UPKAR PRAKASHAN, AGRA–2

Editorial BoardCompetition Science Vision

2015

(According to the Revised Syllabus)Objective Type Questions

Practice Work-Book—NDA Exam. 285/-N.D.A. Mathematics

New Pattern Test of Objective English 175/-Correct English How to Write It 240/-Ever Latest General Knowledge 170/-

Other Useful Books

185/-

Jain & Gupta) (By :

-/012srepaP devloS ADN

General Knowledge Overview with Current Affairs

60/-

Upkar’sUpkar’sUpkar’sUpkar’sUpkar’sUpkar’sUpkar’s

-/994.maxE .A.D.NUpkar’s Dr. H.P. Sharma & Yash Srivastava) (By :

-/543.maxE .A.D.NUpkar’s

© Publishers

PublishersUPKAR PRAKASHAN(An ISO 9001 : 2000 Company)

2/11A, Swadeshi Bima Nagar, AGRA–282 002Phone : 4053333, 2530966, 2531101Fax : (0562) 4053330, 4031570E-mail : care@upkar.in, Website : www.upkar.inBranch Offices :4845, Ansari Road, Daryaganj,New Delhi—110 002Phone : 011–23251844/66

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The publishers have taken all possible precautions in publishing this book, yet ifany mistake has crept in, the publishers shall not be responsible for the same.This book or any part thereof may not be reproduced in any form byPhotographic, Mechanical, or any other method, for any use, without writtenpermission from the Publishers.All disputes shall be subject to the jurisdiction of courts at Agra.

ISBN : 978-81-7482-028-0

Price : 540.00(Rs. Five Hundred Forty Only)

Code No. 319

Printed at : Upkar Prakashan (Printing Unit) Bye-pass, AGRA

Contents● Previous Years’ Papers Fully Solved

MATHEMATICS

● Algebra 3–711. Sets 32. Relation 83. Complex Numbers 134. Arithmetic Progression 195. Geometric Progression 256. Harmonic Progression 317. Miscellaneous Series 358. Permutations and Combinations 409. Quadratic Equations 45

10. Binomial Theorem 5011. Binary Number System 5712. Representation of Real Numbers on

a line 6013. Linear Inequations in two variables 64

● Matrices and Determinants 72–85● Trigonometry 86–115

1. Identities and Trigonometric Ratios 862. Simple Identities 953. Properties of Triangles 994. Inverse Trigonometrical Functions 1045. Height and Distance 109

● Coordinate Geometry 116–1551. Rectangular cartesian coordinates

and straight lines 1162. The Circle 1213. The Parabola 1254. The Ellipse 1305. The Hyperbola 1356. Geometry of Three Dimensions 1407. The Plane 1458. The Sphere 152

● Differential Calculus 156–2091. Function 1562. Limit and Continuity 1643. Differentiation 182

4. Increasing and Decreasing,Maxima and Minima 194

● Integral Calculus and DifferentialEquations 210–2481. Indefinite Integrals 2102. Definite Integrals 2233. Differential Equations 2334. Problems on applications of

differential Equation growth andDecay 246

● Vector Algebra 249–263● Statistics and Probability 264–273

Frequency Distribution, mean,median, mode and standarddeviation 264

● Graphical Representation 274–2921. Histogram, Frequency Polygon

and Pie chart 2742. Correlation and Regression 2813. Probability 284

GENERAL ENGLISH

1. Common Error 2–34

— Articles, Nouns, Pronouns 2

— Adjectives, Adverbs, Adverbial order 8

— Verb, Infinitive, Verbal noun,

Gerund, Participle 13

— Conjunctions, Prepositions 19

— Miscellaneous Sentences 24

2. Antonyms 35–40

3. Synonyms 41–47

4. Sentence Completion 48–57

5. One Word Substitution 58–61

6. Comprehension 62–75

7. Passage Completion 76–80

8. Completion of Paragraphs andSentences 81–88

( iv )

