No,You cannot sit in NDA exam after 10th standard. The candidate must be an Indian national. Only unmarried male candidates can apply for NDA exam. The candidate must have passed 12th from a recognized Board.
If you want to join the army wing of NDA then you can choose any subject after 10th because the eligibility criteria states that for Army Wing of NDA the candidate should be 12th passed by State Education Board or a University but for Air Force and Naval Wings of NDA AND 10+2 Cadet Entry Scheme of Indian Naval Academy you need to have math and physics as subjects in your 10+2 level as the eligibility criteria states that the candidate should be 12th passed with Physics and Mathematics by State Education Board or a University. Please click the below link to know more.