Hopes of lower interest rates and more oil off Canada helped fuel a strong rise in stock prices today.

The Dow Jones average of 30 industrial issues rose 10.92 to 785.92.

The dollar fell sharply against foreign currencies. It has benefited from high interest rates, which made investments in the American currency more attractive.

Oil stocks moved up sharply, aided by rumors that Mobil would announce results of new tests at the Hibernia Well off the coast of Newfoundland. Mobil said there were no plans for an announcement.

Some interest rates have come down sharply in the last several weeks. The rate on six-month Treasury bills has fallen from a high of 15.7 percent to 14.226 percent at this week's auction.

ylate in the day, a small New York bank, UMB Bank and Trust Co., lowered its prime lending rate to 19 3/4 percent from the record 20 percent charged by other banks. The Dow industrial average moved up more than 4 points in the last half-hour of trading following the UMB statement.

Among oils, Mobil climbed 6 to 70 1/2, Standard of California was up 1/2 to 67, Standard of Indiana rose 5 3/4 to 98 3/4, and Exxon was up 2 1/2 to 57 1/2. On the American Stock Exchange, Gulf Canada moved up 14 1/2 to 129 1/2.

The Dow Jones utility average was up 1.72 to 103.99. American Telephone & Telegraph led the NYSE active list and was up 1/2 to 49 3/8.

Volume on the Big Board was a moderate 33.02 million shares, up from 31.70 million the previous day.

The NYSE's composite common stock index rose 1.03 to 58.41 while the Amex market value index rose 7.10 to 244.10.

In the over-the-counter market, the NASDAQ composite index was up 1.57 to 136.04.