Question 10
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a..
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a..Question 6
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 ..
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 ..Suggested answer:
The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -2, A 1 3 = 18 A 2 ..
The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -2, A 1 3 = 18 A 2 ..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 = 6...
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 = 6...Examples:
1, 3, 5, 7..... (adding 2 to every term) 1, 4, 16, 64 (Multiplying by 4 every term) 20, 17, 14 . (add -3 to every term) The different numbers in a sequence are called terms of sequence. The subscripts denote the position of the term. In the..
1, 3, 5, 7..... (adding 2 to every term) 1, 4, 16, 64 (Multiplying by 4 every term) 20, 17, 14 . (add -3 to every term) The different numbers in a sequence are called terms of sequence. The subscripts denote the position of the term. In the..Example:
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..
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..Consistency of a system of linear equation
The above discussion leads to find the solution of a system of linear equations in two variables by using Cramer's rule. Cramer's rule suggests the use of determinants to solve a system of linear equations. Let us denote a 1 b 2 - a 2 b 1 (Denominators of x and y in (4..
The above discussion leads to find the solution of a system of linear equations in two variables by using Cramer's rule. Cramer's rule suggests the use of determinants to solve a system of linear equations. Let us denote a 1 b 2 - a 2 b 1 (Denominators of x and y in (4..Question 6
Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..
Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..Summary
>A system of linear equations is said to be consistent if it has at least are solution, otherwise it is inconsistent. Let A be asquare matrix of order n. Following are the steps to find the inverse of a matrix. Step 1: Find the value of the determinants A. That is, find |A| Step 2: If |A|..
>A system of linear equations is said to be consistent if it has at least are solution, otherwise it is inconsistent. Let A be asquare matrix of order n. Following are the steps to find the inverse of a matrix. Step 1: Find the value of the determinants A. That is, find |A| Step 2: If |A|..Examples:
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common differ..
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common differ..See what our Users say :
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