12th Business Maths and Statistics - TamilNadu State Board (English Medium)

12th Business Maths and Statistics - TamilNadu State Board (English Medium)

Business Maths 12th Std - 12th Business Maths and Statistics

Chapter 1: Applications of Matrices and Determinants

1. Introduction - Applications of Matrices and Determinants
2. Rank of a Matrix: Concept
3. Elementary Transformations and Equivalent matrices - Rank of a Matrix
4. Echelon form and finding the rank of the matrix (upto the order of 3�4)
5. Testing the consistency of non homogeneous linear equations (two and three variables) by rank method - with Solved Example Problems
6. Rank of a Matrix: Solved Example Problems
7. Exercise 1.1 : Rank of a Matrix - Problem Questions with Answer, Solution
8. Cramer�s Rule - Theorem with Solved Example Problems
9. Cramer�s Rule - Non Homogeneous linear equations upto three variables: Solved Example Problems
10. Exercise 1.2 : Cramer�s Rule - Problem Questions with Answer, Solution
11. Transition Probability Matrices
12. Transition Probability Matrices: Solved Example Problems
13. Exercise 1.3: Transition Probability Matrices - Problem Questions with Answer, Solution
14. Choose the correct answer - Applications of Matrices and Determinants
15. Miscellaneous problems - Applications of Matrices and Determinants
16. Summary - Applications of Matrices and Determinants

Chapter 2: Integral Calculus - I

1. Introduction - Integral Calculus - I
2. Concept of Indefinite Integral
3. Two important properties of Integral Calculus
4. Methods of Integration - Indefinite Integrals
5. Integration by decomposition: Type I - Exercise and Example Solved Problems with Answer, Solution | Methods of integration
6. Integration by decomposition: Type II - Exercise and Example Solved Problems with Answer, Solution | Methods of integration
7. Integration by decomposition: Type III - Exercise and Example Solved Problems with Answer, Solution | Methods of integration
8. Integration by decomposition: Type IV - Exercise and Example Solved Problems with Answer, Solution | Methods of integration
9. Integration by parts Method - Exercise and Example Solved Problems with Answer, Solution | Methods of integration
10. Integration by substitution (or) change of variable method - Exercise and Example Solved Problems with Answer, Solution | Methods of integration
11. Some special types of Integrals Method - Exercise and Example Solved Problems with Answer, Solution | Methods of integration
12. Definite integrals
13. The fundamental theorems of Integral Calculus - Definite integrals
14. The fundamental theorems of Integral Calculus: Exercise and Example Solved Problems - Definite integrals
15. Properties of definite integrals
16. Evaluation of Problems using properties of definite integrals - Exercise and Example Solved Problems with Answer, Solution
17. Gamma Integral - Exercise and Example Solved Problems with Answer, Solution
18. Definite integral as the limit of a sum - Exercise and Example Solved Problems with Answer, Solution
19. Choose the correct answer - Integral Calculus
20. Miscellaneous problems - Integral Calculus - I
21. Summary - Integral Calculus - I

Chapter 3: Integral Calculus - II

1. Introduction - Integral Calculus - II
2. Geometrical Interpretation of Definite Integral as Area under a curve - Integral Calculus - II
3. The area of the region bounded by the curves: Example Solved Problems - Integral Calculus
4. Exercise 3.1: The area of the region bounded by the curves - Problem Questions with Answer, Solution
5. Application of Integration in Economics and Commerce - Integral Calculus
6. Integration: Cost functions from marginal cost functions - Example Solved Problems with Answer, Solution, Formula
7. Integration: Revenue functions from Marginal revenue functions - Example Solved Problems with Answer, Solution, Formula
8. Integration: The demand functions from elasticity of demand - Example Solved Problems with Answer, Solution, Formula
9. Exercise 3.2: Application of Integration in Economics and Commerce - Problem Questions with Answer, Solution
10. Integration: Consumer�s surplus - Example Solved Problems with Answer, Solution, Formula
11. Integration: Producer surplus - Example Solved Problems with Answer, Solution, Formula
12. Exercise 3.3: Application of Integration in Economics and Commerce - Problem Questions with Answer, Solution
13. Choose the best answer form the given alternatives - Integral Calculus
14. Miscellaneous problems - Integral Calculus
15. Summary - Integral Calculus - II

