Financial General Bankshares Inc., the large District-based bank holding compnay, yesterday reported the best single quarter in the company's history, a 9 percent profits junp over the first quarter last year.

The company reported 1981 first-quarter profits of $4.9 million (67 cents a share), compared with profits of $4.51 million (62 cents) for the 1980 first quarter. Financial General said that without an after-tax gain on the sale of an investment during the first quarter last year, the profits rise would have been 20 percent.

The bank company said the gain was primarily the result of 16 percent growth in net interest income. Assets rose to $2.47 billion at the end of the quarter, compared with $2.26 billion at the end of the same quarter last year. Toal deposits rose to $2.1 billion, compared with $1.94 billion last year.

First American Bank of Virginia reported record earnings of $9.1 million ($5.39) for 1980 compared with earnings of $8.2 million ($4.89) in 1979.

First American President and Chief Executive Officer Milton L. Drewer Jr. told shareholders that substantial gains in assets, overall growth in deposits and loans and growth in commerical and personal banking programs had helped offset the problems of inflation and high interest rates.

The bank's assets at year's end were more than $888 million.

First-quarter earnings in 1981 were $3 million. Return on assets was 1.38 percent, compared with a 1.11 percent return for the first quarter in 1980. Earnings per share were $1.81, up 50 cents from the first quarter of 1980.

First Maryland Bancorp, whose principal subsidiary is the First National Bank of Maryland, reported earnings before securities transactions for the first quarter of 1981 of $5.265 million ($1.16), compared with $4.921 million ($1.05) for the same quarter last year.

As of March 31, 1981, the bank holding company had assets of $2.396 billion.

Dominion Bankshares reported income before securities transactions for the first quarter of 1981 of $5.92 million (72 cents), compared with $5.93 million (73 cents) in the first quarter of 1980.

As of March 31, 1981, the corporation's total assets were $2.5 billion. Deposits were $2 billion, with most of the increase concentrated in money market certificates of deposit and interest checking deposits. Net loans were $1.4 billion as of March 31, compared with $156.5 million a year before.

Pargas Inc. reported that the company's first-quarter profits rose sharply to $5.4 million ($1.53 a share), compared with $4.7 million ($1.32) for the same period last year. Sales increased to $83.3 million for the quarter, up from $74.6 million reported for the first quarter of 1980.