GENERAL KNOWLEDGE● History and Culture 3–17

● Indian Polity and Constitution 18–40

● Indian National Movement 41–54● Geography 55–68

— Geography of India 55— World Geography 63

● Indian Economy 69–79

● International Organisation 80–81

● Books and Authors 82–85

● Awards 86–89

● Sports 90–93

● Final Population Results–

Census of India 2011 94–96● Physics 1–140

1. Measurement and DimensionalAnalysis 3–7

2. Rectilinear Motion 8–123. Motion in Two and Three

Dimensions 13–19

4. Laws of Motion 20–265. Work, Energy and Power 27–316. Rotatory Motion of Rigid Body 32–357. Gravitation 36–408. Heat and Thermodynamics 41–479. Oscillations 48–51

10. Wave Motion 52–56

11. Electrostatics 57–64

12. Current Electricity 65–69

13. Thermal and Chemical Effectsof Current 70–72

14. Magnetic Effect of Current 73–76

15. Magnetism 77–79

16. Electromagnetic Induction and

Alternating Current 80–84

17. Electromagnetic Waves 85–86

18. Ray Optics and Optical

Instruments 87–95

19. Electrons and Photons 96–98

20. Atoms, Molecule and Nuclei 99–102

21. Solids and Semiconductor

Devices 103–105

22. Primary and Secondary Cells 106–113

23. X-rays 114–116

24. General Physics 117–139

● Chemistry 1–60

— General Chemistry 3

— Physical Chemistry 16

— Inorganic Chemistry 28

— Organic Chemistry 42

● General Science 1–16

IMPORTANT INSTRUCTIONS AND SYLLABUS

A. SCHEME OF THE EXAMINATION1. The subjects of the written examination,

the time allowed and the maximum marksallotted to each subject will be as follows :

SubjectSubject

CodeDuration

Max.

Marks

Mathematics 01 212 hours 300

General Ability Test 02 212 hours 600

Total 900

SSB Test/Interview 900

2. THE PAPERS IN ALL THE SUBJECTS WILLCONSIST OF OBJECTIVE TYPE QUESTIONSONLY. THE QUESTION PAPERS (TEST BOOK-LETS) OF MATHEMATICS AND PART ‘B’ OFGENERAL ABILITY TEST WILL BE SETBILINGUALLY IN HINDI AS WELL AS ENGLISH.

3. In the question papers wherever necessary,questions involving the Metric System of Weightsand Measures only will be set.

4. Candidates must write the papers in theirown hand. In no circumstances will they beallowed the help of a scribe to write the answersfor them.

5. The Commission have discretion to fixqualifying marks in any or all the subjects at theexamination.

6. The candidates are not permitted to usecalculators or Mathematical or logarithmic tablefor answering objective type papers (Test Book-lets). They should not, therefore, bring the sameinside Examination Hall.

B. SYLLABUS OF THE EXAMINATION

Paper–I (Code No. 01)

MATHEMATICS

(Maximum Marks–300)

1. Algebra :Concept of a set, operations on sets, Venn

diagrams. De Morgan laws. Cartesian product,relation, equivalence relation.

Representation of real numbers on a lineComplex numbers—basic properties, modulus,argument, cube roots of unity. Binary system ofnumbers. Conversion of a number in decimalsystem to binary system and vice-versa.Arithmetic, Geometric and Harmonic progres-sions. Quadratic equations with real coefficients.Solution of linear inequations of two variables bygraphs. Permutation and Combination. Binomialtheorem and its applications. Logarithms and theirapplications.

2. Matrices and Determinants :Types of matrices, operations on matrices.

Determinant of a matrix basic properties ofdeterminants. Adjoint and inverse of a squarematrix Applications—Solution of a system oflinear equations in two or three unknowns byCramer’s rule and by Matrix Method.

3. Trigonometry :Angles and their measures in degrees and in

radians. Trigonometrical ratios. Trigonometricidentities Sum and difference formulae. Multipleand Sub-multiple angles. Inverse trigonometricfunctions. Applications—Height and distance,properties of triangles.

4. Analytical Geometry of Two and ThreeDimensions :

Rectangular Cartesian Coordinate system.Distance formula. Equation of a line in variousforms. Angle between two lines. Distance of apoint from a line. Equation of a circle in standardand in general form. Standard forms of parabola,ellipse and hyperbola. Eccentricity and axis of aconic. Point in a three dimensional space, distancebetween two points. Direction Cosines anddirection ratios. Equation of a plane and a line invarious forms. Angle between two lines and anglebetween two planes. Equation of a sphere.

