Complete Companion For Jee Main 2020 Mathematics Vol 1

677 Pages·2019·33.065 MB·English

by  Dinesh Khattar, Rohan Sinha

FIFTH EDITION
Complete Companion for FIFTH EDITION
2020
JEE Main
Complete Companion for
MATHEMATICS
2020
JEE Main
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The Complete Resource Book for JEE Main series has been designed to be an independent E (cid:31)(cid:30)(cid:29)(cid:28)(cid:27)(cid:26)(cid:25)(cid:24)
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resource to enable faster and effective learning. This series includes three separate books on Y
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(Joint Entrance Examinations) and other key engineering entrance examinations.
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HIGHLIGHTS  Coverage of key topics along with
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solved examples
 Complete coverage of JEE Main curriculum with emphasis on important concepts
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 Provides varieties of solved example after each concept for better understanding T
complete solutions
 Key points highlighted within text along with features like – ‘Concepts at a glance’, H
 Chapter-wise Previous 18 years’
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‘info boxes’, and ‘concept notes’ to aid in quick last-minute revision AIEEE/JEE Main questions
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 Includes ample number of solved examples along with NCERT Exemplar over Im M  Fully-solved JEE Main 2019
 Updated Practice Exercises as per recent patterns of JEE Main for result-oriented preparation age: Seno AT questions (April & Jan)
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FIFTH EDITION
Complete Companion for
2020
JEE Main
MATHEMATICS
(cid:31)(cid:30)(cid:29)(cid:28)(cid:27)(cid:26)(cid:25)(cid:24)(cid:24)
Dinesh Khattar
Rohan Sinha
This page is intentionally left blank.
FIFTH EDITION
Complete Companion for
2020
JEE Main
MATHEMATICS
(cid:31)(cid:30)(cid:29)(cid:28)(cid:27)(cid:26)(cid:25)(cid:24)
Dinesh Khattar
Rohan Sinha
Copyright © 2019 Pearson India Education Services Pvt. Ltd

Published by Pearson India Education Services Pvt. Ltd, CIN: U72200TN2005PTC057128.

