Mathematics for IIT JEE main and Advanced Two Dimensional Coordinate Geometry Vector And Three Dimensional Geometry Integral Calculus Algebra Sanjiva Dayal

354 Pages·2019·11.61 MB·English

by  Sanjiva Dayal

Mathematics
for IIT-JEE

Two Dimensional Coordinate Geometry
Vector And Three Dimensional Geometry
Integral Calculus
Algebra

Volume-2

Second Edition 2015

This book contains theory and a large collection of about 7500 questions and is useful for
students and learners of IIT-JEE, Higher and Technical Mathematics; and also for the students
who are preparing for Standardized Tests, Achievement Tests, Aptitude Tests and other
competitive examinations all over the world

Er. Sanjiva Dayal,
B.Tech. (I.I.T. Kanpur)
First Edition 2014
Second Edition 2015

Sanjiva Dayal Classes For IIT-JEE Mathematics
Head Office: A-602, Twin Towers, Lakhanpur, Kanpur-208024, INDIA.
Phone: [phone].
Mobile: [phone].
Email: [email protected].
Website: www.amazon.com/author/sanjivadayal.
Website: www.sanjivadayal-iitjee.blogspot.com.

ISBN-13: 978-1511497176
ISBN-10: 1511497173

Copyright © Sanjiva Dayal, Author

All rights reserved. No part of this publication may be reproduced, distributed or transmitted
in any form or by any means electronic, mechanical, photocopying and recording or
otherwise, or stored in a database or retrieval system, including, but not limited to, in any
network or other electronic storage or transmission, or broadcast for distance learning
without the prior written permission of the Author.
i
ABOUT THE AUTHOR

Indian Institute of Technology Joint Entrance Examination (IIT-JEE) is considered to be one of
the toughest competitive entrance examinations in the world with success ratio well below 1%. The author of
this book Sanjiva Dayal was selected in IIT-JEE in his first attempt. After completing B.Tech. from IIT Kanpur,
since the last more than 25 years, he has been teaching IIT-JEE Mathematics to the students aspiring for
success in IIT-JEE and other engineering entrance examinations with an objective to provide training of the
highest order by way of specialized and personalized oral coaching, teaching, training, guidance, educational
facilities including tutorials, tests, assignments, reading materials etc. and all such facilities which are helpful to
the students seeking admission in the IIT and other Engineering Institutes of India.
His excellent teaching and result-oriented methods have combined to produce outstanding
performance by his students in the past years. A large number of his students were selected in their First
Attempt with top ranks. Most of his students have secured admission in the IIT and other Engineering
Institutes of India and they are doing well in their engineering education and professional career also.
Conceptual understanding of Mathematics provided by him not only helps his students to do
well in the IIT-JEE and other engineering entrance examinations but also helps them to do well in their
engineering studies where they are pitted against the best students of the country and competition is much
more intense.
ii
ACKNOWLEDGEMENTS

I thank the Almighty God for my very existence and for providing me the opportunity and
resources to write this book.
Mother is the first teacher and father is the second teacher. My respects and deepest gratitude
to my mother Late Pushpa Dayal, my father Late Chandra Mauleshwar Dayal, my grandfather Late
Lakshmeshwar Dayal, my grandmother Late Sarju Dayal, my maternal grandfather Late Ranbir Jang Bahadur
and my maternal grandmother Late Chandra Kishori Bahadur who are no longer in this world but their
blessings are always with me.
I am extremely thankful to all my school teachers and all my IIT Kanpur Professors who have
taught and trained me.
I am also extremely thankful to all my batch mates in IIT Kanpur because studying and training
with such brilliant persons was an amazing experience for me which will be cherished by me throughout my
life.
I am also extremely thankful to all my students because teaching and interacting with such
brilliant minds has been an amazing learning experience for me which will be cherished by me throughout my
life.
I am also extremely thankful to my wife Dr. Vidya Dayal, my sister Ms. Smita Prakash and my
niece Ms. Somya Prakash for their love, cooperation and moral support.
I am also extremely thankful to my childhood friends Mr. Navneet Butan, Mr. Pankaj Agarwal,
Mr. Akhil Srivastava and Mr. Subir Nigam for their love, cooperation and moral support.
I am also thankful to all other persons who have ever helped me directly or indirectly.
I am also thankful to my student Mr. Ashutosh Verma for his help and efforts in publishing this
book.

