A bench of justices B D Ahmed and Siddharth Mridul has fixed the PIL for hearing on May 9.
The PIL filed by Pushpanjali Das is seeking a direction to the CBSE and 16 IITs to "re-conduct JEE (Main), 2014 within a week's time and not on multiple days."
It has also sought a direction that the CBSE and the IITs be not allowed to go ahead with the JEE as different sets of question papers for the exams, which would be held on multiple dates, will not provide equal oppotunities to all students.
"This results in questions of varying levels of difficulty on each day, as a result an average student may score more marks thereby denying deserving student a chance of getting admission in prestigious premium Institutes of India," the petition said.
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According to the plea, CBSE, since 2002, started independent engineering entrance examination known as AIEEE for admission to 30 NITs and 5 IIITs.
However, later it was agreed that IITs be allowed to conduct own examination separately but only for those first 1,50,000 students, who qualify AIEEE based on some cut-off marks, the petition said.