NDA Exam Pattern
Paper  Subject Name  Duration  Containing Marks  No. of Questions 
I  Mathematics  2.5 Hours (150 Min)  300  120 
II  General Ability Test  2.5 Hours (150 Min)  600  150 
Total Marks  900  270 
Pattern of General Ability Test
Section  Subject Name  Marks  No. of Questions 
I  English  200  50 
II  General Knowledge  400  100 
Total Marks  600  150 
General Knowledge Marks distribution
Subject Name  Marks 
Physics  100 
Chemistry  60 
General Science  40 
History, Freedom Movement  80 
Geography  80 
Current Events  40 
NDA Maths Syllabus
YOU CAN ALSO DOWNLOAD SYLLABUS PDF GIVEN AT THE BOTTOM OF THE PAGE
Trigonometry
 Trigonometric ratios
 Inverse trigonometric functions
 Properties of triangles
 Angles and their measures in degrees and in radians
 Trigonometric identities Sum and difference formulae
 Applications – Height and distance
 Multiple and Submultiple angles.
Algebra
 Complex numbers
 Basic properties
 Modulus
 Argument
 Cube roots of unity
 Conversion of a number in decimal system to binary system and viceversa
 Arithmetic
 Geometric and Harmonic Progressions
 Solution of linear inequations of two variables by graphs
 Binomial theorem and its application
 Representation of real numbers on a line
 Binary system of numbers
 Quadratic equations with real coefficients
 Permutation and Combination
 Logarithms and their applications.
Differential Calculus
 Composite functions – one to one, onto and inverse functions
 Continuity of functions
 Algebraic operations on continuous functions
 Geometrical and physical interpretation of a derivative – applications
 Increasing and decreasing functions
 Application of derivatives in problems of maxima and minima
 Concept of a real valued function – domain, range, and graph of a function, Notion of limit,
 Standard limits – Derivative of a function at a point.
 Geometrical and Physical interpretation of a derivative – Applications, Derivatives of Sum, Product and quotient of functions.
 Derivative of a function with respect to another function
 The derivative of a composite function and Second order derivatives.
Vector Algebra:
 Vectors in two and three dimensions
 Magnitude and direction of a vector
 Scalar multiplication of vector
 Scalar product or dot product of two vectors
 Applications – work done by a force and moment of a force, geometrical problems, Unit and null vectors, the addition of vectors, Vector product and cross product of two vectors.
Integral Calculus and Differential equations
 Integration by substitution and by parts
 Trigonometric
 Exponential and hyperbolic functions
 Definition of order and degree of a differential equation
 Formation of a differential equation by examples
 A solution of the first order and firstdegree differential equations of various types – examples, Integration as the inverse of differentiation, Standard integrals involving algebraic expressions.
 Evaluation of definite integrals
 Determination of areas of plane regions bounded by curves – applications, General and particular solution of a differential equation, Application in problems of growth and decay.
Matrices and Determinants
 Types of Matrices
 Determinant of a matrix
 Adjoint and inverse of a square matrix
 Operations on matrices
 Basic properties of determinant
 Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.
Analytical Geometry of two and three dimensions:
 Distance formula
 Angle between two lines
 Equation of a circle in standard and in general form
 Ellipse and hyperbola
 Rectangular Cartesian Coordinate system
 Equation of a line in various forms
 Distance of a point from a line
 Standard forms of parabola
 Eccentricity and axis of a conic.
Three dimensions:
 Point in a threedimensional space
 Distance between two points
 Equation of a plane and a line in various forms
 Equation of a sphere
 Direction Cosines and direction ratios
 An angle between two lines and an angle between two planes.
Statistics:
 Frequency distribution
 Measures of Central tendency – mean, median and mode, Classification of data
 Cumulative frequency distribution – examples
 Graphical representation – Histogram, Pie Chart
 Frequency Polygon – examples,
 Variance and standard deviation – determination and comparison, Correlation and regression.
Probability:
 Outcomes and associated sample Space
 Bayes’ theorem
 Simple problems
 Binomial distribution
 Random experiment
 Examples of random experiments giving rise to Binominal distribution

Events
 Mutually exclusive and exhaustive events,
 Impossible and certain events
 Complementary
 Elementary and composite events
 Union and Intersection of events
 Definition of probability
 Classical and statistical – examples,
 Elementary theorems on probability
 Simple problems
 Conditional probability
 Random variable as function on a sample space
 Binomial distribution
 Examples of random experiments giving rise to Binomial distribution.
