The National Defence Academy (NDA) admits students to the Army, Navy and Air Force wings through an entrance examination held twice a year, generally in the months of April and September. This examination is conducted by the Union Public Service Commission. Age and marital status: A candidate must be an unmarried male, at least 161/2 years old but below the age of 19 as of January 1, or July 1, of the year succeeding the examination year.

Educational Qualifications:

  1. For Army Wing of National Defence Academy: Must have successfully completed Class XII in the 10 + 2 pattern of school education or equivalent examination conducted by a State education board or a university.
  2. 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 Class 12 of the 10 + 2 pattern of school education or equivalent with Physics and Mathematics conducted by a State education board or a university. Candidates currently in Class XII in the 10 + 2 pattern of school education, or equivalent examination, can also apply.


Plan of the Examination:

The examination comprises

  1. a written examination and,
  2. intelligence, obstacles and group tests of the candidates who qualify in the written examination.

Examination Subjects: The subjects of the written examination, the time allowed and the maximum marks allotted to each subject are as follows

S.No Subject Duration Max. Marks
1. Mathematics 21/2 hours 300
2 General Ability Test (English, GK and Science) 21/2 hours 600
  • The papers in all subjects will consist only of objective-type questions.
  • The question papers (test booklets) will be set in English.

Syllabus for Mathematics

Trigonometry :

Angles and their measures in degree and in radians. Trigonometrical ratios. Trigonometry identities. Sum and difference formulae. Multiple and sub-multiple angles trigonometric functions. Applications – height and distance, properties of triangles.

Matrices and Determinants :

Types of matrices, operations on matrices. Determinant of a matrix. Basic properties of determinants. Adjoint and inverse of a square matrix applications – solution of a system of linear equations in two or three unknowns by Cramer’s rule and by matrix method.

Algebra :

Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation equivalence relation.

Analytical Geometry of Two and Three Dimensions :

Rectangular Cartesian coordinate system. Distance formula. Equation of a line in various forms. Angle between two lines. Distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three dimensional space, distance between two points. Direction cosines and direction ratios. Equation of plane and a line in various forms. Angle between two lines and angle between two planes. Equation of a sphere.

Differential Calculus :

Concept of a real valued function – domain, range and graph of a functions, one to one, onto and inverse functions. Notion of limit, standard limits – examples. Continuity of functions- examples, algebraic operations on continuous functions. Derivative of function at a point, geometrical and physical interpretation of a derivative – applications. Derivatives of sum, product and quotient of functions, derivatives of a function with respect to another function, derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

Integral Calculus and Differential Equations:

Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications, Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equations of various type – examples. Application in problems of growth and decay.

Vector Algebra :

Vectors in two and three dimensions, magnitude and direction of vector. Unit and null vectors, addition of vectors, scalar multiplication of a vector, scalar product or dot product of two vectors. Vector product or cross product of two vectors. Applications work done by a force and moment of a force, and in geometrical problems.

Statistics and Probability :

Statistics: Classification of data, frequency distribution, cumulative frequency distribution- examples. Graphical representation-histogram, pie chart, frequency polygon-examples. Measures of central tendency-mean, median and mode. Variance and standard deviation-determination and comparison. Correlation and regression. Probability: random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and intersection of events. Complementary, elementary and composite events. Definition of probability-classical and statistical examples. Elementary theorems or probability. Simple problems, conditional probability, Bayes’ theorem-simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to binomial distribution.