maths from class 5

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)...

Question: Answer: ..

Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the sum of the series...

8! = 8 x 7 x 6 x 5 x4 x 3 x 2 x 1 = 40320 ..

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 = ..

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.units..

skew-symmetric for every square matrix A. That is any square matrix is expressible as the sum of a symmetric matrix and a skew-symmetric matrix. 5. A matrix which is both symmetric and skew symmetric is a zero matr..

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..

= (32.16.8.4.2)(33.31.30.18.17.15.14.13.12.11.10....3.1) = (2 5 .2 4 .2 3 .2 2 .2 1 )(33.31.30.....3.1) which is divisible by 2 1 5 . vi) (n! + 1) is not divisible by any natural number between 2 and ..