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IAF | IAF 2022 | Syllabus | IAF Syllabus

Home » List of Examinations » IAF Examination » IAF Exam Syllabus

IAF Exam Syllabus

IAF Exam Syllabus

National Defence Academy Examination (I) - NDA Syllabus2009 - Page2

PaperSubjectCode NoMaximumMarks

1. Algebra:

Concept of a set,operations on sets, Venn diagrams. De Morgan laws. Cartesian product,relation, equivalence relation.

Representationof real numbers on a line. Complexnumbers - basic properties, modulus,argument, cube roots of unity.Binary system of numbers. Conversion ofa number in decimal system tobinary system and vice-versa.

Arithmetic,Geometric and Harmonic progressions.Quadratic equations with realcoefficients. Solution of linearinequations of two variables bygraphs. Permutation and Combination.Binomial theorem and itsapplication. Logarithms and theirapplications.

2. Matrices andDeterminants:

Typesof matrices,operations on matrices Determinant of a matrix, basicproperties ofdeterminant. Adjoint and inverse of a square matrix,Applications -Solution of a system of linear equations in two or threeunknowns byCramer's rule and by MatrixMethod.


Anglesand theirmeasures in degrees and in radians. Trigonometricalratios.Trigonometric identities Sum and difference formulae. MultipleandSub-multiple angles. Inverse trigonometric functions. Applications-Height and distance, properties oftriangles.

4. AnalyticalGeometry of two and threedimensions:

RectangularCartesian Coordinate system. Distanceformula. Equation of a line invarious forms. Angle between two lines.Distance of a point from aline. Equation of a circle in standard and ingeneral form. Standardforms of parabola, ellipse and hyperbola.Eccentricity and axis of aconic.

Point ina three dimensionalspace, distance between two points. DirectionCosines and directionratios. Equation of a plane and a line in variousforms. Angle betweentwo lines and angle between two planes. Equation ofa sphere.

5. DifferentialCalculus:

Conceptof a realvalued function - domain, range and graph of a function.Compositefunctions, one to one, onto and inverse functions. Notion oflimit,Standard limits - examples. Continuity of functions -examples,algebraic operations on continuous functions. Derivative of afunctionat a point, geometrical and physical interpreatationof a derivative -applications. Derivatives of sum, product and quotientof functions,derivative of a function with respect of another function,derivativeof a composite function. Second order derivatives. Increasinganddecreasing functions. Application of derivatives in problems ofmaximaand minima.

6. Integral Calculus andDifferential equations:

Integrationas inverse of differentiation, integrationby substitution and byparts, standard integrals involving algebraicexpressions,trigonometric, exponential and hyperbolic functions.Evaluation ofdefinite integrals - determination of areas of planeregions bounded bycurves - applications. Definition of order and degreeof a differentialequation, formation of a differential equation byexamples. General andparticular solution of a differential equation,solution of first orderand first degree differential equations ofvarious types - examples.Application in problems of growth anddecay.

7. VectorAlgebra:

Vectorsin two andthree dimensions, magnitude and direction of a vector. Unitand nullvectors, addition of vectors, scalar multiplication of vector,scalarproduct or dot product of two-vectors. Vector product and crossproductof two vectors. Applications-work done by a force and moment ofa force,and in geometrical problems.

8. Statistics andProbability:-

Statistics:Classification of data, Frequencydistribution, cumulative frequencydistribution - examples Graphicalrepresentation - Histogram, PieChart, Frequency Polygon - examples.Measures of Central tendency -mean, median and mode. Variance andstandard deviation - determinationand comparison. Correlation andregression.

Probability:Randomexperiment, outcomes and associated sample space, events,mutuallyexclusive and exhaustive events, impossible and certainevents. Unionand Intersection of events. Complementary, elementary andcompositeevents. Definition of probability - classical and statistical-examples. Elementary theorems on probability - simpleproblems.Conditional probability, Bayes' theorem - simple problems.Randomvariable as function on a sample space. Binomial distribution,examplesof random experiments giving rise to Binominal distribution.

PaperSubjectCode NoMaximumMarks
IIGeneral AbilityTest02600

Thequestion paper in English will be designed to testthe candidate’sunderstanding of English and workman like use of words.The syllabuscovers various aspects like : Grammar and usage,vocabulary,comprehension and cohesion in extended text to test thecandidate’sproficiency inEnglish.

