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

Paper | Subject | Code No | MaximumMarks |
---|

I | Mathematics | 01 | 300 |

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.

3.Trigonometry:

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.

Paper | Subject | Code No | MaximumMarks |
---|

II | General AbilityTest | 02 | 600 |

Part‘A’ | English | | 200 |

Part‘B’ | GenralKnowledge | | 400 |

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.

Note:

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**

**Standard**

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.

**Syllabus**

**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)**

**Arithmetic**

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.

**Algebra**

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.

**Trigonometry**

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.

**Geometry**

Lines and angles, Planeand plane figures, Theorems
on

- Properties of angles at a
point
- Parallel
lines,
- Sides and
angles of atriangle,
- Congruency of
triangles,
- Similar
triangles,
- Concurrence of medians
andaltitudes,
- Properties of angles, sides and diagonals of
aparallelogram, rectangle
andsquare
- Circles
and its properties including tangents
andnormals,
- Loci.

**Mensuration**

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.

**Statistics**

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.