The Complete PHI Learning Guide to Mathematics for IIT JEE (main)

1050 Pages·1995·19.26 MB·English

by  Prem Kumar

Guide to

— for J EE (Main)
The Complete PHI Learning
Guide to

~ MATHEMATICS

for JEE (Main)

PREM KUMAR
Head of MATHS POINT
An Falycorionnl Insttation

PHI Learning [recite Lintiec
New Delhi-110001
2013
‘THE COMPLETE PHI LEARHING GUIDE TO MATHEMATICS FOR JEE WMA)
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Contents

Sebtabns.
Preface
4 Sigggestion Jor Students

. Sets, Relitipns and Functiom

Camplen Numbers...
. Quadratic Equations
Matrices.

Deter
Perquufations and Combinations

ANU

7. Mathematical Induction .
ynial Theorem
1. Sequences aud Series.
|. Functions.
init, € ry
Differentiabitity
>. Differentiation.
. Applications of Derivatives.
1. Indefinite Integrals
5. Definite Integral
5. Applications of Integrat

3-13.32
14.1 1448
15.1 1538
1 W611634

1 recta TT ITER

Coordinates and Straight

Lines. 1s.-1848
19, Cieles 19.1-19.36
20, Parabola 20.1 20.20
AL, Ellipse ..
22, Hyperhola..
23, Vectors.
24, Three Dimensional Geometry... 24.1-24.36
25, Statistics, 5.
26, Probability
27, Trigonometric Ratios, Identities
and Equations.

28, Properties of Irlangles 28.10
29, inverse ‘Ikigouometric

291-2930
30, eights and 30.1-30.20
31. Mathematical Reasoning sense 31.1 31-12
Mock Tast Papers MIMI0
Sample Papers 8H S16

Syllabus

UNIT 1: SETS, RELATIONS AND FUNCTIONS: Som and thsie representation: Union, inerscerion and
complement nPsets an ther algebraie propesties; Paver aet: Relation, lypes of reac, equivalence relat,
functions; owe-one, into and uate Tuncliogs, composition of luaclivas,

UNE 2: COMPLEX NUMBERS AND QUADRATIC EQLATIONS: Complex numhert as nrdened pics
‘of teal, Repiesealation of complex aunbers in the lume i aad Iheie eepeevealation in a plaue, ‘tsand
stggraut algebra of complex numbers. modulus and argument (or amplitade> of a complex number squate Toot
‘of a eamplex minher, triangle inequality, Quacratie equitiont in real and complex rannher ayacem and their
sulutivns. Relason between touls and coelticienls,pature of fous, loemalivg of quadratic equations with given
UNIT 3: MATRICES AND DETERMINANTS: Maticesslgebin of mauices. ypes of matics, determinants
and matrices of order tw and three, Propertios of determinants, svalnation of detorminans, arsa of angles,
using delerminguts. Adjuint and evuluution af inverse ow square matrix usin deleronnants and elewentury
lronsfomatioas. Test of cousisleney and solution of simultaneous linear equations in two ot thiee vasiles
using determinants and maces,

UNIT 4; PERMUTATIONS AND COMBINATIONS: Furusanental principle of counting, petmutaioa at
4am arrongsment and combination as selection, Meaning af Pin, m1 and C1 >), sample applications

ON:

unr

UNIT 6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS: | Binotslal theorem ova positive
integral inces, general tom and middle srr, praportics of Binomial cactfictents and simple applications,

Prmoiple of MachematicalTneuction and its simple applivtions,

MATHEMATICAL INDUC

UNIT 7: SEQUENCES AND SERIES: Arithmetic aud Geometric peoguessioas, Invention of atinetic,
_Beometrie means between to given mumbers, Relation herwssn A.M, and GM, Sum Dp ta terms of spect
nevis Sy Sis Sg Arithmetion-Cisnmetrie progression,

