Family discord was believed to be the reason behind the three taking the extreme step, they said adding the incident happened near Hathiani village here yesterday.
Gayatri Devi, aged 45, jumped before the oncoming train along with her 13-year-old son Ritesh and daughter Kavita, police said.
Kavita was killed, Gayatri suffered head injuries and Ritesh lost his wrist, they said.
The mother and her son were admitted to hospital, police said.
Gayatri was allegedly beaten up her husband's brother before she leapt before the moving train along with her daughter and son, they said.
An FIR had been registered in connection with the incident.
