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MATHEMATICS

Contents

1.     Basic Tips For Calculation

2.     Arithmetic

2.1 Number System

2.1.1 Introduction

2.1.2 Classification of Numbers

2.1.3 Classification of Natural Numbers

2.1.4 Properties of Rational and Irrational Numbers

2.1.5 Some important results on Numbers

2.1.6 Tests of Divisibility

2.1.7 Modulus of a Real number 

2.2 HCF and LCM                                                                                                               

2.2.1 Factors and multiples

2.2.2 Common factors

2.2.3 Highest Common factor (HCF)

2.2.3.1 Prime factorization method

2.2.3.2 Division method

2.2.3.3 HCF of Decimals

2.2.3.4 HCF of vulgar fractions

2.2.4 Least Common multiple (LCM)

2.2.4.1 Prime factorization method

2.2.4.2 Common Division method

2.2.4.3 LCM of Decimals

2.2.4.4 LCM of Fractions

2.2.5 Relation between HCF and LCM

2.2.6 Comparison of fractions using LCM

2.3 Simplification

2.3.1 VBODMAS Rule

2.3.2 Basic arithmetic operations and symbols

2.3.3 Short cut methods for basic operations

2.3.3.1 Short cuts in Addition

2.3.3.2 Short cuts in Subtraction

2.3.3.3 Short-cuts in Multiplication

2.3.3.4 Short cuts in Division

2.3.4 Some algebraic formulae for Simplification

2.4 Approximation

2.4.1 Addition and subtraction

2.4.2 Multiplication

2.4.3 Division

2.5 Ratio and Proportion

2.5.1 Definition and basic concepts

2.5.2 Ratio between more than two quantities

2.5.3 Compound ratio

2.5.4 Comparison of ratios

2.5.5 Proportion

2.5.6 Types of Proportion

2.5.7 Some specific cases

2.6 Average

2.6.1 Definition

2.6.2 Weighted average

2.6.3 Specific cases of average

2.6.3.1 Average speed

2.6.3.2 Average of Series of Numbers

2.6.3.3 Miscellaneous cases

2.7 Additional Topics in Arithmetic

2.7.1 Problems on Trains                       

2.7.1.1 Basic concepts

2.7.1.2 Specific cases

2.7.1.2.1 Train moving past a stationary point object

2.7.1.2.2 Train moving past a stationary lengthy object      

2.7.1.2.3 Train moving past a moving point object

2.7.1.2.4 Train moving past a moving lengthy object

2.7.2 Unitary Method

2.7.2.1 Time and Distance

2.7.2.1.1 Basic definitions and concepts

2.7.2.1.2 Formulae for specific cases

2.7.2.2 Time and Work

2.7.2.2.1 Basic concepts

2.7.2.2.2 Formulae for specific cases

2.7.2.3 Pipes and Cisterns

2.7.2.3.1 Basic concepts

2.7.2.3.2 Basic principles

2.7.2.3.3 Specific cases and formulae

2.7.2.4 Boat and Streams

2.7.2.4.1 Basic concepts

2.7.2.4.2 Specific cases

 

3.     Commercial Maths

 

3.1 Interest

3.1.1 Simple Interest

3.1.1.1 Basic definitions and concepts

3.1.1.2 Some specific cases

3.1.2 Compound Interest

3.1.2.1 Basic definitions and concepts

3.1.2.2 Compounding for different time periods and rates

3.1.2.3 Some specific cases

3.1.2.4 Cases relating Simple and Compound interest

3.2 Percentage

3.2.1 Definition

3.2.2 Conversion between Percent, fraction and decimal

3.2.3 Specific cases of Percentage

3.2.3.1 Percent relationship between quantities

3.2.3.2 Examinations and marks

3.2.3.3 Geometry

3.2.3.4 Depreciation

3.2.3.5 Population growth

3.2.3.6 Price and consumption

3.3 Profit and Loss

3.3.1 Definition

3.3.2 Rule of fraction

3.3.3 Specific cases of Profit and Loss

3.3.3.1 Relation between Cost price and selling price

3.3.3.2 Using false weights

3.3.3.3 Discounts

3.3.3.4 Multiple transactions

3.4 Partnership

3.4.1 Basic concepts

3.4.2 Basic principle of profit sharing

3.4.2.1 Simple partnership

3.4.2.3 Compound partnership

3.4.3 Specific cases

 

 

 

4.      Series

 

