Jimmy Carter marched ever closer to the Democratic nomination last night with landslide victories over Sen. Edward Kennedy in the Indiana, North Carolina and Tennessee primaries.

While Kennedy has staked his hopes on strong showings in the final primaries next month, the possibility of his overtaking the president became ever more remote as Carter moved within 300 delegates votes of the nomination. International projected he would pick up 164 convention delegates, bringing his total to 1,368 of the 1,666 needed to be nominated. Kennedy was projected to pick up 58 bringing his total to 734 1/2. n

The failed Iranian rescue mission apparently did little to damage Carter, according to interviews by ABC News in Indiana, the largest of the three states holding primaries.

In an obvious rallying around the flag, Democratic voters in the conservative state said they approved of the president's handling of the hostage situation by a 2-to-1 ratio. Republicans disapproved by 53 to 41 percent.

The Indiana primary also saw the re-emergence of the personal morality issue that has plagued Kennedy in other states in the nation's heartland.

It was the most crowded primary night of the presidential season, beginning a month of primaries that wind up on June 3. The wins brought Carter's total to 13 primaries; Kennedy, who won the District of Columbia last night, has won five, all in the East.

In Indiana. the only state where Kennedy actively contested the president, Carter led by 68 percent to 32 percent with 75 percent of the precincts counted.

With 95 percent of the precincts reported in North Carolina, Carter led 70 percent to 18 percent.

In Tennessee, Carter led 75 percent to 18 percent with 98 percent of the vote counted.

Although wins were expected, the margins surpassed even the fondest hopes of the Carter camp.

At the White House, press secretary Jody Powell said, "The president appreciates the strong support in today's primaries, especially in these difficult times."

He claimed the delegates won during the day bring Carter within 160 delegates of the nomination, although UPI leaves him about 300 short. "It is not mathematically impossible" for Kennedy to win the nomination," Powell said, but to do so, he said, the challenger would need to win about nine of every 10 delegates to be selected at the remaining primaries and party caucuses.

The White House, Powell said, is now "going to have to prepare for a general election battle" in the fall with GOP front-runner Ronald Reagan.

"There were no real surprises this evening," Kennedy said in Baltimore, where he was campaigning last night.

"We did well, in some areas but not so well in other areas. So we've got to work a little harder now."

Kennedy's loss in Indiana was total and devastating. He lost among almost every population group and in every region, raising serious questions about his claims of a growing disillusionment with Carter's foreign and domestic policies.

In large part, the vote was a personal rejection of him in the Midwest heartland, much as in the March primaries in Wisconsin and Illinois.

Half the Democratic voters interviewed by ABC News as they left Indiana polling places said they found the Massachusetts Democrat an unacceptable candidate. Only one Democrat in 10 found him truthful. About the same proportion approved of his personal morality an apparent spill over from his marital problems and the Chapaquiddick incident.

Carter, as in earlier primaries, scored strong on personal characteristics. He was given high marks for truthfulness, sticking to principles and personal morality. Many Democrats in Indiana apparently don't blame him for inflation, which they regard as the nation's most important issue, or for the Iranian hostage situation. Asked if they thought any president could effectively solve problems, 58 percent of the Democrats interviewed said no.

Republicans were much more confident of a president's ability to manage affairs, and those who felt strongest on the matter favored Ronald Reagan by an overwhelming margin.

Although a total of 204 delegates were at stake, the presidential campaign caused scarcely a ripple in the three states. Kennedy campaigned only in Indiana. This was largely a recognition of political realities. He trailed badly in all three states and lacked the time and money to reverse the situation. His only realistic hope was to hold down Carter's margin, and hope to pick up a few scattered delegates.

Indiana was his best shot. Kennedy's brother Robert won there in 1968 and this year it has a high unemployment rate.

Kennedy tried to capitalize on the state's ailing economy in stumping through industrial areas of Gary, Kokomo and Indianapolis. He also used a television commercial featuring Carroll O'Conor, TV's Archie Bunker, but the Massschusetts senator was hurt by the neutrality of the state's leading liberal Democrat, Sen. Birch Bayh, and its two most powerful labor groups, the United Auto Workers and the AFL-CIO.

Carter won 68 percent of the state's primary vote in 1976, and some observers felt he might match that this time. Indiana's delegates to the Democratic convention are apportioned by a percentage of the popular vote, thus assuring Kennedy one delegate in each congressional district where he scored 16 percent or more of the vote. But the most optimistic projections by aides to the senator were for no more than 30 of the state's 80 delegates.

"Indiana is a very conservative state," said Richard Drayne, a Kennedy operative.

A far tigher race was that for the Democratic gubernatorial nomination. It pitted conservative John Hillenbrand, heir to a coffin-manufacturing fortune, against Wayne Townsend, a state senator with strong labor support.

Bayh, seeking a fourth term, had no primary opponent. He is expected to face difficulties in November, however.

Tennessee and North Carolina are both longtime Carter Strongholds.

Four years ago, the Volunteer State gave the president more primary votes than any except his home state of Georgia. Kennedy hadn't even visited the state since last fall.

He did, however, have the endorsements of Nashville Mayor Richard Fulton and the Nashville Tennesseean newspaper. He hoped to squeeze out a few delegates from Nashville and Memhis areas.

Carter derailed George Wallace in the 1976 North Carolina primary. This year the president had the support of incumbent Gov. Jim Hunt, of Hunt's primary election opponent, former governor Bob Scott, and of former governor Sanford.

Hunt was heavily favored to beat Scott, a Carter appointee to the chair of the Appalachian Regional Commission. Hunt had widespread business support.

Carter had hopes of picking up all 69 North Carolina delegates. "We've seen nothing to indicate Kennedy has picked up any support," Joseph Grimsley, Hunt's campaign manager, told Associated Press. "I thought at one time he would pick up some support . . . but now it's marginal."