Karmashala Parikalan

Author(s): Gurubachansingh Narang
Publisher: Hariyana Sahitya Academy Chandigarh
Catalog link: https://jainqq.org/explore/010393/1

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karmazAlA parikalana [WORKSHOP CALCULATION] -

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yAMtrika tathA vidyut TreDasa ke lie karmazAlA parikalana (bhArata sarakAra ke zrama mantrAlaya dvArA prakAzita pustaka WORKSHOP CALCULATION kA hindI rUpAntara) rUpAMtarakAra gurabacana siMha nAraMga vibhAgAdhyakSa yAMtrika vibhAga hariyANA bahutakanIkI nIlokher3I sAhitya akAdamI hariyANA sAla :: - viNyA'mRtamaznute hariyANA sAhitya akAdamI, caNDIgar3ha

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__ (c) hariyANA sAhitya akAdamI, caNDIgar3ha (hindI saMskaraNa) : 1987 (c) zrama mantrAlaya, bhArata sarakAra, dillI (aMgrejI saMskaraNa) : 1971 bhArata sarakAra ke mAnava saMsAdhana vikAsa mantrAlaya kI prAdezika bhASAoM meM vizvavidyAlaya starIya grantha nirmANa yojanA ke antargata hariyANA sAhitya akAdamI ke tatvAvadhAna meM prakAzita / prathama saMskaraNa: 1987 pratiyAM : 2200 : bAIsa rupaye (Rs. 22/-) mUlya ___ mudraka : maisarja paranAmI priMTiMga presa, mahezapura, paMcakUlA (ambAlA)

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prastAvanA vizvavidyAlaya stara para mAnavikI tathA vijJAna meM vibhinna viSayoM kA zikSaNa hindI mAdhyama se ho sake, isake lie hindI bhASA meM mAnaka granthoM kA upalabdha honA Avazyaka hai / aise granthoM ko upalabdha karavAne meM anya hindI grantha akAdamiyoM ke sAtha hariyANA sAhitya akAdamI bhI kAryarata hai / isa akAdamI dvArA vibhinna viSayoM ke aba taka aneka aise grantha prakAzita kie gae haiM jinameM se atyadhika ke dvitIya, tRtIya evaM caturtha saMskaraNa nikAle jA cuke haiM / prastuta pustaka karmazAlA parikalana isa zrRMkhalA kI 125vIM kar3I hai / karmazAlA parikalana kI mUla aMgrejI pustaka zrama mantrAlaya, bhArata sarakAra dvArA taiyAra kI gaI hai aura isakA hindI rUpAntara zrI gurabacana siMha nAraMga, vibhAgAdhyakSa yAntrika vibhAga hariyANA bahutakanIkI, nIlokher3I dvArA kiyA gayA hai / yaha pustaka takanIkI zikSA vibhAga ke parAmarza para AI0 TI0 AI0 ke vidyArthiyoM ke lie prakAzita kI jA rahI pAMca pustakoM meM se eka hai / pustaka meM abhyAsoM ko rekhAcitroM dvArA sahaja banAyA gayA hai / AzA hai ki AI0 TI0 AI0 ke adhyApakoM aura chAtroM ke lie prastuta pustaka upayogI siddha hogI / TROL 2141 nidezaka hariyANA sAhitya akAdamI, caNDIgar3ha

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paricaya isa pAThya pustaka meM kiyA jAne vAlA saMgraha 'karmazAlA parikalana' (Workshop Calculation) se sambandhita hai jo ki krAphTasa maina TrenIja ke nirdhArita pAThyakrama ke anusAra hai tathA dhAtu kArya aura vidyut zAlA ke TreDoM ke apareMTisa ke lie bhI hai| karmazAlA parikalana kA jJAna bahuta hI anivArya hai kyoMki isase krAphTasa maina kI samasyAoM ko karmazAlA sthala meM pratyeka TreDa ko sahAyatA milatI hai| lekina vidyArthiyoM ko yaha viSaya par3hAne meM bahuta hI kaThinAI hotI hai kyoMki mArkITa meM krAphTasamaina stara kI yogya pustakoM kA abhAva hai| pustakeM jo ki Ama taura para mArkITa meM upalabdha haiM, ve bahuta atyadhika zaikSaNika haiM jinakI vidyArthiyoM dvArA prazaMsA nahIM kI jaatii| kucha pustakoM meM kevala kAryazAlA kI hI samasyAoM ko diyA gayA hai tathA aMkagaNita, bIja gaNita aura rekhAgaNita ke AdhArabhUta (maukhika) siddhAMtoM ko nahIM diyA gayA hai| isa pustaka meM kie jAne vAle saMgraha kA dhyeya vidyArthiyoM ko aisI yogya pustaka upalabdha karAnA hai joki karmazAlA parikalana se sambandhita ho aura jisa meM gaNita tathA kAryazAlA kI samasyAoM kI vibhinna TreDasa kI mUla jAnakArI ho| isa bAta kI bhI saMbhAvanA hai ki isa se nidezakoM ko krAphTasamaina kA viSaya par3hAne meM mArga darzana ke lie sahAyaka ho| isa pustaka meM mITarika paddhati kA anusaraNa kiyA gayA hai aura vizeSa prayatna kiye gaye haiM tAki vidyArthiyoM ko esa. AI. yUniTa kI jAnakArI bhI dI jA ske| AkRtiyoM meM sabhI paimAIza milImITara meM darzAye gaye haiM / phAinala TaisTa peparasa meM kucha mahatvapUrNa praznoM ko liyA gayA hai aura isa pustaka meM diyA gayA hai| tAki vidyArthiyoM ko phAinala TreDa TaisTa ke sTaiMDarDa praznoM ke bAre meM jAnakArI ho ske| -gurabacana siMha nAraMga

