Shrawan Karn

Vector Geometry Class 12 |Basic Formula Of Vectors|

  Permutation Definition of Permutation: The arrangement of any finite number of objects or the given numbers in a certain order is called Permutation. Examples:  1) In how many ways can three letters A,B and C  be arranged in a row taking all three at a time? Solution:  In order to arrange the given three letters A,B,C taking all three at a time(without repetition)  in the form of row; we have the following three choices to fill up the three letters in the first ,second and third places:                 Choice for letter  in the first place           = 3 ways Choice for letter in the second place  = 2 ways Choice for letter in the third place       = 1 way Now, using the basic principle of counting, Total no. of ways= 3x2x1                               ...

Arithmetico-Geometric Series    Definition :  If each part of a series is the product of the terms of the terms of an arithmetic progression and the terms of a geometric progression, then the series is known as  the Arithmetico-Geometric series. The terms of the  arithmetic progression in the general form are:-  a,a+d,a+2d,a+3d, ....... a+(n-1)d and  The terms of a geometric progression are 1,r,r²,r³, ... then the series  a.1+(a+d).r+(a+2d).r²+...............+a+(n-1)d.r^n is called the arithmetico-geometric series.

1.Solution of System of 2-linear Equations using Cramer's Rule. Example-1  Formula: x=D1/D and y=D2/D 2.Solution of System of 3-linear Equations using Cramer's Rule. Example-2 Formula:x=D1/D,  y=D2/D and z=D3/D Step- by-Step method 

Exponential and Logarithmic  Series Solved Examples Of Exponential and Logarithmic  Series

Solved Examples of Binomial Theorem Model-01 Model-01