NDA Syllabus 2026: Maths, GAT, English & GK Syllabus PDF Download

Algebra

Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in the Binary system to Decimals and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear inequations, Permutation and Combination, Binomial theorem and Logarithms.

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-application. 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

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.

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 differential equations, solution of first order and first-degree differential equations of various types—examples. Application in problems of growth and decay.

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.

Vector Algebra

Vectors in two and three dimensions, magnitude, and direction of a vector. Unit and null vectors, the 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 and in geometrical problems.

Analytical Geometry Of Two and Three Dimensions

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 in a 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. Angle between two lines and angle between two planes. Equation of a sphere.

Statistics and Probability

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 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 Binomial distribution.

Calculus

20-25

Quadratic equation

20-15

Matrices & Determinants 

30

Probability

10

Trigonometry

30

Complex number 

10-15

Total Marks

300 Marks

Total No. of Questions

120

Correct Answer 

2.5 marks

Marks deducted for the wrong answer

- 0.83

Total duration of Mathematics Paper 

2 Hours 30 Minutes

Physical Properties and States of Matter

Modes of Transference of Heat

Mass

Sound waves and their properties

Weight

Simple musical instruments

Volume

Rectilinear propagation of Light

Density and Specific Gravity

Reflection and refraction

Principle of Archimedes

Spherical mirrors and Lenses

Pressure Barometer

Human Eye

Motion of objects

Natural and Artificial Magnets

Velocity and Acceleration

Properties of a Magnet

Newton’s Laws of Motion

Earth as a Magnet

Force and Momentum

Static and Current Electricity

Parallelogram of Forces

Conductors and Non-conductors

Stability and Equilibrium of bodies

Ohm’s Law

Gravitation

Simple Electrical Circuits

Elementary ideas of work

Heating, Lighting, and Magnetic Effects of Current

Power and Energy

Measurement of Electrical Power

Effects of Heat

Primary and Secondary Cells

Measurement of Temperature and Heat

Use of X-Rays ,General Principles in the working of 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.

Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon Dioxide, Oxidation and Reduction. Acids, bases and salts. Carbon— different forms

Physical and Chemical Changes

Fertilizers—Natural and Artificial

Elements

Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and Gunpowder

Mixtures and Compounds

Elementary ideas about the structure of Atom

Symbols, Formulae, and simple Chemical Equation

Atomic Equivalent and Molecular Weights

Law of Chemical Combination (excluding problems)

Valency

Properties of Air and Water

Common Epidemics, their causes and prevention

Difference between the living and non-living

Food-Source of Energy for man

Basis of Life—Cells, Protoplasms and Tissues

Constituents of food

Growth and Reproduction in Plants and Animals

Balanced Diet

Elementary knowledge of Human Body and its important organs

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

Forces shaping the modern world; Renaissance

A broad survey of Indian History, with emphasis on Culture and Civilisation

Exploration and Discovery; War of American Independence, French Revolution, Industrial Revolution and Russian Revolution

Freedom Movement in India

Impact of Science and Technology on Society

Elementary study of Indian Constitution and Administration

Concept of one World

Elementary knowledge of Five Year Plans of India

United Nations, Panchsheel, Democracy, Socialism and Communism

Panchayati Raj

Role of India in the present world

Co-operatives and Community Development

A broad survey of Indian History, with emphasis on Culture and Civilisation

Bhoodan, Sarvodaya, National Integration and Welfare State

Basic Teachings of Mahatma Gandhi

-

The Earth, its shape and size

Ocean Currents and Tides Atmosphere and its composition

Latitudes and Longitudes

Temperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anticyclones; Humidity; Condensation and Precipitation

Concept of time

Types of Climate

International Date Line

Major Natural regions of the World

Movements of Earth and their effects

Regional Geography of India—Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and Industrial activities

Origin of Earth. Rocks and their classification

Important Sea ports and main sea, land and air routes of India

Weathering—Mechanical and Chemical, Earthquakes and Volcanoes

Main items of Imports and Exports of India

Knowledge of Important events that have happened in India in the recent years

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

Current important world events

-

Figures

Completion of Series

Analogies

Blood Relation

Figure Matrix

Shorter and Taller Problems

Locating Hidden Figure

Logical Venn Diagram

Odd one out

Jumbled Words

Classification of data

Coding-Decoding

Paper Cutting

One word Substitution

Problem on Dice

Problem on Ranks

Problem on Cubes

Interchanging 2 signs

Visualizing Patterns

Identification of letters

Spatial Ability

Reconstruction of test

• Mathematics for NDA and NA: National Defence Academy and Naval Academy by RS Aggarwal
• Quantitative aptitude for competitive examinations by RS Aggarwal

• History Of Modern India (History) by Bipan Chandra
• Science and Technology in India (Science and Technology) by Kalpana Rajaram: Spectrum
• Objective General English for Competitive Exams by S P Bakshi
• Manorama Yearbook by Mammen Mathew

Paper 1

Mathematics

300

2 ½

Paper 2

GAT

600

2 ½

Total

900

5 hours