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NDA Written Exam Syllabus
The National Defence Academy (NDA) is a premier joint training institution and center of excellence for grooming young aspirants for the Indian Armed Forces and the armed forces of friendly foreign countries. The NDA syllabus undergoes modifications and amendments from time to time. The NDA syllabus covers several subjects including mathematics, English, general knowledge and current affairs. Candidates appearing for the NDA written exam are required to analyze subjectwise topics. Check out the complete NDA syllabus as per different subjects.
Particulars  Details 
Exam  NDA Entrance Exam 
Exam Mode  Offline (OMR Sheet) 
Types of Questions  Objective 
Total Papers  Two 
Paper 1  Mathematics 
Paper 2  General Ability Test (GAT) 
Negative Marking  Applicable 
Total Shifts  Two 
NDA Math Syllabus
Topics Covered in NDA Math Paper
 Algebra
 Matrices and Determinants
 Trigonometry
 Analytical Geometry of Two and ThreeDimensions
 Differential Calculus
 Integral Calculus and Differential Equations
 Vector Algebra
 Statistics and Probability
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 viceversa
 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
Matrices and Determinants
 Types of matrices
 Operations on matrices
 Determinant of a matrix
 Basic properties of determinants
 Adjoint and inverse of a square matrix
 ApplicationsSolution of a system of linear equations by Cramer’s rule
 ApplicationsSolution of a system of linear equations by Matrix Method
Trigonometry
 Angles and their measures in degrees and radians
 Trigonometrical ratios
 Trigonometric identities
 Sum and difference formulae
 Multiple and Submultiple angles
 Inverse trigonometric functions
 ApplicationsHeight and distance
 Properties of triangles
Analytical Geometry of Two and ThreeDimensions
 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 axis of a conic
 Point in a threedimensional space
 Distance between 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
Differential Calculus
 Concept of a realvalued function
 Domain, range and graph of a function
 Composite functions, onetoone, onto and inverse functions
 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
 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
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 a differential equation
 Solution of firstorder and firstdegree differential equations of various types
 Application in problems of growth and decay
Vector Algebra
 Vectors in two and threedimensions
 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
 Applications—work done by a force
 Moment of a force in geometrical problems
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 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 (Binomial distribution)
NDA GAT Syllabus
Particulars  Details 
Subject  GAT 
GAT Full Form  General Ability Test 
Paper  Paper 2 
Paper Code  02 
Shift  Second 
Total Parts  Two – “A” and “B” 
GAT Part “A”  English 
GAT Part “B”  General Knowledge 
Topics Covered in NDA GAT Paper
Part “A” – English
 
Part “B” – General Knowledge

NDA GAT Paper Part “B”  General Knowledge
Sections  Weightage 
Section ‘A’ (Physics)  25% 
Section ‘B’ (Chemistry)  15% 
Section ‘C’ (General Science)  10% 
Section ‘D’ (History, Freedom Movement, etc.)  20% 
Section ‘E’ (Geography)  20% 
Section ‘F’ (Current Events)  10% 
Section ‘A’ (Physics) Syllabus
 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
 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 XRays
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
Section ‘B’ (Chemistry) Syllabus
 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 and Oxygen
 Preparation and Properties of Nitrogen and Carbon dioxide
 Oxidation and Reduction
 Acids, bases and salts
 Different forms of carbon
 Natural and Artificial Fertilizers
 Elementary ideas about the structure of Atom
 Atomic Equivalent and Molecular Weights
 Valency
Material used in the preparation of the following substances:
 Soap
 Glass
 Ink
 Paper
 Cement
 Paints
 Safety Matches
 Gun Powder
Section ‘C’ (General Science) Syllabus
 Difference between the living and nonliving
 Basis of Life—Cells, Protoplasms and Tissues
 Growth and Reproduction in Plants and Animals
 Elementary knowledge of 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
Section ‘D’ (History and Freedom Movement) Syllabus
 A broad survey of Indian History
 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 System
 Cooperatives 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
 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
Section ‘E’ (Geography) Syllabus
 The Earth
 Shape and size of the Earth
 Latitudes and Longitudes
 Concept of the 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 Anticyclones
 Humidity, Condensation and Precipitation
 Types of Climate
 Major Natural regions of the World
 Regional Geography of India
 Climate and Natural vegetation
 Mineral and Power resources
 location and distribution of agricultural and Industrial activities
 Important Sea ports
 Main sea, land and air routes of India
 Main items of Imports and Exports of India
Section ‘F’ (Current Events) Syllabus
 Important happenings and events in India
 Important international happening and events
 Prominent Indian personalities
 Prominent International personalities
 Prominent personalities connected with cultural activities
 Prominent personalities connected with sports
 Heritage and Culture
 Military exercises and locations
 Defence deals and countries
 Recent wars between countries
 Geographical locations of countries involved in war
 Important appointments
 Latest sports events held in India and abroad
 New schemes launched by the Government of India
 Important international seminars and their venues
 Important days and their themes
 Latest books and authors
 National and international awards and ceremonies
 Recent seminars and meetings related to climate change
 Important constructions such as tunnels and bridges
 Constitutional articles and provisions in the news
 Important places covered in the news recently