find the number of ways of dividing 12 distinct books into 3 groups of 5 4 3 books respectively.

Find the number of ways of dividing 12 distinct books into 3 groups of 5, 4, 3 books respectively. => 1 2 P 1 2 or ( 1 2 C 5 )( 1 2 C 4 )( ..

Imaginary Number - Square root of a negative number is known as an imaginary number. a > 0 is an imaginary number. or A number whose square is negative is known as an imaginary number. . . . The symbol i, We write, Powers of ..

The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing respectiv..

>Now let us consider the following. 1. Assume that there is some book 'k' which doesn't fall over i.e., k is the first book which behaves in a different manner. 2. Since k is the first book, the book right before k must have fallen over. 3. But we k..

p(x) = x 3 -3x 2 +4x-12 is divided by x-3. R = p(3) = 3 3 - 3 x 3 2 + 4 x 3-12 = 27-27+12-12=0..

Find 'a.c ', the product of the coefficient of x 2 and the last term. Find all the factor pairs of 12. (1,12), (3,4), (2,6) are the factor pairs of 12. The factor pair (3,4) is such that 3 + 4 = 7and ..

Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...

Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can b..

The above discussion leads to find the solution of a system of linear equations in two variables by using Cramer's rule. Cramer's rule suggests the use of determinants to solve a system of linear equations. Let us denote a 1 b 2 - a 2 b 1 (Denominators of x and y in (4) and (..

Ratio - Ratio is the numerical relation of one quantity to another of the same kind. To find the ratio of 2 m 25 cm to 75 cm, we first change 2 m 25 cm into cm, which equals 225 cm. Now, we have to find 225 cm to 75 cm ratio is = 3 : 1 We can write the above ratio as (..