The fights broke out last night after the results were announced, when Akhil Bharatiya Vidyarthi Parishad members were celebrating their victory, police said.
A roadways bus and other vehicles passing by were also damaged during the melee, they said.
Police force has been deployed to maintain law and order Superintendent of Police Om Prakash said, adding that no complaint has been lodged in the case so far.
However, SP district chairman Vipin Bhandana alleged that ABVP workers first attacked the SP members.
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ABVP's Virat Kumar Godara became President, polling 2373 votes against SP candidate Anuj Kumar Bhabisa's 1395 votes.
ABVP's Gaurav Singh bagged the post of General Secretary with 1,236 votes, beating NSUI's Ankit Soni by 464 votes, while Aakriti Gupta became the new vice president with 1,642 votes, defeating SP student wing's Garima Kain by 505 votes.
ABVP also won top posts in D N College here, but in Ismail Ladies College, it only got the President's post. The remaining seats in Ismail Ladies College went to Samajwadi Chhatra Sabha.