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The quartet of Muhammed Anas Yahiya, Tom Noah Nirmal, Rajiv Arokia and Amoj Jacob finished fourth in the second heat with a timing of 3:00.25sec.
The 50km distance has been part of the Games since 1936 but Friday's race might have been the last at an Olympics.
American teenager Mu Athing won the 800 metres gold.
His best attempt of 19.99m was well short of the qualifying mark of 21.20m. Toor finished 13th.
Germany’s Kristin Pudenz had a personal best 66.86 metres for silver and Cuba’s Yaime Perez took bronze with 65.72.
American world record holder Kendra Harrison won silver in 12.52 and Jamaican Megan Tapper took bronze in 12.55.
Indian sprinter Dutee Chand continued her disappointing run at the Olympics as she failed to qualify for the women's 200m semifinals after finishing last in her heat.
Both Barshim, 30, and the 29-year-old Tamberi ended with jumps of 2.37 metres and had no failed attempts until they attempted to clear 2.39.
Ann Rose Tomy of Idukki clocked 13.98 seconds to fetch silver in the Federation Cup Jr Championship in Punjab to meet the worlds' qualifying mark
Fred Kerley of United States won the silver while Andre de Grasse of Canada took the bronze.
Results 291-300 of 386