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1.Multiplication of 2(Two) digit numbers where the first(1st) digit of both the numbers are same and last digit of the two numbers sum to 10

Example1 : Calculate 56*54
Solution :Multiply 5 by 5+1,So 5*6=30
Now,Multiply together the last digits 6*4=24
So,56*54 =[5*(5+1)][6*4]=3024
Example2 : Calculate 78*72
Solution :[7*(7+1)][8*2]=5616

2.Square of a 2 digit number ending with 5(You can’t use this rule for other numbers)

Example1 : 35^2 = 3*(3+1)—25 = 1225 
Example2 : 95^2 = 9*(9+1)—25 = 9025
Example3 : 105^2=10*(10+1)—25=11025

3.To calculate Remainder on dividing the number by 3

Let me explain you by giving some examples :

Example1: What would be the remainder of 1342568 dividing by 3?
Solution :  The sum of digits is 29.Dividing 29 by 3 gives Remainder 2
Example2: What would be the remainder of  34259677858 dividing by 3?
Solution :  The sum of the number is 64.Dividing 64 by 3 gives Remainder 1

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  1. Number System

    Interesting Facts
    Properties of Prime Number
    Squaring Techniques
    Cubing Techniques
    Finding Square Root & Cube Root of Number
    Divisibility Rules
    Factors / Divisors of Given Composite Number
    HCF / LCM of Numbers
    Applications of HCF / LCM of Numbers
    Digital Sum of a Number
    Concept of Cyclicity / Power Cycle
    Remainder Theorem
    Finding the Last / Unit Digit
    Finding the Last Two Digits of a Number
    Number of Exponents / Highest Power / Number of Zeroes
    Percentages & Its Application

    Quick Calculation of Percentages
    Successive Percentage
    Percentage Apti-Tips
    Profit - Loss Concepts
    Various Problem Types on Profit - Loss Concepts
    Commercial Mathematics - I
    - Simple Interest (S.I)
    - Compound Interest (C.I)
    - Difference Between Simple & Compound Interest
    - Application of Digital Sum in S.I & C.I
    - Application of Successive Percentage in S.I & C.I
    - Population Formula
    - Growth Rates
    Commercial Mathematics-II
    - Stocks & Share
    Ratio & Proportions

    Type of Proportions
    Compounded Ratio
    Rule of Three
    Double Rule of Three
    Ratio in Investment/Partnerships
    Time, Speed & Distance

    Basic Relationships
    Concept of Average Speed
    Various Problem Types on TSD Concepts
    Concept of Relative Speed
    Boats and Streams Problems
    Application of Relative Speed in Train Problems
    The Escalator Problems
    Circular Motion
    Concept of Races
    Time & Work

    Universal Rules (Rule 1 - Rule 8)
    Pipes & Cisterns
    Examples & Problem Types
    Permutations & Combinations (P & C)

    Fundamental Principle of Counting
    Introduction to Permutations & Combinations
    Different Corollaries of Permutations
    Circular Permutations
    Different Corollaries of Combinations
    Selection out of Identical / Non-Identical things
    Distribution of Things
    Groupings & Dividing of Things
    Derangement Principle
    Geometrical Applications of P & C
    Use of P & C in Solution of Equations
    Trick for Finding the Rank of a Given Word

    Introduction to Probability
    Occurrence of Events
    Addition Theorem of Probability
    Conditional Probability
    Baye's Theorem of Probability
    Trick for Solving 2-Dice Problems
    Trick for Solving 3-Dice Problems
    Pascal's Triangle, Coin Toss & Genetic Probabilities
    The Birthday & Telegram Problems
    Miscellaneous Problem Types

    Properties of Lines & Angles
    Properties of Triangles
    Properties of Circles
    Geometrical Mensuration

    Basic Geometrical Mensuration
    Facts About Quadrilaterals
    Properties of Polygons
    Areas of Miscellaneous Figures
    Quadratic Equations

    Roots of Quadratic Equation
    Nature of Roots
    To find Equation with given roots
    Graphical Representation of Quadratic Equations
    Higher Order Equations
    Relation between Roots & Coefficients
    Descarte's Rule of Signs
    Finding the Common Root
    Sets, Venn Diagram & Averages

    Properties of Sets
    Properties of Venn Diagrams
    De-Morgan's Laws
    Problems Based on Venn-Diagrams
    Problems Based on Averages
    Clocks & Calendars

    Properties of Clocks
    Doomsday Algorithm for Calendar Problems
    Mixtures & Alligations

    Rule of Weighted Averages
    Rule of Alligation
    Alligation Cross
    Alligation Line
    Successive Replacement


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