The policemen were asked to run for 10 km as a part of physical test at the Police Lines in Kanpur and Meerut. At least 250 policemen appeared for the physical test in both districts.
13 constables fainted in Meerut and were later hospitalised.
"One of them (Agresh Dubey, head constable) has died while the condition of two is stated to be serious," said SK Singh, Superintendent of Police (Traffic) in Meerut.
Similarly, 7 policemen fell unconscious in Kanpur after running for 6 km.
"All the policemen are being treated at the Ursala Hospital. The condition of one of them is serious," said a police officer.