fourth grade math

Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h..

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 = ..

General Series - 1. To find the sum of first n natural numbers. ..

To insert n Harmonic Means between two given quantities - Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h..

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 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: Given five different green dyes, four different blue dyes and three different red dyes, how many combinations of dyes can be chosen taking atleast one green and one blue dye? Answer: The least number of dyes that a combination can have is 2. (one blue and one green). Maximum ..

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..

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..