General Ability Syllabus

Part A
English
 Vocabulary
 Grammar and usage
 Comprehension and cohesion in extended text to test the candidate’s proficiency in English.
Part B
NDA Syllabus for General Knowledge
The question paper comprises of general knowledge and covers the subjects that include Physics, Chemistry, General Science, Social Studies, Geography and Current Events.
Section A – NDA Exam Syllabus – Physics
 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
 Sound waves and their properties
 Simple musical instruments
 Natural and Artificial Magnets
 Properties of a Magnet
 Earth as a Magnet
 Simple Pendulum – Simple Pulleys, Balloon, Siphon, Pressure Cooker, Levers, Pumps, Hydrometer, Gramophone, Thermos Flask, Telegraphs, Periscope, Telephone, Microscope, Telescope, Mariner’s Compass.
 Lightning Conductors
 Safety Fuses
 Physical Properties and States of Matter – Mass, Weight, Volume, Density and Specific Gravity
 Principle of Archimedes
 Pressure Barometer
 Effects of Heat
 Measurement of temperature and heat
 Change of State and Latent Heat
 Modes of transference of Heat
 Rectilinear propagation of Light
 Reflection and refraction.
 Spherical mirrors and Lenses – Human Eye
 Static and Current Electricity
 Conductors and Nonconductors
 Ohm’s Law – Simple Electrical Circuits, Lighting and Magnetic effects of Current, Heating, Measurement of Electrical Power, Primary and Secondary Cells, Use of XRays.
Section B – UPSC NDA Syllabus of Chemistry
 Preparation and Properties of Hydrogen
 Oxygen
 Nitrogen and CarbonDioxide
 Oxidation and Reduction
 Carbon – different forms, Material used in the preparation of substances like soap, Ink, Glass, Cement, Paper, Paints, Safety Matches, and GunPowder, Physical and Chemical changes.
 Elements, Symbols, Mixtures and Compounds, Formulas and simple Chemical Equations, Law of Chemical Combination (excluding problems).
 Properties of Air and Water, Acids, bases, and salts.
 Fertilizers – Natural and Artificial, Elementary ideas about the Structure of Atom, Atomic, Equivalent and Molecular Weights, Valency.
Section C – Syllabus of NDA – General Science
 The basis of Life – Cells, Protoplasms and Tissues, Elementary knowledge of human Body and its important organs.
 Food – Source of Energy for man, Balanced Diet, Constituents of food, Achievements of Eminent Scientists, Difference between the living and nonliving, Common Epidemics, their causes, and prevention
 The Solar System – Meteors and Comets, Eclipses.
Section D – Syllabus for NDA Exam – History
 Freedom Movement in India
 Elementary knowledge of Five Year Plans of India
 Bhoodan
 Sarvodaya
 National Integration and Welfare State
 Basic Teachings of Mahatma Gandhi
 A broad survey of Indian History
 With emphasis on Culture and Civilisation
 Elementary study of Indian Constitution and Administration
 Panchayati Raj, Cooperatives, and Community Development
 Forces shaping the modern world; Renaissance
 Exploration and Discovery
 War of American Independence.
 French Revolution, Industrial Revolution and Russian Revolution.
 The 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 – Syllabus for NDA Entrance Exam – Geography
 Origin of Earth
 Rocks and their classification
 Weathering – Mechanical and Chemical, Atmosphere and its composition, Earthquakes, and volcanoes.
 Temperature and Atmospheric Pressure
 Planetary Winds
 Cyclones and Anticyclones
Humidity  Condensation and Precipitation
 Types of Climate
 Major Natural regions of the World
 Important Sea ports and main sea
 Land and air routes of India.
 Main items of Imports and Exports of India
 The Earth, its shape, and size
 Latitudes and Longitudes
 Concept of time
 International Date Line
 Movements of Earth and their effects
 Ocean Currents and Tides
 Regional Geography of India – Climate, Natural vegetation.
 Mineral and Power resources
 Location and distribution of agricultural and industrial activities.
Section F – Current Events
 Current important world events.
 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.
NDA MATH SYLLABUS PDF
NDA GAT SYLLABUS PDF