Oswaal IIT JEE Main Solved Papers Mathematics Chapterwise and Topicwise 2019 and 2020 All shifts 32 Papers IITJEE IIT-JEE NTA

353 Pages·2021·11.511 MB·English

by  Oswaal Teachers

MATHEMATICS
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1st EDITION, YEAR 2020-21
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“978-93-5423-013-4”
SYLLABUS JEE (MAIN)
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PREFACE
Logical thinkers, problem solvers, creators, engineers are definitely the most recognisable and
valued people around the world. But many students preparing for JEE still ask; how good is
engineering as a career option?
Engineering has become the most lucrative profession now more than ever, with the demand
for engineers exceeding their supply. Engineers bring ideas to life. In every field, engineers play
a very important role in devising and executing new and better technologies. Thus, to take up
engineering as a profession cracking the JEE (Main) exam is the first and the most important step.
Every aspiring engineer in the country works diligently for this exam. This makes JEE a highly
competitive exam.
With the core objective of “Learning Made Simple” Oswaal Editorial Board has designed
Oswaal JEE (Main) Solved Papers to help these aspiring candidates crack one of the most difficult
examinations in the country. The book includes Previous Years’ Papers; to tell the students what
to expect and familiarise them with the exam pattern that has been followed year on year along
with the Scheme of Examination issued by the NTA on 16th Dec 2020.
Benefits of studying from this book are:
1. Based on the Scheme of Examination issued by the NTA on 16th Dec 2020
2. Fully Solved Papers of 2019 & 2020 JEE (Main)
3. Chapter-wise & Topic-wise presentation for systematic learning
4. Subjective (Integer Types) Questions for extensive practice
5. Concept Revision (Video Based) for hybrid learning
6. Commonly Made Errors to polish concepts
7. Mind Maps for better retention
8. Mnemonics for memorise the concepts.
This book aims to make students exam-ready, boost their confidence and help them achieve
better results.
We hope that OSWAAL JEE (Main) Solved Papers 2019 & 2020 will help you at every step as
you move closer to your educational career goal. We wish you all great success ahead!

TEAM OSWAAL
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CONTENTS
g Latest Syllabus for Academic Year 2021 9 - 11
g 10 Tips & Tricks to Crack JEE (Main) 12 - 13
g Trend Analysis JEE (Main) 2019 & 2020 14 - 14
g Mnemonics 15 - 24
1. Sets, Relations and Functions 1 - 15
Topic 1. Sets and their Properties
Topic 2. Relations, Functions and their Properties
2. Complex Numbers and Quadratic Equations 16 - 33
Topic 1. Complex Numbers
Topic 2. Quadratic Equations
3. Matrices and Determinants 34 - 56
Topic 1. Matrices, Matrix operations and their Properties
Topic 2. Determinants & Properties of Determinants
Topic 3. Simultaneous Linear Equations in two or three Variables
4. Permutations and Combinations 57 - 63
5. Mathematical Induction 64 - 66
6. Binomial Theorem and Its Simple Applications 67 - 79
7. Sequence and Series 80 - 95
Topic 1. A.P., G.P. and H.P., Insertion of A.M., G.M. and H.M.
Topic 2. A.G.P. and sum of Σn, ∑n2,∑n3,
8. Limit, Continuity and Differentiability 96 - 132
Topic 1. Limit
Topic 2. Continuity and Differentiability
Topic 3. Differentiation
Topic 4. Application of Derivatives
9. Integral Calculus 133 - 163
Topic 1. Indefinite Integrals
Topic 2. Definite Integrals
Topic 3. Area of Bounded Regions
10. Differential Equations 164 - 179
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...CONTD.
11. Coordinate Geometry 180 - 224
Topic 1. Straight Lines
Topic 2. Circle
Topic 3. Conic Sections
12. Three Dimensional Geometry 225 - 240
13. Vector Algebra 241 - 251
14. Statistics and Probability 252 - 271
Topic 1. Statistics
Topic 2. Probability
15. Trigonometry 272 - 288
16. Mathematical Reasoning 289 - 296
 Appendix 297 - 327
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JEE (Main) Latest Syllabus for Academic Year (2021)
MATHEMATICS
UNIT 1 : Sets, Relations and Functions
Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power
set; Relation, Type of relations, equivalence relations, functions; one-one, into and onto functions, composition of
functions.
UNIT 2 : Complex Numbers and Quadratic Equations
Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their
representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of
a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex
number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic
equations with given roots.
UNIT 3 : Matrices and Determinants
Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of
determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of
a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous
linear equations in two or three variables using determinants and matrices.
UNIT 4 : Permutations and Combinations
Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P
(n,r) and C (n,r), simple applications.
UNIT 5 : Mathematical Induction
Principle of Mathematical Induction and its simple applications.
UNIT 6 : Binomial Theorem and Its Simple Applications
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients
and simple applications.
UNIT 7 : Sequences and Series
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers.
Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n, Sn. Arithmetic-Geometric progression.
2 3
UNIT 2 : Limit, Continuity and Differentiability
Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential
functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of
the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric,
logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle’s and Lagrange’s
Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and
decreasing functions, Maxima and minima of functions of one variable, tangents and normals.
UNIT 9 : Integral Calculus
Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and
logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric
identities.
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