UPSC NDA & NA (National Defence Academy) Syllabus 2026

The complete UPSC NDA & NA (National Defence Academy) syllabus for 2026 — 3 sections and 25 topics in all, organised exactly as the Union Public Service Commission (UPSC) prescribes. Use it as your revision checklist, then test yourself with a free UPSC NDA & NA (National Defence Academy) mock below.

Mathematics (Paper I, 300 marks) — NCERT Class 11 + 12 backbone10 topics

Algebra: sets, Venn diagrams, relations and functions, complex numbers (modulus, argument, Argand plane, cube roots of unity), quadratic equations and inequations, arithmetic / geometric / harmonic progressions, binomial theorem and its applications, logarithms (laws and applications), permutations and combinations
Matrices and Determinants: types of matrices, operations on matrices, determinant of a matrix, properties of determinants, adjoint and inverse of a square matrix, application — solving systems of linear equations by Cramer's rule and by matrix method
Trigonometry: angles and their measures in degrees and radians, trigonometric ratios and identities, sum and difference formulas, multiple and sub-multiple angle formulas, inverse trigonometric functions and their principal values, properties of triangles (sine rule, cosine rule, projection formulas), heights and distances
Analytical Geometry of Two and Three Dimensions: rectangular Cartesian coordinate system, distance formula, equations of a line in various forms, angle between two lines, distance from a point to a line, equation of a circle in standard and general form, standard forms of parabola, ellipse and hyperbola — eccentricity and axes, three-dimensional coordinates — distance formula, direction cosines and direction ratios, equation of a plane and a line in 3D, angle between two lines and between two planes
Differential Calculus: concept of a real-valued function — domain, range and graph, composite functions, one-to-one / onto / inverse functions, notion of a limit, standard limits, continuity of functions, derivative of a function at a point — geometrical and physical interpretation, derivatives of sum / product / quotient, derivatives of composite functions, chain rule, derivatives of implicit functions and parametric functions, 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 / trigonometric / exponential / hyperbolic functions, evaluation of definite integrals — area under a curve and area enclosed between two curves, definition of order and degree of a differential equation, formation of a differential equation, solution of first-order and first-degree differential equations of various types, application in growth and decay problems
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 (dot product) and vector product (cross product) of two vectors, scalar triple product, applications in geometry — work done by a force, moment of a force
Statistics and Probability: classification of data, frequency distribution, cumulative frequency distribution, graphical representation — histogram, pie chart, frequency polygon, measures of central tendency (mean, median, mode), variance and standard deviation, correlation and regression (basic), random experiment, outcomes and associated sample space, events — mutually exclusive and exhaustive, impossible and certain events, union and intersection of events, complementary events, elementary and composite events, definition of probability — classical and statistical, elementary theorems on probability, conditional probability, Bayes' theorem (simple problems), random variable as function on a sample space, binomial distribution and examples of random experiments giving rise to it
Indicative weight distribution (averaged across recent cycles): Calculus 25-30 questions, Trigonometry 18-22 questions, Algebra 15-18 questions, Analytical Geometry 12-15 questions, Vector Algebra 8-10 questions, Statistics + Probability 8-12 questions, Matrices + Determinants 6-8 questions, Complex Numbers 4-6 questions
High-yield NCERT chapters that consistently produce questions cycle after cycle: Class 11 — Sets, Trigonometric Functions, Complex Numbers, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Limits and Derivatives, Statistics, Probability; Class 12 — Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three-Dimensional Geometry, Probability (conditional + Bayes' + Binomial)