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nidezaka mArgadarzaka isa pustaka meM viSaya sAmagrI ko tIna bhAgoM meM bAMTA gayA hai| pahalA bhAga aMkagaNita, bIjagaNita trikoNamiti tathA mainsurensa kI mUla jAnakArI se sambandhita hai tathA zApa (karmazAlA) kI samasyAoM ke prayoga ke bAre meM zAmila kiyA gayA hai| isa prakAra pahalA bhAga sAmAnya hai tathA sabhI TreDoM ke vidyArthiyoM ke lie hai| isa pAThya pustaka kA dUsarA bhAga vibhinna TreDoM ke lie alaga se dikhAyA gayA hai| tIsare bhAga meM gaNita kI prasiddha sAraNiyAM dI gaI haiM joki vidyArthiyoM tathA nidezaka ke lie sahAyaka haiM jisase kaThinAIyoM kA samAdhAna kiyA jA sake / isa bhAga meM nidezaka ke patha pradarzana ke lie nirdeza pustakeM adhyAya anusAra dI gaI haiN| prastuta adhyAya meM viSaya sacI kramAnusAra dikhAI gaI hai jo ki prazikSaNa zAstra ke niyama krameza, vidita se avidita, sarala se kaThina para AdhArita hai tAki vidyArthiyoM ko manacAhI jAnakArI ucita DhaMga se prApta ho| pratyeka adhyAya meM paryApta accha-acche udAharaNa die hue haiM tAki vidyArthiyoM ne sidvAMta jo ki unhoMne pahale par3he hue hai ke upayoga se jAnakArI kara ske| pratyeka adhyAya ke anta meM ucita abhyAsa udAharaNe vidyArthI ke pUrNa abhyAsa ke lie die gaye haiM / yaha bhI prAzA kI jAtI hai ki nidezaka isa yogya hogA ki vaha atirikta praznoM kA rUpAMkana kara skegaa| usI dizA meM vaha socegA ki isameM aura abhyAsa kI kyA AvazyakatA hai| deza meM aba mITrika praNAlI apanAI gaI hai| isalie pustaka meM vahI prayoga meM lAI gaI hai| parantu phira bhI yadi nidezaka cAhe to koI udAharaNa phUTa-pAuMDa-saikiMDa / antarASTrIya paddhati meM ucita sudhAra sahita pratyeka adhyAya ke anta meM die gae udAharaNoM se le sakatA hai| kakSA meM esa. AI (antarASTrIya praNAlI) praNAlI kA paricaya dete samaya nidezaka ko vizeSa dhyAna denA caahie| yaha antarASTrIya praNAlI hone ke nAte isa pustaka meM dI gaI hai yadyapi ise pAThyakrama meM zAmila nahIM kiyA gayA hai| sabho maulika ikAIyoM tathA guNanakhaNDa, rUpAntara kA bhI isa pustaka ke adhyAya 2 meM varNana kiyA gayA hai|

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anukrama bhAga : 1 sabhI TreDasa ke liye sAmAnya prazna (yAntrika tathA vidyut adhyAya 1 saMkhyAe~ aura prArambhika aMkagaNita kArya 1-12 jor3a sambandhI ghaTAnA, guNA aura sArI saMkhyAoM kI bhAga, bhinna aura dazamalava, bhinna ko dazamalava meM badalanA aura usake viparIna yAni (dazamalava kI bhinna meM badalanA) sarala karanA, Upara ke Aparezana kI karmazAlA prazna ke lie eplIkezana adhyAya 2 ikAI aura mApa 12 22 briTiza ikAI kI praNAlI, miTrika aura esa AI ikAIyAM, lambAI kI vibhinna ikAIyAM, kSetraphala Ayatana, dhAritA bhAra, samaya, koNa, tApamAna, bala, kArya, ghAta aura UrjA, unakA samAntara, prazna / adhyAya 3 ghAta aura mUla 23-26 guNanakhaNDa, ghAta, AdhAra, ghAtAMka, guNA aura ghAta kI bhAga, eka saMkhyA kA mUla, vargamUla aMkagaNita dvArA aura prazna / 27-29 adhyAya 4 pratizata pratizata, pratizata ko dazamalava aura bhinna meM badalanA tathA isake viparIta prazna ! adhyAya 5 anupAta aura samAnupAta 30-36 anupAta, pada nikAlanA aura anupAta, samAnupAta, pratyakSa samAnupAta aura apratyakSa samAnupAta, karmazAlA prazna ke lie anupAta aura samAnupAta kI eplIkezana-samAna tribhujeM, ajJAta UMcAI jJAta karanA, uttolaka, dravacAlita mazIna ityAdi mizrita pratyakSa aura apratyakSa samAnupAta ! adhyAya 6 bIjagaNita cihna aura prArambhika bIjagaNita Aparezana 37-43 cihna aura pratIka bIjagaNita meM prayoga hone vAle, guNAka, vyajaka, sajAtIya pada aura vijAtIya pada, bIjagaNita jor3a, ghaTAnA, guNA aura bhAga, ghAta aura ghAtAMka ke niyama, peja sarala karanA, prazna adhyAya 7 guNanakhaNDa aura samIkaraNa 44-55 bIjagaNita sUtra, guNanakhaNDa aura vibhinna prakAra kI bhinna, sarala samIkaraNa, yugagata. dvighAta samIkaraNa eplIkezana banAvaTa aura samIkaraNoM dvArA praznoM ke hala ; adhyAya 8 laghaguNAMka aura laghugaNAMka sAraNI ke lAbha 56-61 laghuguNAMka, laghuguNAMka aura ghAtAMka, laghuguNaka ko kaise lete haiM, laghuguNaka kA prayoga aura eNTIlAga sAraNI, aMkagaNiA Aparezana jina meM laghuguNaka lAga kara Akalana praznoM kA hala prazna adhyAya 9 jyAmitI 61-01 maulika jyAmitI paribhASAeM , koNa ora koNoM kI vizeSatAeM, tribhujoM aura tribhujoM kI vizeSatAeM, pAIthAgora prameya, samAna tribhujoM kI vizeSatAeM, Ayata, varga mamAntara caturbhuja rombasa ityAdi ! aura unakI vizeSatAeM, vR aura vRta kI vizeSatAeM, samabAhu bahubhuja, karmazAlA praznoM ke lie jyAmitI kA prayoga ! adhyAya 10 mainasurezana 70-9 plena AkRtiyAM - tribhuja, varga, Ayata, samAntara caturbhuja Taropijama, TarepijAiDa, samabAhu bahubhuja, vRta, khAlI vRra vRta kA maikTara vRta kA segameMTa, aNDAkAra aura phileTa, Thosa AkRtiyAM-prijma, belana, pirAmiDa, koNa, pirAmiDa va pharamaTarama, koNa kA pharasaTarama, golA, Torasa aura sapherikala segameMTa, padArtha bhAra aura kImata, prazna

