hile rising unemployment darkened the holiday season in other parts of the country, figures released this sunny day in Ronald Reagan's southern California homeland show his election has helped keep many businesses here booming.

Seasonally unadjusted U.S. Labor Department statistics show unemployment dropped from 7.5 percent in October to 6.8 percent in November in Los Angeles County, down from 8.1 percent last October.

Even with adjustments, bankers and economists said southern California's economy remains unusually strong because of its diversity and the recent surge of defense contracts. "It's Reagan. It's a basic build-up in defense," said an executive at the Northrop Corp., explaining his company's active hiring here.

Aerospace and technology firms are so short of qualified engineers in this area that they have resorted to radio advertising extolling the challenges of the space age that can open to anyone who knocks on their doors.

Last month, shortly after President Reagan announced plans to go ahead with the B1 bomber, Rockwell International, the principal contractor for the aircraft, processed 3,400 applications in a single morning from job-seekers who formed a line blocks long outside its offices here.

A Bank of America study predicts California will receive $19.6 billion in defense contracts in 1982, a 20 percent increase over this year. About $10 billion of that will be from the MX missile project, which has been enthusiastically supported by Reagan and recently passed a number of congressional hurdles.

Fred Brenner, regional administrator of California's employment development department here, said that the latest Los Angeles employment figures are somewhat inflated by Christmas hiring and that much of the unemployment drop since last year may be the result of large numbers of frustrated job-seekers stopping their search for work.

But in general, he added, the employment situation here remains better than the nation's as a whole "because of the diversity of industry in Los Angeles. We have banking, we have services, we have aerospace," which pick up the slack when a major industry like housing slumps as it is doing now.

The boom extends to other Sun Belt states such as Oklahoma and Texas, where demand for oil and gas have made their economies virtually recession-proof for the time being. The unemployment rate in Texas increased slightly in November but still remained three percentage points below the national average. In October unemployment was only 3.9 percent in Houston and 4.2 percent in Dallas-Fort Worth.

Bernard L. Weinstein, an economist at the University of Texas at Dallas, noted that dependence on some depressed manufacturing businesses and continued high immigration into the state had been a problem, "but Texas and Oklahoma will ride out the recession pretty well."

Random interviews with job-seekers checking work notices and collecting unemployment checks at a state office in Culver City indicated some hardship caused by layoffs in certain industries, but most said they had not been out of work long enough to exhaust their savings or were being supported by spouses or friends.

Asked what she thought of Reagan's economic program, recently fired office worker Barbara Kessler, 49, said "part of me says he has the right idea, but I don't know if he's going about it right. He's not giving people a chance to glide in to some of these changes." Kessler said she waited almost three weeks to even bother to file for unemployment and now thinks she has a good chance at a career in sales working on her own.