Am I eligible to join Indian Army through NDA after Passing X Standard????

You are not eligible to join Indian Army after 10th standard because the minimum educational qualification required is 10+2.

You can Join Indian Army through cracking NDA(National Defence Academy) exam which is conducted by the UPSC

Eligibility for NDA:

Nationality:
-Must be a citizen of India, or Bhutan, or Nepal

Age and Gender
-Candidate must be an unmarried male.
-Age must lie between 16 1/2 years and maximum age 19 years

Educational Qualifications:

For Army wing of National Defence Academy:-

Must have passed 12th Class from any recognized Board

For Air Force and Naval Wings of National Defence Academy and for the 10+2 (Executive Branch) Course at the Naval Academy—

Must have passed 12th Class pass with Physics and Mathematics