free online math games

Question 1 - Question: Find n. Answer: ..

Equality of Matrices - 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 = ..

Some Properties of A.P. - If a,b,c,d are in A.P., then (ii) ka, kc, kb, kd are also in A.P. A remark on finding a few members of an A.P. whose sum is given along with other conditions: i) If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+..

Question: Prove that the number of ways in which (m+n) dissimilar things can be divided into two groups containing m and n Answer: If we select m things out of (m+n) things, then n things are left out . Then, this gives (m+n) that can be divided into two groups containing m and n thin..

Question: A sportsteam of 11 students is to be constituted choosing at least 5 from class XI and 5 at least from XII. If there are 20 students in each of these classes, in how many ways can the team be constituted? Answer: Number of students in each class is 20. Total number of selec..

Question: Find the number of diagonals in a polygon of n sides. Answer: In a polygon, no three points are collinear. To draw a line, we require two distinct points. The polygon of n sides has n distinct points. Number of diagonals that can be drawn ..

The adjoint of a square matrix [a i j ] is defined as the transpose of the matrix [A i j ] where A i j are the cofactors of the elements a i j . Adjoint of A is denoted by adj A. ..

In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matrices of th..

If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2 and the second equation by a 1 , w..

Let A = [a ij ] be a square matrix. We can associate with the square matrix A, a determinant which is formed by exactly the same array of elements of the matrix A. A determinant formed by the same array of elements of the square matrix A is called the determinant of the square matrix A and is denot..