Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1 for IIT JEE CET EAMCET MHT-CET more than 5000+ Questions Examples Solutions of all types 2022

1260 Pages·2022·15.621 MB·English

by  Amit Agarwal

COMPLETE STUDY PACK FOR
ENGINEERING
ENTRANCES
OBJECTIVE
MATHEMATICS
Volume 1
COMPLETE STUDY PACK FOR
ENGINEERING
ENTRANCES
OBJECTIVE
MATHEMATICS
Volume 1
Amit M. Agarwal
ARIHANT PRAKASHAN (SERIES), MEERUT
Arihant Prakashan (Series), Meerut
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PREFACE
Engineering offers the most exciting and fulfilling of careers. As a Engineer you can find satisfaction
by serving the society through your knowledge of technology. Although the number of
Engineering colleges imparting quality education and training has significantly increased after
independence in the country, but simultaneous increase in the number of serious aspirants has
made the competition difficult, it is no longer easy to get a seat in a prestigious Engineering
college today.
For success, you require an objective approach of the study. This does not mean you 'prepare'
yourself for just 'objective questions'. Objective Approach means more than that. It could be
defined as that approach through which a student is able to master the concepts of the subject
and also the skills required to tackle the questions asked in different entrances such as JEE Main &
Advanced, as well other regional Engineering entrances. These two-volume books on Mathematics
‘Objective Mathematics (Vol.1 & 2)’ fill the needs of such books in the market in Mathematics and
are borne out of my experience of teaching Mathematics to Engineering aspirants.
The plan of the presentation of the subject matter in the books is as follows
— The whole chapter has been divided under logical topic heads to cover the syllabi of JEE Main &
Advanced and various Engineering entrances in India.
— The Text develops the concepts in an easy going manner, taking the help of the examples from the
day-to-day life.
— Important points of the topics have been highlighted in the text. Under Notes, some extra points
regarding the topics have been given to enrich the students.
— The Solved Examples make the students learn the basic problem solving skills in Mathematics. Very
detailed explanations have been provided to make the students skilled in systematically tackling
the problems.
— The answers / solutions to all the questions have been provided.
— The Objective Questions have been divided according to their types Single correct option, More
than One, Assertion-Reason, Matching Type, Integer Type, Passage Based, etc. which can take the
students to a level required for various Engineering entrances in the present scenario.
— Entrance Corner includes the Previous Years' Questions asked in JEE Main & Advanced and other
various Engineering entrances. At the end of the book, JEE Main & Advanced & Other Regional
Entrances Solved Papers have been given.
I would open-heartedly welcome the suggestions for the further improvements of this book (Vol.1)
from the students and teachers.
Amit M. Agarwal
CONTENTS
1. SETS 1-19 Ÿ Harmonic Progression (HP)
Ÿ Introduction Ÿ Arithmetico-Geometric Progression (AGP)
Ÿ Set Ÿ Some Special Series
Ÿ Notations
4. COMPLEX NUMBERS 109-181
Ÿ Representation of Sets
Ÿ The Real Number System
Ÿ Types of Sets
Ÿ Modulus of a Real Number
Ÿ Venn Diagram
Ÿ Imaginary Number
Ÿ Operations on SetsLaws of Algebra of Sets
Ÿ Complex Number
Ÿ Formulae to Solve Practical Problems on
Union and Intersection of Sets Ÿ Algebra of Complex Numbers
Ÿ Conjugate of a Complex Number
2. FUNDAMENTALS OF RELATION Ÿ Modulus of a Complex Number
AND FUNCTION 20-40
Ÿ Argument (or Amplitude) of a Complex
Ÿ Ordered Pair Number
Ÿ Cartesian Product of Sets Ÿ Various Forms of a Complex Number
Ÿ Properties of Cartesian Product of Sets Ÿ De-Moivre’s Theorem
Ÿ Relation Ÿ Roots of Unity
Ÿ Representation of Relation Ÿ Geometrical Applications of Complex
