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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 subject-wise topics. Check out the complete NDA syllabus as per different subjects.




NDA Entrance Exam

Exam Mode

Offline (OMR Sheet)

Types of Questions


Total Papers


Paper 1


Paper 2

General Ability Test (GAT)

Negative Marking 


Total Shifts


NDA Math Syllabus

Topics Covered in NDA Math Paper
  • Algebra
  • Matrices and Determinants
  • Trigonometry
  • Analytical Geometry of Two and Three-Dimensions
  • Differential Calculus
  • Integral Calculus and Differential Equations
  • Vector Algebra
  • Statistics and Probability
  • 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
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 by Cramer’s rule
  • Applications-Solution of a system of linear equations by Matrix Method
  • 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
Analytical Geometry of Two and Three-Dimensions
  • 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 three-dimensional 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 real-valued function
  • Domain, range and graph of a function
  • Composite functions, one-to-one, 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 first-order and first-degree differential equations of various types
  • Application in problems of growth and decay
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
  • Applications—work done by a force
  • Moment of a force in geometrical problems
Statistics and Probability
  • 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
  • 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





GAT Full Form

General Ability Test


Paper 2

Paper Code




Total Parts

Two – “A” and “B”

GAT Part “A”


GAT Part “B”

General Knowledge

Topics Covered in NDA GAT Paper

Part “A” – English

  • Grammar
  • Reading Comprehension
  • Vocabulary
  • Synonyms
  • Antonyms
  • Idioms and Phrases
  • Para Jumbles 
  • Spotting the Errors
  • Sentence Sequencing
  • Active and Passive Voices
  • Direct and Indirect Speech

Part “B” – General Knowledge

  • Section ‘A’ (Physics)
  • Section ‘B’ (Chemistry)
  • Section ‘C’ (General Science)
  • Section ‘D’ (History, Freedom Movement, etc.)
  • Section ‘E’ (Geography)
  • Section ‘F’ (Current Events)
NDA GAT Paper Part “B” - General Knowledge



Section ‘A’ (Physics)


Section ‘B’ (Chemistry)


Section ‘C’ (General Science)


Section ‘D’ (History, Freedom Movement, etc.)


Section ‘E’ (Geography)


Section ‘F’ (Current Events)


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 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
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 non-living
  • 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
  • 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
  • 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 Anti-cyclones
  • 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

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