4.1 Definition

4.2 Types of Series

4.2.1 Arithmetic Series

4.2.2 Geometric Series

4.2.3 Series of squares and cubes

4.2.4 Mixed series

4.2.5 Two tier Arithmetic series

4.2.6 Three tier Arithmetic series

4.2.7 Arithmetico-Geometric series

4.2.8 Geometrico-Arithmetic series

4.2.9 Twin series    

4.3 Suggested steps for solving series problems

4.4 Different types of problems on Series

4.4.1 Finding the next term

4.4.2 Finding wrong/missing number

4.4.3 Two line number series

4.5 Some unique series

GENERAL MENTAL ABILITY

Contents

1.     VERBAL TESTS

 

1.1              Reasoning Tests

1.1.1       Direction and Distance Test

1.1.2       Classification (Odd Man Out) Test

1.1.3       Coding-Decoding Tests

1.1.4       Series Test

1.1.5       Relationships Test

1.1.5.1 Blood Relationships Test

1.1.5.2 Coded Relationships Tests

1.1.6       Alphabet Test

1.1.7       Number, Ranking and Time Sequence Test

1.1.8       Mathematical Operations

1.1.9       Logical Word Sequence Test

1.1.10   Cubes and Cubical Dice Tests

1.1.11   Data Arrangement Test

1.1.12   Data Sufficiency Test

1.2              Logic Tests

1.2.1 Syllogism

1.2.2 Statements Conclusions

1.2.2.1 Coded Inequality

 

2.     NON VERBAL TESTS

 

2.1              Problems Based On Symmetry

2.1.1       Problems On Mirror Images

2.1.2       Problems On Water Images

2.1.3       Completion Of An Incomplete Pattern

2.1.4       Problems On Paper Folding

2.1.5       Problems On Paper Cutting

2.2              Problem Based On Visual Ability

2.3              Classification

2.4              Series

2.5              Analogy  

 

GENERAL KNOWLEDGE

Contents

 

1.     General Knowledge (World)

1.1        Books and Authors

1.2   World’s Great Structures (Building)

1.3   Calendars

1.4   Countries

1.4.1    Countries and their Capital

1.4.2    Countries and Their Emblems

    1.4.3    Countries and Their Parliaments

    1.4.4    Lines and Boundaries

    1.4.5    Minerals and Producing Countries

    1.4.6    Major Industrial Towns

    1.4.7    Major Riverside Cities

    1.4.8    Tribes and Races

1.5   Currencies

1.6   Music and Dance

1.7   Disasters

1.8   Famous Places of World

1.9   Famous Personalities

1.10 First, Largest, Longest of World

                 1.10.1 ‘First’ in the World

                           1.10.2    Important Geographical Facts

1.11  Inventions and Discoveries

1.12  Languages

1.13 Religions

1.14  Wars

1.15  Weathers and Climate

1.16 World organization

                 1.16.1 United Nations Organization (UNO)

                 1.16.2 The Commonwealth

                 1.16.3 The Non–Aligned Movement (NAM)

                 1.16.4 South Asian Association for Regional Cooperation (SAARC)

                 1.16.5 European Union (EU)

                 1.16.6 Organisation of Petroleum Exporting Countries (OPEC)

                 1.16.7 North Atlantic Treaty Organisation (NATO)

                 1.16.8 G-7 (Now G-8)

                 1.16.9 Association of South-East Asian Nation (ASEAN)

                 1.16.10 World Trade Prganisation (WTO)

1.17 Statistical Data of World

                           1.17.1   Census of world

1.18 Prize and Awards

           

2.     General Knowledge (India)

2.1        Books and Authors(I)

            2.1.1   Indian Authors (English)

                 2.2.2   Ancient Classical Authors

2.2        Dances(I)          

            2.2.1   Classical Dance of India

            2.2.2   Folk Dance of India

2.3        Famous Places

2.4        Famous Personalities

2.5        First, Largest, Longest(I)

            2.5.1   Record Makers (India)

                 2.5.2   India’s Superlatives Structures

2.6         Music(I)   

                    2.6.1   Hindustani classical music

            2.6.2   Carnatic music

2.7        Religions of India

2.8        Sanctuaries(I)

2.9        National Symbols (I)

2.10    Statistical Data of India

            2.10.1 Census of India

2.11    Prize and Awards(I)

 2.11.1 National Awards

                 2.11.2 Other Awards