Ÿ Domain and Range of Relations Numbers
Ÿ Some Particular Types of Relations Ÿ Loci in Complex Plane
Ÿ Inverse Relation Ÿ Logarithm of Complex Numbers
Ÿ Composition of Relations
5. INEQUALITIES AND
Ÿ Functions or Mappings
QUADRATIC EQUATION 182-268
Ÿ Difference between Relation and Function
Ÿ Inequality
Ÿ Domain, Codomain and Range of a Function
Ÿ Generalised Method of Intervals for Solving
Ÿ Equal Functions
Inequalities by Wavy Curve Method
Ÿ Classification of Functions (Line Rule)
Ÿ Algebra of Real Functions Ÿ Absolute Value of a Real Number
Ÿ Composition of Functions Ÿ Logarithms
Ÿ Arithmetico-Geometric Mean Inequality
3. SEQUENCE AND SERIES 41-108
Ÿ Quadratic Equation with Real Coefficients
Ÿ Introduction
Ÿ Formation of a Polynomial Equation from
Ÿ Arithmetic Progression (AP)
Given Roots
Ÿ Geometric Progression (GP)
Ÿ Symmetric Function of the Roots
Ÿ Transformation of Equations 8. BINOMIAL THEOREM 348-417
Ÿ Common Roots Ÿ Binomial Theorem for Positive Integral Index
Ÿ Quadratic Expression and its Graph Ÿ Multinomial Theorem
Ÿ Maximum and Minimum Values of Rational Ÿ Greatest Coefficient
Expression Ÿ Greatest Term
Ÿ Location of the Roots of a Quadratic Equation Ÿ R-f Factor Relation
Ÿ Algebraic Interpretation of Rolle’s Theorem Ÿ Divisibility Problems
Ÿ Condition for Resolution into Linear Factors Ÿ Properties of Binomial Coefficients
Ÿ Some Application of Graphs to Find the Roots Ÿ Binomial Theorem for any Index
of Equations
Ÿ Approximation
Ÿ Exponential Series
6. PERMUTATION AND COMBINATION 269-332
Ÿ Logarithmic Series
Ÿ Fundamental Principles of Counting (FPC)
Ÿ Factorial
9. TRIGONOMETRIC FUNCTIONS
Ÿ Exponent of Prime p in Factorial n AND EQUATIONS 418-511
Ÿ Representation of Symbols nP and nC Ÿ Introduction
r r
Ÿ Some Basic Arrangements and Selections Ÿ Measure of Angles
Ÿ Summation of Numbers (3 different ways) Ÿ Systems of Measurement of Angles
Ÿ Permutations under Certain Conditions Ÿ Trigonometric Ratios
Ÿ Circular Permutations Ÿ Trigonometric Function
Ÿ Geometrical Applications of nC Ÿ Graph of Trigonometric Functions
r
Ÿ Selection of One or More Objects Ÿ Trigonometrical Identities
Ÿ Number of Divisors and the Sum of the Ÿ Trigonometric Ratios of Allied Angles
Divisors of a Given Natural Number
Ÿ Trigonometrical Ratios of Compound Angles
Ÿ Division of Objects into Groups
Ÿ Trigonometric Ratios of Multiples of an Angle
Ÿ Dearrangements
Ÿ Maximum and Minimum Values of
Ÿ Number of Integral Solutions of Linear Trigonometrical Expressions
Equations and Inequations
Ÿ Trigonometric Equations
Ÿ General Solution of Trigonometric Equations
7. MATHEMATICAL INDUCTION 333-347
Ÿ Solution of Trigonometric Inequality
Ÿ Introduction
Ÿ Statement
10. PROPERTIES OF TRIANGLES,
Ÿ Principle of Mathematical Induction
HEIGHTS AND DISTANCES 512-589
Ÿ Algorithm for Mathematical Induction
Ÿ Introduction
Ÿ Types of Problems
Ÿ Relation between the Sides and Angles of
Triangle
Ÿ Trigonometric Ratios of Half Angles of a Ÿ Locus and its Equation
Triangle Ÿ Combined Equation of a Pair of Straight Lines
Ÿ Area of a Triangle Ÿ Bisectors of the Angle between the Lines
Ÿ Conditional Identities Given by a Homogeneous Equation
Ÿ Solution of Triangles Ÿ General Equation of Second Degree
Ÿ Circles Connected with Triangle Ÿ Equations of the Angle Bisectors
Ÿ The Orthocentre and the Pedal Triangle Ÿ Distance between the Pair of Parallel Lines
Ÿ Cyclic Quadrilateral
13. CIRCLE 695-791
Ÿ Regular Polygon
Ÿ Introduction
Ÿ Heights and Distances
Ÿ Standard Equation of a Circle
Ÿ Some Important Properties of Triangles
Ÿ Circle Passing through Three Points
Ÿ Some Properties Related to Circle
Ÿ Position of a Point with respect to a Circle
11. CARTESIAN SYSTEM OF Ÿ Intersection of a Straight Line and a Circle
RECTANGULAR COORDINATES 590-626 Ÿ Equation of Tangent
Ÿ Introduction Ÿ Normal to a Circle
Ÿ Coordinate System Ÿ Pair of Tangents
Ÿ Distance Formulae Ÿ Director Circle
Ÿ Applications of Distance Formula Ÿ Pole and Polar
