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GATE engineering MATHEMATICS Part 4 NotE : OTHER THEN THESE NOTES I HAVE MY Own gate engineering mathematics note’s which in which I covered more ten 300 gate problem and solution with every topic derivation & their properties and variations if you want you can mail me at my mail id I will make these available on 31 st July to all of you My mail ID : [email protected]

Maths Part 4

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NotE : OTHER THEN THESE NOTES I HAVE MY Own gate engineeringmathematics notes which in which I covered more ten 300gate problem and solution with every topic derivation &their properties and variationsif you want you can mail meat my mail id I will make these available on 31stJuly to allof youMy mail ID : [email protected]&?.Eo/*?. O'*f,o f,onoJ hlecrvrs a1p .Vg : oF:-qr-\-LJz - (q+>)LA - +A,?-J +Zg * + RAMKAMAL.cHouDHARYsslqGMArL.coMsTs423sesl-B'(q-z) ++ (-z+,) + /^ (at:og (ct->l - 4-hA:Lq4 o)Ar)4r'V.P =V'F=htr,-l-Ao1b.7 b,= ( q-zl .i *. bj +/rkcJ;v ,f -*y.F = t+t rtvF-.fnav'cq+i) .ir Azj -ak.2-LPage 92 of 225fo.'I!/n 1oidql-Yeclor3-Cnr* necess eq! 9rlC st-tNfii cieqf Colnd* {-raVe-ch'r Pa^n c- ' F' Jo Ae.+o7ern o i "loJ ri ,oli v:_ f_;_ o iY'F:-OA) lcr"ior''o Pe-re.*ur,V'F:o- Utrr + dF: +Atrr:.oO:c A.y de-L+J+ ):,O3"Fln 4 **e Vc', lue o?-'t '3o *ka{ 1-tne- ve-dtv?q+-,r*)k g-of e,r.r o i "l o.l "co/*?-o/iwD:odFr_+-ehI dts z-odz_o)c bjPage 95 of 225, Y3 -2 AxJ -t- 8x5 +:r*J = oLu>+_ro)xJ:oL- i+-:34.'l"J\'',i+snn ( div Ft , ?RAM [email protected] 8423698L: _A +_ 2_o *_ SnS'. LPF = xJL i f"rLy'i - syz-l c, Y=ot-d* =-a clq=oQs z=o't" z=l-lr,, 7 - *),). =c t',,J ..," (tt]-bluwy ffix- ea tz -LQs _ra, _Lp+e y = Li.2.1V./ illowqDcV =L -,.--- , ?Z:-tt 3) Qx- =-aXI 13 cl:c\- 1a1-- 6 xL f d,. ttz-l * Z4 +\{t-_---r -.xgdr:3ItLr)L-1 plar^r- }"..Ou{17-rflacl i qf3 ---U-n Ll3.t1^!"- LLv*< eetot3iw a4r.r.l)Dl :- : x-+ l)16{ r,reZzar-,-^ItL-*eI qu-7i"fx ? -3 Sivr.Qs- [& LuS&' Si,r,t] q 3)'r a-o! Ls"Jr& tqsi"16LI3 LoJ&_ - 3Sivt= ld nPage 103 of 225q rblL"j Evc'l q61-fe 4ftdt r^,-rlrcre i=)tr n l] 't ' ,+yi uohetI ^t 'L is q ?e-* b aur ,d qd by t =D t >L=-1 evdl \=o ,Yrfq( a { qt 4fl_ cuatidc ck r^:tre-ol,-Tb *:-c=ha.y =bc[.r =-n--_..'-_.Y+bY)AvQbL:o'a3 --Qb-z o'bz!q3-q3Page 104 of 225Jsr-o S q-t ?a y i'r*r-1+ a-l'(Iil .-n Arny ryy mte4vaf uhr c,! i. {v-tq ^"k4 oryt,r-, e Sr-r-vFqee)s cd).4S.rr ?qa f N+ ery alt ."1r} lf ' tltelut ll ahl,e- !e.do:rt q vl--etefltv't-"'-Or,re.t q 9q-r oi"-;tr. o l: JDlAva-.l-t ,)-jJ_J.r r a 0r{-nr {-h,ru v,.r-{rr.l bl z- =e- , z = 6 . -1X*\ - -J*1\Page 105 of 225q l03l^rtLe* \R' be f* Y'i"huI'e' x- 2 oc++ 2 LtL,) = [gIof r, I i+r the \ - z_- FL^r*_grnce jl jr r4e-LtlrruprL_ r!:11 etcwt _ayq f ry_ vg4ut tel, t +rr-kIq-. ^ ^.l.AVA- C-. --*AR\'1.qlCMAl.COV c/8d2'.r81KAIVI-' -!j rr-t ,]5:r -L/ o fr,;;- aac:;_cl_;4*p-.+-?=-Plqt^e -Page 106 of 225Ilo\-iJa=t J? s oB s cfr.H ,, Nl *-'-!-- \>!tertoJe4- D1 A=-SiE+fs -ALA els-'se-.JeJ{.n"{-'c{,\e.l tP n u-u{ t&' a.t e ( -a v,f'nt c.Lo_!.cl_ + rr,r& {=F xClote4 $ i*letcer-hAltilatrv+z*d nt: ///k'Lx1 SrlnIexe p4J-t/LL-rWLuawhtlv-\r)dd-_r]_-z-b.JIIJ(J)C_2-9II: 4 Lrrb: - )t Y,alj x q/ \g3za &{-ll;:- G, -Y ira-llLr'^,, ,)_ : IQ_x-b^Page 113 of 225(!.,t ( tgi - Ptq, ) a* * [ ,v -u\) d,1'lruu,.del U1y .