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NDA (National Defence Academy)

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Before starting the preparation first check the important points of the NDA Syllabus and Exam Pattern by going through the table below. 

Name of the Exam: National Defence Academy (NDA) 

Conducting Body: Union Public Service Commission, UPSC.  

Frequency of Exam: Twice in a Year  

Selection Process: 1. Written Test consisting of Objective Type Questions

                                     2. Intelligence & Personality Test (SSB) 

 Mode of exam: Offline 

Papers in NDA Exam: 1. Mathematics 

                                       2. General Ability Test 

Marks Segregation: 1. Mathematics: 300

                                        2. GAT: 600 Marks  

Total No. of Questions: 1. Mathematics: 120 

                                               2. GAT: 150 

  Negative Marking: 1. Mathematics: -0.83 

                                         2. GAT: -1.33 marks  

 Exam Duration: 2.5 Hours for Each Paper (5 hours total) 

Language of Question Paper: English & Hindi English Language paper has to be attempted in English. 

Subject wise syllabus for NDA-




Algebra: Sets, Venn diagrams, De Morgan laws, Cartesian product, relation, equivalence relation. Real numbers, Complex numbers, Modulus, Cube roots, Conversion of a number in Binary system to Decimals, and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations, Linear in equations, 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. The 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, a derivative of a function concerning another function, the 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 the 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 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 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 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. The angle between two lines and the 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.



Physical Properties and States of Matter

Modes of transference of Heat

Mass, Weight, Volume, Sound waves and their properties

Simple musical instruments

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


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


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)


Properties of Air and Water

General studies

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 the Human Body and its important organs

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


Forces shaping the modern world;


Exploration and Discovery;

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

Freedom Movement in India

French Revolution, Industrial Revolution, and Russian Revolution

War of American Independence,

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,


Panchayati Raj, Democracy, Socialism and Communism

Role of India in the present world

Co-operatives and Community Development

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

Course content

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