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adhyAya 11 trikoNamiti 95-103 trikoNamiti anupAta, trikoNamitIya sAraNI kA prayoga, tribhuja kA kSetraphala, trikoNamitI se UMcAI aura dUrI jJAta karanA ! karmazAlA praznoM ke lie trikoNamiti kI eplIkezanasa ! adhyAya 12 rekhAcitra 8 ; bhAga 2 : bhinna-bhinna prakAra ke viSaya sambandhI prazna - 95 S 1 adhyAya 13 karmazAlA parikalana ke prazna jo ki aparenTisa ke grupa 1,3,6,9 se sambandhita hai ! saraphaiMsa spIDa, DriliMga ke lie mazIniMga samaya jJAta karanA; phIDa kara kI gaharAI gaI usakA Ayatana ; kharAda para kArya karate samaya mazIniMga TAIpa Tepara TarniMga; lie mazIniMga samaya; giyara ke lie hala karanA; giyara ke cihna, DivAIDiMga haiDa; yala inaDeksiMga; helIkala salArasa tathA kI ve kI miliMga karanA roDekzana phaikTara, * adhyAya 14 karmazAlA ke prazna jo ki aparenTisa ke grupa dUsare se sambandhita hai / adhyAya 15 karmazAlA ke prazna jo ki prAparenTisa ke grupa cAra se sambandhita hai ! dhArA; volTeja aura pratirodhitAH kramarUpa se aura samAntara rUpa se sambandha pratirodhitA; vidyuta zakti; giratA huA pratirodha; volTeja meM kamI AnA 130-131 132-138 H bhAga- 2 bhinna- 2 prakAra ke viSaya sambandhI prazna sAraNI - 1 : sAraNI - 2 : sAraNI - 3 : sAraNI - 4 sAraNI - 5 sAraNI -- 6 cunA huA (xii) w Tes : bhAga - 3 pariziSTa rUpAntara sAraNI iMcoM se mi. mITara rUpAntara sAraNI mi. mITara se iMca padArtha kA ghanatva grIka ralphAbeTa : : pratinirdeza aMkagaNita sAraNI laghuguNAMka aura epTIlAgarIyamika sAraNI 91-94 109-129 aura dhAtu jo kharAda para kATI kharAda para cUrI kATanA, miliMga ke sAdhAraNa tathA kampAUMDa DipharensivelDiMga, zITa maiTala yAkiMga 140 140 141 141 142-145 150-155

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bhAga-1 karmazAlA parikalana - - - - sabhI TreDsa ke lie sAmAnya prazna (yAntrika tathA vidyut)

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karmazAlA parikalana/3 adhyAya-1 saMkhyAe~ aura prArambhika aMkagaNita kArya saMkhyAeM: hama apane dainika jIvana meM cIjoM ko ginane ke lie saMkhyAoM kA prayoga karate haiN| kriyAtmaka samasyAoM ko hala karane ke lie saMkhyAe~ prayoga kI jAtI haiM : nimnalikhita pada samasyAoM ko sulajhAne ke lie prayoga kiye jAte haiN| (ka) pUrNa saMkhyA 1, 2, 3, 4 ityAdi (kha) bhinna : eka bhinna eka pUrNa mAtrA kA eka bhAga hai jo ki sAdhAraNa rUpa meM jaise ki jahAM ka tathA kha / pUrNa saMkhyAe~ haiN| ka aMza kha hara udAharaNa: kha bhinna = vA bhAga 1vAM bhAga Fig.? Fig. 1 citra-1 citra-2 cinna eka meM eka vRtAkAra bhAga 4 barAbara bhAgoM meM baMTA huA hai : eka bhAga vRtAkAra kA eka cauthAI hai| isI taraha citra-2 meM eka bhAga barAbara hai hai noTa: yadi hama bhinna yA bhAga ke sAtha kAma kareM to yaha eka kA hissA hai| (ga) dazamalava : eka dazamalava bhinna vaha bhinna hai jo ki 10;100; 1000; yA kucha dUsare 10 ke guNAtmaka, bhinna ke hara, prAyaH pradarzita nahIM, parantu eka bindu ke mAdhyama se aMza ke bAyIM ora saMketika kiyA jAtA hai| likhane meM dazamalava, eka zUnya prAyaH dazamalava bindu ke bAyIM ora rakhA jAtA hai| jaba koI pUrNa saMkhyA na ho| udAharaNa : ___0.9-9 9 kA dazavAM bhAga par3hA jaaegaa|

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karmazAlA parikalana/4 0.09-100 9 kA sauvAM bhAga par3hA jaaegaa| 0.009 =1000 9 kA hajAravAM bhAga par3A jaaegaa| dazamalava sthAnoM kA mAna -ikAI -~-dahAI ---saMkar3A ----hajAra ----dasa hajAra -- -lAkha --0 0 0 0 0 0 100000 maulika aMkagaNita kiyA jamA do yA do se adhika saMkhyAoM ko joDanA / ghaTA eka saMkhyA se dUsarI saMkhyA kA nikaalnaa| bhinna : dI huI sabhI bhinnoM ko isa taraha badalo tAki unakA hara eka jaisA ho ; aba jamA aura ghaTA kro| 2-3-1 2+3 + 34-7-18 - kzamalava : pUrNa saMkhyAoM ke rUpa meM eka ko dUsarI ke nIce isa taraha chipAo tAki dazamalava bindU, dazamalava bindu ke nIce aae| 14.370 2.030 14.370 2.030 - - 16.400 12.340

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karmazAlA parikalana/5 guNAx vaha sAdhana jisake dvArA eka saMkhyA ko dI huI saMkhyA kA gunnaa| bhAga vaha sAdhana jisa ke dvArA yaha patA cale ki kitanI bAra eka saMkhyA dI huI saMkhyA meM rakhI hai| hara ko hara se tathA aMza ko aMza se guNA kro| dUsarI bhinna ke ulTe ko pahalI bhinna se guNA kro| 2x1-2 - -2 pUrNa saMkhyAoM ke rUpa meM dazamalava bindu ko guNanaphala meM utane sthAnoM taka rakho jitane Apa gina sakate haiN| (bAyIM ora se) zUnya ko jamA karo yadi jarUrata pdd'e| 1.4 x 0.02 14x2-28 2.028 pUrNa saMkhyA prApta karane ke lie AvazyakatAnusAra dazamalava bindu ko donoM saMkhyAoM meM dAyIM ora se dUra rkho| dazamalava bindu ko dAyIM ora se 2 dazamalava sthAnoM taka rkho| 1.5-0.25-150:25-6 2 1 2 dazamalava sthAna bAyIM ora se dazamalava bindu do sthAnoM taka / sAdhAraNa bhinna ko vazamalava bhinna meM badalanA sAdhAraNa bhinna ke aMza ko hara se bhAga do / nya zUko dazamalava bindu ke bAda jamA karo; AvazyakatAnusAra / udAharaNa: (1) sAdhAraNa bhinna hai ko dazamalava bhinna meM badalo / 0.4 5) 20 ( 20 4 (2) bhinna 11 ko dazamalava bhinna meM bdlo| 12) 0.91666 110 10.8 20 12