UNIT 8: LIMIT, CONTINUITY AND DIFFERENTIABLLITY: — Resl-valed fumetions algebsn of fmotions,
polynomials, raiuna, Uisonometi, logartmic and exponential Tunetins. inverse Cunetions. Craps ul simple
furious. Lincs, concinuiey and dhfereacabuiry Datfrsutistion of tue sua, difference, product and quocisat
‘of fen Fimariona, Dierentincon af trigomemete, invense trigonomeri, Ingoridhmie, expomentil, comypnsiae
and ipl functions derivatives uC under up i tw, Rolle aud Lagrange's Men Vulue Thorens. pplicalivas
of detivatives: Rate of change of quancties, monotonic inexeasing and decreasing tunetions. Maxima and
minima of fimetions af ane Yarinble, emngenty and. normaly,
Yi_ Syllabus

UNIT 9: INTEGRAL CALCULUS: Iategel as an alinlesheatve, Fundamental imegeals Involving algebraic.
‘rigonomenio, exponential and logarithms fictions, Inxgraton by subsmevaon, by pars and by partial factions,
Integration using tripanomettic identities. valuation of simple integrals of the type. Integral ag limit of a sum.
Fundimeatal Theorem of Calculus, Properties of deliaite mvearals Evaluation of deliaite inegeals. doves
areas of the regions hounded by simple gprees in standard form,

UNIT IU: DIFFERENTIAL EQUATIONS: | Ordinary dffercuril equaous, their order aud degree, Fonnanon,
cof diffeencal eqnicions. Solution of differential equtions by the method of vepacion nf variables, aalution
‘of humiogeceuus and linear didrential equatiuns uf te uype: dvds poewr ~ gle

UNIT TL COORDINATE GEOMETRY: Catesim system of retangolarenomdinates in a plane, distance
formula. section Foraula, locus and its equation. translation of anes, slope ofa Tine. parallel and peupenicular
lines intercepts ofa liae on the coordina axes, Sttight lins. Vasious foun of equations ofa line, ineuseetion,
‘of Fines, angles hetiicen en nee, ennelitions for eoneurrenoe af three Kinet distanee of a point fry a in,
‘equations of iemmal aud eslernal bisecors of angles belieen Us lines cucrdinales of veateud, ontweentie
and circuuicents of « wiangle. equation of funlly of Hines passing tusugh the point of ineseetion af two lines,
Circles, conic acctions. Sundar form of eqnation of a ctcle, general forma ofthe equation ofa cnc, its radius
and centre, equation uf a cicele when the end puinls of a diameler ae yiven, pinks oF intereclian oF lie wad
4 ctcle with the ceae at the origin aud coudition for a line to be taugenc to 4 ciscle, equation of the rangent
Sections of ennes, equations of cone sestions (parable, ellipse and hyperbala) in sendard torms, candhticn far
ome ftw be a tangent and puintls} of unzeney.

UNFIT 12: TIIREE DIMENSIONAL GEOMETRY: Coordinates of « paint in space, ditance hetveea to
points, secon formula ditection ratios and direction cosines, angle between two inersectng Tues. Shes les.
ths showtest distanes betsicen them and 1 equagon, Equations of a line and a plane an dtfforsnt forms,
intentution of w Fine and » plane, eaplar ines

UNIT 1%, VECTOR ALGEBRA: Vectors and scalar, adliton of veceors,componcnts ata YeeKer In
mensions and three dimensional spaoe, aealar und veeter product, sbalne and vovtnr tiple product

UNIT 14; STATISTICS AND PROBARILITY: Measums of Dispersion: Caleulaaon of mean, median,
rede of gmuped and ungrouped data calenltinn nf standaed desiatien, variance and mean deviation fer
geuped aud ungiouped dala, Peobabiliy: Prubabilily of au eveal.aldiiuva and multiplication Ureurens of
probabil, Raye's ehearem, prabebitigsdsmionion ofa random variate, Roma nals and Binomial eistibutin,

UNIT 1S: TRIGONOMETRY: Trigouomouncal ideutises and cquations, Trigonometsical functions, averse
trigonnmetrizal fumetions snd their prnperticx. Heights andl Distances.

