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 161/2years
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 :

S.No | Subject | Duration | Max. Marks |

1. | Mathematics | 21/2 hours | 300 |

2. | General Ability Test (English, GK and Science) | 21/2 hours | 600 |

Total | 900 |

Notes

- 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.

**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.