- 3f , J ,*9ll ir: =!rr! -rjq- ;I L'lc.;h.Pta lris 't*hc -V e1iw1e) )rx-l ^x-\ --L-M1,- t=ncl h:-,c- CtrCeL -. .t1- -1r---)LLp !-\i ::l -l\slv-JoLJj*l)c-oe i+ c i a- -ard r-i-1n ow l]t v pl:---Page 114 of 2256es l, (slL-.r al, t2-L>L'i*tAq'J O*- rLp\q, *{*\,) dl ,uahe'^re 'L' ir+1rt-.bor.r*I-d b1\L-*a ry=o,n*\,>+-tt-aftmp,*. ,.L et l( ' I e qr Ofl eru, qr F{-ce- h n U \d zJ L* qC{o teoJ rr ut4 nora * i 'vrter\ e a-r*r'hq r'L{-rt '-,e- tc ' a f.4 lr-tE/ b ,,\q.i'= -t'j+/j,zt:r,is -ir..'e-ire,Jc.a c{icc >3+.1'LL \ a"d-qrIIZJ-'L-\LtLl__= ?_[-llsurj tt _6 g _ y)ele !14q^2- lktt S *) It,ri tlwp-k lq lcqlvdqe t.#-e---::::.;- -- :>L>-gL* &)-+'-- Lc-t-!s @)-A'M KAMAI.CFrO UDr.l AFiY! 5 I@ G i\4ArL CO\,19 78423698I,L lyd4lLrtg{e 4\anI-(, I - -1t,)vV =1 n^{ L/tPage 118 of 225il62tt-;Lleu-- ltl>-x-IL-;))L-:1 o-3 ,totLrV)L--I L-)L*7 o{x-Lt_f .,; _, :,,-,,(.-:_ __=_ 4_'xla 6 t {til rF.{ ,e:::_*t'tsq,nt- d+lrl *,1 f rEa_**+ -cl*-a ,L'-cl,i'-tQL -{q\[' -a?= =-4? :a, -,!?L -1Z^L7 -zPage 119 of 2251i_7fi1.(JIJolt-lt")o t'l clY f L"rt, +- irial d6-fIIIJa,, ft llwlu --+;1r,t): " )--,aa ltf-elo uL@dtld\9'!"lflinct e=Yl-renttm AY q Cq.rv*, -U) e -V;/- ,t- - {t-t z(elt 3fl' ("-J ic-)1f" u"i- q-0 * t:nl,'l-FI( ULMu-L::tt:y4x,n, 'i-r{-Zl:oPage 120 of 225It Bt,\!L?ffi!:iv1n.n Latua,flom CoYsisliry cl,li?te-'t(-*idJ, Gff{ue"tt,--r.-lMM --irccaeJd.y 4nL 4 r;d "yCi i-+-".-er*-fi d t+&i@Ihp v\rie*he-oL\Yee oF -t)lu^) o L>0r&l t- _ - Lo\ Q--7a uz 4^gal24bqdeY z3 , Aecf"reP-'z-5il'-4)* o.ddu.- 1t e\Lldee- .-Lpts. d*enmit 4"Page 121 of 225If you wantfull notes insame formatpleaseimmediatelymail us at:[email protected] Contact at whatsapp : 09784236981Use full groups for electrical engineering &electronics engineering for subject wisediscussion of gate ies & psUSuper Groups:1. Common Group to get written noteshttps://www.facebook.com/groups/gate.dream2doit/2. Group to discuss about gate ies material & guidance by GATEIES TOPPERs It will active mid of Septemberhttps://www.facebook.com/groups/DreamMission2016/3. GATE GUIDE GROUP :https://www.facebook.com/groups/GateGuidetrue/4. IES GUIDE GROUP :https://www.facebook.com/groups/IESTrueGuide/5. Engineering & PSU JOB Notificationhttps://www.facebook.com/groups/JobNotifyByKamal/6. Aptitude & Mathematicshttps://www.facebook.com/groups/kamal.gatehelp/SUBJECT WISE PROBLEM DISCUSSION GROUP BY TOPPERs STUDENT & TOP COACHING FACULTY ELECTRICAL& ELECTRONICS GROUPS1. https://www.facebook.com/groups/Dream2EEECIN/2. https://www.facebook.com/groups/Dream2ElecEngg/3. https://www.facebook.com/groups/GateEePowerElectro/4. https://www.facebook.com/groups/GateEePowerSystem/5. https://www.facebook.com/groups/GateEeMachine/6. https://www.facebook.com/groups/GateEeEcEMI/7. https://www.facebook.com/groups/GateEcMicrowaveEDC/8. https://www.facebook.com/groups/GateEeEcNetwork/9. https://www.facebook.com/groups/GateEeEcSignal/10. https://www.facebook.com/groups/GateEcEeCommunicationEMFT/11. https://www.facebook.com/groups/GateEcEeAnalog/12. https://www.facebook.com/groups/GateEcEePajjiControl/13. https://www.facebook.com/groups/GateEcEeDigitalMicro/MECHANICAL