UNIT 16; MATHEMATICAL REASONING: Siaromen's, loieal opcroroas aud, of, unelies implicd by
if and only if. Livdersunding nF untology, onnmadiccin, enmvense and enntrapositive
Preface

In pprsuance ofthe ret dirsotives andl changes premulgated by the \insty of Human Resanres Development
{MHD}, Gavernment of India, with regard fo the merger of ALEEE nnd IV-IEE, a combined Joint Rntranee
Eainination TEE} will be held hereiaafer ia two phases. with efleet tom Apail 2013:

1 JRE «Maing

2. TEE (Advanced

he IKE Main, de fats ceplieement nf ALLHE, will he enneducted hy the Cental Hoard nF Seondary
Tduvation ICSE), The JEE (Main) will have the sane syllabus aud paleen of exaination a3 those of AILEE.
dts scores rch 2085 weightage w CBSE stores) will be used for adussious oo BE/BTech courses ar NTs,
111 belbi Technological University (191) and ather Centmilly Funded echnical Inasitaions (CI), a8 per
The hithevto peavice followed by CLSE in sespect ut AIEEC.

‘The JEE (Advaacod), hitherto known 23 UT JBE, will be conducted by the JEE Apsx Boal for only the
‘np 1.50640 candidates in 1H (Main), for admision to Ha, IMT HEL, and ISM Dhanbad

‘The IEE (Muien will bave one sbjecive type question paper as per Paper T ofthe erstwhile AIBC. 1 ill
‘consis af Pinysies. Chemistry auc| Mathematics. The duration of the paper will bs 3 bouts.

The First Jk (Main) sill be held in April 2013. I hay nove heen pmpasl to eondact the JA test tier
in a year The secoud IEE (Ming ll be held ia Novernher"Deverber 2013, the thd in April 2014, and so

hae mathematies book has been specifically designed keeping in mind the standard af die examnation for
he JEE (Min). Taving tough mathesoatie te a Turge number wf students of Classes XT and XT for more thar
a decade wow, Lam well vetsed wilh the areas which equlle special veatateal, Ascoedingly bave given wins!
Jmportance 1 the eanecpts and mechadslegies requited far salving a wide variery af abjeetive type questions,
‘The veal inspiration bebind siting this hook hax been the Feedback of my students ever the year.

1 wish to thank all wy students for theic suggestions without which il would not awe beea possible to bring
‘ur this baok, fam alsa indebted tothe edivial and praccron toams of PHT Learning for many of ther ep fl
suggestions, and alwe care and devotion shown during the production of this bak

Tam aratelul my father Sh, Buh Dev and my laaily meuibels for providing me with mosal support
luring my busy psriads af wting the book,

Aalthnugh every effort hin heen mule tv Keep thie lok free fom encan, 1 shall fel highly obliged 1»
students aud wachers Loe pulnting out eurus au (01 sstking suggestioas towatds he iaproventent uf the book,

Prom Kumar

A Suggestion for Students

ate bea oF penblam ar body of knowledge can be presented bx a form sinple enough so vit aay
ortcalar learner cam sadersiand 4 io a recone form.”
—Bacwa

| fnpe you hove read the Preface carefully, The the (Main paper will be ohiective type im mature and hence
swite diferent from the CDSE Buand exams. The purpose vf tis book is to provide students with a fim
inderstandivg of the concspts along wich rigorous pracace of solving problems with specdl and accuracy

Mathematics is rch, elegant andl beowtfil—but nat necersarily easy. ‘Thece ore three steps for achieving
revficieney in mathematics concept building, proper application ul-concepls ad lst bul rot Teast, peace
and mlere practice, Do every exercise, even sien you eink you can de it casily, There is always a 1eas0u for
every exeruise, so do aut Teave uny out. Muke alla efforts solve every peublem youre siling ox a sludy
lable with paper aad peovil at hand, Try baad 10 ecack aad semember the tisk Develop seeed and accussey
thragh repnlar practice

This at luck, hul youd hard work, patience and perseverance that yuu sluould bank upon ts wie Cough
in the examination

‘Yeo must have realized by’ now thac the JFK (Main) 1s che gateway te JEE (Advanced), You have to by one
‘of the 130,004 up ranken, im JEL (Min) tn heconne eligihle far tuking the tet of the JLL: Advanced.