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1.     Arithmetic


1.1 Number System

1.1.1 Introduction

1.1.2 Classification of numbers

1.1.3 Classification of Natural numbers

1.1.4 Important terms & concepts related to numbers

1.1.5 Basic Arithmetic Operations

1.1.6 Tests of Divisibility

1.1.7 Important results on numbers

1.1.8 Binary & Octal base system

1.1.9 Modulus of a Real number


          1.2 Fractions and Decimals

1.2.1 Basic concept

1.2.2 Classification and terminology of fractions

1.2.3 Calculation with fractions Converting unlike into like fractions Comparing fractions To insert a fraction between two given fractions Arithmetic operations on fractions

1.2.4 Decimal Fractions Inter-conversion between decimal numbers and fractions Arithmetic operations on decimal numbers Types of Decimal numbers Rounding off Significant figures

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            1.3 HCF and LCM                                            

1.3.1 Factors and multiples

1.3.2 Highest Common factor (HCF) Prime factorization method Division method HCF of Decimals of vulgar fractions

1.3.3 Least Common multiple (LCM) Prime factorization method Common Division method LCM of Decimals LCM of fractions

1.3.4 Relation between HCF and LCM

1.3.5 Comparison of fractions using LCM


1.4 Surds and Indices

1.4.1 Square and Cube of a number

1.4.2 Square root and Cube root Square root Methods to find square root of a number Cube root

1.4.3 Indices and Surds Laws of Indices Laws of Surds Rule of cyclicity


1.5 Ratio and Proportion

1.5.1 Definition and basic concepts

1.5.2 Ratio between more than two quantities

1.5.3 Compound ratio

1.5.4 Comparison of ratios

1.5.5 Proportion

1.5.6 Types of Proportion

1.5.7 Some specific cases


1.6 Average

1.6.1 Definition

1.6.2 Weighted average

1.6.3 Specific cases of average Average speed Average of Series of Numbers Miscellaneous cases


1.7 Additional Topics in Arithmetic

1.7.1 Mixtures and Alligation Introduction Rule of Alligation Different cases of Alligation and mixtures

1.7.2 Problems on Trains Basic concepts Specific cases Train moving past a stationary point object Train moving past a stationary lengthy object Train moving past a moving point object Train moving past a moving lengthy object

1.7.3 Unitary Method Time and Distance Basic definitions and concepts Specific cases Time and Work Basic concepts Specific cases Pipes and Cisterns Basic definitions Basic concepts Specific cases Boat and Streams Basic concepts Specific cases


2.     Commercial Maths


2.1 Interest

2.1.1 Simple Interest Basic definitions and concepts Some specific cases

2.1.2 Compound Interest Basic definitions and concepts Compounding for different time periods and rates Some specific cases Cases relating Simple and Compound interest


2.2 Percentage

2.2.1 Definition

2.2.2 Conversion between Percent, fraction and decimal

2.2.3 Specific cases of Percentage Percent relationship between quantities Examinations and marks Geometry Depreciation Population growth Price and consumption


2.3 Profit and Loss

2.3.1 Definition

2.3.2 Rule of fraction

2.3.3 Specific cases of Profit and Loss Relation between Cost price and selling price Using false weight Discount Multiple transactions