Chapter 4: Differential Equations

1. Introduction - Differential Equations
2. Definition of ordinary differential equation
3. Order and degree of a differential equation - Example Solved Problems with Answer, Solution, Formula
4. Formation of ordinary differential equation - Example Solved Problems with Answer, Solution, Formula
5. Exercise 4.1: Formation of ordinary differential equations - Problem Questions with Answer, Solution
6. Solution of a Differential Equation
7. First order and first degree differential - Example Solved Problems with Answer, Solution, Formula | Differential Equations
8. First order and first degree differential: Solved Example Problems - with Answer, Solution, Formula | Differential Equations
9. Exercise 4.2: First order and first degree differential - Problem Questions with Answer, Solution
10. Homogeneous Differential Equations - Example Solved Problems with Answer, Solution, Formula
11. Homogeneous Differential Equations: Solved Example Problems - with Answer, Solution, Formula
12. Exercise 4.3: Homogeneous Differential Equations - Problem Questions with Answer, Solution
13. Linear differential equations of first order - Example Solved Problems with Answer, Solution, Formula
14. Linear differential equations of first order: Solved Example Problems - with Answer, Solution, Formula
15. Exercise 4.4: Linear differential equations of first order - Problem Questions with Answer, Solution
16. A general second order linear differential equation with constant coefficients is of the form
17. Second Order first degree differential equations with constant coefficients: Solved Example Problems - with Answer, Solution, Formula
18. Exercise 4.5: Second Order first degree differential equations with constant coefficients - Problem Questions with Answer, Solution
19. Choose the Correct answer - Differential Equations
20. Miscellaneous Problems - Differential Equations
21. Summary - Differential Equations

Chapter 5: Numerical Methods

1. Introduction - Numerical Methods
2. Finite Differences - Numerical Methods
3. Forward Difference Operator(?) - Finite Differences | Numerical Methods
4. Backward Difference operator(?) - Finite Differences | Numerical Methods
5. Shifting operator (E) - Finite Differences | Numerical Methods
6. Relations between the operators ?, ? and E - Finite Differences | Numerical Methods
7. Finite Differences: Solved Example Problems - Numerical Methods
8. Finite Differences operators: Finding the missing terms - Example Solved Problems with Answer, Solution, Formula
9. Exercise 5.1: Finite Differences - Problem Questions with Answer, Solution | Numerical Methods
10. Interpolation - Numerical Methods
11. Methods of interpolation - Numerical Methods
12. Graphical and Algebraic method of Interpolation: Solved Example Problems - Numerical Methods
13. Lagrange�s interpolation formula - Example Solved Problems with Answer, Solution, Formula
14. Exercise 5.2: Interpolation - Problem Questions with Answer, Solution | Numerical Methods
15. Choose the correct Answer - Numerical Methods
16. Miscellaneous Problems - Numerical Methods
17. Summary - Numerical Methods

Chapter 6: Random Variable and Mathematical Expectation

1. Introduction - Random Variable and Mathematical Expectation
2. Random variable - Introduction
3. Definition and Types of Random Variable
4. Discrete random variable - Definition, Formulas, Solved Example Problems
5. Continuous random variable - Definition, Formulas, Solved Example Problems
6. Exercise 6.1: Random variable - Problem Questions with Answer, Solution
7. Mathematical Expectation - Introduction
8. Expected value and Variance - Definition, Formulas | Mathematical Expectation
9. Properties of Mathematical expectation - Definition, Formulas
10. Mathematical Expectation: Solved Example Problems
11. Exercise 6.2: Mathematical Expectation - Problem Questions with Answer, Solution
12. Choose the correct Answer - Random Variable and Mathematical Expectation
13. Miscellaneous Problems - Random Variable and Mathematical Expectation
14. Summary - Random Variable and Mathematical Expectation

Chapter 7: Probability Distributions

1. Introduction - Probability Distributions
2. Types of Theoretical distributions - Probability Distributions
3. Binomial distribution - Definition, Properties, Derivation, Formulas, Solved Example Problems
4. Exercise 7.1: Binomial distribution - Problem Questions with Answer, Solution | Probability Distributions
5. Poisson Distribution - Definition, Properties, Derivation, Formulas, Solved Example Problems
6. Exercise 7.2: Poisson Distribution - Problem Questions with Answer, Solution | Probability Distributions
7. Normal Distribution - Definition, Properties, Derivation, Formulas, Solved Example Problems
8. Exercise 7.3: Normal Distribution - Problem Questions with Answer, Solution | Probability Distributions
9. Choose the correct Answer - Probability Distributions
10. Miscellaneous Problems - with Answer, Solution | Probability Distributions
11. Summary - Probability Distributions

