"In the past few years, the IIT-JEE has evolved as an examination designed to check a candidate's true scientific skills. The examination pattern needs one to see those little details which others fail to see. These details tell us how much in depth we should know to explain a concept in the right direction. Keeping the present-day scenario in mind, is written for students, to allow them not only to learn the tools but also to see why they work so nicely in explaining the beauty of ideas behind the subject. The central goal of this series is to help the students develop a thorough understanding of Mathematics as a subject. This series stresses on building a rock-solid technical knowledge based on firm foundation of the fundamental principles followed by a large collection of formulae. The primary philosophy of this book is to guide the aspirants towards detailed groundwork for strong conceptual understanding and development of problem-solving skills like mature and experienced mathematicians. Each book in this new Mathematics series is to help the aspirants prepare for both Advanced and Main levels of JEE conducted for IITs and other elite engineering institutions in India. The books in this series is to strengthen the basic understanding of the concepts and their applications. The books will be equally useful for the students preparing for Mathematics Olympiads. This book is enriched with detailed exhaustive theory that introduces the concepts of Mathematics in a clear, concise, thorough and easy-to-understand language. A large collection of relevant problems is provided in eight major categories (including updated archive for JEE Advanced and JEE Main), for which the solutions are demonstrated in a logical and stepwise manner. These not only make students exam-ready but also helps them gain analytical skills. We have carefully divided the series into five parts to make the learning of different topics seamless for the students. These parts are &bull Coordinate Geometry &bull Algebra &bull Trigonometry &bull Calculus &bull 3-D and Vector Finally, I would like to thank all my teacher friends who had been a guiding source of light throughout the entire journey of writing this book. I apologise in advance for the errors (if any) that might have inadvertently crept in the text. I would be grateful to the readers who bring errors of any kind to my attention. I truly welcome all comments, critiques and suggestions. I hope this book will nourish you with the concepts involved so that you get a great rank at JEE. Wish you all the best! Om Sharma"