Yes you are eligible to apply for NDA entrance examination organized by Union public service commission . to apply for jobs in Indian army you have to passed minimum 12th grade examination .

NDA Exam Eligibility :
For Army: Candidates must pass in Class 12th from any recognized board with any discipline.

For Navy and AIF: Candidates must pass in Class 12th with Science Discipline from any recognized Board.

Age limit
16 ½ to 19 Years
Marital Status unmarried


UPSC NDA EXAM PATTERN
The written exam consist of two papers.
Written Examination Paper Subject Duration Maximum Marks
I Mathematics 2.5 hours 300
II General Ability Test 2.5 hours 600
Total 900

The General Ability Test
Part Subject Maximum Marks
Part A English 200
Part B General Knowledge 400
Total 600

UPSC NDA NA I Exam Syllabus 2014
Paper I Mathematics :
Matrices and Determinants
Analytical Geometry of two and three dimensions
Algebra
Statistics and Probability
Differential Calculus
Trigonometry
Vector Algebra
Integral Calculus and Differential equations

Paper II General Ability :
Paper II General Ability have two section
1. English Section and
2. General Knowledge Section.

English Section :
Vocabulary
Grammar and usage
Proficiency in English
Use of words
Comprehension
Cohesion in extended text

General Knowledge Section :
General Science
Physics
Chemistry
Geography
Social Study
Current Events