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.
(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 (i) a written examination and (ii) intelligence, obstacles and group tests of the candidates who qualify in the written examination.
The subjects of the written examination, the time allowed and the maximum marks allotted to each subject are as follows:
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
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.
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.
Concept of a set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation equivalence relation.
Rectangular Cartesian coordinate system. The Distance formula. The Equation of a line in various forms. The Angle between two lines. The Distance of a point from a line. The Equation of a circle in standard and in general form. Standard forms of the parabola, ellipse and hyperbola. Eccentricity and axis of a conic. Point in a three-dimensional space, the distance between two points. Direction cosines and direction ratios. The Equation of plane and a line in various forms. The Angle between two lines and the angle between two planes. The Equation of a sphere.
The Concept of a real valued function – domain, range and a graph of a functions, one to one, onto and inverse functions. The Notion of limit, standard limits – examples. Continuity of functions- examples, algebraic operations on continuous functions. The Derivative of a function at a point, geometrical and physical interpretation of a derivative – applications. Derivatives of the 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.
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.
The Vectors in two and three-dimensions, magnitude and direction of a vector. Unit and null vectors, the addition of a 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: 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 the binomial distribution.
Syllabus for General Studies
The question paper in English will be designed to test the candidate’s understanding of English and workman like use of words. The syllabus covers various aspects like : Grammar and usage, vocabulary, comprehension and cohesion in extended text to test the candidate’s proficiency in English.
The question paper on General Knowledge will broadly cover the subjects : Physics, Chemistry, General Science, Social Studies, Geography and Current Events.
The syllabus given below is designed to indicate the scope of these subjects included in this paper.
The topics mentioned are not to be regarded as exhaustive and questions on topics of similar nature not specifically mentioned in the syllabus may also be asked.
Candidate’s answers are expected to show their knowledge and intelligent understanding of the subject.
•Physical Properties and States of Matter, Mass, Weight, Volume, Density and Specific Gravity, Principle of Archimedes, Pressure Barometer.
•Motion of objects, Velocity and Acceleration, Newton’s Laws of Motion, Force and Momentum, Parallelogram of Forces, Stability and Equilibrium of bodies, Gravitation, elementary ideas of work, Power and Energy.
•Effects of Heat, Measurement of temperature and heat, change of State and Latent Heat, Modes of transference of Heat.
•Sound waves and their properties, Simple musical instruments.
•Rectilinear propagation of Light, Reflection and refraction. Spherical mirrors and Lenses. Human Eye.
•Natural and Artificial Magnets, Properties of a Magnet, Earth as a Magnet.
•Static and Current Electricity, conductors and Non-conductors, Ohm’s Law, Simple Electrical Circuits, Heating, Lighting and Magnetic effects of Current, •Measurement of Electrical Power, Primary and Secondary Cells, Use of X-Rays.
•General Principles in the working of the following :
Simple Pendulum, Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs, Telephone, Periscope, Telescope, Microscope, Mariner’s Compass; Lightening Conductors, Safety Fuses.
•Physical and Chemical changes.
•Elements, Mixtures and Compounds, Symbols, Formulae and simple Chemical Equations, Law of Chemical Combination (excluding problems).
•Properties of Air and Water.
•Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbondioxide, Oxidation and Reduction.
•Acids, bases and salts.
•Carbon – different forms
•Fertilizers – Natural and Artificial
•Material used in the preparation of substances like soap, Glass, Ink, Paper, Cement, Paints, Safety Matches, and Gun-Powder.
•Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.
•Difference between the living and non- living.
•Basis of Life – Cells, Protoplasms and Tissues.
•Growth and Reproduction in Plants and Animals.
•Elementary knowledge of human Body and its important organs.
•Common Epidemics, their causes and prevention.
•Food – Source of Energy for man. Constituents of food, Balanced Diet.
•The Solar System – Meteors and Comets, Eclipses.
•Achievements of Eminent Scientists.
•A broad survey of Indian History, with emphasis on Culture and Civilisation.
•Freedom Movement in India.
•Elementary study of Indian Constitution and Administration.
•Elementary knowledge of Five Year Plans of India.
•Panchayati Raj, Co-operatives and Community Development.
•Bhoodan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi.
•Forces shaping the modern world; Renaissance, Exploration and Discovery; War of American Independence. French Revolution, Industrial Revolution and Russian Revolution.
•Impact of Science and Technology on Society.
•Concept of one World, United Nations, Panchsheel, Democracy.
•Socialism and Communism.
•Role of India in the present world.
•The Earth, its shape and size.
Lattitudes and Longitudes, Concept of time.
•International Date Line.
•Movements of Earth and their effects.
•Origin of Earth.
•Rocks and their classification; Weathering – Mechanical and Chemical, Earthquakes and volcanoes.
•Ocean Currents and Tides
•Atmosphere and its composition; Temperature and Atmospheric Pressure, Planetary Winds, cyclones and Anti-cyclones; Humidity; Condensation and Precipitation.
•Types of Climate.
Major Natural regions of the World.
•Regional Geography of India – Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and industrial activities.
•Important Sea ports and main sea, land and air routes of India. Main items of Imports and Exports of India.
•Knowledge of Important events that have happened in India in the recent years.
•Current important world events.
•Prominent personalities – both Indian and International including those connected with cultural activities and sports.