school of mathematics

Question: vi) (n! + 1) is not divisible by any natural number between 2 and n. vii) Simplify Answer: ..

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Question: How many three letter words (with or without meaning) can be formed out of the letters of the word LOGARITHMS if repetition of letters is not allowed? Answer: Number of letters in the word LOGARITHMS is 10. The three letter words formed by using these letters will be ..

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: 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: Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many different ways can we place the balls so that no box remains empty? Answer: Given 5 balls can be placed in 3 boxes as follows: i. 1 ball can be pl..

Question: Find the number of triangles that can be drawn through 12 distinct points, no three of which are collinear. Answer: To draw a triangle, we require three non-collinear points. Hence, the number of triangles that can be drawn is ..

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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..

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..