Chapter-Wise Solutions JEE Main Mathematics 2002-2014

249 Pages·2014·14.677 MB·English

by  Bhupinder Singh Tomar, Hansa Soni,

CHAPTER-WISE SOLUTIONS
2002-2014
I
Bhupinder Singh Tomar Hansa Soni
with 10 SOLVED TEST PAPERS
PEARSON
ALWAYS LEARNING
Chapter-wise Solution:
JEE Main Mathematics
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Chapter-wise Solution:
JEE Main Mathematics
Bhupinder Singh Tomar
Hansa Soni
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No part of this eBook may be used or reproduced in any manner whatsoever without the
publisher’s prior written consent.
Copyright © 2014 Dorling Kindersley (India) Pvt. Ltd.
This eBook may or may not include all assets that were part of the print version. The publisher
reserves the right to remove any material in this eBook at any time.
ISBN: 9789332537804
e-ISBN: 9789332541863
First Impression
Head Office: 7th Floor, Knowledge Boulevard, A-8(A) Sector 62, Noida 201 309, India.
Registered Office: 11 Community Centre, Panchsheel Park, New Delhi 110 017, India.
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ConTEnTS
Preface vii
Chapter 1 Set and Relation 1–2
Chapter 2 Quadratic Equations 3–8
Chapter 3 Sequence and Series 9–12
Chapter 4 Permutation and Combination 13–16
Chapter 5 Binomial Theorem 17–21
Chapter 6 Complex Number 22–27
Chapter 7 Matrices and Determinants 28–35
Chapter 8 Probability 36–43
Chapter 9 Mathematical Reasoning 44–46
Chapter 10 Statistics 47–51
Chapter 11 Trigonometric Ratios and Identities 52–55
Chapter 12 Trigonometric Equations 56–58
Chapter 13 Solution of Triangle 59–61
Chapter 14 Heights and Distances 62–63
Chapter 15 Inverse Trigonometry 64–66
Chapter 16 Straight Line 67–74
Chapter 17 Circles 75–80
Chapter 18 Parabola 81–83
Chapter 19 Ellipse 84–86
Chapter 20 Hyperbola 87–88
Chapter 21 Vector 89–97
Chapter 22 Three-dimensional Geometry 98–107
Chapter 23 Function 108–111
Chapter 24 Limits of Function 112–115
Chapter 25 Continuity and Derivability 116–120
Chapter 26 Differentiation 121–123
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vi | Contents
Chapter 27 Application of Derivatives 124–130
Chapter 28 Indefinite Integration 131–133
Chapter 29 Definite Integration 134–141
Chapter 30 Area under Curve 142–146
Chapter 31 Differential Equations 147–152
Test Paper 1 153–160
Test Paper 2 161–168
Test Paper 3 169–176
Test Paper 4 177–184
Test Paper 5 185–192
Test Paper 6 193–201
Test Paper 7 202–208
Test Paper 8 209–216
Test Paper 9 217–225
Test Paper 10 226–233
JEE MAIN 2014 234–240
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prEfaCE
Chapter-wise Solutions: JEE Main Mathematics has been designed as per the requirements of stu-
dents aspiring to make it big in the JEE Main. The book has been divided into 31 chapters and 10 Test
Papers which will help the students to understand the syllabus as well as the latest pattern of the exami-
nation. The solutions provided will give the students an insight into the various methodologies which
will help them solve various questions as well as understand the subject better.
We hope that this book will be well received by the students. Though we have taken utmost care
to make this book error free but feedback regarding any error will be highly appreciated. Readers are
requested to mail their queries to [e-mail].
Bhupinder Singh Tomar
Hansa Soni
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1
SET And RELATIOn
1. If R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} is a 12! 12!
relation on the set A = {1, 2, 3, 4}, the relation (a) 3!(4!)2 (b) 3!(3!)4
R is
[AIEEE 2004] 12! 12!
(c) (d)
(a) transitive (b) not symmetric (4!)3 (3!)4
(c) reflexive (d) a function 5. Condider the following relation:
2. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), R = {(x, y) |x, y are real numbers and x = wy
(3, 9), (3, 12), (3, 6)} be relation on the set A for some rational number w}
= {3, 6, 9, 12}. The relation is
m p
[AIEEE 2005] S ={ , |m,n,p and q are integers such
 n q
(a) reflexive and transitive only
(b) reflexive only that n, q ≠ 0 and qm = pm}
(c) an equilvalence relation [AIEEE 2010]
(d) reflexive and symmetric only
(a) Neither R nor S is an equivalence relation
3. Let W denote the words in the english diction- (b) S is an equivalence relation but R is not an
ary. Define the relation R by: R = {(x, y) ∈ W × equivalence relation
W | the words x and y have at least one letter in
(c) Both R and S are equivalence relations
common}. Then R is
(d) R is an equivalence relation but S is not an
[AIEEE 2006]
equivalence relation
(a) reflexive, symmetric and not transitive
(b) reflexive, symmetric and transitive
6. Let R be the set of real numbers
(c) reflexive, not symmetric and transitive
[AIEEE 2011]
(d) not reflexive, symmetric and transitive
4. The set S:{1, 2, 3,...12} is to be partitioned Statement-1: A = {(x, y) ∈ R × R:y – x is an
into three sets, A, B, C of equal size. Thus A ∪ integer} is an equivalence relation on R .
B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = f. The Statement-2: B = {(x, y) ∈ R × R:x = ay for
number of ways to partition S is some rational number a) is an equivalence
[AIEEE 2007] relation on R.
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