#### Topics

##### Applications of Matrices and Determinants

##### Complex Numbers

##### Theory of Equations

- Introduction to Theory of Equations
- Basics of Polynomial Equations
- Vieta’s Formulae and Formation of Polynomial Equations
- Nature of Roots and Nature of Coefficients of Polynomial Equations
- Roots of Higher Degree Polynomial Equations
- Polynomials with Additional Information
- Polynomial Equations with No Additional Information
- Descartes Rule

##### Inverse Trigonometric Functions

- Inverse Trigonometric Functions
- Some Fundamental Concepts
- Sine Function and Inverse Sine Function
- The Cosine Function and Inverse Cosine Function
- The Tangent Function and the Inverse Tangent Function
- The Cosecant Function and the Inverse Cosecant Function
- The Secant Function and Inverse Secant Function
- The Cotangent Function and the Inverse Cotangent Function
- Principal Value of Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions

##### Two Dimensional Analytical Geometry-II

##### Applications of Vector Algebra

- Introduction to Applications of Vector Algebra
- Geometric Introduction to Vectors
- Scalar Product and Vector Product
- Scalar Triple Product of Vectors
- Vector Triple Product
- Jacobi’S Identity and Lagrange’S Identity
- Application of Vectors to 3-dimensional Geometry
- Different Forms of Equation of a Plane
- Image of a Point in a Plane
- Meeting Point of a Line and a Plane

##### Applications of Differential Calculus

##### Differentials and Partial Derivatives

##### Applications of Integration

- Applications of Integrations
- Definite Integral as the Limit of a Sum
- Fundamental Theorems of Integral Calculus and Their Applications
- Bernoulli’s Formula
- Improper Integrals
- Reduction Formulae
- Gamma Integral
- Evaluation of a Bounded Plane Area by Integration
- Volume of a Solid Obtained by Revolving Area About an Axis

##### Ordinary Differential Equations

- Introduction to Ordinary Differential Equations
- Differential Equation, Order, and Degree
- Classification of Differential Equations
- Formation of Differential Equations
- Solution of Ordinary Differential Equations
- Solution of First Order and First Degree Differential Equations
- First Order Linear Differential Equations
- Applications of First Order Ordinary Differential Equations

##### Probability Distributions

##### Discrete Mathematics

#### description

- Statement of Descartes Rule
- Attainment of bounds

- Bounds for the number of real roots
- Bounds for the number of Imaginary (Nonreal Complex)roots

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