Hearing a batch of petitions filed by some students, Justice M V Muralidharan of the court's Madurai bench also directed the Medical Council of India, the director of the Central Broad of Secondary Education and the Union health ministry to file their counter affidavits on June seven.
Over 11 lakh MBBS and BDS aspirants had appeared for the NEET at more than 1,900 centres across the country on May seven.
They demanded that the NEET be cancelled and a fresh examination with a uniform question paper be conducted.
They claimed that different sets of question paper had been used at various places, though a common syllabus had been announced.
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The petitioners also submitted that officials had not informed them that different sets of question paper would be circulated.
In Tamil Nadu, the question papers were different for those who opted for English and Tamil, they said, adding that the one in Tamil was easier.
"Hence, the NEET should be cancelled and fresh examination with uniform question papers be conducted," the petitioners submitted.