NDA Syllabus 2026: Download the Maths and GAT Syllabus PDF Here

Exam Conducting Body

Union Public Service Commission (UPSC)

Exam Name

National Defence Academy & Naval Academy Exam

Selection Process

Written Test & SSB Interview

Total Papers

2 (Mathematics & General Ability Test)

Total Marks (Written)

900

Exam Mode

Offline (Pen & Paper)

Negative Marking

Yes (1/3rd for wrong answers)

Exam Duration

Each paper: 2.5 hours

NDA 1 Syllabus 2026

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Topic

Complete Syllabus

Algebra

• Concept of sets, operations on sets, Venn diagrams, De Morgan’s laws, Cartesian product, relations and equivalence relations.
• Representation of real numbers on a number line.
• Complex numbers: basic properties, modulus, argument, cube roots of unity.
• Binary number system and conversion between decimal and binary systems.
• 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.
• Logarithms and their applications.

Matrices and Determinants

• Types of matrices and operations on matrices.
• Determinants and their basic properties.
• Adjoint and inverse of a square matrix.
• Applications: Solution of system of linear equations in two or three unknowns using Cramer’s Rule and Matrix Method.

Trigonometry

• Angles and their measures in degrees and radians.
• Trigonometric ratios and identities.
• Sum and difference formulae.
• Multiple and sub-multiple angles.
• Inverse trigonometric functions.
• Applications: height and distance and properties of triangles.

Analytical Geometry (2D & 3D)

• 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 axes of conics. 
• Point in three-dimensional space and distance between two points. 
• Direction cosines and direction ratios. 
• Equation of a line and a plane in various forms. 
• Angle between two lines and angle between two planes. 
• Equation of a sphere.

Differential Calculus

• Concept of real-valued functions: domain, range and graphs. 
• Composite functions, one-one, onto and inverse functions. 
• Limits and standard limits. 
• Continuity of functions and algebra of continuous functions. 
• Derivative at a point: geometrical and physical interpretation. 
• Derivatives of sum, product and quotient of functions. 
• Chain rule. Second-order derivatives. 
• Increasing and decreasing functions. 
• Applications of derivatives in maxima and minima problems.

Integral Calculus & Differential Equations

• Integration as inverse of differentiation. 
• Integration by substitution and by parts. 
• Standard integrals involving algebraic, trigonometric, exponential and hyperbolic functions. 
• Evaluation of definite integrals and applications in finding areas bounded by curves. 
• Differential equations – order and degree. 
• Formation of differential equations. 
• General and particular solutions. 
• Solution of first-order first-degree differential equations. 
• Applications in growth and decay problems.

Vector Algebra

• Vectors in two and three dimensions. 
• Magnitude and direction of vectors. 
• Unit and null vectors. 
• Addition of vectors and scalar multiplication. 
• Scalar (dot) product and vector (cross) product. 
• Applications: work done by a force, moment of a force, and geometrical problems.

Statistics and Probability

• Statistics: Classification of data, frequency and cumulative frequency distributions.
• Graphical representation: histogram, pie chart, frequency polygon.
• Measures of central tendency – mean, median and mode. 
• Variance and standard deviation. 
• Correlation and regression. 
• Probability: Random experiments and sample space. 
• Events: mutually exclusive, exhaustive, impossible and certain events. 
• Union and intersection of events. 
• Complementary, elementary and composite events. 
• Classical and statistical definition of probability. 
• Elementary probability theorems. 
• Conditional probability and Bayes’ theorem. 
• Random variables and Binomial distribution with examples.

Subject

Complete Syllabus

Physics

• 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.

• 21 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; Lightning Conductors, Safety Fuses.

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 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.

General Science

• Difference between the living and non-living.

• Basis of Life: Cells, Protoplasms 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: Source of Energy for man. Constituents of food, Balanced Diet.

• The Solar System: Meteors and Comets, Eclipses. Achievements of Eminent Scientists

History

• 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.

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 and air routes of India. Main items of Imports and Exports of India.

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.