There is no certainty about the postponement of JEE Main 2021 April session as if the exam date is deferred, it will clash with the postponed class 12 boards and also the May session of JEE Main. However, NTA might postpone both the April and May sessions if the situation gets worse.
While NEET 2021 will only be postponed if the situation is too bad until August. NDA exam will be conducted on 18 April 2021, so there are chances that the exam might be postponed. However, no official notice has been made for the same. Students appearing for the competitive exams are strongly against holding the exam amidst the huge COVID-19.