The rowers, Diya Anna Correa and Upamanyu Dutta, have sought directions to the Ministry of Youth Affairs and Sports to reinstate their category saying they are willing to go to the Games at their own cost.
Their plea was mentioned today before a bench of justices Badar Durrez Ahmed and Siddharth Mridul which ordered listing of the matter before a single judge bench of Justice Vibhu Bakhru.
However, the matter could not be taken up today and was listed for hearing tomorrow.
In their petition, filed through advocate Rahul Mehra, they have contended they have also received accreditation from both Indian Olympic Association (IOA) and Olympic Committee of Asia (OCA) to participate in the Games.
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They have also sought retaining their category saying it would be their last oppostunity to participate in the Games in the under-19 age group of the 420 class sailing event.
They have also submitted that they have "complied with all the requirements such as selection trials, international exposure, focused coaching among others in order to prepare themselves for the forthcoming competition so as to be able to represent India to the best of their abilities."
The Asian Games is scheduled to take place in Incheon, South Korea, from September 19 to October 4, 2014 with 439 events in 36 sports and disciplines.