NDA Syllabus 2025: Subject-Wise Exam Details

Particulars

Details

Exam Name

National Defence Academy & Naval Academy Examination, 2025

Conducting Authority

Union Public Service Commission (UPSC)

Exam Frequency

Twice a Year

Exam Mode

Offline (Pen & Paper Based)

Papers/Subjects

Mathematics and General Ability Test (GAT)

Total Marks

900 Marks

Negative Marking

1/3rd Marks Deducted for Each Wrong Answer

Duration of Each Paper

2 Hours 30 Minutes (Each Paper)

Official Website

upsc.gov.in

Subjects

Important Topics

Mathematics

Algebra, Matrices and Determinants, Trigonometry, Analytical Geometry (2D and 3D), Differential Calculus, Integral Calculus and Differential Equations, Vector Algebra, Statistics and Probability, Set Theory, Complex Numbers, Linear Equations, Quadratic Equations, Arithmetic and Geometric Progressions, Binomial Theorem, Logarithms, Mensuration

English (Part of GAT)

Grammar and Usage, Vocabulary, Comprehension and Unseen Passages, Spotting Errors, Fill in the Blanks, Synonyms & Antonyms, Idioms and Phrases, Sentence Improvement, Para Jumbles, Cloze Test

General Knowledge (Part of GAT)

Physics (NDA Physics Syllabus)

Physical Properties and States of Matter, Motion and Laws of Motion, Force, Gravitation, Work and Energy, Power, Sound Waves, Heat, Thermodynamics, Light – Reflection and Refraction, Optics, Static and Current Electricity, Magnetism, Electromagnetic Induction, Nuclear Physics, Modern Physics, Units and Measurements, Simple Machines, Principles of Archimedes and Pascal

Chemistry

Matter and Its States, Atomic Structure, Chemical Bonding, Elements, Compounds and Mixtures, Chemical Reactions and Equations, Acids, Bases and Salts, Periodic Table, Metals and Non-metals, Carbon and Its Compounds, Fertilizers, Petroleum and Natural Gas, Environmental Chemistry, Important Chemicals in Daily Life

General Science

Basic Biology, Human Body Systems (Digestive, Respiratory, Circulatory), Reproduction, Genetics, Food and Nutrition, Diseases and Prevention, Immunity, Ecology and Environment, Bio-diversity, Plant and Animal Kingdom, Cell Structure and Functions, Biotechnology Basics

History (NDA History Syllabus)

Indian Ancient, Medieval, and Modern History, Indian Freedom Struggle, Revolt of 1857, Indian National Congress, Important Movements and Leaders, Constitution of India, Fundamental Rights and Duties, Basic Governance Structure, Indian Monuments and Culture, World History (Renaissance, French Revolution, Industrial Revolution, World Wars)

Geography

Earth and Its Structure, Rocks and Minerals, Mountains, Rivers and Lakes, Climate and Weather, Soil Types in India, Natural Vegetation, Agriculture and Industries, Important Sea Ports and Airports, Latitudes and Longitudes, Time Zones, Earthquakes and Volcanoes, Oceans and Continents, Environmental Issues, Population and Urbanization

Current Affairs

National and International Events, Defence Exercises and Agreements, Government Schemes, Awards and Honours, Important Personalities, Science and Technology Developments, Sports, Economy and Finance Updates, Environmental Issues, Space and Defence Technology (like ISRO, DRDO), International Organizations (UN, WHO, IMF, World Bank)

NDA Exam Pattern 2025 for Maths & GAT

Subject

Mathematics

General Ability Test

Total Number of Questions

120

150

Maximum Marks

300

600

Marks for Correct Answer

2.5 mark

4 mark

Marks for Incorrect Answer

-0.83 mark

-1.33 mark

Duration

2.5 hours

2.5 hours

NDA Exam Pattern 2025 for SSB Test/Interview

Subject

Total

SSB Test/Interview

900

NDA Syllabus 2025 for Mathematics

Subject

UPSC NDA Maths Syllabus 2025

NDA Syllabus for Algebra

Concept of set, operations on sets, Venn diagrams.  De Morgan laws, Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbers—basic properties, modulus, argument, cube roots of unity. Binary system of numbers. 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 inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its applications. Logarithms and their applications.

NDA Syllabus for 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.

NDA Syllabus for Trigonometry

Angles and their measures in degrees and radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications-Height and distance, properties of triangles.

NDA Syllabus for Analytical Geometry of Two and Three Dimension

Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. The 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, the distance between two points. Direction Cosines and direction ratios. Equation two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. The angle between two lines and the angle between two planes. Equation of a sphere.

NDA Syllabus for Differential Calculus

Concept of a real-valued function–domain, range, and graph of a function. Composite functions, one-to-one, onto, and inverse functions. The 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, derivative of a function concerning another function, derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima

NDA Syllabus for 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. A general and particular solution of differential equations, solution of the first order, and first-degree differential equations of various types—examples. Application in problems of growth and decay

NDA Syllabus for 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. Application work done by a force and moment of a force and in geometrical problems

NDA Syllabus for 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, associated sample space, 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 on 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 Binominal distribution

NDA GAT Syllabus 2025

Subject

NDA Important Topics

NDA Syllabus for English

• Spotting Errors

• Comprehension

• Selecting Words

• Synonyms

• Antonyms

• Sentence Improvements

• Ordering of Words in a Sentence, etc.

NDA Syllabus for Physics

• Physical Properties and States of Matter, Mass, Weight, Volume, Density, and Specific Gravity, the Principle of Archimedes, and the 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 Nonconductors, 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.

NDA Syllabus for Chemistry

• 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 carbon dioxide, 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

NDA Syllabus for General Science

• The difference between living and nonliving things. The basis of Life—cells, Protoplasms, and Tissues. Growth and Reproduction in Plants and Animals.

• Elementary knowledge of the Human Body and its vital organs. Common Epidemics, their causes, and prevention.

• Food is a source of Energy for man. Its constituents include a balanced Diet. The Solar System includes meteors, comets, and Eclipses. Eminent Scientists have achieved many achievements.

NDA Syllabus for History, Freedom Movement, etc.

• 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.

NDA Syllabus for Geography

• 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.

NDA Syllabus for Current Events

• Knowledge of Important events that have happened in India in recent years. Current important world events.

• Prominent personalities—both Indian and International including those connected with cultural activities and sports

UPSC NDA Syllabus 2025 for SSB

Subject

Important Topics

Stage I

• Officer Intelligence Rating (OIR) tests

• Picture Perception Description Test (PP&DT)

Stage II

• Interview

• Group Testing Officer Tasks

• Psychology Tests

• Conference