preparation for discrete variable exam

We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..

We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan method e..

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) and (5)) as the de..

Question: Find n. Answer: i) ii) \ n = 8..

Question: When n = 5 and r = 2, find the values of Answer: i) ii) ..

Question: Answer: ..

Question: Find n if P(n,4) = 20P(n,2) Answer: ..

Question: Answer: = 5 + 10 + 10 + 5 + 1 = 31 = RH..

Question: At an election, three wards of a town are canvassed by 4, 5 and 8 men respectively. If 20 men volunteer, in how many ways can they be allotted to the different wards? Answer: Let the three wards be labelled as A, B and C respectively. Let us select 4 men for ward A. 4 men can ..

Question: How many words of different 4 letters can be formed out of 7 capital letters, 3 vowels and 8 consonants, if each word starts with a capital letter and contains at least one vowel? Answer: Any capital letter can be chosen as the first letter of each word. So there are 7 ways of..