The woman was identified as Preeti, who lived at a slum cluster in Bhalswa Dairy with her husband, Heera, who is an e-rickshaw driver, and two daughters -- Anushka (5) and Kanika (2), said police.
"Prima facie Preeti strangled Anushka and Kanika, and then hanged herself from the ceiling fan. Locals sensed that something was wrong and informed Heera, who broke open the door and rushed the three to a hospital," said DCP (northwest) Vijay Singh.
"The bodies have been sent for postmortem examination. The cause and time of death can be ascertained only after the report is obtained," said Singh, adding that the police are now questioning the couple's relatives and neighbours for leads into the probe.
The incident came to light around 4.30 PM when officials of a hospital called up the police and reported that three persons were brought dead there, said police.
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A police team rushed to the spot and investigation was taken up. A case under relevant sections of IPC was also registered at Bhalswa Dairy police station, said police.
When some locals found the children missing, they went on to check on the family. The door was locked from inside. When Preeti did not open the door for a long time, they called up Heera, said police.
Heera rushed home and had to break open the door. He found his daughters lying motionless and his wife hanging from the ceiling with a stole. He rushed the three to a hospital, where they were declared brought dead, and police were informed.
Their relatives have been informed and the case is being investigated from all possible angles, police added.