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karmazAlA parikalana/6 dazamalava bhinna ko sAdhAraNa bhinna meM badalanA dazamalava, bhinna ke hara 10, 100, 1000 Adi kI taraha mAnA jAtA hai / . 6875 275 udAharaNa : (1) isI taraha 0.6875-16 + 10 + 1000 + 10000 25 se kATa kara -10000-400 aura dobArA 25 se kATa kara ' - 27-11 (2) isI prakAra 2.375 25 se kATa kara -2 + 373 dobArA 5 se kATa kara -2 +3 -2 +3 + 1000 dobArA 5 se kATa kara 000 udAharaNa : (ka) dazamalava likho jaise : 00 (kha) bhinna likho jaise : 0.25; 0.125 (grupa 5, 2 varSa, prArambhika) (ka) / isa prakAra 10) 70 ( 0.7 uttara : 70 0.09 5- isa prakAra 100) 900 ( 900 x (ba) isalie 0.25 5 se kATane para) isalie 0.125-12 + 10 + Tbo 1255 , 1000-40 (25 se kATane para (5 se kATane para)

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karmazAlA parikalana/7 2. eka karmazAlA meM cAra phiTara tathA do sAthiyoM (meTasa) kA sAptAhika vetana 48 ru0 thaa| yadi phiTara, sAthI (meTa) se 11 ganA kamAtA ho to pratyeka kA sAptAhika vetana nikAlo ? (grupa 2, krAphTasamaina TreDa TesTa, julAI, 1972) phiTara, sAthI (meTa) se 11 gunA kamAtA hai .:. 4 phiTara kamAte haiM = 4x11=4x =6 gunA 2 sAthI kamAte haiM =2 -2 gunA kula -8 gunA (phiTara+sAthI) kamAte haiM =48 ru0 isalie eka sAthI kamAtA hai 36 ru0 :. eka phiTara kamAtA hai -6X11 =9 ru0 uttara 3. sarala kIjie : 77x16-0.04x150 .16x.25+116x.25 _0x16-box 150 iioxii+kxi _0x18-tox150 -rixristix 1600 4. sarala kIjie : --1+24-1+ [2-=}

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diyA hai : -1+ = 127 - 81 3x5 2 T1 = 5 T2-4 fg=3 5. aneka pratirodha, jo ki samAnAntara meM jur3e hue haiM, kA kula pratirodha nimnalikhita phArmUle se diyA jAtA hai : 1 1 1 kath Ta yadi - 5, Tg 4 tathA rg - 3 hoM to R jJAta kiijie| diyA huA phArmUlA : 1 .. R-5+7+7 [1 1 R uttara R -1+ Ts For Tg kI kImata diye hue phArmUle meM rakhane para 12+15+20 R = 3+4+3= 60 + 47 60 = DaiThe abhyAsa : nimnalikhita kA mAna nikAliye: 1. (i) 4+11+5 uttara : 12 20 60 -- 1 47 karmazAlA parikalana / 8 - 1 x 9 - 13 ghaMTe 15 2 13 47 6. tIna pAipa eka TaiMka ko kramaza: 6, 5 tathA 4 ghaMTe meM khAlI kara sakate haiN| TaiMka khAlI hone meM kitanA samaya lagegA yadi tInoM pAIpa ikaTThe calA die jAeM / uttara : 13 ghaMTe / kyoMki pahalA pAIpa Teka ko 6 ghaMTe me khAlI kara sakatA hai, isalie yaha TaiMka kA bhAga 1 ghaMTe meM khAlI kara sakatA hai| isI prakAra dUsarA pAIpa Teka 1/2 bhAga 1 ghaMTe meM khAlI kara sakatA hai tathA tIsarA pAipa 1/2 bhAga 1 ghaMTe meM khAlI kara sakatA hai| isalie tIna pAipa 2 + 3 + 4 = 30 bhAga 1 ghaMTe meM khAlI kara sakate haiN| TaiMka ko pUrI taraha se khAlI karane ke lie, jabaki tInoM pAIpa ikaTThe calAe jAeM, samaya lagegA, 1 - uttara (ii) 1478+613+}+258 +}} uttara 4743 :

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karmazAlA parikalana/9 (iii) jamA kIjie : 36.036, 7.004, 0.00236, 427, 723.0026 uttara : 1193.04496 (iv) jamA kIjie : 8.4, 0.0105, 1.0055 uttara : 9.416 (i) -3d 16 (ii) 18100-15 uttara : uttara : 3100 (iii) 9876.5-0.0011 uttara : 9876.4989 (iv) 6.5-1.4142 uttara : 5.0858 3. (i) x 108 uttara : 20 (ii) 11x3x51 x 3degx72 uttara : 4143 (iii) 8.4x0.0105x1.0055 (iv) 90.58X2.2046 uttara: 0.0887 uttara : 199.6927 uttara : 70118 4. (i) 9101:13 ixix 18x3+32x3 (iii) 0.4375:0.125 (iv) 33 (6.25): 8.25 uttr| / uttara : 3.5 uttara : 25 5. nimnalikhita ko hala kIjie : uttara : 1I (grupa 2, julAI, 1970) 1x18+ 1.125 uttara : 13 8.2x2.5x10.8X0.96 41X200x1.2 dazamalava ke cAra aMkoM taka uttara: 0.0216 (1:31)x0.00025 0.075 uttara: 0.0005128 ko jamA karo, pariNAma ko ( 8 8) se bhAga karo tathA pariNAma ko dazamalava meM bdlo| uttara : 9.10625 aura zAphaTa tathA iseMTarika meM kama se kama dUrI 7. iseMTarika zAphaTa kA aiMDa viyU citra meM dikhAyA gayA hai|

Page #18
karmazAlA parikalana/10 0.168 sai. mI hai jaisA ki dikhAyA gayA hai| isainTrIsiTI jJAta kro| uttara : 17 se. mI. 12480 8. eka tAlAba meM do inasaiTa pAIpa lage hue haiN| eka meM tAlAba ko bharane kI kSamatA 3 ghaNTe meM hai aura dUsarA 4 ghaNTe meM bharatA hai| khAlI karane vAle pAIpa usako 5 ghaNTe meM khAlI kara dete haiN| yadi sabhI eka hI bArI khola die jAeM to kitanA samaya lagegA usa ko bharane meM / uttara : 23 ghaNTe (grupa 2, TreDa TaisTa krAphaTsamaina ke lie, julAI, 1972) 9. citra ke Upara dUrI aba sa aura za jJAta karo nIce dikhAyA gayA hai sArI sAmAnya bhinnoM ko dazamalava bhinnoM meM badalate hue| . 10. a, ba, sa ko sAmAnya bhinna meM jJAta karo : -2-125-+-1975-+500-+0900-40875+0-750 11. yadi a, ba tathA sa kramaza: 35 mi0 mI0, 5 sai0 mI0 tathA 45.5 mi0 mI0 hoM to dakitane milI mITara hogA? uttara : 130.5 mi. mI. -

