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Quiz by Dr. Dishant Pandya
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A function f(x) can always be expressed as an arithmetic mean of an even or odd function.
Partial differential equation might have only independent variable.
The method of Lagrange is applicable to only linear partial differential equations.
Charpit's method can also be applied to the Clairaut's equation.
While solving first order nonlinear PDEs, it may be possible to convert general equation to Type - 1.
There are two components of a general solution of any partial differential equation: a complementary function & a particular integral. Now, based upon the knowledge we have gained, can we say that, complementary function may be a particular integral?
IA-1 for those who have missed for whatsoever reasonIA - 1 - Mathematics - II for Sciences - B.Sc. - Sem - 2 - PhysicsEN8LC-ia-5.1: Listen for important points signaled by volume, projection, pitch, stress, intonation, juncture, and rate of speech. Eff..rs of ott.-PoFllat i What woLrld hoppen ro our colnrry i, it is ovetsp.pulored? When our counrry is ov€.-populdted, re @ €xp€ri.nce rh€ foll.wirg: Food is our bdsic h@d. Wh€n th€.Cs an ih.re.se ir populdtion it neans thar hore ,@d is iealed. It rheds ho .naJgh food, rrtrple irll srruggle wirh eddr oth€r in ordeLro €!'r- As o l!fllr, lhde rill be o f@d -- , ond ou, now]nert of on ihdiyiduol fron d c..tair - the move$eni o, on individudl our of o cerrain pla.e which help r€duce ihe populotion of th6t fr Arcih€. b.sic ned is w.ra. Wde. shorroge ocu.s when there is on ircreare of hu,nber of p@ple ro be $pptied. rn owr-popur.t d ore.s, woler is rdior€d, Ir rEB rhoi supplies like ti,tWSS ond ,IWSI can'i $pply enoish worer. Do you hdve enough supply of sai.. in your oreo? Aside f.om food alld worer, shelier is olso ohe o, our inportant heeds. As the populoiion ihcre.!e!, building n.w hoLr!€s or rhelt€r is limit.i. To find solulion to this prcbl€n, some goverihent og.ncies dnd orhs non{ov€Ihrehl offi.iofs (N6O) .onvefied sot@ ti.elields, du,np site. dnd nountcirlr inlo flbdivisions dnd relidentiols. Sut whot uould be ths effect o{ coMrtiig .i@fields to .6id€nri6l uits in our food supply? z , 2 Z Z :'", becouse there ore no enough space for prcpex garbage dkposol. ^s o r€sulr, sore peoPle lend to ihrow'their gorbdge onywh.f€. oorbdge baones brc{niry ond rursing ground of iEecrs and onidols ihot @se horm ro pe.ple. Dec.yiry garboge olso produces r,hpleaiant odor ard ehen burn if pmduces pois.nour qds @lled nelhohe As ihe populdtion incr€a3*, the 9d6.9e dso incraes. nris is T't ,,8 T H Wha you de living in on oa-populdi.d pla@, you moy oqaiae halrh prcblerns. Ir is be@@. the woi.r srpply is limit.d ihct will l..d you to poor hygi.ni. hobirs. In plo.4 like rhis, the surrouhdiigs naybe uniidy. o focrorthoi @uld oko cfFe.t your h4l'th. The common oilments rhot yd @uld oc$rire in ovesfDpllar€d ploces ore bEnchil is, o5l hnq. diqrrha and rube.culosis. 7,\ ,\\ \1" 6. Lnck of Herlrh sarvice llosi Pelple in 6n oM-populci€d 6ra 90 ro rubli. heilrh @trtas ond governhent hospirols be6u.e ii prcvides fr@ @Eulrorion oid los @sr rEdicdrions. A3 a ..suli, lh€s€ gow.nnenr dg€rciB b.@ne itud.4$re in mcetiig ihe n eds b..ou!€ df ihsrffici€nr funds. Lock of medicol personnel ,o odmaiisi€I is also s problen in mosr hosptols ev€n rhere or. od.audtc supply of hedicire!. 7_ Do you how wlry rhe crim€ roi€ hexs ih becdur€ fiDre pe.ple o.e fnJrrct€d d@ ro sLffici€.i naE io supp.rr their forniliG. ouf country inclY{ses? If is uh.mploym€ni dnd hdve no arinet .re u$dv gr€{rer ia dn dq-popltdled ra whq. tl, , a, v, tlr I E. Air ard Wat€r Pollutioh How dir be.o'nes pollut€d? I11€ dir b@'n€s p.llurn be.4ne of rhe hormfolgoees thot ser. produ.4 by the fdciori€s and vehicles. Itete {octories ond whi.l6 @ fuel ro run nochiB ond .JBin6. In ,h€ prc.ess, they give our Cdrboh Dioxide ond other ho.6ful gars.r such 6 Nittugei Oxide, Corbon l oioxide dnd Le.d iiio the oir. Do you know whot .ontdbute io ihe incr€asing number of whides qnd foctories? It is ihe inc.6e o, populdtion. As whdt I hove dis.!sse!, wirh a lihired sra.e 9@bd9e disposalie one of the problens thot .o!ld ise i, dh o!er-pop!,.t€d ploce. exn,jple ot thie orc rhos€ pelpl€ livi,rg oh the raverside teid 'ro ,hrou, lheir gEr&ge Hde you seen 'th. P6si9 river or the Tulyahan river? Did you {ind it Whdr do you think i! ihe eff€.t of ihis ih the.re4iures sho lives ih Ahothd f6do.s thal could.on rlbule to wdtd pollutioh dre oil s?ills, gorbqg€ fro,n boa, or ships ahd som€ ihdust.iol wosre. 