Radha Devi had yesterday strangled the three daughters aged 8 months, 3 and 8 years, and attempted suicide by hanging from a tree behind her house.
Police said the eldest daughter, aged 10 years, had a narrow escape as she had gone out at the time of the incident.
The police is waiting to record the mother's statement. She is believed to be in depression and was admitted to Safdarjung hospital, police said.
"After giving birth to a fourth girl child, Radha became extremely upset. She would often leave house for hours and not return. She had threatened earlier about killing their daughters," Singh added.
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Singh works as a tailor and has been staying in Ambedkar Nagar for the past 15 years. He is a native of Mainpuri in Uttar Pradesh. The couple has been married for ten years.
Police said that they are probing the matter from all possible angles and will take action accordingly.
"Police will soon ascertain the motive behind the extreme act and are waiting to record Radha's statement," said a senior police official.