Algebra

This chapter discusses the Principles of Mathematical Induction, a technique used to prove certain mathematically accepted statements. We will study how these statements are formulated using positive integers through examples.

In this chapter, we will study the conjugate, equality, product, modules, and sum and difference of Complex Numbers. The properties of addition, multiplication, and division of Complex Numbers and Quadratic Equations with complex roots are described.

This chapter discusses Linear Inequations in One Variable. It describes the standard form of linear inequalities in one variable. The method of finding the solution of these inequalities is also covered.

This chapter discusses Linear Inequations in Two Variables. It describes the standard form of linear inequalities in two variables. The method of finding the solution of these inequalities is also covered.

This chapter discusses the fundamentals of Permutation. It provides us with the formulae for calculating Permutation. It also describes calculating Permutation of distinct objects and 'n' distinct objects taken all at a time.

This chapter discusses the basics of Combination. It highlights the formulae used to evaluate the Combination of any kind. It also explains the Fundamental Principles of Counting (FPC) along with the addition principle.

This chapter discusses the Binomial Theorem. It describes this theorem for non-negative integers and positive integral index, along with some deductions. We will also learn about the Binomial Theorem for a rational index.

This chapter discusses the concept of Arithmetic Progression (AP) by defining sequence and progressions. It explains how to determine the general term, the nth term from the end, and the sum of n terms of an AP, along with its properties.

This chapter sheds light on the concept of Geometrical Progression (GP). We will understand GP with its first term, common ratio, and nth term. The general term and the sum of n terms of a GP are discussed. It also explains the properties of GP.

This chapter explores Infinite Geometric Series. It includes the formula to find the sum of first n natural numbers and the sum of the cubes of first n odd natural numbers. It also presents the sum of the squares and cubes of first n natural numbers.