The questionpaperon General Knowledge will broadly cover the subjects :Physics,Chemistry, General Science, Social Studies, Geography andCurrentEvents.

The syllabus givenbelow isdesigned to indicate the scope of these subjects included inthispaper. The topics mentioned are not to be regarded as exhaustiveandquestions on topics of similar nature not specifically mentioned inthesyllabus may also be asked. Candidate’s answers are expected toshowtheir knowledge and intelligent understanding of thesubject.

Section ‘A’(Physics)

PhysicalPropertiesand States of Matter, Mass, Weight, Volume, Density andSpecificGravity, Principle of Archimedes, PressureBarometer.

Motionof objects,Velocity and Acceleration, Newton’s Laws of Motion, forceand Momentum,Parallelogram of forces, Stability and Equilibrium ofbodies,Gravitation, elementary ideas of work, Power andEnergy.

Effects of Heat,Measurement of temperature and heat, change of State and Latent Heat,Modes of transference of Heat.

Soundwaves and their properties, Simple musicalinstruments.

Rectilinearpropagation of Light, Reflection and refraction. Spherical mirrors andLenses. Human Eye.

Natural andArtificial Magnets, Properties of a Magnet, Earth as aMagnet.

Staticand CurrentElectricity, conductors and Non-conductors, Ohm’s Law,Simple ElectricalCircuits, Heating, Lighting and Magnetic effects ofCurrent, Measurementof Electrical Power, Primary and Secondary Cells,Use ofX-Rays.

National Defence Academy Examination (I) - NDA Syllabus2009 - Page1

General Principlesin the working of the following:

SimplePendulum,Simple Pulleys, Siphon, Levers, Balloon, Pumps, Hydrometer,PressureCooker, Thermos Flask, Gramophone, Telegraphs, Telephone,Periscope,Telescope, Microscope, Mariner’s Compass; LighteningConductors, SafetyFuses.

Section ‘B’(Chemistry)

PhysicalandChemical changes. Elements, Mixtures and Compounds, Symbols,formulaeand simple Chemical Equations, Law of Chemical Combination(excludingproblems). Properties of Air andWater.

Preparation andProperties of Hydrogen, Oxygen, Nitrogen and Carbondioxide, Oxidationand Reduction.

Acids, bases andsalts.

Carbon - differentforms.

Fertilizers -Natural and Artificial

Material used inthe preparation of substances like soap, Glass, Ink, Paper, Cement,Paints, Safety Matches, andGun-Powder.

Elementary ideasabout the Structure of Atom, Atomic, Equivalent and Molecular Weights,Valency.

Section ‘C’(General Science)

Difference betweenthe living and non- living.

Basis ofLife - Cells, Protoplasms andTissues.

Growth andReproduction in Plants andAnimals.

Elementaryknowledge of human Body and its importantorgans.

Common Epidemics,their causes and prevention.

Food -Source of Energy for man. Constituents of food, BalancedDiet.

The Solar System -Meteors and Comets, Eclipses.

Achievements of EminentScientists.

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

A broadsurvey of Indian History, with emphasis on Culture andCivilisation.

Freedom Movement inIndia.

Elementary study ofIndian Constitution andAdministration.

Elementaryknowledge of Five Year Plans ofIndia.

Panchayati Raj,Co-operatives and CommunityDevelopment.

Bhoodan, Sarvodaya,National Integration and Welfare State, Basic Teachings of MahatmaGandhi.

forcesshaping themodern world; Renaissance, Exploration and Discovery; Warof AmericanIndependence. French Revolution, Industrial Revolution andRussianRevolution. Impact of Science and Technology on Society.Concept of oneWorld, United Nations, Panchsheel, Democracy. Socialismand Communism.Role of India in the presentworld.

Section ‘E’(Geography)

TheEarth, its shapeand size. Lattitudes and Longitudes, Concept of time.International DateLine. Movements of Earth and theireffects.

Origin of Earth.Rocks and their classification; Weathering - Mechanical and Chemical,Earthquakes and volcanoes.

OceanCurrents and Tides

Atmosphereand itscomposition; Temperature and Atmospheric Pressure, PlanetaryWinds,cyclones and Anti-cyclones; Humidity; Condensation andPrecipitation;Types of Climate. Major Natural regions of theWorld.

RegionalGeographyof India - Climate, Natural vegetation. Mineral and Powerresources;location and distribution of agricultural andindustrialactivities.

Important Sea portsand main sea, land and air routes of India. Main items of Imports andExports of India.