Chapter 8: Sampling Techniques and Statistical Inference

1. Introduction - Sampling Techniques and Statistical Inference
2. Basic concepts of sampling - Definition, Solved Example Problems, Merits, Demerits
3. Types of Random sampling or Probability sampling - Solved Example Problems, Merits, Demerits
4. Sampling and Non-Sampling Errors
5. Sampling distribution - Definition, Formulas
6. Computing standard error in simple cases - Example Solved Problems with Answer, Solution | Sampling and Non-Sampling Errors
7. Exercise 8.1: Sampling Techniques - Problem Questions with Answer, Solution
8. Statistical Inference
9. Estimation - Definition, Characteristic | Statistical Inference
10. Point and Interval Estimation - with Solved Example Problems | Statistical Inference
11. Hypothesis Testing - Statistical Inference
12. statistical hypothesis: Null Hypothesis and Alternative Hypothesis, Level of Significants, Type of Errors - Statistical Inference
13. Testing Procedure : Large sample theory and test of significants for single mean - Hypothesis Testing | Statistical Inference
14. Hypothesis Testing: Solved Example Problems - with Answer, Solution | Statistical Inference
15. Exercise 8.2: Statistical Inference - Problem Questions with Answer, Solution
16. Choose the correct Answer - Sampling Techniques and Statistical Inference
17. Miscellaneous Problems - Sampling Techniques and Statistical Inference
18. Summary - Sampling Techniques and Statistical Inference

Chapter 9: Applied Statistics

1. Introduction - Applied Statistics
2. Time Series Analysis - Definition | Applied Statistics
3. Meaning, Uses and Basic Components of Time Series Analysis - Applied Statistics
4. Measurements of Trends - Time Series Analysis | Applied Statistics
5. Measurements of Trends: Freehand or Graphic Method - Procedure, Example Solved Problem | Time Series Analysis
6. Measurements of Trends: Method of Semi-Averages - Procedure, Example Solved Problem | Time Series Analysis
7. Measurements of Trends: Method of Moving Averages - Procedure, Example Solved Problem | Time Series Analysis
8. Measurements of Trends: Method of Least Squares - Procedure, Example Solved Problem | Time Series Analysis
9. Measurements of Trends: Methods of measuring Seasonal Variations By Simple Averages - Procedure, Example Solved Problem | Time Series Analysis
10. Exercise 9.1: Time Series Analysis and Measurements of Trends - Problem Questions with Answer, Solution | Applied Statistics
11. Index Number - Applied Statistics
12. Meaning, Classifications, Construction and Uses of Index Numbers - Applied Statistics
13. Weighted Index Number - Definition, Solved Example Problems | Applied Statistics
14. Test of adequacy for an Index Number - Definition, Solved Example Problems | Applied Statistics
15. Construction of Cost of Living Index Number - Uses, Methods, Solved Example Problems | Applied Statistics
16. Exercise 9.2: Index Number - Problem Questions with Answer, Solution | Applied Statistics
17. Statistical Quality Control (SQC) - Applied Statistics
18. Process Control and Product Control - Statistical Quality Control (SQC) | Applied Statistics
19. Construction of X and R charts - Statistical Quality Control (SQC) | Applied Statistics
20. Statistical Quality Control (SQC): Example Solved Problems - with Answer, Solution | Applied Statistics
21. Exercise 9.3: Statistical Quality Control (SQC) - Problem Questions with Answer, Solution | Applied Statistics
22. Choose the correct Answer - Applied Statistics
23. Miscellaneous Problems - Applied Statistics
24. Summary - Applied Statistics

Chapter 10: Operations Research

1. Introduction - Operations Research
2. Transportation Problem - Definition and formulation, Structure | Operations Research
3. Methods of finding initial Basic Feasible Solutions - Solved Example Problems | Transportation Problem | Operations Research
4. Methods of finding initial Basic Feasible Solutions: North-West Corner Rule (NWC) - Solved Example Problems | Transportation Problem | Operations Research
5. Methods of finding initial Basic Feasible Solutions: Least Cost Method (LCM) - Solved Example Problems | Transportation Problem | Operations Research
6. Methods of finding initial Basic Feasible Solutions: Vogel�s Approximation Method(VAM) - Solved Example Problems | Transportation Problem | Operations Research
7. Exercise 10.1: Transportation Problem - Problem Questions with Answer, Solution | Operations Research
8. Assignment Problem - Introduction | Operations Research
9. Definition and formulation of Assignment Problem - Operations Research
10. Solution of assignment problems (Hungarian Method) - Procedure, Example Solved Problem | Operations Research
11. Exercise 10.2: Assignment problems(Hungarian Method) - Problem Questions with Answer, Solution
12. Decision Theory - Introduction | Operations Research
13. Meaning of Decision Theory - Operations Research
14. Situations- Certainty and uncertainty - Decision Theory | Operations Research
15. Decision Theory: Maximin and Minimax strategy - Operations Research
16. Exercise 10.3: Decision Theory - Problem Questions with Answer, Solution | Operations Research
17. Choose the correct Answer - Operations Research
18. Miscellaneous Problems - Operations Research
19. Summary - Operations Research