The infant and his two-year-old sister were both asleep in their home in Faridabad district, around 25 miles (40 kilometres) outside New Delhi, when the attackers doused the building with petrol and set it alight.
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Both children died at the scene while their parents were rushed to hospital in the capital, according to police. The mother is in critical condition although the father's life is no longer in danger.
Three people have been arrested over the attack on the family who are members of the Dalit community, according to the detective leading the murder inquiry, although no one has yet to be formally charged.
Subhash Yadav, Faridabad's police commissioner, said the attack appeared to have been part of a long-running feud between the area's Dalit community and the higher Rajput caste, which also claimed the lives of three people a year ago.
"We are trying to maintain calm," Yadav told AFP after the killings, saying officers were still trying to confirm if it was a revenge attack.
Vishnu Dayal, who is leading the investigation, told AFP that three people have been arrested but without giving details of their suspected role in the attack.
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Dalits, formerly known as untouchables, are frequently the victims of violence and prejudice. Their lowly status means that investigations into attacks on Dalits are often treated as a low priority by police.
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