English (Paper II / GAT Section A, 200 marks)7 topics

Grammar and usage — spotting the error, sentence improvement, sentence correction, parts of speech, articles, prepositions, tenses, subject-verb agreement, voice (active and passive), narration (direct and indirect), conditionals, modals
Vocabulary — antonyms, synonyms, one-word substitution, idioms and phrases, commonly confused words, foreign words and phrases used in English
Reading comprehension — one or more passages of NCERT class 11-12 difficulty with vocabulary-in-context, inference and main-idea questions
Cohesion of sentences — cloze test (passage with blanks), ordering of sentences / jumbled paragraphs, ordering of words within a sentence (para-jumbles)
Recommended depth: Wren & Martin (chapters on tense, voice, narration, prepositions, articles, conditionals) end-to-end, plus Norman Lewis Word Power Made Easy for systematic vocabulary building
Indicative weight distribution across 50 English questions: spotting errors and sentence improvement 12-15, antonyms-synonyms 8-10, one-word substitution 5-8, idioms and phrases 3-5, reading comprehension 8-10, cloze test 5-8, jumbled sentences / para-jumbles 3-5
Cohesion sub-skill — sentence ordering (PQRS-type questions) and cloze test together account for 8-12 questions and reward fast pattern-matching rather than deep grammar; treat them as scoring engines, not as time-sinks, by capping each set to 60-90 seconds

General Knowledge (Paper II / GAT Section B, 400 marks) — six sub-sections8 topics

Physics (heavy weight) — physical properties and states of matter, mass, weight, volume, density, specific gravity, Archimedes' principle, pressure barometer, motion (uniform, accelerated, Newton's laws), gravitation, work / energy / power, sound waves and 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 / magnetic effects of current, measurement of electrical power, primary and secondary cells, use of X-rays, modern scientific instruments — telescope, microscope, mariner's compass, lightning conductor
Chemistry — physical and chemical changes, elements / mixtures / compounds, symbols / formulas and simple chemical equations, law of chemical combination (excluding stoichiometry), properties of air and water, preparation and properties of hydrogen / oxygen / nitrogen / carbon dioxide, oxidation and reduction, acids / bases / salts, carbon and its different forms, fertilisers (natural and artificial), materials used in industry — soap, glass, ink, paper, cement, paints, safety matches, gunpowder, structure of the atom, atomic equivalent and molecular weights, valency
General Science (Biology) — difference between living and non-living, basis of life — cells, protoplasm and tissues, growth and reproduction in plants and animals, elementary knowledge of the human body and its important organs, common epidemics — their causes and prevention, food and nutrition (sources of food, balanced diet), the solar system — meteors and comets, eclipses, achievements of eminent scientists
History and Freedom Movement — broad survey of Indian history with emphasis on culture and civilisation, freedom movement in India (1857 to 1947 — major events and personalities), elementary study of the Indian Constitution and administration, elementary knowledge of the Five-Year Plans, Panchayati Raj, co-operatives and community development, Bhoodan, Sarvodaya, national integration and welfare state, Indian national renaissance and modern world — Renaissance, Industrial Revolution, French and Russian revolutions, impact of science and technology on society, concept of one-world, the United Nations, panchsheel, democracy, socialism and communism, the role of India in the present world
Geography — the Earth — its shape and size, latitudes 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 / air routes of India, main items of imports and exports
Current Events — 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, recent defence acquisitions, ISRO milestones, awards (Padma / military gallantry / Olympic / sports), recent appointments — Chief of Defence Staff, Service Chiefs, key civilian officials
Indicative weight distribution across 100 GK questions: Physics 22-25, Chemistry 15-18, General Science / Biology 8-10, History (with Freedom Movement) 15-18, Geography 12-15, Current Affairs 18-22 — Physics-Chemistry-Biology together at roughly 50% of GK marks is what distinguishes NDA GK from CDS GK (where they account for only 15-20%)
Static GK side-topics that appear regularly: Indian Constitution basics (Preamble, Fundamental Rights and Duties, key Articles — 14/19/21/32/352/356/370, schedules, key amendments), Indian and world organisations (UN structure and key agencies, SAARC, BRICS, G20, ASEAN), Indian defence structure (Chief of Defence Staff role, three Service Chiefs, integrated theatre commands progress, key indigenous platforms), space and nuclear milestones (ISRO mission timeline, key DRDO test events, NPCIL reactors)

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