Charan Singh, a 77-year-old farmer's son who has made no secret during the past five years of his ambition to rule India, was asked yesterday to become that country's fifth prime minister.

To get the bare majority of the Parliament to allow him to form a new government, Singh said he put together a fragile coalition that includes dropouts from the Janata Party of former Prime Minister Morarji Desai, whose government fell 11 days ago, and supporters of Indira Gandhi, who once jailed Singh for his political opposition to her.

Singh's coalition could fall apart, but he said he expects to be sworn in Saturday. President N. Sanjiva Reddy, who asked Singh to form the government, said he should get a vote of confidence from the Parliament by the third week of August.

Singh, who had been deputy prime minister and finance minister in the Desai government and whose resignation precipitated its fall, attacked Desai for having brought India "to the brink of economic and administrative chaos."

He said the government he hopes to form will aim at eliminating poverty and unemployment, narrowing the wide gap between rich and poor in a country where the average per capita income is $150 a year and build "a healthy classless society."*tThroughout the last 10 days, however, personalities rather than issues have played the major role in the battle three old men of Indian politics - Singh, Desai, 83, and Jagjivan Ram, the 71-year old former defense minister - to form the new government.

Singh thought that he should have been named prime minister over Desia in 1977, when the Janata Party defeated Gandhi's authoritarian government.

Moreover, Singh, whose roots run deep among the farmers and small landowners of northern India and Ram, the leader of India's 100 million untouchables, do not get along politically or personally.

Ram agreed to bow out of the battle to give Desai a chance to form the new government. But after looking into conflicting claims of parliamentary support, Reddy ruled that Singh had the greatest number of members behind him.

Singh never held national office until 1977, and his entire political orientation revolves around the state of Uttar Pradesh. He has been out of India just once - to the neighboring nation of Sri Lanka - and has no record in foreign policy, State Department officials here said.

"He's a north Indian who generally considers Madras [a city in South India] as foreign," said one diplomat.

The most surprising part of Singh's coalition is the support from Gandhi's 72-vote parliamentary bloc.

Singh was one of the many Indian politicians - including Desai - who was jailed by Gandhi and he quit the government temporarily last year because he did not think it was prosecuting her vigorously enough for the abuses of her "emergency rule."

With the Gandhi bloc representing one-fourth of Singh's support, there was speculation in New Delhi that he would drop the prosecution of Gandhi and her son Sanjay in several cases now before special courts. Singh branded suggestions of a deal with Gandhi as "an unmitigated lie."

While Gandhi's bloc promised to support Singh in forming the new government, its members will not become part of that government. The 75-vote Congress Party group headed by U.B. Chavan, who earlier failed to muster enough support in Parliament to allow him to form the government, also agreed to support Singh, even though Chavan's group rivals the Gandhi bloc.

The rest of Singh's strength comes mainly from the 92 members of his Janata Secular Party, which split from Desia's Janata over charges that he allowed the Hindu-chauvinist Jana Sangh faction too much influence in the government.

Singh accused the Jana Sangh of fomenting Hindu-Moslem clashes in the country.

Despite their personal differences, most Indian politicans were united in the desire to avoid a midterm election.

According to observers here an in New Delhi, the only political factions organized well enough for an election campaign now are Gandhi's and the Jana Sangh. Gandhi has told her supporters that she will back Singh only until her political star has risen from its current low point and then will try to force new elections.

Their strengthens the felling here that India's political instability will not go away with Singh as prime minister.*t"For the first time," said one observer here "India will be governed at its center by an unstable coalition. The question is whether India can take a series of unstable coalition governments." CAPTION: Picture, Charan Singh reads a letter from Indian President Reddy, left, asking him to form a new government. AP