Section ‘F’(Current Events)

Knowledge ofImportant events that have happened in India in the recentyears.

Current importantworld events.

Prominentpersonalities - both Indian and International including those connectedwith cultural activities andsports.


Outof maximum marksassigned to part ‘B’ of this paper, questions onSections ‘A’, ‘B’, ‘C’,‘D’, ‘E’ and ‘F’ will carry appoximately 25%,15%, 10%, 20%, 20% and 10%weightages respectively.

Intelligence and PersonalityTest:

Inaddition to the interview the candidates will be putto IntelligenceTests both verbal and non-verbal, designed to assesstheir basicintelligence. They will also be put to Group Tests such asgroupdiscussions, group planning, outdoor group tasks, and asked togivebrief lectures on specified subjects.

Allthese tests areintended to judge the mental calibre of a candidate. Inbroad terms,this is really an assessment of not only his intellectualqualities butalso his social traits and interests in currentaffairs.

UPSC - CDS Examination (I) 2009 -Syllabus

Standard and Syllabus of theExamination


Thestandard of the papers in Elementary Mathematics will be ofMatriculation level.

The standard ofpapers in other subjects will approximately be such as may be expectedof a graduate of an IndianUniversity.


English (Code No.01)

Thequestion paper will be designed to test the candidates’ understandingof English and workmanlike use ofwords.

General Knowledge (Code No.02)

General Knowledgeincluding knowledge of currentevents and of such matters of everydayobservation and experience intheir scientific aspects as may beexpected of an educated person whohas not made a special study of anyscientific subject.

Thepaper will alsoinclude questions on History of India and Geography ofa nature whichcandidate should be able to answer without specialstudy.

Elementary Mathematics (Code No.03)


NumberSystem-Natural numbers, Integers, Rational andReal numbers.Fundamental operations addition, subtraction,multiplication, division,Square roots, Decimalfractions.

Unitarymethod-timeand distance, time and work, percentages, applications tosimple andcompound interest, profit and loss, ratio andproportion,variation.

Elementary NumberTheory-Division algorithm. Prime and composite numbers. Tests ofdivisibilityby 2,3,4,5,9 and 11. Multiples andfactors.

FactorisationTheorem. H.C.F. and L.C.M. Euclideanalgorithm, Logarithms to base 10,laws of logarithms, use of logarithmictables.


BasicOperations, simple factors, Remainder Theorem,H.C.F., L.C.M. Theory ofpolynomials, solutions of quadratic equations,relation between itsroots and coefficients (Only real roots to beconsidered).

Simultaneouslinearequations in two unknowns-analytical and graphicalsolutions.Simultaneous linear equations in two variables and theirsolutions.

Practicalproblemsleading to two simultaneous linear equations or inequations intwovariables or quadratic equations in one variable &theirsolutions.

Set language andset notation, Rational expressions and conditional identities, Laws ofindices.


Sinex,cosine x, Tangent x when 00 x 900 Values of sin x, cos x and tan x,forx = 00, 300, 450, 600 and 900 Simple trigonometricidentities.

Use oftrigonometric tables. simple cases of heights anddistances.


Lines and angles, Planeand plane figures, Theorems on

  1. Properties of angles at a point
  2. Parallel lines,
  3. Sides and angles of atriangle,
  4. Congruency of triangles,
  5. Similar triangles,
  6. Concurrence of medians andaltitudes,
  7. Properties of angles, sides and diagonals of aparallelogram, rectangle andsquare
  8. Circles and its properties including tangents andnormals,
  9. Loci.


Areasofsquares, rectangles, parallelograms, triangle and circle. Areasoffigures which can be split up into these figures (Field Book),Surfacearea and volume of cuboids, lateral surface and volume ofrightcircular cones and cylinders, surface area and volume ofspheres.


Collectionand tabulation of statistical data, Graphicalrepresentation frequencypolygons, histograms, bar charts, pie chartsetc. Measures ofcentraltendency.

Intelligence and personalitytest

Inaddition to the interview the candidates will be putto IntelligenceTests both verbal and non-verbal, designed to assesstheir basicintelligence.

They willalso be put toGroup Tests such as group discussions, group planning,outdoor grouptasks, and asked to give brief lectures on specifiedsubjects.

Allthese tests areintended to judge the mental calibre of a candidate. Inbroad terms,this is really an assessment of not only his intellectualqualities butalso his social traits and interests in currentaffairs.

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