The Federal Home Loan Mortgage Corp. reported a 39 percent increase in profits for its fourth quarter, earning $71.6 million, compared with the $51.4 million the company earned during the same quarter last year.

For the year, earnings totaled $267.4 million, up 67 percent over last year, when profits were $159.7 million. There is no earnings-per-share figure because the company's stock is held in trust by the Federal Home Loan Bank System.

Freddie Mac, as the company is widely known, buys residential mortgage loans to provide funds for lenders to make new loans. It then sells most of these loans.

The company's president, Kenneth J. Thygerson, attributed the record earnings for 1984 to the increase in the company's mortgage portfolio, including the firm's Guarantor program and mortgages purchased to back Collateralized Mortgage Obligations.

* General Physics Corp. said its fourth-quarter earnings dropped 5 percent to $864,000 (23 cents a share), compared with $912,000 (24 cents) during the same period last year.

The Columbia high-technology company, which provides training, operations, engineering and research services for the power and defense industries, reported a 35 percent increase in revenue to $12.7 million, compared with $9.4 million for the fourth quarter of 1983.

For the year, General Physics said its net income rose 8 percent to $2.95 million (79 cents) on revenue of $41.57 million, compared with $2.73 million (73 cents) on revenue of $35 million during 1983.

These results include a portion of the fourth-quarter 1984 revenue and net income of Taurio Corp., the Alexandria defense technical services firm that General Physics acquired in November.

The company's president, Robert W. Deutsch, said that the acquisition of Taurio positions General Physics to expand its defense business and he predicted that revenue from defense contracts should increase to about one-third of total revenue, which is more than double the 1984 share.

* Washington Homes Inc., a Waldorf firm that builds and sells single-family homes, reported that its second-quarter earnings rose 21 percent to $626,817 (34 cents), compared with $519,375 (28 cents) during the same quarter last year.

Sales for the firm rose to $13.7 million, compared with $12.3 million during the same period last year. For the first six months, Washington Homes said its earnings rose to $1.37 million (75 cents) on sales of $30.1 million, compared with $1.3 million (72 cents) on sales of $27.1 million for the same period in 1983.

The company said per-share figures for the second quarter and six-month periods last year were restated to reflect the higher number of shares outstanding as a result of a stock dividend issued on Jan. 18.

* PHH Group Inc., a management services and vehicle and aircraft leasing company, said that its net income for the third quarter rose to $10.6 million (67 cents) on revenue of $182.9 million, compared with $9.4 million (59 cents) on revenue of $126.2 million during the same period last year.

For the year, the Hunt Valley, Md., firm said its net income increased to $29.9 million ($1.88), compared with $26.8 million ($1.69) for 1983.

Revenue for the year increased to $487.1 million, compared with $391.4 million for the same period last year.

The company's chairman, Jerome W. Geckle, said the number of vehicles under management is 13 percent larger than a year ago.