Page #19
karmazAlA parikalana/11 12. eka mizraNa, jo ki gharSaNa viruddha dhAtu hai, meM 1370 tAMbA, 111 Tina tathA 43 enTImanI hai| 1250 kilogrAma mizraNa meM pratyeka dhAtu kA bhAra jJAta kiijie| uttara : 461 ki0 grA0, 1110 ki0 grA0,933 ki. grA0 13. tIna pAIpa jinake nambara 1, 2 tathA 3 haiM, eka TaiMka se nikalate haiN| pAIpa naM0 / TaiMka ko 8 meM ghaMTe khAlI kara sakatA hai; pAIpa 2 ise 6 ghaNTe meM khAlI kara sakatA hai; tathA pAIpa 3 ise 2 ghaNTe meM khAlI kara sakatA hai| Teka ko khAlI hone meM kitane ghaMTe lagegeM yadi sabhI tIna pAIpa ikaTe khola die jaaeN| uttara : 11 ghaNTe 14. eka ThekedAra ne eka ghara 40 dina meM banAnA hai| yadi 16 AdamI 30 dina ke lie kAma karate haiM aura AdhA kAma karate haiM, agale 10 dinoM meM kitane AdamI kAma kareM tAki ghara samaya para bana jAe? uttara : 48 15. eka kharAda kA TUla eka cakkara meM 0.16 sai0 mI0 Age baDhatA hai| TUla ko 2.4 saM0 mI0 Age bar3hAne ke lie kitane cakkara cAhieM ? Tala ko apanI prArambhika avasthA se 1.44 sai0 mI0 taka le jAne ke lie ulaTI dizA meM kitane cakkara cAhieM ? uttara : 15 cakkara tathA 6 cakkara 16. eka moTara zakti kA bhAga detI hai jitanA ki ye letI hai| yadi ye 6 azva zakti letI hai to kitanI zakti degI? uttara : 51 azva zakti 17. kula volTeja jJAta karo jaba tIna 11 volTa ke zuSka saila sIrIja meM jor3e gae hoM ? uttara : 41 volTa 18. tIna 11 volTa ke DrAI saila jo ki sIrIja meM jor3e gaye haiM unakI kula volTeja saplAI jJAta karo? uttara : 41 volTa 19. yadi bhAga UrjA kA eka moTara meM lagAyA gayA hai aura vaha gharSaNa, kApara tathA Ayarana lausisa meM calA jAtA hai| yadi moTara kilovATa prApta kareM to kitane kilovaTAsa kA nukasAna huA hai ? uttara : 5 kilovATa 10. DisTrIbiyUsana sisTama meM kula volTeja DrApa jJAta karo yadi pratyeka saMkzana meM volTeja DrApa 1.06, 36.4 tathA 8 volTa hai| uttara : 45.46 volTaz2a ___ RIXR 21. Rr = B.R. phArmUlA prayoga karake, samAnAntara dhArAmaNDala, kA kula pratirodha (RT ) jJAta kIjie, yadi R-30 om tathA R,-60 om ho| uttara : 20 oma -

Page #20
ikAI : ikAI aura mApa ikAI saMhati, lambAI, TAIma ityAdi kI eka nizcita mAtrA hai / yaha sarakAra, borDa oNpha TreDa, antarrASTrIya kameTI Adi janatA dvArA AsAnI ke lie rakhI hai / O mITrika paddhati, yahA~ mITara mITrika paddhati bahuta se dezoM meM sI. jI. esa. aura saikiNDa hai / ikAI paddhatiyAM : 0 briTiza paddhati ko phuTa-pAMUDa - saikiNDa (epha. pI. esa. ) paddhati bhI kahate haiN| yahAM phuTa, pAMUDa tathA saikiNDa; lambAI, saMhati aura samaya kI maulika ikAIyAM haiM / karmazAlA parikalana / 12 mAtA 1. lambAI 2. bhAra adhyAya-2 O esa. AI. ikAIyAM : 'arntarASTrIya paddhati' ikAIyAM (choTe rUpa meM esa. AI. ikAIyAM) mITrika paddhati meM sudhAra hai / aura yaha dUsarI paddhati ikAIyoM kI jagaha prayoga aura lAgU ho sakatI hai joki gaNita, sAiMsa (vijJAna), abhiyatikI aura TaikanolojI aura sabhI prakAra kI zikSA, phaikTarI aura komarsa Adi zAkhAoM para lAgU hai / 6. 7. kilogrAma aura saikiMDa; lambAI saMhati aura samaya kI kramAnusAra maulika ikAIyAM haiM / paddhati ke nAma se phaila cukI hai| isa paddhati meM maulika ikAIyAM seMTI mITara- grAma 3. samaya 4. vidyut dhArA 5. USNa yantra kriyA tApa prakAziya tIvratA padArtha kI mAtrA sAraNI - I 7 mukhya ikAIyAM esa. AI. meM ikAI mITara kilogrAma saikiNDa | empIyara kailavina kainDelA maula 1 saMketa mI0 ki0grA0 #o e kai sIDI maoNla abhI taka esa. AI. praNAlI pUrI taraha pracalita nahIM huI / lekina kaimisTrI ke phIlDa meM zIghra hI pracalita ho jAyegI /

Page #21
eTo phemaTo pIko nAno mAikro milI seMTI haMsI IkA haikaTo kilo maMgA gIgA TerA upasarga mAtrA sama kSetra koNa 1. 2. Thosa koNa VECE LECCE ES sAriNI 2 esa. AI. sapalImenTarI ikAIyAM aura saMketa ikAI DIe eca PA (miyU) ema sI karmazAlA parikalana / 13 saMketa reDiyana sTreDiyana sAriNI-3 esa AI mAnaka ke upasarga pUrNa bhAjaka aura bhAjaka saMketa Ara eDI esadhAra mAna 0.000 000 000 000 000 001 0.000 000 000 000 001 0.000 000 000 001 0.000 000 001 0.000 001 0.001 0.01 0.1 10 100 1000 1000 000 1000 000 000 1000 000 000 000 10-18 10-15 10-12 10-9 10-6 10-3 10-2 10-1 10 102 103 106 100 1012

