Question 10
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 boo..
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 boo..Question 8
Question: There are three different rings to be worn in 5 fingers with at most one in each finger. In how many ways can this be done? Answer: For the first ring, there are 4 options as one finger cannot have more than one ring. The remaining two f..
Definition of a Matrix
Matrices - Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x..
Matrices - Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x..Consistency of a system of linear equation
If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2h..
If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2h..Summary
) ka, kb, kc are in G.P. (b) a/k, b/k, c/k are in G.P. (x) (a) If the product of three numbers in G.P. is given, then the numbers should be taken as a/r, a, ar. (b) If the product of four numbers in G.P. is given, then the numbers should be taken as a/r 3 , a..
) ka, kb, kc are in G.P. (b) a/k, b/k, c/k are in G.P. (x) (a) If the product of three numbers in G.P. is given, then the numbers should be taken as a/r, a, ar. (b) If the product of four numbers in G.P. is given, then the numbers should be taken as a/r 3 , a..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, ..
>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, ..Question 2
Question: A lady wants to select one cotton saree and one polyster saree from a collection of 8 cotton sarees and 11 polyster sarees. In how many ways can the lady choose the two sarees? Answer: Here, there are two events E 1 and E 2 . E 1..
Question: A lady wants to select one cotton saree and one polyster saree from a collection of 8 cotton sarees and 11 polyster sarees. In how many ways can the lady choose the two sarees? Answer: Here, there are two events E 1 and E 2 . E 1..Question 2
= (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! + ..
= (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! + ..Example 1:
Using matrix method solve the following systems of linear equations 2x - y + z = -3 3x - z = - 8 2x + 6y = 2..
Properties of adjoint of a matrix
1. A.(adj A) = (adj A). A = |A| I 2. adj (AB) = (adj B) . (adj ..
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