Suppose you roll a number cube 10 times. You get an even number 3 time..
Suppose you roll a number cube 10 times. You get an even number 3 times. Find the experimental probability that you get an even number. => 1 2 or 3 5 or 3..
Summary
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing respectively t..
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing respectively t..Sub-triplicate Ratio:
The ratio obtained by taking the cube root of the given ratio a : b is called sub-triplicate ratio. is sub-triplicate ratio of a : b. For example the sub-triplicate ratio of 8a 3 : 27b 6 is or 2a : 3b 2 . Find the compounded ratio of the duplicate ..
The ratio obtained by taking the cube root of the given ratio a : b is called sub-triplicate ratio. is sub-triplicate ratio of a : b. For example the sub-triplicate ratio of 8a 3 : 27b 6 is or 2a : 3b 2 . Find the compounded ratio of the duplicate ..Question 2
Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Since there are infinite numb..
Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Since there are infinite numb..Co-factors
The co-factor of the element a ij is (-1) i+j times its minor a ij . We shall denote the cofactor of an element by the corresponding capital letter. Cofactor of a i j = A i j = (-1) i + j M i j Consider the determinant The minor of a 1 1 can be obtained by deleting the fir..
The co-factor of the element a ij is (-1) i+j times its minor a ij . We shall denote the cofactor of an element by the corresponding capital letter. Cofactor of a i j = A i j = (-1) i + j M i j Consider the determinant The minor of a 1 1 can be obtained by deleting the fir..Sequences and Series Summary
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, ..
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, ..3rd Method:
(i) RHS (ii) From (i) and (ii), LHS = RHS Hence proved. Which number should be added to each of the numbers 7, 22 and 62 so that the sums would be in continued proportion? Let the number added to each of them be 'x..
(i) RHS (ii) From (i) and (ii), LHS = RHS Hence proved. Which number should be added to each of the numbers 7, 22 and 62 so that the sums would be in continued proportion? Let the number added to each of them be 'x..Complex number
Imaginary Number - Square root of a negative number is known as an imaginary number. a > 0 is an imaginary number. or A number whose square is negative is known as an imaginary number. . . . The symbol i, We write, Powers of ..
Imaginary Number - Square root of a negative number is known as an imaginary number. a > 0 is an imaginary number. or A number whose square is negative is known as an imaginary number. . . . The symbol i, We write, Powers of ..Rational and Irrational Numbers Introduction
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} T..
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} T..Summary
1. Problems involving rational numbers are simplified using 'BODMAS' rule. 2. A rational number can be represented in the decimal form. 3. When a rational number is represented as a decimal, it will be either a terminating decimal or a recur..
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