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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 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..