What was going on when I was born?

Expectations of lower interest rates helped push stocks strongly ahead yesterday with both prices and volume reaching their best levels of the new year. The Dow Jones industrial average, lost some ground in late trading but still ended the day 11.04 points higher, at 1,202.74. It had been up nearly 14 points in the early afternoon. Advances on the New York Stock Exchange outnumbered declines by 1,075 to 519.

The Air Force announced today that the General Electric Company would continue to produce the majority of its combat jet aircraft engines in 1986. But in a move that marked a significant recovery for G.E.'s main competitor, the Air Force awarded 46 percent of next year's engine production work to the Connecticut-based Pratt & Whitney division of the United Technologies Corporation. A year ago, the Pentagon concluded what had become known as the ''Great Engine War'' by awarding G.E. 75 percent of the engine production for F-15 and F-16 warplanes in 1985. Pratt & Whitney, which had dominated the industry for decades and had never had to share an award with a competitor, received only 25 percent of the work. The split award in favor of G.E. was seen as an attempt to invigorate competition and hold down costs. The Air Force saw potential savings of $3 billion over the engines' life cycles of about 20 years.

An investment group yesterday said that it had acquired a stake in the Petro-Lewis Corporation, the beleaguered oil and gas production company, and was ''exploring several options,'' including seeking to take it over. In a disclosure statement with the Securities and Exchange Commission, the investor group, Jakobson, Kass Partners of New York, said that it owned 1,367,100 shares of Petro- Lewis common stock. The stake represents 6.3 percent of the Denver- based company's outstanding common shares.

A report in the Finance Briefs column of Business Day yesterday misnamed the company that affirmed the senior debt rating of the Montana Power Company. It was Standard & Poor's.

A blast of Arctic air plunged the temperature in the New York area to the winter's lowest levels, bringing complaints from thousands of residents without heat, stalling commuters whose cars would not start and sending record numbers of homeless men and women to shelters. New York City filled all 863 of its beds for homeless women Tuesday night and was adding emergency beds yesterday to make room for more homeless women last night, according to a spokesman for the city's Human Resources Administration, Jack Deacy. ''We are at record numbers, there's no doubt,'' Mr. Deacy said. ''We do expect with this cold wave continuing that they will go up.''

President Reagan is expected to nominate Energy Secretary Donald P. Hodel as Secretary of the Interior and to consider merging the Energy and Interior Departments, White House officials said today. The officials, who discussed the proposed changes on condition that they not be identified, said Mr. Hodel's selection was assured whether or not Mr. Reagan decided to recommend the merger to Congress. They said the President had yet to consider the merger plan, which they acknowledged could face an uphill battle in Congress. Mr. Reagan pledged in the 1980 campaign to abolish the Energy Department to streamline the Federal Government. He Would Replace Clark Mr. Hodel, 49 years old, was Under Secretary of the Interior when James G. Watt was Secretary, and he later became Energy Secretary. Mr. Hodel would replace William P. Clark, a longtime Reagan confidant, who notified the President last week that he would return to California in several months.

The teen-ager whose spine was severed when Bernhard Hugo Goetz shot him on a subway train last month stopped breathing briefly yesterday, but was revived and placed on a respirator, a spokesman for St. Vincent's Hospital and Medical Center said. The youth, Darrel Cabey, 19 years old, slipped into a coma early yesterday morning and was placed on the critical list, according to the director of public relations for the hospital, Dan Sorrenti. Mr. Cabey is paralyzed from the waist down and contracted pneumonia late last week. Mr, Goetz appeared yesterday in Criminal Court in Manhattan at a hearing in which the prosecutor sought and won a week's postponement in the case. Mr. Goetz has said that he shot Mr. Cabey and three other youths on an IRT train last Dec. 22. He said they were trying to rob him.

Only four years ago, New York's financial potpourri had only one Arab ingredient: the UBAF Arab American Bank. Today there are more than 20 Arab banks in New York, beneficiaries of liberalized banking laws and of their own vision of this city as their new frontier. No one is entirely sure what they are all doing here, or if they will all survive. In fact, some are finding it exceedingly difficult to get much business in the highly competitive New York market. ''I actually tried to get an account from the P.L.O. mission here,'' said one Arab banker who asked not to be named, referring to the Palestine Liberation Organization. ''But they said they were very happy at Chemical,'' the only bank with an office at the United Nations.

IT has been said that great rooms begin with great custom-made upholstered furniture. To make great rooms, when fireplaces must be flanked and nooks must be filled, decorators have long relied on two basic chair shapes, the Lawson and the Bridgewater. The Lawson chair is the little black dress of the upholsterer: comfortable and safe. A squared-off club chair with a loose cushion, the Lawson has appealed to decorators and conservative clients for half a century.

As glass, brick, mortar and dust littered West 44th Street, city officials tried yesterday to figure out why four buildings there were partly demolished in the dark. The buildings, at 143, 145, 147 and 149 West 44th Street were partly torn down well after 6 P.M. Monday, according to city officials, by workers who used unorthodox methods at a distinctly unorthodox time of day. The demolition forced the city to close the street, between the Avenue of the Americas and Broadway, causing traffic jams in Times Square, and left the block covered in dirt and rife with confusion. The buildings' owner of record, according to Charles M. Smith Jr., the city's Buildings Commissioner, is Margo Properties, a company controlled by Sol Goldman, one of the largest real-estate operators in the metropolitan area, where he is estimated to hold nearly 500 properties. The demolition contractor, Mr. Smith said, was Mitran Associates Inc., of 600 Smith Street in Brooklyn. Mr. Goldman could not be reached at his office yesterday.

Despite a solid gain in the number of people working, the national unemployment rate edged up slightly in December, to 7.1 percent from 7 percent, the Labor Department reported today. Gains in automobile and construction jobs, aided by unseasonably warm weather, helped create 340,000 new jobs in December, a stronger performance than most private analysts expected. The December report was also a fresh sign, analysts said, that the autumn lull in the economy was only a pause and did not portend a recession. ''I think it's comforting evidence that the slowdown is nothing more than that, and that the economy will show continuing growth,'' said Bernard Schoenfeld, vice president and economist for the Irving Trust Company.

''From the beginning of this nation's history New York has always been the place where people come to fulfill their dreams.'' - Governor Cuomo. (B5:3.)