# CLASS 12 MATHS

### Syllabus & Solved Exercise Problems

Video Syllabus

#### Applications of Matrices and Determinants

1.1 Introduction Zero Matrix Ex 1.1.1 (i) Find the Adjoint of 2 x 2 Matrix Ex 1.1.1 (ii) Find the Adjoint of 3 X 3 Matrix Ex 1.1.1 (iii) Adjoint of 3 X 3 Matrix Ex 1.1.2 (i) Find the Inverse of 2 x 2 Matrix Ex 1.1.2 (ii) Find the inverse of 3 X 3 Matrix Ex 1.1.2 (iii) Find the inverse of 3 X 3 Matrix Ex 1.1.3 Ex 1.1.4 Ex 1.1.5 Ex 1.1.6 Ex 1.1.7 Reversal Law for Inverses Ex 1.1.8 How to Find a Matrix from its Adjoint Ex 1.1.9 Find the inverse of 3 X 3 Matrix Using Adjoint Ex 1.1.10 Ex 1.1.11 Matrices & Determinants Ex 1.1.12 Ex 1.1.13 Ex 1.1.14 Ex 1.1.14 Unit Matrix
1.2 Inverse of a Non-Singular Square Matrix
1.3 Elementary Transformations of a Matrix
1.4 Applications of Matrices: Solving System of Linear Equations
1.5 Applications of Matrices: Consistency of system of linear equations by rank method
2 Complex Numbers
2.1 Introduction to Complex Numbers
2.2 Complex Numbers
2.3 Basic Algebraic Properties of Complex Numbers
2.4 Conjugate of a Complex Number
2.5 Modulus of a Complex Number
2.6 Geometry and Locus of Complex Numbers
2.7 Polar and Euler form of a Complex Number
2.8 de Moivre's Theorem and its Applications

#### 3 Theory of Equations

3.1 Introduction
3.2 Basics of Polynomial Equations
3.3 Vieta’s Formulae and Formation of Polynomial Equations
3.4 Nature of Roots and Nature of Coefficients of Polynomial Equations
3.5 Applications to Geometrical Problems
3.6 Roots of Higher Degree Polynomial Equations
3.7 Polynomials with Additional Information
3.8 Polynomial Equations with no additional information
3.9 Descartes Rule
4 Inverse Trigonometric Functions
4.1 Introduction
4.2 Some Fundamental Concepts
4.3 Sine Function and Inverse Sine Function
4.4 The Cosine Function and Inverse Cosine Function
4.5 The Tangent Function and the Inverse Tangent Function
4.6 The Cosecant Function and the Inverse Cosecant Function
4.7 The Secant Function and Inverse Secant Function
4.8 The Cotangent Function and the Inverse Cotangent Function
4.9 Principal Value of Inverse Trigonometric Functions
4.10 Properties of Inverse Trigonometric Functions
5 Two Dimensional Analytical Geometry-II
5.1 Introduction
5.2 Circle
5.3 Conics
5.4 Conic Sections
5.5 Parametric form of Conics
5.6 Tangents and Normals to Conics
5.7 Real life Applications of Conics
6 Applications of Vector Algebra
6.1 Introduction
6.2 Geometric Introduction to Vectors
6.3 Scalar Product and Vector Product
6.4 Scalar triple product
6.5 Vector triple product
6.6 Jacobi’s Identity and Lagrange’s Identity
6.7 Different forms of Equation of a Straight line
6.8 Different forms of Equation of a plane
6.9 Image of a point in a plane
6.10 Meeting point of a line and a plane
7 Applications of Differential Calculus
7.1 Introduction
7.2 Meaning of Derivatives
7.3 Mean Value Theorem
7.4 Series Expansions
7.5 Indeterminate Forms
7.6 Applications of First Derivative
7.7 Applications of Second Derivative
7.8 Applications in Optimization
7.9 Symmetry and Asymptotes
7.10 Sketching of Curves
8 Differentials and Partial Derivatives
8.1 Introduction
8.2 Linear Approximation and Differentials
8.3 Functions of Several Variables
8.4 Limit and Continuity of Functions of Two Variables
8.5 Partial Derivatives
8.6 Linear Approximation and Differential of a Function of Several Variables
9 Applications of Integration
9.1 Introduction
9.2 Definite Integral as the Limit of a Sum
9.3 Fundamental Theorems of Integral Calculus and their Applications
9.4 Bernoulli’s Formula
9.5 Improper Integrals
9.6 Reduction Formulae
9.7 Gamma Integral
9.8 Evaluation of Bounded Plane Area by Integration
9.9 Volume of a Solid obtained by Revolving Area about an Axis
10 Ordinary Differential Equations
10.1 Introduction
10.2 Differential Equation, Order, and Degree
10.3 Classification of Differential Equations
10.4 Formation of Differential Equations
10.5 Solution of Ordinary Differential Equations
10.6 Solution of First Order and First Degree Differential Equations
10.7 First Order Linear Differential Equations
10.8 Applications of First Order Ordinary Differential Equations
11 Probability Distributions
11.1 Introduction
11.2 Random Variable
11.3 Types of Random Variable
11.4 Continuous Distributions
11.5 Mathematical Expectation
11.6 Theoretical Distributions: Some Special Discrete Distributions
12 Discrete Mathematics
12.1 Introduction
12.2 Binary Operations
12.3 Mathematical Logic