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I don't think that bringing caste certificate to the exam hall will solve your problem because the invigilator present at the exam hall just the teachers of the college or school which will be present there so they don't have anything to do with the procedure of the exam in other formalities there just invigilator also for appearing the exam the caste does not matter what matters is when you are result will be declared so based on the your category you will be your result will be declared so I think you should write a mail to the organising authority of JEE main that is national testing agency mentioning all the issues in the detail format and then wait for the reply.