davis were rejected in 1973 and again in 1974. A lower court ruled 13 months ago that the school turned him away solely because he is white and thereby violated the Constitution.

For the university, Archibald Cox pleaded for a flat-out reversal of the lower court ruling. He said the school's special admissions program, which reserved 16 of 100 places mainly for blacks, Hispanics, and Asian-Americans, obeyed the command of the 14th Amendment that no state shall deny any person the equal protection of the laws.

For the United States, Solicitor General Wade H. McCree Jr. argued that race may be a factor in a state university admissions program seeking to remedy past societal discrimination. But he urged that the case be sent back to the California Supreme Court for reconsideration of its order that the school admit Bakke, now 37.

For Bakke, Reynold H. Colvin urged unqualified affirmance of the lower court ruling. He said that an admissions program designed to benefit disadvantaged persons complies with civil rights laws as well as the Constitution only so long as race isn't a factor.

The arguments lasted two hours, elicited dozens of questions from the nine justices and ended at high noon. The spectator seats were filled. Extra chairs were added for the press. Security was unusually tight.

Such factors aside, little in the demeanor or lawyer-like probing of the justices, in the arguments of counsel, or in the hused, controlled atmosphere suggested that the case has aroused more public interest than any since the Brown v. Board of Education school desegregation case of 1954.

The justices will decide the Bakke case by the end of the term in late June or early July. As usual, they made it their business to give no reliable clues to their thinking, or even to indicate if they share the common view - evidenced by demosstrators outside - that the case may have cosmic implications for affirmative-action programs of all kinds.

Much of the questioning focused on whether the school had established quotas by setting aside 16 places for minority applicants. In the two years in which Bakke applied, all of the 245 whites who applied to the special admissions program, were rejected.

In replies to Justices Potter Stewart and John Paul Stevens, Cox said he regarded neither the 16 minority seats nor the 84 in the regular program as a quota. ". . . this was not pointing the finger at a group which had been marked as inferior in any sense," Cox said. ". . . it was not stigmatizing in the sense of the old quota against Jews was stigmatizing, in any way."

Justice Lewis F. Powell Jr. wondered, "Does it really matter what we call this program?" Cox thought not, because nothing about the program warrants labeling it a quota if that is "a bad word."

Justice William H. Rehnquist inquired whether there would be more constitutional infirmity in a set-aside of 50 rather than 16 places, so long as that would be needed to overcome past discrimination.

Cox said that increasing the numbers increases the possible infirmity. But he said such a set-aside should not be condemned so long as it reasonably relates to a proper goal. He said later that a comparison may be drawn to public program that train only Indians to work with other Indians.

A few minutes before Chief Justice Warren E. Burger took the case under advisement, Cox raised a question of his own: "Is there something about the use of the number 16 that renders this program peculiarly vulnerable?"

The method used to put a racially sensitive policy into practice does not attain "constitutional dimension" when someone reduces it to a number, Cox said.

He warned against using the number as a basis for sending the case back as urged by Solicitor General McCree, saying it would convert lower federal courts "into being the supervisors of the admissions policies of certainly state and perhaps rpivate institutions."

Questions about quotas also were asked of Colvin. Bakke's lawyer, who plainly taxed Justice Powell's patience by spending 20 minutes on facts without making constitutional arguments.

Colvin replied that he had "the deepest difficulty" in dealing with the question of numbers. What's appropriate? he asked rhetorically. Eight? 16? 32? 64? 100? Would the court be satisfied to let the school decide?

Justice Thurgood Marshall asked if his argument would "be the same if one, instead of 16 seats, were left open."

"Yes," Colvin replied. "Numbers are unimportant. It is the principle of keeping a man out because of his race that is important."

Justice Marshall responded. "You are arguing about keeping somebody out and the other side is arguing about getting somebody in."

"That's right," Colvin said.

Chief Justice Burger approached the validity of the special admissions program with a series of questions concerning Asian-Americans. In 1973 and 1974, the school admitted a total of 17 applicants in this category into its regular program and five more into the special program. The comparable figures for blacks were zero and 12, and for Hispanics six and 15. The school admitted an Indian to the regular program in 1974.

In questions to Cox and McCree, the Chief Justice poted without contradiction that the record contains no specific finding that Asian-Americans as a group have been disadvantaged, or that there isn't a far larger proportion of them than blacks and Hispanics in the professions.

McCree, answering a question by Justice Rehnquist, emphasized that he believes the record to be deficient partly because it "makes it difficult, if not impossible, to determine the extent of . . . the continuing impact of racial discrimination upon that segment of our society." That segment "isn't monolithic," consisting of Chinese, Japanese, Korean, Philippine, Cambodian and other persons, he said.

Colvin opened and closed his argument by emphasizing that he is Allan Bakke's lawyer, and that his purpose is to get his client into medical school.

In a reply to a question by Justice Byron R. White, he said, however, that the factor of race "was permissible to the extent that it gave some clue to the admissions committee," meaining that it "ought to consider" whether an applicant has "a prior history of economic, educational, or whatever, deprivation, persecution, or whatever it may be."

Cox contended that the alternatives to the special admissions program suggested by the lower court - building more medical schools, better recruitment, setting crieria for he "disadvantages," avoidance of the word "race" - "simply won't work."

The California Supreme Court invalidated the special program on constitutional grounds. But Justice William J. Brennan Jr. raised the possiblity that a federal civil rights law reflecting the 14th Amendment, which had figured strongly in the case earlier, might come into the justices' deliberations and conclusions.