Basic Mathematics

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Unit 1
1. Logarithm
1.1 Introduction
1.2 Laws of Logarithm
1.3 Types of Logarithm
2. Partial Fractions
2.1 Introduction
2.2 Partial Fraction of Proper fraction
2.3 Partial Fractions of Improper Fraction
3. Determinants
3.1 Introduction
3.2 Definition and Expansion of Determinants
3.3 Cramer’s Rule to Solve Simultaneous Equations in 2 and 3 unknowns
4. Matrices
4.1 Introduction
4.2 Algebra of Matrices
4.3 Transpose of Matrix
4.4 Adjoint of Matrix
4.5 Solution of Simultaneous Equations
5. Binomial Theorem
5.1 Introduction 3
5.2 Factorial Notation n! or
5.3 Binomial Theorem
5.4 General Term 12
5.5 Binomial Theorem for Negative Index
5.6 Use of Binomial Theorem for Approximate values
6. Trigonometric Ratio
6.1 Introduction
6.2 Angle
6.3 Standard Position of an Angle
6.4 Trigonometric Ratios of Acute Angle
6.5 Trigonometric Ratios of any Angle
6.6 Signs of Trigonometric Ratios
6.7 Trigonometric Ratios of Special Angles viz. 0°, 30°, 45°, 60° and Quadrantal angles 90°, 180°, 270°
6.8 Trigonometric Ratios at (– q)
6.9 Trigonometric Ratios at (90° – q)
7. Trigonometric Ratios of Allied and Compound Multiple and Submultiple Angles
7.1 Introduction
7.2 Compound Angles
7.3 Allied Angles
7.4 Trigonometric Ratios of Multiple Angles
7.5 Trigonometric Ratios of submultiple Angles
8. Factorization and Defactorization Formulae
8.1 Introduction
8.2 Factorization Formulae (or Product Formulae)
8.3 Defactorization Formula
9. Inverse Trigonometric Function
9.1 Introduction
9.2 Principal Values
9.3 Properties of Inverse Trigonometric Functions
10. Points and Distance
10.1 Introduction
10.2 Distance Formula
10.3 Section Formula
10.4 Midpoint formula
10.5 Centroid of Triangle
10.6 Area of a Triangle
11. Straight Line
11.1 Introduction
11.2 Slope of a Line
11.3 Equation of line in Different forms
11.4 Angle between two lines
11.5 Intersection of two lines
11.6 Length of perpendicular from a point on the line and distance between parallel lines
12. Circle
12.1 Definition of Circle
12.2 General Equation of Circle and its Centre and Radius
13. Vectors
13.1 Introduction
13.2 Product of 2 Vectors
13.3 Application of Vectors
solved papers of winter 12,winter 13

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