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• Examples of Simple Interest

Example 1: Find simple interest on Rs. 3000 at 7% rate of interest for one year. Solution: Let Principal = 3000, Rate of interest = 7%, Simple interest Example 2: Find simple interest on Rs. 10,000 at the rate of 5% for 5 years. Also find the amount for 5 years. Solution: Let Principal = […]

• More Examples of Simple Interest

To Find Principal When interest, time, rate are given: Example 01: What amount was borrowed, for which amount of interest is 200 at the rate of 5% for 4 years. Solution: Let P = Principal , Rate = 5%, Interest = 200, time = n = 4, I = Interest We know that To Find […]

• Formulas and Results of Permutations Combinations and Binomial Theorem

1. Factorial of is defined as , where is natural number. 2. (Permutation) 3. (Combination) 4. 5. 6. 7. 8. For large , is called Striling Approximation Formula. 9. 10. , , , 11. , 12. If is positive integer, then 13. 14. General Term 15. If is not positive integer, then the binomial expansion […]

• Basic Formulas and Results of Vectors

1) If then magnitude or length or norm or absolute value of is 2) A vector of unit magnitude is unit vector. If is a vector then unit vector of is denoted by and 3) Important unit vectors are , where 4) The components of unit vectors of are called the direction cosines of , […]

• Introduction to Set Theory

Set theory which was developed by Gorge Cantor (1845-1918) between1874-1895, is a basic mathematical tool that is used by various branches of Mathematics, such as Group Theory, Topology, Probability Theory, Calculus, Geometry etc. Cantor was born in Russia in 1845, but moved to Germany in 1856. In 1863 he entered the University of Berlin, where […]

• Definition and Representation of Set

Definition of Set: Set is a well-defined collection of distinct objects (i.e. The nature of the object is the same or in other words object in a set may be anything: number, people, place, letters etc.) These objects are called the elements or members of the sets. Notation: Set is usually denoted by capital letters […]

• Empty Set or Null Set

In set theory the concept of empty set or null set is very important and interesting, it defined as the “a set which contains no elements is called as empty set or null set”, it is sometimes known as void set or vacuous set. It is usually denoted by this Greek symbol is known as […]

• Concept of Subset

The concept of subset is defined as, a set is said to be the subset of a set if every element of set is also an element of set , this relationship is usually denoted by and mathematically this relationship is written as, if implies .  The concept of subset is also written in the […]

• Introduction to Matrices

The word matrix was first introduced by English Mathematician Jame Sylverter (1814-1897). Another Mathematician Arther Caylay (1821-1895) also developed the theory of matrices independently and used it for solving the linear equations. Now a days, matrices (plural of matrix) are used in high speed computers and other branches of natural & social sciences to solve […]

• Concept of Matrices

Matrix: Now, we write formal definition of Matrix. An arrangement of number into m-rows and n-columns is called a Matrix of order . Matrix always denoted by capital letters whereas their elements or entries by small letters e.g. This form of matrix is called matrix in tabular form, matrix can also be written in short […]

• Types of Matrices

There are several types of matrices, but most commonly used are: Rows Matrix Columns Matrix Rectangular Matrix Square Matrix Diagonal Matrix Scalar Matrix Identity Matrix Triangular Matrix Null or Zero Matrix Transpose of a Matrix Row Matrix: A matrix is said to be row matrix if it has only one row. e.g. Column Matrix: A […]

• Algebra of Matrices

The algebra of matrices includes Addition of Matrices Subtraction of Matrices Multiplication of a Matrix by Scalar Multiplication of Matrices Addition of Matrices: Two matrices and can be added only if order of matrix is equal to order of matrix . Then addition of matrices and can be obtained by adding the corresponding elements and […]