5. Differential Calculus :Concept of a real valued function-domain,

range and graph of a function. Composite

( vi )

functions, one to one, onto and inverse functions.Notion of limit, Standard limits—examples.Continuity of functions—examples, algebraicoperations on continuous functions. Derivative offunction at a point, geometrical and physicalinterpretation of a derivative-applications.Derivatives of sum, product and quotient offunctions, derivative of a function with respect toanother function, derivative of a compositefunction. Second order derivatives. Increasing anddecreasing functions. Application of derivatives inproblems of maxima and minima.

6. Integral Calculus and DifferentialEquations :Integration as inverse of differentiation,

integration by substitution and by parts, standardintegrals involving algebraic expressions, trigono-metric, exponential and hyperbolic functions.Evaluation of definite integrals—determination ofareas of plane regions bounded by curves—applications. Definition of order and degree of adifferential equation, formation of a differentialequation by examples. General and particularsolution of a differential equation, solution of firstorder and first degree differential equations ofvarious types—examples. Application in problemsof growth and decay.

7. Vector Algebra :Vectors in two and three dimensions,

magnitude and direction of a vector. Unit and nullvectors, addition of vectors, scalar multiplicationof a vector, scalar product or dot product of twovectors. Vector product or cross product of twovectors. Applications-work done by a force andmoment of a force, and in geometrical problems.

8. Statistics and Probability :Statistics : Classification of data. Frequency

distribution, cumulative frequency distribution-examples. Graphical representation—Histogram,Pie Chart, frequency polygon—examples. Measureof Central tendency—Mean, median and mode.Variance and standard deviation—determinationand comparison. Correlation and regression.

Probability : Random experiment, outcomesand associated sample space, events, mutuallyexclusive and exhaustive events, impossible andcertain 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 asfunction on a sample space. Binomial distribution,examples of random experiments giving rise toBinomial distribution.

Paper–II (Code No. 02)

GENERAL ABILITY TEST

(Maximum Marks–600)

PART ‘A’

ENGLISH

(Maximum Marks–200)

The question paper in English will bedesigned to test the candidate’s understanding ofEnglish and work-man-like use of words. Thesyllabus covers various aspects like : Grammarand usage, vocabulary, comprehension andcohesion in extended texts to test the candidate’sproficiency in English.

PART ‘B’

GENERAL KNOWLEDGE

(Maximum Marks–400)

The question paper on General Knowledgewill broadly cover the subjects : Physics,Chemistry, General Science, Social Studies,Geography and Current Events.

The syllabus given below is designed toindicate the scope of these subjects included inthis paper. The topics mentioned are not to beregarded as exhaustive and questions on topics ofsimilar nature not specifically mentioned in thesyllabus may also be asked. Candidate’s answersare expected to show their knowledge andintelligent understanding of the subject.

Section ‘A’ (Physics)

Physical Properties and States of Matter,Mass, Weight, Volume, Density and SpecificGravity, Principle of Archimedes, Pressure Baro-meter.

Motion of objects, Velocity and Acceleration,Newton’s Laws of Motion, Force and Momentum,Parallelogram of Forces, Stability and Equilibriumof bodies, Gravitation, elementary ideas of Work,Power and Energy.

( vii )

Effects of Heat. Measurement of Temperatureand Heat. Change of State and Latent Heat. Modesof transference of Heat.

Sound waves and their properties, Simplemusical instruments.

Rectilinear propagation of Light. Reflectionand refraction, Spherical mirrors and Lenses,Human Eye.

Natural and Artificial Magnets. Properties ofa Magnet, Earth as a Magnet.

Static and Current Electricity. Conductors andNon-conductors, Ohm’s Law. Simple ElectricalCircuits. Heating, Lighting and Magnetic effectsof Current. Measurement of Electrical Power, Pri-mary and Secondary Cells. Use of X-rays.

General Principles in the working of thefollowing :

Simple Pendulum, Simple Pulleys, Siphon,Levers, Balloon, Pumps, Hydrometer, PressureCooker, Thermos Flask, Gramophone, Telegraphs,Telephone, Periscope, Telescope, Microscope,Mariner’s Compass, Lightning Conductors. SafetyFuses.

Section ‘B’ (Chemistry)

Physical and Chemical changes. Elements,Mixtures and Compounds, Symbols, Formulaeand Simple Chemical Equations. Law of ChemicalCombination (excluding problems). Properties ofAir and Water.