Page #22
karmazAlA parikalana/14 sAriNI-4 mApa kI ikAIyAM lambAI kI mApa briTiza ikAIyAM mITrika ikAI rUpAntara khaNDa phuTa 1 phuTa=12" yArDa (gaja) 1 gaja = 3 phuTa milImITara 1 mi. mI saiTImITara 1 sai0 mI0-10 mi0 mI0 DesImITara 1 Dai0 sI0-10 sai0 mI0 mITara 1 mI0=10 De0 mI0 ___100 sai0 mI0-1000 mi0 mI0 kilomITara 1 ki0 mI0 1000 mI. mAIkrAna 1-0.001 mi0 mI0 1 iMca-25.4 mi0 mI0 1 phuTa = 30.48 sai0 mI0 1 gaja= 0.914 mI0 1 mIla=1.61 ki0mI0 1 sai0 mI0-0.3937 1 mI0-1.09 gaja | ki0 mI0-0.62 mIla pharalAMga 1 -220 gaja mIla 1 = 8 pharalAga -1760 gaja mApa kI ikAI sAraNI-4 kSetraphala ke mApa: kSetraphala ke do parimApa hote haiM isalie sIdhe mApa ke lie prayukta mAnaka --- briTiza ikAI mITrika ikAI varga inca varga phuTa varga gaja 1 ekar3a 640 ekar3a 1 iMca 1 phuTa-144 iMca 1 gaja =9 phuTa -4840 varga gaja =1 varga mIla varga milImITara 1 ema.ema. varga sai0mI0 1 sai0mI0-100 ema.ema varga DesImITara 1 De0mI0-106 saM0mI0 varga mITara 1 mI0-100Da0mI0 __ 1 e =100mI 1 haikTara = 100 e 100 haikTara-1 ki0mI0 esa. AI. ikAIyAM kSetraphala kI: varga mITara rUpAntara khaNDa 1 iMca 6.45 sai0mI02 1 phuTa2-0.093 mI. 1 gaja =0.836 mI0 1 ekar3a=0.404 haikTara 1 varga mIla=2.59 ki0mI01 1 sai0mI02-0.155 Ica 1 mI0 =1.196 gaja 1 haikTara-2.47 ekar3a 1 ki0mI0=0.386 varga mIla

Page #23
briTiza ikAIyAM kyUbika iMca (kyu Ica) 1 Ica kyuvika phuTa (kyu phuTa) 1 phuTa kyubika gaja (kyu gaja ) / gaja- 27 phuTa 17288 briTiza ikAIyAM Ayatana kA mApa 4 gilla - 1 piTa 2 piTa= 1 kvArTa 4 kvArTa -1 gailana (yU. ke.) 1 maMlana (yU.esa.) = 0.832 gailana (yU.ke.) - 1 kyu iMca = 16.387 saM0mI0 3 1 kyu phuTa - 28.317 De0mI0 esa AI Ayatana kI ikAI kyubika mI0 ( mI0 dhana parimANa kA mApa : esaAI ikAIyo milIliTara saM0mI0 DesIliTara 1 liTara laikToliTara 1 liTara karmazAlA parikalana / 15 bhAra kA mApa rUpAntara khaNDa kyubika milImITara 1 ema ema kyUbika se0 mI0 1 seM. mI. - 1000 ema ema kyubika De0mI0 1 De0mI0- 1000 se0 mI0 kyUbika mI0 / mI0- 1000 I0mI0 1 saM0mI0 0.061 kyU iMca 61.0234 kyu iMca 1 I0mI0 - mApa kI ikAIyoM sAriNI - 4 mITrika ikAIyAM ghana parimANa Ayatana aura jagaha ko darzAtA hai aura yaha tarala ko mApane ke lie prayoga kiyA jAtA hai| mITrika ikAIyAM 1 mi0lI0 1 sI. ela. 1 I0li0 - Dai0li0 = 1000 mi0li0 1 ofre 100 fire - 1 kapa IsI moTara ke lie liTara (ela) 10 ema ela 100 sI esa rUpAntara bhAjya khaNDa 1 piTa = 0.568 liTara 1 gailana (yU. ke. ) - 455 liTara 1 liTara - 1.76 piTa 0.219 galana (yU.ke.) bhAra vaha bala hai jisa ke dvArA pRthvI kisI vastu ko apanI ora AkarSita karatI hai|

Page #24
auMsa pAUMDa cauthAI Tana 14 pAUMDa 1 oja 1 pauMDa 1 Tana (2 saikinDa minTa ghaNTA dina saptAha sAla esa AI saMhati kI ikAI ki0grA0 esa AI bala isalie bhAra kI ikAI - nyUTana briTiza ikAIyo 1 oja (o0ja0 ) 1 pAUMDa - 16 oja 1 cauthAI - 28 pAUMDa 1 Tana 80 cobAI saikiMDa 12 fave 1'-60" [DigrI] 1deg = 60* = 2240 pAUMDa = 1 sTona 360deg = 1 bUta - 28.35 grAma = 0.453 ki0grA0 - 1.01 TanI briTiza ikAIyAM 1 saMki0 1 mi0 60 saiki0 1 eca Ara 1 dina - 24 ghanTe 1 saptAha = 7 dina 1 sAla 90deg - 1 samakoNa samaya kA mApa 60 minTa 52 saptAha koNa kA mAha karmazAlA parikalana / 16 peDa greDa rUpAntara khaNDa mi0 grAma grAma ki0grA0 kvinTala mITrika Tana mITrika ikAIyAM senaTensImala 1<< sekinDa sainaTensImala 1<- 100<< minTa mApa kI ikAI sAraNI - 4 1 grA0 1 ki0grA0 1 mITrika Tana 18 100 < =90deg-1008 1 mahInA - 30 dina mITara ikAIyAM 1 milI grAma 1 grAma - 1000 mi grA0 samaya kA yaha mAnaka dvivya vastuoM ko ghUmane para nirbhara karatA hai| samaya kA yaha mAtraka sabhI paddhatiyoM ke lie samAna hai| 1 ki0grA0 1000 grA0 1 kvinTala 100 ki0grA0 = = 1 Tana = 1000 ki0grA0 1 sAla = 12 mahIne - 0.035 oja - 2.2 pauMDa - 0.984 Tana yA 4 saptAha yA 365 dina 1 saincurI = 100 sAla esa AI ikAIyAM esa AI koNa kI ikAI reDiyana hai A reDiyana - 180deg 1 reDiyana - 57.3deg -57deg 17'44" rUpAntara 1deg - 180 reDa -0.017