Place: Kanpur, India.
Date: 28th March, 2015. Sanjiva Dayal
B.Tech. (I.I.T. Kanpur)
Author
iii
PREFACE TO THE SECOND EDITION 2015

"If there is a God, he's a great mathematician."~Paul Dirac
"How is an error possible in mathematics?"~Henri Poincare
"Go down deep enough into anything and you will find mathematics."~Dean Schlicter

 About Indian Institute of Technology Joint Entrance Examination (IIT-JEE)
Indian Institute of Technology (IIT) are the premier Engineering Institutes of India.
Career in engineering calls for high level of confidence, motivation and capacity to do hard work besides
intelligence and analytical & deductive thinking. Therefore, in order to select the brightest students for
admission in the Indian Institute of Technology (IIT), National Institute of Technology (NIT) and other
Engineering Institutes of India, the competitive entrance examination Indian Institute of Technology Joint
Entrance Examination (IIT-JEE) is conducted on all India basis every year, along with other state level
engineering entrance examinations. IIT-JEE is considered to be one of the toughest competitive entrance
examinations in the world with success ratio well below 1%. The number of candidates appearing in IIT-
JEE as well as the level of competition has grown tremendously in the past years thus creating a need for
highly specialized course content and result-oriented coaching and training.
 About the student
An engineering aspirant should possess sharp mental reflexes, acumen and skill to
understand and master the fundamental concepts of Science and Mathematics; should have the basic
qualities of an ideal student; should be capable of going through the rigorous and tough training schedule
to achieve the standards set by the IIT-JEE and other engineering entrance examinations; and must be
hungry for achievement. With specialized coaching and training, such talented students can achieve
success in IIT-JEE and other engineering entrance examinations.
iv
 Purpose of the book
This book is useful for students and learners of IIT-JEE, Higher and Technical
Mathematics; and also for the students who are preparing for Standardized Tests, Achievement Tests,
Aptitude Tests and other competitive examinations all over the world.
 Organization of the book
This book is a part of book series which is divided into two volumes, seven parts and
twenty eight chapters as under:-
Volume-1
Part-I: Differential Calculus
Chapter-1: Real Functions, Domain, Range
Chapter-2: Limit
Chapter-3: Continuity
Chapter-4: Derivatives
Chapter-5: Applications Of Derivatives
Chapter-6: Investigation Of Functions And Their Graphs
Part-II: Algebra
Chapter-7: Equations And Inequalities
Chapter-8: Quadratic Expressions
Chapter-9: Progressions
Chapter-10: Determinants And Matrices
Part-III: Trigonometry
Chapter-11: Trigonometric Identities And Expressions
Chapter-12: Trigonometric And Inverse Trigonometric Functions, Equations And Inequalities
Chapter-13: Properties Of Triangles
Volume-2
Part-IV: Two Dimensional Coordinate Geometry
Chapter-14: Point And Straight Line
Chapter-15: Circle
Chapter-16: Parabola
Chapter-17: Ellipse
Chapter-18: Hyperbola
Part-V: Vector And Three Dimensional Geometry
Chapter-19: Vector
Chapter-20: Three Dimensional Coordinate Geometry
Part-VI: Integral Calculus
Chapter-21: Indefinite Integrals
Chapter-22: Definite Integral
Chapter-23: Differential Equations
Chapter-24: Applications Of Calculus
Part-VII: Algebra
Chapter-25: Complex Numbers
Chapter-26: Binomial Theorem
v
Chapter-27: Permutations and Combinations
Chapter-28: Probability
This book contains theory and a large collection of about 7500 questions. In each
chapter, theory is divided into Sections and questions are divided into Question Categories. For each
Section there are one or more corresponding Question Category/ Categories in order to make this book
more readable and more useful for the readers and students.
 Using the book
Each Section and its corresponding Question Category/ Categories is the prerequisite of
its following Sections and their corresponding Question Category/ Categories. It is recommended that
readers and students should read a Section and then solve the questions of its corresponding Question
Category/ Categories; and thereafter go to the next Section and so on. This approach is necessary for
proper conceptual development and problem solving skills.
 Reader's feedback
All readers and students are requested and welcome to send their feedback, comments,
corrections, suggestions, improvements, mathematical theory and questions on my email ID
[email protected]. This will help in continuous improvement and updation of this book. All readers
and students are invited to join me as friends on Facebook at URL www.facebook.com/sanjiva.dayal and
they are also invited to join my Facebook Group "Mathematics By Sanjiva Dayal".
Place: Kanpur, India.
Date: 28th March, 2015. Sanjiva Dayal
B.Tech. (I.I.T. Kanpur)
Author
vi
CONTENTS

