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 16^{1/2} 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.

**Examination**

**Plan of the Examination:** The examination comprises (i) a written examination and (ii) 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 :

Subject | Duration | Max Marks |
---|---|---|

Mathematics | 2.5 hrs | 300 |

General Ability Test (English, GK and Science) | 2.5 hrs | 600 |

**Note:**

1. The papers in all subjects will consist only of objective-type questions.

2. 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 identitity. Sum and difference formulae. Multiple and sub-multiple angles trigonometric functions. Applications of 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.