2.4 Partnership

2.4.1 Basic concepts

2.4.2 Basic principle of profit sharing Simple partnership Compound partnership

2.4.3 Specific cases


3.     Geometry       


3.1     Lines and Angles

3.1.1    Basic properties of lines and angles

3.1.2    Parallel lines


3.2     Triangles

3.2.1    Basic properties

3.2.2    Interior points in a triangle

3.2.3  Special types of triangles

3.2.4  General theorems on proportionality

3.2.5    Congruence and similarity of triangles

3.2.6    Properties of similar triangles


3.3 Quadrilaterals

3.3.1  Parallelograms

3.3.2  Rhombus

3.3.3  Rectangle

3.3.4  Square

3.3.5  Trapezium

3.3.6    Regular polygons

3.3.7    Cyclic quadrilateral


 3.4 Circles: properties of chords, tangents and secants


4             Mensuration


4.1 Plane Mensuration

4.2.Solved examples on Plane Mensuration

4.3 Solid Mensuration                       

4.4 Solved examples on Solid Mensuration


5            Algebra


  5.1Basic concepts


5.2 Arithmetic operations on algebraic expressions

5.2.1 Addition and subtraction

5.2.2 Multiplication

5.2.3 Division

5.3 Algebraic Identities

5.4 Factors of Polynomials

5.5 HCF and LCM of Polynomials

5.6 Linear Equations

5.6.1 Solving a Linear Equation

5.6.2 Word problems on Linear Equations


5.7 Simultaneous Equations

5.7.1 Solving Simultaneous equations

5.7.2 Word problems on Simultaneous Equations


5.8 Quadratic Equations

5.8.1 Methods of solving Quadratic equation

5.8.2 Relation between roots and coefficients

5.8.3 To form a Quadratic equation with given roots

5.8.4 Nature of roots of a Quadratic Equation

5.8.5 Word problems on Quadratic equations

5.8.6 Equation reducible to Quadratic Equation


5.9 Inequalities


6       Series


6.1 Definition


6.2 Types of Series

6.2.1 Arithmetic Series

6.2.2 Geometric Series

6.2.3 Series of squares and cubes

6.2.4 Mixed series

6.2.5 Two tier Arithmetic series

6.2.6 Three tier Arithmetic series

6.2.7 Arithmetico-Geometric series

6.2.8 Geometrico-Arithmetic series

6.2.9 Twin series   


6.3 Suggested Steps for solving series problems


6.4 Different types of problems on Series

6.4.1 Finding the next term

6.4.2 Finding wrong/missing number

6.4.3 Two line number series


6.5 Some unique series




1.     Set theory


1.1     Basic concepts

1.2     Representation of sets

1.3     Different type of sets

1.4     Venn Diagrams

1.5     Union and Intersection of sets

1.6     Operations on sets

1.7     Cardinal number

1.8     De Morgan’s laws


2.     Functions


2.1     Definition of function

2.2     Domain, co-domain and range

2.3     Classification of functions

2.3.1    One-one and Many-one functions

2.3.2    Into and onto functions

2.4     Composite and Inverse functions

2.5     Some common functions


3.     Sequences and Series


3.1     Basic definitions and concepts

3.2     Types of Progressions

3.2.1    Arithmetic Progression

3.2.2    Geometric Progression

3.2.3    Harmonic Progression

3.3 Some important series


4.     Permutation and Combination


4.1     Fundamental principle of counting

4.2     Permutations

4.2.1    Important cases of Permutations

4.2.2    Circular Permutations

4.3     Combinations

4.3.1    Relation between Permutation and Combination

4.3.2    Important cases of Combination


5.     Probability


5.1     Basic terms and concepts

5.2     Conditional Probability and independent events


6.     Logarithms


6.1     Definition

6.2     Laws of Logarithm

6.3     Solved examples


7.                 Co-ordinate Geometry


7.1     Cartesian co-ordinate system

7.2     Distance formula

7.3     Section formula

7.4     Application to Geometrical figures

7.5     Straight line

7.5.1    Different forms of equation of a straight line

7.5.2    Angle between two lines

7.5.3    Distance from a line

7.6  Equation of a circle


8.                 Graphing Equations and In-equations


8.1  Graphs on one axis

8.2  Graphs on two axis

8.2.1    Equations and In-equations in one variable

8.2.2    Equations and In-equations in two variables

8.2.3    Simultaneous equations and in-equations in two variables


9.     Trigonometry


9.1     Angles

9.2     Definition of Trigonometric ratios

9.3     Trigonometric Identities

9.4     Trigonometric ratios of some angles

9.5     Relation between Complementary and Supplementary angles

9.6     Height and distances

9.7     Law of Sine and Cosine


10.             Derivatives


10.1 Definition and concept

10.2 Finding derivative of functions

10.3 Higher order derivatives

10.4 Application of derivatives

     10.4.1 Velocity and acceleration

     10.4.2 Finding tangent to a curve

     10.4.3 Marginal cost

     10.4.4 Finding maxima and minima       








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

1.5.1   Blood Relationships Test

1.5.2   Coded Relationships Tests

1.1.6       Alphabet Test

1.1.7       Conditions and Grouping Test

1.1.8       Number, Ranking and Time Sequence Test

1.1.9       Mathematical Operations

1.1.10   Cubes and Cubical Dice Tests