No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s
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ISBN 978-93-534-3509-7
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Contents
Preface xi Chapter 3 Quadratic Equations and
Mathematics Trend Analysis (2011 to 2019) xiii Expressions 3.1
Quadratic Equation 3.1
Chapter 1 Set Theory 1.1
Common Roots 3.7
Set 1.1 Symmetric Function of the Roots 3.9
Representation of a Set 1.1 Graph of a Quadratic Expression 3.9
Types of Sets 1.1 G reatest and Least Values of a Quadratic
Operations on Sets 1.2 Expression 3.9
Algebra of Sets 1.4 N ature of Roots of a Quadratic Equation with
Respect to One or Two Real Numbers 3.10
Cartesian Product of Two Sets 1.4
R elation Between Roots and Coefficients
Relations 1.9
of a Polynomial Equation 3.11
Types of Relations on a Set 1.10
F ormation of a Polynomial Equation From
Equivalence Relation 1.10
Given Roots 3.11
Congruence Modulo m 1.10
Sign of a Polynomial Expression 3.11
NCERT Exemplars 1.14
Rational Algebraic Expression 3.16
Practice Exercises 1.17
NCERT Exemplars 3.19
Practice Exercises 3.23
Chapter 2 Complex Numbers 2.1
Imaginary Numbers 2.1 Chapter 4 Permutations and Combinations
Integral Powers of i 2.1 4.1
Complex Numbers 2.2
Factorial Notation 4.1
Conjugate of a Complex Number 2.3 Fundamental Principles of Counting 4.1
Modulus of a Complex Number 2.4 Permutation 4.4
Square Roots of a Complex Number 2.6 Combination 4.7
A rgand Plane and Geometrical Representation Key Results on Combination 4.8
of Complex Numbers 2.7 Derangement 4.13
Polar Form of a Complex Number 2.7 Exponent of prime p in n! 4.14
Particular Cases of Polar Form 2.9 Number of Divisors 4.15
Eulerian Representation of a Complex Number 2.10 NCERT Exemplars 4.16
Logarithm of a Complex Number 2.10 Practice Exercises 4.19
Vectorial Representation of a Complex Number 2.10
Chapter 5 Mathematical Induction 5.1
Roots of a Complex Number 2.12
Geometry of Complex Numbers 2.15 Mathematical Induction 5.1
Practice Exercises 2.21 NCERT Exemplars 5.4
Practice Exercises 5.5
viii Contents
Chapter 6 Binomial Theorem Chapter 10 Coordinates and Straight
Lines 10.1
Binomial Expression 6.1
Binomial Theorem 6.1 Distance Formula 10.1
Special Cases 6.1 Section Formulae 10.3
Pascal’s Triangle 6.2 Area of a Triangle 10.5
Middle Term in the Binomial Expansion 6.9 Condition for Collinearity of Three Points 10.5
NCERT Exemplars 6.14 Stair Method for Finding the Area 10.6
Practice Exercises 6.16 Area of a Quadrilateral 10.8
Area of a Polygon 10.8
Chapter 7 Sequence and Series 7.1
Stair Method 10.8
Sequence 7.1 Locus 10.9
Series 7.1 Translation of Axes 10.9
Progressions 7.1 Rotation of Axes 10.10
Arithmetic Progression (A.P.) 7.1 Reflection (Image) of a Point 10.10
Sum of n Terms of an A.P. 7.3 General Equation of a Straight Line 10.12
Properties of A.P. 7.4 Slope of a Line 10.12
Arithmetic Mean (A.M.) 7.7 Intercept of a Line on the Axes 10.12
Geometric Progression (G.P.) 7.9 Equation of a Straight Line in Various forms 10.13
Geometric Mean (G.M.) 7.14 Reduction of the General Equation to Different
Standard Forms 10.17
Some Special Sequences 7.16
Angle Between Two Intersecting Lines 10.17
Arithmetico-Geometric Progression (A.G.P.) 7.18
Condition for Two Lines to be Coincident,
Method for Finding Sum of A.G. Series 7.18
Parallel, Perpendicular or Intersecting 10.18
NCERT Exemplars 7.21
Equation of a Line Parallel to a Given Line 10.18
Practice Exercises 7.24
Equation of a Line Perpendicular to a Given Line 10.19
Chapter 8 Limits 8.1
Point of Intersection of Two Given Lines 10.19
Limit of A Function 8.1
Concurrent Lines 10.19
Indeterminate Forms 8.2
Position of Two Points Relative to a Line 10.19
Algebra of Limits 8.3
Length of Perpendicular from a Point on a Line 10.20
Evaluation of Limits 8.3
Distance between Two Parallel Lines 10.21
Algebraic Limits 8.3
Equations of Straight Lines Passing through
Limit of an Algebraic Function when x → ∞ 8.4 a Given Point and Making a Given
Trigonometric Limits 8.6 Angle with a Given Line 10.21
Exponential and Logarithmic Limits 8.8 Reflection on the Surface 10.21
Evaluation of Limits using L’Hospital’s Rule 8.12 Image of a Point with Respect to a Line 10.22
Practice Exercises 8.16 Equations of the Bisectors of the Angles
Between Two Lines 10.23
Chapter 9 Differential Equations 9.1 Equations of Lines Passing through the Point
of Intersection of Two Given Lines 10.24
Differential Equation 9.1
Standard Points of a Triangle 10.24
Linear and Non-linear Differential Equations 9.3
Orthocentre 10.26
Initial Value Problems 9.7
Coordinates of Nine Point Circle 10.26
Homogeneous Differential Equations 9.10
NCERT Exemplars 10.28
Solution by Inspection 9.13
Practice Exercises 10.33
NCERT Exemplars 9.17
Practice Exercises 9.26
Contents ix
Chapter 11 Circles 11.1 Centre of Conic 12.3
Parabola 12.3
Circle 11.1
Some Terms Related to Parabola 12.3
Standard Equation of a Circle 11.1
Intersection of a Line and a Parabola 12.5
General Equation of a Circle 11.1
Equation of a Chord 12.5
Conditions for an Equation to Represent a Circle 11.1
Point of Intersection of tangents 12.5
Equation of a Circle in some Special Cases 11.2
Position of a Point with Respect to a Parabola 12.6
Equation of A Circle In Diameter Form 11.4
N umber of Tangents Drawn from a Point
Intercepts Made by a Circle on the Axes 11.5
to a Parabola 12.6
Parametric Equations of a Circle 11.5
Equation of the Pair of Tangents 12.6
Position of a Point with Respect to a Circle 11.6
Equations of Normal in Different Forms 12.6
Circle Through Three Points 11.7
Point of Intersection of Normals 12.6
Intersection of a Line and a Circle 11.8
Co-normal Points 12.7
Length of Intercept Made by a Circle on a Line 11.8
Chord of Contact 12.7
T he Least and Greatest Distance of a Point
Chord with a Given Mid Point 12.7
from a Circle 11.9
Ellipse 12.14
Contact of Two Circles 11.10
Position of a Point with Respect to an Ellipse 12.16
Tangent to a Circle at a Given Point 11.11
Equation of Normal in Different Forms 12.18
Equation of the Tangent in Slope form 11.11
Equation of the Pair of Tangents 12.18
Condition of Tangency 11.11
Chord with a Given Mid Point 12.19
Tangents From a Point Outside the Circle 11.11
Optical Property of Parabola 12.25
Length of the Tangent From a Point to a Circle 11.12
Equation of a Hyperbola in Standard Form 12.26
Normal to the Circle at a Given Point 11.12
S ome Terms and Properties Related to a
Pair of Tangents 11.13
Hyperbola 12.26
Common Tangents to Two Circles 11.13
Conjugate Hyperbola 12.27
Power of a Point with Respect to a Circle 11.15
P osition of a Point with Respect to a
Director Circle 11.15
Hyperbola 12.28
Equation of Chord of Contact 11.16
Equation of the Pair of Tangents 12.29
Equation of Chord if its Mid Point is Known 11.16
Chord with a Given Mid Point 12.29
Common Chord of Two Circles 11.17
Chord of Contact 12.29
Diameter of a Circle 11.17
NCERT Exemplars 12.35
Angle of Intersection of Two Circles 11.18
Practice Exercises 12.38
Orthogonal Intersection of Two Circles 11.18
Chapter 13 Vector Algebra 13.1
Family of Circles 11.19
Image of the Circle by the Line Mirror 11.20 Scalars and Vectors 13.1
Practice Exercises 11.21 Representation of Vectors 13.1
Types of Vectors 13.2
Chapter 12 Conic Sections (Parabola,
Equal Vectors 13.2
Ellipse and Hyperbola) 12.1 Fixed Vectors 13.2
Conic Section 12.1 Free Vectors 13.2
Important Terms 12.1 Angle between Two Vectors 13.2
S ection of a Right Circular Cone by Different Addition (Sum or Resultant) of Two Vectors 13.3
Planes 12.1 Position Vector 13.4
Equation of Conic 12.2 Component of a Vector 13.8
General Equation 12.2 Linear Combination 13.8