In that case you have to decide which exam you want to give and want to pursue. Both the tests are national level and there are many students like you who will will be missing the exam. Try to mail the administration of both the exams informing about your case and giving an argument that many students will be losing an opportunity. They might consider the case and change the schedule before it's too late. One more thing, JIPMER schedule is tentative, that means if any problem arises they can consider it. Make the case clear as soon as possible.
All the best.
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