1.1.11   Data Arrangement Test

1.11.1   Linear Arrangement Test   Linear Sitting Arrangement

   Linear Arrangement of Letters & Numbers

1.11.2   Complex Arrangement Test

1.1.12   Data Sufficiency Test

1.1.13   Sequential Output Tracing (Input)


2. Logic Tests


2.1     Syllogism

2.2     Statements Assumptions

2.3     Statements Arguments

2.4     Statements Conclusions

2.4.1   Coded Inequality

2.5     Statements Action

2.6     Inferences (Deriving Conclusions from Passages)

2.7     Cause and Effect

2.8     Logical Diagrams (Venn diagram)




1.     English Grammar


1.1         Parts of Speech

1.1.1          Nouns Classification of Nouns Gender Number Case Rules

1.1.2          Adjectives Classification of Adjectives Degrees of Adjectives Rules

1.1.3          Pronouns Classification of Pronouns Rules

1.1.4          Verbs Classification of Verbs Subject Verb Agreement Rules

1.1.5          Adverbs Classification of Adverbs Comparison of Adverbs Rules Related to the Use of Adverbs

1.1.6          Prepositions Short List of One-Word Prepositions General Rules Regarding Certain Prepositions

1.1.7          Conjunctions Classification of Conjunctions Rules

1.1.8          Interjections

   List of Commonly Used Interjections

1.1.9          Articles Classification of Articles         The Indefinite Article         The Definite Article

1.1.10      Punctuation and Capitals      List of Important Punctuation Marks      Rules      Use of Capital Letters

1.1.11      Active Voice and Passive Voice      Active Voice  Passive Voice  Rules for changing the voice  Transformation of Sentences-Voice Change  Summary of Rules with Examples in Tabular Form


1.1.12      Direct and Indirect Speech      Direct Speech      Indirect Speech      Rules for Changing Direct into Indirect Speech


2        English Vocabulary

2.1           Synonyms

2.1.1    Strategies for Synonyms

2.2 Antonyms

2.2.1          Strategies for Antonyms

2.3           Analogies

2.3.1    Common Relationships

2.3.2          Strategies for Analogies

2.4    Odd Man Out

2.4.1    Types of Odd Man Out Questions


3        English Proficiency

3.1           Idioms, Phrases and Clauses      

3.1.1    Idioms

3.1.2    Phrases

3.1.3       Clauses


3.2           Sentence Improvement

3.2.1        Types of Format

3.2.2         Strategies for Sentence Improvement


3.3              Rearrangement of Words in Sentence

3.3.1     Strategies for Rearrangement of Words in Sentence


3.4          Rearrangement of Sentence in Paragraph

3.4.1         Types of Formats

3.4.2     Strategies for Rearrangement of Sentence in Paragraph


3.5          Fill in the Blanks

3.5.1       Types of Fill in the Blanks Logical Fill in the Blanks Paired Logical Fill in the Blanks Grammar Based Fill in the Blanks Missing Link in a Paragraph    Complete the Theme    Maximum Number of Times

3.5.2   Strategies for Fill in the Blanks


4.   English Usage Errors

4.1           Types of Errors

4.1.1          Error in Case

4.1.2          Error in Subject Verb Agreement

4.1.3    Error in the Tense or Form of a Verb

4.1.4          Error in Subjunctive Mood

4.1.5          Error in Comparison

4.1.6          Error in the Use of Adjective for Adverb or Vice-Versa

4.1.7          Error of Parallel Construction

4.1.8          Error in Diction or Idiom

4.2           Types of Common Errors

4.2.1          Common Errors in the Use of Articles

4.2.2          Common Errors in the Use of Nouns

4.2.3          Common Errors in the Use of Pronouns

4.2.4          Common Errors in the Use of Adjectives

4.2.5          Common Errors in the Use of Verbs

4.2.6          Common Errors in the Use of Adverbs

4.2.7          Common Errors in the Use of Prepositions

4.2.8          Common Errors in the Use of Conjunction

4.2.9          Common Errors in the Use of Tenses

4.2.10 Common Errors in the Use of Modals


5. Critical Reasoning

5.1    Basic terms

5.2    Types of Questions

5.3           Methodology


6. Summary


7. Definition Based Questions

7.1           Basic Terms

7.2           Strategies


8. Verbal Ability Test




1.     Introduction and Fundamental Concepts


1.1       Introduction

1.2       Aspects of Reading in the Context of a Test

1.3       Methodology for Effective Reading

1.4       Précis Writing

1.5       Central Idea

1.6       Multiple Choice Questions

1.6.1       Types of Questions


2.     Avoiding Verbosity in Text and Determining Title of a Passage


2.1       Avoiding Verbosity in Text

2.2       Determining Title of a Passage


3.     Combining Speed with Efficiency


3.1       Techniques for Reading Effectively

3.1.1       Skimming

3.1.2       Scanning


4.     Identifying Style and Tone of Passage


4.1       Style of Writing

4.1.1       Various Styles

4.2       Tone of Author

4.1.2       Subjective Tone        Types of Subjective Tones 

4.1.3       Objective Tone


5.     Example Passages


6.     English Comprehension Test


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