Ÿ Section Formulae Ÿ Diameter of a Circle
Ÿ Area of a Triangle Ÿ Angle of Intersection of Two Circles
Ÿ Area of a Quadrilateral Ÿ Family of Circles
Ÿ Some Standard Points of a Triangle Ÿ Coaxial System of Circles
Ÿ Locus Ÿ Limiting Points
Ÿ Transformation of Axes
14. PARABOLA 792-853
12. STRAIGHT LINE AND PAIR Ÿ Conic Sections
OF STRAIGHT LINES 627-694 Ÿ Parabola
Ÿ Straight Line Ÿ Other Standard Forms of Parabola
Ÿ Angle between Two Lines Ÿ Position of a Point with respect to a Parabola
Ÿ Point of Intersection of Two Lines Ÿ Intersection of a Line and a Parabola
Ÿ Image of a Point with Respect to a Line Ÿ Equation of Tangent
Ÿ Family of Lines through the Intersection of Ÿ Angle of Intersection of Two Parabolas
Two Given Lines Ÿ Equation of Normal to Parabola
Ÿ Number of Normals and Conormal Points Ÿ Conjugate points
Ÿ Combined Equation of Pair of Tangents Ÿ Conjugate Lines
Ÿ Director Circle Ÿ Diameter
Ÿ Diameter of a Parabola Ÿ Asymptotes
Ÿ Pole and Polar of a Parabola Ÿ Rectangular Hyperbola
Ÿ Lengths of Tangent, Subtangent, Normal Ÿ Tangent to a Rectangular Hyperbola
and Subnormal Ÿ Normals to a Rectangular Hyperbola
15. ELLIPSE 854-918 17. INTRODUCTION TO THREE
Ÿ Introduction DIMENSIONAL (3D) GEOMETRY 972-986
Ÿ Position of a Point with respect to an Ellipse Ÿ Coordinate Axes and Coordinate Planes in
Ÿ Equation of the Chord Three Dimensional Space
Ÿ Intersection of a Line and an Ellipse Ÿ Coordinates of a Point in Space
Ÿ Tangent Ÿ Distance between Two Points
Ÿ Combined Equation of the Pair of Tangents Ÿ Section Formulae
Ÿ Director Circle Ÿ Centroid of a Triangle
Ÿ Normal
18. INTRODUCTION TO LIMITS
Ÿ Number of Normals and Conormal Points
& DERIVATIVES 987-1040
Ÿ Pole and Polar
Ÿ Limits
Ÿ Conjugate Lines
Ÿ Existence of Limit
Ÿ Diameter
Ÿ Algebra of Limits
Ÿ Evaluation of Limits by Using L' Hospital’s Rule
16. HYPERBOLA 919-971
Ÿ Evaluation of Algebraic Limits
Ÿ Introduction
Ÿ Evaluation of Trigonometric Limits
Ÿ Conjugate Hyperbola
Ÿ Evaluation of Exponential and Logarithmic
Ÿ Position of a Point with respect to a
Limits
Hyperbola
Ÿ Evaluation of Exponential Limits of the
Ÿ Intersection of a Line and a Hyperbola
Form 1¥
Ÿ Tangent to a Hyperbola
Ÿ Sandwich Theorem for Evaluating Limits
Ÿ Director Circle
Ÿ Some Useful Expansions
Ÿ Normals to a Hyperbola
Ÿ Use of Newton-Leibnitz’s Formula in
Ÿ Equation of the Pair of Tangents
Evaluating the Limits
Ÿ Equations of Chord
Ÿ Derivative
Ÿ Pole and Polar
Ÿ Geometrical Meaning of a Derivative 20. STATISTICS 1058-1094
Ÿ Derivative from First Principle Ÿ Measures of Central Tendency
Ÿ Differentiation of Some Important Functions Ÿ Measures of Dispersion
Ÿ Algebra of Derivative of Functions Ÿ Skewness
Ÿ Chain Rule Ÿ Some Results to be Remembered
Ÿ Logarithmic Differentiation Ÿ Correlation Analysis
Ÿ Characteristics of Correlation Coefficient
19. MATHEMATICAL REASONING 1041-1057
Ÿ Regression Analysis
Ÿ Statements or Propositions
Ÿ Properties of Regression Coefficients
Ÿ Use of Venn Diagrams in Checking Truth and
Ÿ Properties of Lines of Regression
Falsity of Statements
Ÿ Truth Table 21. FUNDAMENTALS OF
Ÿ Logical Connectives/Operators PROBABILITY 1095-1132
Ÿ Quantifiers and Quantified Statements Ÿ Introduction
Ÿ Negation of a Quantified Statement Ÿ Some Basic Definitions
Ÿ Logical Equivalence Ÿ Event
Ÿ Negation of a Compound Statement Ÿ Important Events
Ÿ Converse, Inverse and Contrapositive of an Ÿ Algebra of Events
Implication Ÿ Probability
Ÿ Tautologies and Contradictions Ÿ Geometrical Probability
Ÿ Algebra of Statements Ÿ Addition Theorem of Probability
Ÿ Duality Ÿ Independent Events
Ÿ Booley’s Inequality
JEE Advanced Solved Paper 2015 1135-1140
JEE Main & Advanced Solved Papers 2016 1-12
JEE Main & Advanced/ BITSAT/Kerala CEE/ KCET/AP & TS EAMCET/
VIT/MHT CET Solved Papers 2017 1-32
JEE Main & Advanced/ BITSAT/ KCET/AP & TS EAMCET/
VIT/MHT CET Solved Papers 2018 1-35
JEE Main & Advanced/ BITSAT/ AP & TS EAMCET/
MHT CET/WB JEE Solved Papers 2019-20 1-31