President Carter will leave Washington Nov. 22 on a whirlwind 11-day trip to eight countries on four continents, during which he will make the first state visit by an American President to a black African nation, White House officials announced yesterday.

The trip, one of the most ambitious ever planned by a President, will take Carter to Caracas, Venezuela; Brasilia, Brazil; Lagos, Nigeria; New Delhi, India: Tehran, Iran; Paris, Warsaw and Brussels. He is scheduled to return to the United States on Dec 2.

In anticipation of questions about why the President would choose to make such a hopscotching trip around much of the world during his 10th month in office. Zbigniew Brzezinski, his national security affairs adviser, said the trip has four objectives:

To "conduct important bilateral business" with each of the countries, to "underline traditional ties of alliance, of beliefs, of values," to "widen the scope of international cooperation," and to "symbolize our willingness to cooperate with systems that are different than ours socially, politically, economically."

Nonetheless, even in the White House there was considerable bafflement about the trip, during which the President will spend no more than two days in any of the countries.

"It seems utterly insane to me, especially since Carter said he wanted to concentrate on domestic issues his first year in office," one aide said.

Asked about the President's frequent statements that he would not travel abroad his first year in office, Brzezinski replied:

"Of course, you know, his preference is to be at home, and he has stayed at home . . . This trip, however, does seem to us to be an important need. It reflects our continued efforts to promote the kind of world we all want to live in, and we think it is useful."

The trip will be Carter's second out of the country since talking office in January. In May, he traveled to London to attend an economic summit conference with U.S. allies and, as part of that journey, made a quick flight to Geneva to meet Syrian President Hafez Assad.

But that trip was part of a continuing commitment by American presidents to attend a yearly summit in economic matters with U.S. allies. In contrast, the trip planned for November, in part over the Thanksgiving holiday, is clearly a Carter creation, particularly with its emphasis on developing nations in Latin America, Africa and Asia.

White House secretary Jody Powell said the President first asked Brzezinski to begin exploring the possibility of a foreign journey last spring. It was Carter, Powell said, who emphasized the importance of Latin America and Africa in the planning.

"To some extent it is also a tribute to the work Andy Young has done," Powell siad in reference to United Nations Ambassador Andrew Young, who early in the administration traveled extensively through Africa.

Rosalynn Carter will accompany the President. Brzezinski said he expects that Secretary of State Cyrus R. Vance will also go along for most or all of the trip, and Powell said Young may accompany Carter too, particularly during the Latin American and African legs of the journey.

Some questions to Brzezinski suggested skepticism about the timing of yesterday's announcement, which the White House had advertised as one of major importance and which came just two days after Carter's first presidential crisis - the resignation of budget director Bert lance.

Brzezinski said "serious planning" had been going on for a month, and the overall schedule was put into place on Monday. He said the announcement was delayed until Friday because it had to be coordinated with the governments of the countries to be visited.

The trip was scheduled for late November, Brzezinski said, because by then Congress is due to have adjourned and the President will have "more flexibility in his schedule."

Brzezinski said there are no plans for Carter to meet Soviet President Leonid I. Brezhnev while in Warsaw, but he did not rule out that possibility from developing. By the same token, he said there was no reason why, while in Nigeria, the President could not meet with leaders of other African nations if it "proved to be desirable."

The only other American President to visit a black African nation was Franklin D. Roosevelt, who stopped briefly in Liberia on Jan. 26, 1943, while returning from a conference of World War II Allied leaders at Casablanca.

In recent years, frequent overseas travel by Presidents has come to be expected in the United States. Such visits, however, are of major importance to other natons, and Carter can except 11 days of tumultuous receptions accompanied by saturation media coverage back home.