The basic Educational qualification to appear for NDA exam is that the candidate must have passed class 12th from any recognised board or the candidates who are appearing in class 12th same year are also eligible to appear for NDA exam, however if you are in class 11th then sorry but you are not eligible to appear for NDA exam.
Yes you can apply for national defense service examination after passing 11th grade examination. but firstly you have to pass 12th grade examination than you will be eligible to apply for national defense service examination organized by union public service commission to Join Indian Army.