i
About The Author
ii
Acknowledgements
iii
Preface
Part-IV: Two Dimensional Coordinate Geometry
Chapter-14: Point And Straight Line 14.1
Chapter-15: Circle 15.1
Chapter-16: Parabola 16.1
Chapter-17: Ellipse 17.1
Chapter-18: Hyperbola 18.1
Part-V: Vector And Three Dimensional Geometry
Chapter-19: Vector 19.1
Chapter-20: Three Dimensional Coordinate Geometry 20.1
Part-VI: Integral Calculus
Chapter-21: Indefinite Integrals 21.1
Chapter-22: Definite Integral 22.1
Chapter-23: Differential Equations 23.1
Chapter-24: Applications Of Calculus 24.1
Part-VII: Algebra
Chapter-25: Complex Numbers 25.1
Chapter-26: Binomial Theorem 26.1
Chapter-27: Permutations and Combinations 27.1
Chapter-28: Probability 28.1
Mathematics for IIT-JEE
Er. Sanjiva Dayal,
By B.Tech. (I.I.T. Kanpur)

PART-IV
TWO DIMENSIONAL COORDINATE GEOMETRY

CHAPTER-14
POINT AND STRAIGHT LINE

SANJIVA DAYAL CLASSES FOR IIT-JEE MATHEMATICS
HEAD OFFICE: A-602, TWIN TOWERS, LAKHANPUR, KANPUR-208024, INDIA.
PHONE: [phone]. MOBILE: [phone].
EMAIL: [email protected]. WEBSITE: sanjivadayal-iitjee.blogspot.com.
14.2 MATHEMATICS FOR IIT-JEE/VOLUME-II
CHAPTER-14
POINT AND STRAIGHT LINE

LIST OF THEORY SECTIONS

14.1. Locus, Coordinates, Equation
14.2. Points
14.3. General Equation Of A Straight Line
14.4. Equation Of A Straight Line In Different Standard Forms
14.5. Transformation Of General Equation Of A Line In Different Standard Forms
14.6. A Straight Line And Point(s)
14.7. Two Or More Lines
14.8. General Second Degree Equation Representing A Pair Of Lines
14.9. Transformation Of Axes

LIST OF QUESTION CATEGORIES

14.1. Locus Plotting
14.2. Distance Formula
14.3. Section Formula
14.4. Area Of A Triangle, Collinearity Of Points
14.5. Coordinates Of Centroid, Incenter, Excenters Of A Triangle
14.6. Finding Equation Of A Straight Line From Its Properties
14.7. Finding Properties Of A Straight Line By Its Equation
14.8. Position Of Point(s) W.R.T. A Straight Line, Length Of Perpendicular From A Point On A Straight Line
14.9. Angle Between Two Lines, Parallel And Perpendicular Lines
14.10. Distance Between Two Parallel Lines
14.11. Point Of Intersection Of Two Non-Parallel Lines
14.12. Angular Bisector Of Two Lines
14.13. Family Of Lines Passing Through The Point Of Intersection Of Two Given Lines
14.14. Concurrency Of Three Lines
14.15. A Variable Line Passing Through A Fixed Point
14.16. Equation Representing More Than One Straight Lines
14.17. A General Second Degree Equation Representing A Pair Of Straight Lines
14.18. Homogeneous Second Degree Equation Representing A Pair Of Straight Lines
14.19. Homogeneous Equation Of Lines Joining The Origin To The Points Of Intersection Of A Given Line
And A Given Second Degree Curve
14.20. Locus Problems In Straight Lines
14.21. Transformation Of Axes
14.22. Additional Questions

SANJIVA DAYAL CLASSES FOR IIT-JEE MATHEMATICS. Head office: A-602, Twin Towers, Lakhanpur, Kanpur-208024, INDIA.
Phone: [phone]. Mobile: [phone]. Email: [email protected]. Website: sanjivadayal-iitjee.blogspot.com.