The incidents happened in Siwan and Begusarai districts, they said.
In the first incident, four persons, including three women and a child, were killed after they fell down from a railway bridge, an official said.
They were crossing the bridge over Daha river on foot to reach the Siwan Kutchery railway station, the District Magistrate (DM) of Siwan, Mahendra Kumar, told PTI.
The deceased were residents of Kuchaykot police station in the neighbouring district of Gopalganj and they were approaching the railway station to catch a train back home, he said.
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The Chief Public Relations Officer (CPRO) of North Eastern Railway, headquartered at Gorakhpur, Sanjay Yadav said, "The driver of the train gave a message upon reaching the next station confirming that none of the persons walking on the bridge were run over".
The DM said, another person, who was seriously injured, was referred to the PMCH hospital in Patna.
The deceased were identified as Khushboo Nishan, Jhuni Khatoon, Saraswati Devi and Munna, the child. The injured person was identified as Aslam Ansari, the DM added.
The incident happened under the jurisdiction of Teghra police station in the district, he said.
The man has been identified as Suresh Sah, a resident of Jagdar village under the jurisdiction of Veerpur police station, the SHO said, adding, the identity of the woman was yet to be established.
The injured were sent to a hospital, he said.
Though, the three-wheeler and the truck were seized, the driver of the truck fled the spot, he added.