Profits of General Motors Corp. fell sharply in the fourth quarter last year as car and truck sales declined by 416,000 vehicles, the world's largest automobile manufacturer announced yesterday.

Largely because of an even weaker July-September quarter and the decline in fourth-quarter business. GM's earnings also declined for the full year while the company's profit margin (earnings as a percentage of sales) dipped to 4.4 percent from 5.5 percent the previous year and 6.1 percent in 1977.

Although GM Chairman Thomas Murphy and President Elliott Estes noted that their business had operated with a profit margin of 10.3 percent back in 1965, unit sales last year were the third best in the company's history and total profits were the fourth highest on record.

In a statement, they blamed "a less favorable" mix of vehicles produced at GM factories, which translates into a larger volume of lower-profit cars or trucks. In addition, "competitive factors which continued to limit our ability to recover cost increases in product prices" were cited.

GM directors approved a regular dividend of $1.15 a share on common stock, unchanged from the three previous quarters but up from $1 a share at this time last year. Total dividends by GM on common shares fell to $5.30 a share last year from $6 in 1978 but actually represented a higher percentage of net income (53 percent) than in 1978 (49 percent). The latest payout will be distributed March 10 to owners of record Feb. 14.

In the fourth quarter, GM's profits declined 58 percent to $426 million ($1.46 a share) from $1 billion ($3.51) as sales dipped to $16.1 billion from $17.7 billion.

For the year, profits were $2.9 billion ($10.04 a share), down 18 percent from the record $3.5 billion ($12.24) in 1978. Revenues rose only $3 billion to $66.3 billion, as GM lost its ranking as top corporate industrial giant in the country to Exxon Corp., with sales of $84.4 billion in 1979.

GM's earnings as a percentage of stockholders' investment fell to 15.1 percent from 20 percent in 1978.

Worldwide factory sales of GM cars and trucks totaled 8.99 million units, down 5 percent from the 9.48 million record of the previous year, U.S. operations accounted for 79 percent of 1979 profits compared with 87 percent a year earlier.

In an effort to boost sales now, with a large inventory to unsold vehicles still parked around the country, GM has started a selective $500-a-vehicle consumer rebate offer designed to unload big cars and vans. GM, which has criticized use of such promotional efforts in the past, thus joins the troubled Chrysler Corp. in a new sales drive. Chrysler has offered unprecedented money-back guarantees.

The rebates will apply until March 10 to about 50,000 V-8 and six-cylinder Chevrolet Impalas and Caprice Classics, Pontiac Catalinas and Bonnevilles, Oldsmobile, Delta 88s, Buck LeSabres and some 25,000 Chevy vans.

Other corporate earnings statements yesterday, compiled from news dispatches:

United Technologies Corp. said net income rose 39 percent last year to a record $325.6 million ($6.49 a share) from $234.1 million ($5.45) in 1978 as sales increased 45 percent to $9.1 billion.

Earnings for the fourth quarter totaled $89.1 million ($1.64), up 44 percent from $62 million ($1.34) for the same period in 1978. Sales for the last quarter of 1979 increased 75 percent to $2.98 billion.

Boeing Co. reported sales for 1979 soared to $8.13 billion from $5.5 billion and declared a three-for-two stock split. T. A. Wilson, board chairman, said that, based on current programs and schedules, 1980 sales should be in the range of $9.5 billion.

Earnings of Boeing were $505.4 million ($7.88 a share) compared with $322.9 million ($5.04) in 1978.

Wilson also announced the board increased the quarterly dividend to 45 cents per share from 35 cents per share, payable March 10.

Time Inc. reported that net income for the fourth quarter of 1979 rose 16.3 percent to $43.13 million ($1.54 a share) from $37.09 million ($1.51) in the comparable period of 1978. Revenues rose to $716.96 million from $541.97 million.

The nation's largest magazine publisher reported a 20.9 percent increase in earnings for the full year to $143.92 million ($5.15 a share) from $119.02 million ($5.31) in 1978. Revenues rose 47 percent of $2.50 billion.In 1978, an extraordinary gain of $6.72 million (30 cents a share) from the sale of timberland made final net earnings equal to $125.7 million.