DETROIT, MAY 25 -- During a stormy annual meeting, General Motors Corp. stockholders today overwhelmingly approved a plan to substantially increase executive pensions and to nearly double the one that outgoing Chairman Roger B. Smith will get to $1.2 million a year.

The proposal to raise pensions for about 3,350 GM executives was approved by 83.3 percent of stockholder votes.

Smith, attending his 10th and final annual meeting, retires Aug. 1 but will remain on GM's board of directors. GM President Robert C. Stempel will take over as head of the giant automaker.

''We think Roger Smith could eke out a retirement at $749,000 a year,'' said Michigan state Treasurer Robert Bowman, who attended the meeting. Michigan's pension fund, which holds some 8.8 million shares, or 1.5 percent of GM's outstanding stock, voted against the proposal.

Smith was roundly booed by shareholders when he tried to cut off corporate gadfly Evelyn Y. Davis of New York from speaking out about the pensions.

''This is absolutely outrageous ... absolutely absurd,'' Davis told Smith at the meeting attended by about 900 of the company's approximately 1 million shareholders. ''Roger, in due respect to you, you don't need this type of a pension.''

Jim Musselman of Michigan, who translated Smith's pension into $20,000 a week for fellow shareholders, pointed out that Smith will have made in two weeks what an average auto assembler earns in a year.

Smith defended the new pensions and other retirement benefits for GM executives by saying that the automaker currently ranks in the lower fifth of all U.S. corporate plans and that the proposal puts the company only in the bottom 39 percent.

''That means that 61 percent of corporations in this country will have better pensions than GM,'' Smith said.

Smith also told the stockholders that GM will begin making cars in East Germany later this year. If GM starts production as planned in October, the world's largest corporation will become the first U.S. automaker to make vehicles in the region, which is undergoing rapid political and economic reform.

Smith said the company will make Opel Vectra cars for sale in Europe under a joint venture with East Germany's Automobilewerke Eisenach. The company will assemble about 10,000 of the cars this year. Production of the four-door sedans, about the same size as the Chevrolet Cavalier, is expected to increase to about 150,000 annually by the mid-1990s, GM spokesman Jack Harned said. In addition, GM will begin building engines and assembling a small number of cars in Hungary by early 1992.

At the annual meeting, Smith's continued presence on the board was another matter that drew dissent.

''We voted against Roger Smith continuing on the board because it is our position that a chief executive officer should fully retire,'' said Richard Koppes, general counsel for California's Public Employees Retirement System, which owns 6.2 million shares of assorted GM stock that was voted by proxy late last week.

The other three company proposals, including one to increase the number of GM's Class E stock, were approved by shareholders.

Eight other proposals put before the shareholders were soundly defeated, including ones relating to limiting or ending GM's presence in South Africa and one to restore preemptive rights to stockholders.