Page #25
karmazAlA parikalana/17 tApamAna kA mApa phArenahAiTa mApa : pAnI kA jamAva bindu 32deg epha pAnI kA ubalane kA bindu 212deg epha vibhAjita nambara -212-32-180 saiTIgreDa mApa: pAnI kA jamAva bindU 0deg sI pAnI kA ubalane kA darjA -100deg sI vibhAjita nambara-100 esa AI tApamAna kI ikAI : kelavina (ke) 9/5deg sI+ 32degephaepha 0deg sI-273.15 (ke) 5/9 (degF-32)=degsI TIdegC-TI---273.15 (ke) (kelavina tApamAna meM) mApa kI ikAI sAriNI-4 - ---- bala kA mApa bala saMhati aura tvaraNa kA guNAtmaka hai| bala-sahati - tvaraNa briTiza ikAIyAM mITrika ikAIyAM epha pI esa sI jI esa ema ke esa *gurutvAkarSaNa zuddha gurutvAkarSaNa zuddha gurutvAkarSaNa | zuddha pAUMDa bala (ela bI epha) pAuDala (pI DI ela) grAma bala (jI epha) DAina-1 grA0 sai0mI/02 ki0 grA0 bala | nyUTana eca(ke.jI.epha.) | ki. grA. mI sai.2 esa AI bala kI ikAI : nyUTana (ena) (zuddha ema ke esa mAtraka kI taraha) ___ rUpAntara bhAjya (khaNDa) 1 ela bI epha-jI+(g) pAUDala =32.2 pAUDala 1 ena=105 DAIna = 0.2448 ela bI epha 1 jI epha-jI (g) DAina =981 DAina 1 ki0 grA0 epha =jI ena -9.81 eca *gurutvAkarSaNa ikAI kriyAtmaka mAtraka hai aura Amataura para TaikanolojI meM prayoga hotA hai tathA ikAI eka akriyAtmaka ikAI hai aura sAIsa meM prayoga hotI hai| +jI (8) kA mAna mAnaka kI paddhati ke anusAra badalatA hai|

Page #26
karmazAlA parikalana/18 - 7 kAma (yAMtrika) kA mApa kAma (DablyU) = bala (epha)x dUrI (esa) briTiza mAtraka mITrika mAtraka epha pI esa sI jI esa ena ke esa gurutvAkarSaNa gurutvAkarSaNa gurutvAkarSaNa zuddha phuTa pAUMDa bala | phuTa pAUDala grAma bala se. mI. | arga = DAIna | kilogrAma bala mITara | jyUla (je) - nyUTana : (phuTa ela bI epha) | (phuTa pI DI ela) / (grA0 sai0 mii0)| sai0 mI0 / (ki0graa0eph0mii0)| mITara | (je esa ema) ___ esa AI kAma ke mAtra ka jyUla (J) (zuddha ema ke esa mAtraka kI taraha) mApa ke mAnaka sAriNI-4 rUpAntara bhAjya (khaNDa) ... 1 phuTa pAUMDa-32.2 phuTa pAUDala 1 jyUla-107 aga 1jI epha0 mI0-981 arg| =0.7375 phuTa pAUMDa bala 1 ki0 grA0 bala mI0 = 9.81 jyUla kAma / vidyutI)=volTa (vI)x dhArA (AI) x samaya (TI) = bI AI TI aura kriyAtmaka mAnaka jyUla hai| isalie DablyU (W) =vI AI TI jyuul| UrjA aura kAma kI mAnaka samAna haiM / vidyuta urjA ke do vizeSa mAtraka (i) vATa hAvara (Wh) aura (ii) kilovATa hAvara (KWH) 1 vATa hAvara =3600 jyUla aura kilovATa hAvara = 36 x 10 jyUla -ine... - - - - yAMtrika zakti kA mApa zakti kisI mAtraka samaya meM kiyA gayA kAma hai| briTiza mAtraka mITrika mAtraka epha. pI. esa. | sI. jI. esa. ema. ke esa , gurutvAkarSaNa / zuddha ! gurutvAkarSaNa | zuddha / gurutvAkarSaNa / zuddha / phuTa pAUMDa bala prati | phuTa pAUDala | grAma bala sai0 mI0 prati | arga prati | kilogrAma bala mI0 prati | vATa jyUla saiMkiDa tathA briTiza | prati saiMkiDa | saMkiDa grA0 bala / saiMkiDa = | saMkiDa ki0 grA0 bala prati saikaDa hArsa pAvara (zakti) | phuTa pAUDala|| sai0 mI0sai0 DAIna se. mI. mI0|sai0 tathA mITrika | (DablyU = (eca. pI.) | maiM | prati saikiDa | hArsa zakti / je/esa.) 1 esa AI zakti ke mAtraka : vATa (DablyU) [zuddha ema ke esa mAtraka kI taraha

Page #27
karmazAlA parikalana/19 1 eca pI (briTiza) -550 phuTa pAUMDa bala/se | 1 eca pI (mITrika) =75 ki0grA0 bala mo0/se. =746 vATa =735.5 vATa -746 jyUla/saM0 -735.5 jyUla/sai0 1 ecapI (briTiza) =1.014 eca pI (mITrika) - 1 vATa =107 arga sai0 | 1 ke DablyU (kilo vATa) =1 36 eca pI (mITrika) =0.737 phuTa pAUMDa bala maiM vidyut zakti kA kriyAtmaka mAtraka : vATa aura yaha vibhava tathA dhArA kA guNAtmaka hai| 1 vATa=1 vibhavax1 dhArA tApa yA garmI kailorI : eka grAma pAnI ke tApa ko eka DigrI seMTIgreDa bar3hAne ke lie Avazyaka garmI yA tApa kI mAtrA ko kailorI kahate hai| USNatA sambandhI briTiza mAtraka : yaha eka pAuMDa pAnI ke tApa ko eka DigrI phArenahAITa taka bar3hAne ke lie Avazyaka garmI yA tApa kI mAtrA hai| tApa saMbaMdhI saiMTIgreDa mAnaka: yaha eka pAUMDa pAnI ke tApa ko 1deg epha taka bar3hAne ke lie Avazyaka tApa kI mAtrA hai| esa. AI. meM tApa kA mAtraka jyUla hai / rupAMtara mAjya (khaMDa) 1 kailorI =4.18 je23.08 phuTa pAUMDa bala 1 USNatA sambandhI briTiza mAnaka = 252 kailorI = 1055 jyUla = 778 phuTa pAUMDa bala 1 tApa saiTIgreDa mAtraka = 1.8 USNatA briTiza mAnaka =1899 jyUla =1400 phuTa pAUMDa bala udAharaNa: nimnalikhita mAtrAoM meM saMbaMdha sthApita kro| (i) pAUMDa vATa aura nyUTana (ii) phuTa pAUMDa aura jyUla (iii) bI. TI. yU. aura ke DablyU ec| | hala : (i) 1 pAUMDa bhAra = 453.6 grAma bhAra =0.4536 ki0 grA0 bhAra aba 1 ki0 prA0 bhAra =9.81 nyUTana (sAriNI-4 peja 19 para) .:. 1 pAUMDa bhAra = 0.4536x9.81 =4.45 nyUTana (ena) uttara (ii) eka phuTa pAUMDa (bhAra) = 0.3045 mI0x4.45 (ena) =1.357 ena ema (nyUTana mITara) =1.36 jyUla (iii) 1 bI TI yU =1055 jyUla ___ aba 1 kilo vATa hAvara = 36 x 106 je (sArigI 4, peja 20 para) :. 1 bI. TI. yU. 105563 ke DablyU eca = 29.3x106 ke DablyU eca (kilovATa hAvara) uttara uttara 1. rikta sthAna bharo: (ka) 80 DigrI seMTIgreDa =......DigrI phArenahAiTa (kha) 6'-10" =......seM0 mI0

