The hydraulic brakes caught fire as soon as the driver pressed them at a station
Rescuers are still searching for the remaining two students.
All of them were students of Chakaria Grammar School adjacent to the river.
The missing students have been identified as Md Sayeed, Aminul Hossain, Md Farhan, Turja Bhattacharya and Sohrab Hossain.
Sayeed, Aminul, Farhan and Turja were the tenth graders while Sohrab was the eighth grade student.
After finishing the exams, some students were playing football at a playground near the school and six of them went bathing in the river around 5pm, said Chowdhury.
“One of them swam ashore and five went missing as they were hit by a strong current of the river,” he said citing teachers and students.