A wide-ranging D.C. government investigation of reports of cheating on a fire department promotion examination is focusing on allegations that some firemen may have been given test questions in advance and other firemen may have shared answers while taking the exam, knowledgeable sources said yesterday.

Also involved in the alleged irregularities, many of which have been made by the union representing city firefighters, are the actions of a highranking fire official and a federal civil servant, both of wom helped to prepare the examination.

Mayor Marion Barry, who has imposed a delay of up to one month on fire department promotions, said yesterday that he has ordered the probe because of "some circumstantial evidence" that resulted in unresolved "gray areas" in an earlier investigation by one of his special assistants.

The probe was prompted by several charges of irregularities that were made by the union representing the city's firefighters, and the fact that the scores from the test, which was given last June, are the highest recorded in several years, city officials said.

Barry said yesterday that a comparison done by his office had shown "some broad discrepancies" in the scores some individual firemen received in 1976 and the scores those same firemen received last June.

For example, according to sources familiar with the test results, the fireman who finished first last year -- scoring 98 out of a possible 100 -- was not among the top 50 in 1976, the last time the exam for promotion to sergeant was given.

The controversy over the examinations, the first public employe quarrel Barry has had to referee since becoming mayor Jan. 2, has been tinged with racial overtones in a city department long divided by racial tensions and rivalry.

In sharp contrast to previous years, the 12 highest scorers on the 1978 examination are black. The allegations of irregularities in the development and administration of the test have come largely from the union representing the firefighters, which is predominantly white.

Union officials insist they are not implying that the blacks had to cheat to finish on top, but representatives of the black firefighters sharply disagree.

Barry said yesterday he is aware of the racial connotations of the controversy and of his actions, which have angered some black city firemen. "My own view is that if it had been all white (firemen at the top), I'd have done the same thing,' Barry said.

The test, developed jointly by a panel of six high-ranking city fire officials and the then U.S. Civil Service Commission, was given June 17 to 285 privates in the fire department who were seeking promotion to sergeant.

On two other similar tests given that day -- those for promotion to lieutenant and to captain -- blacks were less concentrated in the upper ranks and no allegations of irregularities have been made concerning those tests.

The examination scores are the major determinants of the rank of firemen on lists for promotion to the higher-paying upper-level jobs in the department. Blacks, who make up about one-third of those on the city's firefighting force, have been traditionally concentrated in the lower posts.

The allegations of irregularities that have been turned over to Acting Inspector General David Legge, the city's chief auditor, include at least one matter dating back to the 1976 test, according to knowledgeable sources.

Investigators have been told that the top scorer in 1978 had previously told four of his superiors that in 1976, when his test results were much lower, several persons finished ahead of him because they had been provided questions before the examination.

Lt. Michael D'Amico said yesterday that he had talked with that fireman after the 1976 tests. "He said he had known people who had answers for that exam," D'Amico said. "He was a little upset that he had studied hard and these other fellas who did have the exam had come out ahead of him. There was no doubt in my mind that he was serious."

Sources said yesterday that the union, Local 36 of the International Association of Firefighters, has told investigators that four firemen who took the examination may have been given the test questions in advance.

The U.S. Office of Personnel Management (formerly the Civil Service Commission), has also been told, sources said, that during its administration of the examination, three firefighters were observed exchanging answers during a break in the fivehour test.

One investigator for the city has interviewed the three regarding the alleged exchange of information, but all refused to answer questions, a source said. "They basically took the Fifth (Amendment) on it," the source said.

Investigators indicated they have no hard evidence to support the charges that information about the test was given to some firefighters before the examination.

However, the union has charged that one of the six high-ranking officers who helped develop examination questions had advised some firemen that they need not study some subjects because they would not be included in the test.

The six officials met with a city investigator several weeks ago to discuss that charge. All denied it. Five of them volunteered to take a lie-detector test. The sixth refused. Lie-detector tests have not been given to any of them.

One other area under examination is the conduct of the GS-9 federal civil service test specialist who served as a technical expert for the six highranking fire officials in the preparation of the promotion examination.

As the panel's guide on how questions should be written, their applicability to job requirements and their conformity with federal law, this person was in a position to know in advance which questions would be on the multiple-choice exam and how they would be worded.

The civil servant, a woman, was once seen by a ranking city fireman attending a social function as the date of a fireman who had taken the examination in 1976 and finished among the top three on the list.

This has raised suspicions that the woman may have provided information to persons taking the examination last June.

The woman's supervisor said yesterday, however, that the woman did not participate in the development of the 1976 examination taken by her acquaintance. Nor, said the supervisor, did she meet the acquaintance until August 1978 -- two months after the latest promotional examination had been given.

At a press conference yesterday, Goldie C. Johnson, president of the predominantly black Metropolitan Police Wives Association, said she planned to protest the union's action next week at the District Building.

"As long as the white firemen were first on the list, nothing was said. But as soon as 16 out of 20 are black, they want to say they cheated," Johnson said later.

"They want to say blacks are not smart enough," Johnson said. She criticized Barry for delaying the promotions, the first of which were to have occurred Sunday.