9. Ite l@96f p4.enroge group. Individuols who orc this grclp. of olr popllarioh is compos.n of the working @pobla of s'rpporting ,heir fomilies nok !-up Though rhas group hol& the lojgeei percenroge of d. populaiion, rhis olso becomer one o{ oveFpopulored probl€]ns b€4use there ore rc jobs awildble fo. oll of iha10. Erergy Shortdge ltere will be on energy shortdge iJ ihe populdtion incre63"l be.dise rhe d.,nand i. €le.iriciry is high. Why is thai wh.n th. PoPqldion inclE.g, rhe d4ord in el4tricity is high? Ir B be.ouse there $,ould be 8to.e hdsat dnd blildirys to lighr ond nore el?riric oPPliohces ro run. rt.6rcznho!3.Ef+ed Whor is rhe grernho@ eff€.r? In whoi say il c.uld offect c2 6re.hhG. effed is rhe wdrniltg of rhe drltlosphee. lvhen the 5un worft rhe.nrrh s1jrf.@, sone of rhe h@r go€J bo.k ro rhe ornos?herc. Air an the dtnDsphere which is C@boi Dioxid. ,rops ihe heot 6hd it mok6 the a.th very worm. As ihe populdtion coniinuou!|,l gtol4 , the gt@rl$use etfe.t b@res no.e visible. Ir is becaosu ,hera ore mo.e focrories snd whicl.s iha, produce wdst€s ond fuma5 which cduses more C{.bo. Diodde ir the ormosphere. As a rcsutt, ,herc eiould be nore h4, ,rop in the ornosphere uhich osk6 th. @ih nuch wornerIf this will hoppen continuously, ,h€ fish ih th€ ocah *ill di€, ricerields/f@mlands will dry too due to lh€ wcm clitnole 12. Destruction of rhe Ozone Loyer A5 whot you hove l@med lrheh you de in v5-6, rhot the qzore ldver is 'the proiecrive loy€. of the olnosPhd€. ft protects us {rom the homful effects of ultrdviolei rays of the su. Do you khow ,hot our Ozore lol€t q4. dQ4tt\!ci.d? Il olreadY hod holes lhai dllow the ulrroviolet rdys to .4dt ihe @rrh. How do6 this hdpPei? Does th. in rc$e of poPuldioh h@€ sonething 'to do tr,lh ir? Yes, rhe I6i grov/irts PoPuldiion .odribuied o lot be@use 6 th' populotion incre3es, rhe u5e of refrigerd'tors, d€rosol lProvs 6nd pl4srics 6bo ihcre&s6. The sid producls coiiojn chemicol called Chlorofluorocdrbons (CFCS) which is mix wafh ihe dir in ihe ormosPher€. As o resulr. ihe hcrmfirl chernicol r€oches the Prolectiw ldver dnd lhrowh. hole in {hid ult@iolzi cahders aid cai4.ct3 ,F.*Y.iis hi!586$q€9.7,- Ho$ doas dcid rdin form? Is cid roii hdmful ro rEn? In the prcvious dis.ussions, yodt€ t.on€d rhd more vel .1e3 dnd fdctori€s or€ necded fo het the iii:.e.siry number o{ P@Pla. Lefs now fihd af hd f@tot.i€s dnd vehicle! .ontribure in the forrEtion of ocid When foctories 6nd whi.ler give off woste gd..3 ,hot will ,nix on lhe noisture i. rhe oir, it will ihen Produ.e sulPhu.i. ocld dnd Nitri. o.id. 'Ihe clol,Jd folb will ,h€h obsorb rhese ccids ond ehei ihe clold f.lls os .oin, ih. ccid is ahady Pdrr of itU/ha d.id ftin falls oh lok"!, ,46 or ocan ih€ fish sill die d.d if h fdlls oh fopnlonds,lhe pldni. together oith the soil B desrroyed. When you inhole dir with Niiric acid, your blood will los. irs @pobilily io fonspori Oxyg€h to your diff€.ai bodY Po.i3. ScieniisB include other rorns oJ dcidic pr€cipiigrion. Thes€ drc nisi, Do you krcw ihot Nuclerr power slotionr Use .adiodctive ,ndie.ials in producirE fuels, yet, rhey do and those .odioactiw rndlqlotE gi\e otf radio'ting en.rgy thoi is harmrul 'to livirq thilEs. wlren rodiotion enlert ihe body ot living things it {ill srq rhere for o lorg ,eriod of ri'ne. Exonple fhe rodiqtion vG srilled to the c.m. Then rhe @rn will be aie by rhe chicken, the .odiotion o the c.rn 'rill also 'tronsf€r to the chi.k€n. Wha on individuol als ihe nat of the chickeh sith mdiarion, helshe rill .ko oblorb ihe rodi@.tirc mtaid that will destrcy hB/her .€lls ond ruket hnn/hd si.r. Over-populoiion .on leld to food shoridg€, wdter shorroqe, housiB probl€ms, qdrbog€ probl€rs, lock of halrh sdi.e. tisa ol clit@ rote, oir ond woi€r pollution, uhanpl6ynat, eiergy 5horr69e, grenhoq3€ efreci, desrruction o( th. ozo@ lat/e?, rci.l roi. olld e.l€d. wattaIA-1IA - 1IA - 1 - B.Sc. Data Science - 01 - 09 - 2025IA - 1 - Python - 01 - 09 - 2025