free online math games

Question 1 - Question: Answer: As n represents all positive integers, we have Multiplying the above terms of both sides respectively, we get Multiplying both sides of inequality by n!, we g..

Harmonic Progression (H.P.) - A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..

Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..

Question: Prove that n!(n + 2) = n! + (n + 1)!. Answer: L.H.S = n!(n + 2) = n![(n+1)+1] ..

Question: A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee? Answer: Let the two ladies who refuse to work on the same committee be d..

Question: From 12 books, in how many ways can 5 be chosen i. to surely include a particular book ii. never to include a particular book iii. to have no restrictions at all? Answer: i. To include a particular book, one particular book has already been chosen. We have to select 4 books fr..

Let R i denotes the i t h row of the matrix A = [a i j ] then the elementary row operations on the matrix A are defined as: 3. R i g R i + kR j means multiply each element of j t h row by k and add it to the corresponding elements of i t h row. The corresponding column transformatio..

Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 Since area has to be a positive quantity, it is given by 47.5 sq.uni..

A - 1 does not exist But if (adj A) B = 0, then the system is consistent with infinite number of solutions or has no solution. the system is inconsistent i.e., it has no solutio..

Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 columns and is thus of order 3 x 2. The p..