National Defence Academy

The NDA exam is conducted by UPSC for admission to the Army, Navy and Air Force wings of the NDA. This exam is a gateway for candidates looking forward to joining Defence Forces including Army, Navy and Air Force.

This is a national level exam conducted twice a year: NDA I and NDA II to help candidates make a career in Defence services. National Defence Academy & Naval Academy (NDA & NA) Examination will be a two-step process where candidates first need to take the exam and then qualify the personality test or interview conducted by the Service Selection Board (SSB). The UPSC is solely responsible for issuing guidelines for selection and the final conduct of the entrance examination.

The Supreme Court has passed an interim order to allow women to join UPSC National Defence Academy & Naval Academy (NDA & NA) exam.

SubjectCodeDurationMaximum Marks
Mathematics (120 Questions)012 Hours & 30 Minutes300
General Ability Test (150 Questions) English + General Knowledge022 Hours & 30 Minutes600
Total  900
SSB Test/Interview900

The marks distribution of NDA exam GAT section is highlighted below:

NDA General Ability TestMaximum marks
Part A English200
Part B – General Awareness 
History, Freedom Movement, etc.80
General Science40
Current Events40

NDA Syllabus For Mathematics – Paper 1

Mathematics TopicNDA Topic-wise syllabus
AlgebraSets, 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 inequations, Permutation and Combination, Binomial theorem and Logarithms.
CalculusConcept 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 DeterminantsTypes 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 EquationsIntegration 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.
TrigonometryAngles 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 AlgebraVectors 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 and moment of a force and in geometrical problems.
Analytical Geometry Of Two and Three DimensionRectangular 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 in 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 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 ProbabilityProbability: 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.

NDA Paper II Syllabus

EnglishGrammar and usage, vocabulary, comprehension and cohesion in extended text
Physical Properties and States of MatterModes of transference of Heat
MassSound waves and their properties
WeightSimple musical instruments
VolumeRectilinear propagation of Light
Density and Specific GravityReflection and refraction
Principle of ArchimedesSpherical mirrors and Lenses
Pressure BarometerHuman Eye
Motion of objectsNatural and Artificial Magnets
Velocity and AccelerationProperties of a Magnet
Newton’s Laws of MotionEarth as a Magnet
Force and MomentumStatic and Current Electricity
Parallelogram of ForcesConductors and Non-conductors
Stability and Equilibrium of bodiesOhm’s Law
GravitationSimple Electrical Circuits
Elementary ideas of workHeating, Lighting and Magnetic effects of Current
Power and EnergyMeasurement of Electrical Power
Effects of HeatPrimary and Secondary Cells
Measurement of Temperature and HeatUse 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; Lightning Conductors, Safety Fuses.
Preparation and Properties of Hydrogen, Oxygen, Nitrogen and Carbon Dioxide, Oxidation and Reduction. Acids, bases and salts. Carbon— different formsPhysical and Chemical Changes
Fertilizers—Natural and ArtificialElements
Material used in the preparation of substances like Soap, Glass, Ink, Paper, Cement, Paints, Safety Matches and GunpowderMixtures and Compounds
Elementary ideas about the structure of AtomSymbols, Formulae and simple Chemical Equation
Atomic Equivalent and Molecular WeightsLaw of Chemical Combination (excluding problems)
ValencyProperties of Air and Water
General Science
Common Epidemics, their causes and preventionDifference between the living and non-living
Food—Source of Energy for manBasis of Life—Cells, Protoplasms and Tissues
Constituents of foodGrowth and Reproduction in Plants and Animals
Balanced DietElementary knowledge of Human Body and its important organs
The Solar System—Meteors and Comets, Eclipses. Achievements of Eminent Scientists 
Forces shaping the modern world; RenaissanceA broad survey of Indian History, with emphasis on Culture and Civilisation
Exploration and Discovery; War of American Independence, French Revolution, Industrial Revolution and Russian RevolutionFreedom Movement in India
Impact of Science and Technology on SocietyElementary study of Indian Constitution and Administration
Concept of one WorldElementary knowledge of Five Year Plans of India
United Nations, Panchsheel, Democracy, Socialism and CommunismPanchayati Raj
Role of India in the present worldCo-operatives and Community Development
A broad survey of Indian History, with emphasis on Culture and CivilisationBhoodan, Sarvodaya, National Integration and Welfare State
 Basic Teachings of Mahatma Gandhi
The Earth, its shape and sizeOcean Currents and Tides Atmosphere and its composition
Latitudes and LongitudesTemperature and Atmospheric Pressure, Planetary Winds, Cyclones and Anticyclones; Humidity; Condensation and Precipitation
Concept of timeTypes of Climate
International Date LineMajor Natural regions of the World
Movements of Earth and their effectsRegional Geography of India—Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and Industrial activities
Origin of Earth. Rocks and their classificationImportant Sea ports and main sea, land and air routes of India
Weathering—Mechanical and Chemical, Earthquakes and VolcanoesMain items of Imports and Exports of India
Current Affairs
Knowledge of Important events that have happened in India in the recent yearsProminent personalities—both Indian and International including those connected with cultural activities and sports
Current important world events