GROUPS1. https://www.facebook.com/groups/Dream2Mech/2. https://www.facebook.com/groups/mech.dream2doit/3. https://www.facebook.com/groups/CrackMeGateIn51Day/4. https://www.facebook.com/groups/MechFMandEnggMechanics/5. https://www.facebook.com/groups/MechMachineDesign/6. https://www.facebook.com/groups/MechICenginceRAC/7. https://www.facebook.com/groups/MechProduction/8. https://www.facebook.com/groups/MechPowerPlantEngg/9. https://www.facebook.com/groups/GateMeHeatMassTransfer/10. https://www.facebook.com/groups/MechIndustrialEngg/11. https://www.facebook.com/groups/MechThermodynamics/12. https://www.facebook.com/groups/MechSOM/13. https://www.facebook.com/groups/MechTheoryofMachine/CIVIL ENGINEERING GROUPS1. https://www.facebook.com/groups/Dream2Civil/2. https://www.facebook.com/groups/GateCivilRailwasyBuildingCPM/3. https://www.facebook.com/groups/GateCivilHydroHighwaySurvey/4. https://www.facebook.com/groups/GateCivilEnvironIrregation/5. https://www.facebook.com/groups/GateCivilGeotechFM/6. https://www.facebook.com/groups/GateCivilRccSteel/7. https://www.facebook.com/groups/GateCivilStructuralSOM/CS-IT GROUPS1. https://www.facebook.com/groups/Dream2CS/2. https://www.facebook.com/groups/GateCsSoftDigi/3. https://www.facebook.com/groups/GateCsDiscreteMaths/4. https://www.facebook.com/groups/GateCsComputerNetwork/5. https://www.facebook.com/groups/GateCSDBMS/6. https://www.facebook.com/groups/GateCSComputerOrgandOperatingSystem/7. https://www.facebook.com/groups/GateCSAutomataandCompiler/8. https://www.facebook.com/groups/GateCSAlgoDS/14. SUBNOTE: IF YOU WANT TO HELP AND ANY GUIDANCE REGARDING YOURPRERATION AND PROBLEM DISCUSSION PLEASE IMMEDIALTY JOIN OURGROUP Because we want to share our ethics and share ourknowledge with youReason:1. We dont want to invest of fake advertising and showing us2. We want direct communication with students & want to showthat we have best experience to guide you for choosing rightpath that is most important factor of your career..... so3. First test us & then join US4. Maths & aptitude preparation notes guidance will 100% free5. On other subject we will give you 20-30% only subject wise..ThanksWarm Regards:Kamal ChOUDHARY09784236981 (Whatsapp)[email protected] CS-IT EC EE MECH CIVIL IN1. Algorithm Analog Analog Fluid Mechanics Building Material Analog2. Data Structure Signal System Signal System M/C Design SOM Signal System3. TOC Communication Communication M/C Tool Fluid Mechanics Communication4. Compiler Control Control IC Engine Surveying Control System5. 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GK & GS GK & GS GK & GS GK & GS GK & GS GK & GS IF YOU WANT ANY KIND OF NOTES FROM ABOVE THESE ACCORDING TO BRANCHWISE YOU CAN MAIL US AT [email protected] These Notes are prepared by GATE-IES toppers from Top Engineering Institution which cover fully syllabus with topic wise GATE Question Solution Best Groupto Join : GATE Handwritten Notes for all Branch : https://www.facebook.com/groups/gate.dream2doit/IF you are 100% ready to get these notes then only call me at 09784236981 between 7:00PM-9:00PMI will manage its xerox copy at least price for you because I don't have money for scanning and don't have time for free service All Technical Subjectavailable in Xerox and all not tech part will available in PDF format