The National Defence Academy (NDA) Examination is conducted by the Union Public Service Commission (UPSC) for admission to the Army, Navy, and Air Force wings of the NDA. The exam comprises two main sections: Mathematics and the General Ability Test (GAT). Below is a detailed breakdown of the syllabus, including key subjects, unit-wise topics, recommended study materials, and the exam format to guide aspirants in their preparation.
1. Overview of Key Subjects
| Section | Description |
|---|---|
| Mathematics | Assesses mathematical aptitude and problem-solving skills. |
| General Ability Test (GAT) | Evaluates proficiency in English and general knowledge across various subjects. |
2. Unit-wise Breakdown and Essential Topics
a. Mathematics
| Unit No. | Unit Name | Essential Topics |
|---|---|---|
| 1 | Algebra | Concept of sets, operations on sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation, mappings, real numbers, complex numbers, modulus, argument, cube roots, conversion of a number in decimal system to binary system and vice-versa, arithmetic, geometric and harmonic progressions, quadratic equations with real coefficients, solution of linear inequalities of two variables by graphs, permutation and combination, binomial theorem and its applications. |
| 2 | 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. |
| 3 | Trigonometry | Angles and their measures in degrees and in radians, trigonometric ratios, trigonometric identities, sum and difference formulae, multiple and sub-multiple angles, inverse trigonometric functions, applications—height and distance, properties of triangles. |
| 4 | 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 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 a plane and a line in various forms, angle between two lines and angle between two planes. |
| 5 | Differential Calculus | Concept of a real-valued function, domain, range and graph of a function, composite functions, one-to-one, onto and inverse functions, notion of limit, standard limits, continuity of functions, algebraic operations on continuous functions, derivative of function at a point, geometrical and physical interpretation of a derivative, derivatives of sum, product and quotient of functions, derivative 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. |
| 6 | 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 types—examples, application in problems of growth and decay. |
| 7 | Vector Algebra | Vectors in two and three dimensions, magnitude and direction of a 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, geometrical problems. |
| 8 | Statistics and Probability | Statistics: Classification of data, frequency distribution, cumulative frequency distribution, graphical representation—histogram, pie chart, frequency polygon, measures of central tendency—mean, median and mode, variance and standard deviation, correlation and regression. Probability: Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events, complementary, elementary and composite events, definition of probability—classical and statistical, elementary theorems on probability, simple problems on probability, conditional probability, Bayes’ theorem, random variable as function on a sample space, binomial distribution, examples of random experiments giving rise to binomial distribution. |
b. General Ability Test (GAT)
Part A: English
| Unit No. | Unit Name | Essential Topics |
|---|---|---|
| 1 | Grammar and Usage | Spotting errors, sentence improvement, vocabulary, synonyms, antonyms, idioms and phrases. |
| 2 | Comprehension | Reading comprehension, inference, and interpretation of passages. |
Part B: General Knowledge
| Unit No. | Unit Name | Essential Topics |
|---|---|---|
| 1 | Physics | Physical properties and states of matter, mass, weight, volume, density, principles 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, elementary knowledge of light and sound, reflection and refraction, spherical mirrors and lenses, human eye. |
| 2 | Chemistry | Physical and chemical changes, elements, mixtures and compounds, symbols, formulae and simple chemical equations, law of chemical combination, properties of air and water, preparation and properties of hydrogen, oxygen, nitrogen and carbon dioxide, oxidation and reduction, acids, bases and salts, carbon—different forms, fertilizers—natural and artificial, materials used in the preparation of substances like soap, glass, ink, paper, cement, paints, safety matches and gunpowder, elementary ideas about the structure of atom, atomic equivalent and molecular weights, valency. |
| 3 | General Science | Difference between living and non-living, basis of life—cells, protoplasms and tissues, growth and reproduction in animals and plants, 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. |
| 4 | History, Freedom Movement, etc. | A broad survey of Indian history, with emphasis on culture and civilization, freedom movement in India, elementary study of Indian Constitution and administration, |