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

Acids, Bases and Salts.

Carbon–Different forms.

Fertilizers–Natural and Artificial.

Materials used in the preparations ofsubstances like Soap, Glass, Ink, Paper, Cement,Paints, Safety Matches and Gun-powder.

Elementary ideas about the Structure ofAtom, Atomic Equivalent and Molecular Weights.Valency.

Section ‘C’ (General Science)Difference between the living and non-living.Basis of Life—Cells Protoplasms and Tissues.

Growth and Reproduction in Plants andAnimals.

Elementary knowledge of human Body andits important organs.

Common Epidemics, their causes and preven-tion.

Food—Source of Energy for Man, Consti-tuent of food, Balanced Diet.

The Solar System Meteors and Comets, Ecli-pses.

Achievements of Eminent Scientists.

Section ‘D’ (History, Freedom Movementetc.)

A broad survey of Indian History, withemphasis on Culture and Civilisation.

Freedom Movement in India.

Elementary study of Indian Constitution andAdministration.

Elementary knowledge of Five Year Plans ofIndia.

Panchayati Raj, Co-operatives and Commu-nity Development.

Bhoodan, Sarvodaya, National Integrationand Welfare State, Basic teachings of MahatmaGandhi.

Forces shaping the modern World; Renais-sance Exploration and Discovery. War of Ameri-can Independence, French Revolution, IndustrialRevolution and Russian Revolution, Impact ofScience and Technology on Society. Concept ofOne World, United Nations Panchsheel, Demo-cracy, Socialism and Communism. Role of Indiain the Present World.

Section ‘E’ (Geography)

The Earth, its shape and size, Latitudes andLongitudes. Concept of Time, International Dateline, Movements of Earth and their effects.

Origin of Earth, Rocks and their classifica-tion; Weathering—Mechanical and Chemical,Earthquakes and Volcanoes.

Ocean Current and Tides.

Atmosphere and its composition; Temperatureand Atmospheric Pressure, Planetary winds,Cyclones and Anti-cyclones; Humidity; Conden-sation and Precipitation; Types of Climate. MajorNatural regions of the World.

( viii )

Regional Geography of India—Climate,Natural Vegetation. Mineral and Power resources;location and distribution of agricultural and indus-trial activities.

Important Sea Ports and main sea, land andair routes of India. Main items of Imports andExports of India.

Section ‘F’ (Current Events)

Knowledge of Important events that havehappened in India in the recent years.

Current important world events.

Prominent personalities—both Indian andInternational including those connected with cul-tural activities and sports.

Note—Out of maximum marks assigned toPart ‘B’ of this paper questions on Sections ‘A’,‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ will carry approximately25%, 15%, 10%, 20%, 20% and 10% weightagesrespectively.

INTELLIGENCE AND PERSONALITYTEST

The SSB procedure consists of two stageSelection process-stage-I and stage-II. Only thosecandidates who clear the stage-I are permitted toappear for stage II. The details are :

(a) Stage-I comprises of Officer IntelligenceRating (OIR) tests are Picture Perception*Description Test (PP & DT). The candidateswill be shortlisted based on combination ofperformance in QIR Test and PP and DT.

(b) Stage-II comprises of Interview, GroupTesting Officer Tasks, Psychology Tests andthe Conference. These tests are conductedover 4 days. The details of these tests aregiven on the website www.joinindianarmy.nic.in.

The personality of a candidate is assessed bythree different assessors viz. the InterviewingOfficer (IO), Group Testing Officer (GTO) andthe Psychologist. There are no separate weightagefor each test. The mks are allotted by assessorsonly after taking into consideration theperformance of the candidate holistically in all thetest. In addition, marks for Conference are alsoallotted based on the initial performance of theCandidate in the three techniques and decision ofthe Board. All these have equal weightage.

The various tests of IO, GTO and Psych aredesigned to bring out the presence/absence ofOfficer Like Qualities and their trainability in acandidate. candidates are Recommended orNot Recommended at the SSB

⎯⎯⎯⎯⎯⎯⎯⎯

National Defence AcademyExamination

Solved Paper

National Defence Academy Examination.

Publisher : Upkar Prakashan ISBN : 978817482028 Author : CompetitionScience Vision

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