Page #28
karmazAlA parikalana/20 - (ga). 4000 ki0 mI0 =......mIla __(grupa-4, 2 varSa, julAI, 1972) hala : (ka) 80degC =2x80+ 32 =144+32 =176 :.80degC =176"F (kha) 6-10" 1' = 30.48 sai0 mI. 1" = 2.54 sai0 mI0 = (6x30.48+ 10x2.54) saM0 mI0 (182.88+25.4) seM. mI. =208.28 se. mI. (ga) 4000 ki0 mI0 1 ki. mI0 = 0.62 mIla 4000 ki0 mI0-4000x0.62 mIla 2480.00 mIla 2. reDiyo taraMgeM lagabhaga 18,6000 mIla yA 300,000,000 mITara prati sa kiDa calatI hai| kyA yaha saca hai ? 1000 mITara -1 ki0 mI0 1 ki0 mI0 =0.62 mIla 300,000,0ki0 mI0 300,000,000 mITara = 100 ki0 mI0 -300,000x0.62 mIla =186000 mIla 3. 14.7 pauMDa prati varga iMca dabAva kitane grAma prati varga seMTImITara hai? hala : 14.7 pauMDa/iMca = 4 pauMDAsai0 mI2 (1 iMca = 6.45 seM. mI. ( / pauDa-453 grAma 14.7x453 yAma sai0 mI0 6.45 = 1033 5 grAma abhyAsa : 1. nimnalikhita ko badaliye : (ka) 31 ki0 mI ko mIla, yArDa tathA phuTa meM (kha) 2.546 iMca ko milImITara meM (ga) 5.08 seM. mI ko iMca meM (gha) 19.05 mi0 mI0 ko iMca meM (Ga) 10 liTara ko gailana meM (ca) 88 ki0 prA0 ko pauMDa meM uttara : 19 mIla, 496 yArDa, 1 phuTa uttara : 64.69 mi 0 mI0 uttara : 2 ica uttara : ica uttara : -2.641 gailana uttara : 193.952 pauMDa . .

Page #29
karmazAlA parikalana/21 (cha) 400deg ko degC meM uttara : 204.44degC (na) 15 ki0 grA0/0 mI0 ko pauMDa/iMca meM uttara: 213375 pauMDa/iMca 2. eka patthara ke Tukar3e kA bhAra 7643 ki0 grA0 hai| patthara ke eka kyUbika DesImITara kA bhAra 2.7 ki0 prA0 hai / TukaDe kA dhanaphala kyUbika mITara meM jJAta kro| uttara : 2.83 (mITara) 3. eka kharAda mazIna kA bhAra 5609 pauMDa hai| isakA bhAra mITrika Tana meM jJAta kro| uttara : 2.545 Tana 4. eka sTIla zAphTa kA kraoNsa saMkzanala kSetraphala 64.52 varga sai0mI0 hai| kSetraphala ko varga inca meM jJAta kro| uttara : 21.6 varga inca 5. tumhArI U~cAI 174 sai0mI0 hai| tumhArI UMcAI phuTa aura inca meM kitanI hai ? uttara : 5 phuTa, 8.5 inca 6. mITrika praNAlI kI anupasthitI meM kucha kAbaloM ko aMgrejI praNAlI meM badalanA hai| 8 mi0mI0, 12 mi0mI0 16 mi0mI0 kAbaloM ke lie sabase ucita mApa btaaie| .5 uttara : 16 inca, inca, hai inca 7. 723 mi0mI0 ko mITara meM badalo tathA isa mApa ko phuTa aura inca ke solahaveM hisse taka jJAta kro| uttara : 0.723 mITara . 2 phuTa, 45 inca 8. (ka) 10 ki.grA0/varga saM0mI0 dabAva pauMDa prati varga inca meM bdlo| uttara : 142.2 pauMDa/varga inca (kha) nIce dikhAe gae citra meM pUrje kA phrI haiMDa citra banAo tathA isako incoM meM aMkita kro| mApa ko inca ke 1000veM hisse taka dazamalava meM badalo: -10+ // + --104 - +-20 -09 -3 | 9. (ka) nIce dikhAe gae citra meM khule muMha kI cAbI kA phrI haiMDa citra banAo tathA mi0mI0 meM paimAiza darzAo / dazamalava bindu mi0mI0 ke 100veM hisse taka honA caahie| sabhI mApa inca meM haiN| MN

Page #30
karmazAlA parikalana/22 (kha) eka sTIla letha sainTara nIce diyA gayA hai tathA isako mi0mI0 meM paimAiza kro| dazamalava cihna mi0mI0 ke 100veM hisse taka honA cAhie / sabhI mApa inca meM haiN| --02 (ga) mIla tathA kilomITara meM sambandha jJAta karo tathA 60 mIla prati ghaMTe ke anurUpa mITrika gati mAlUma kiijie| - mola _ 1.61 ka uttara - 11, 96.6 ki0mI0/ghaMTA ro tara ki0mI0- 1 10. nimnalikhita ko badaliye : (i) 500 kailorI ko bI.TI.yU. meM uttara : 1.98 bI.TI.yU. (grupa 3, sitambara 73) (ii) ki0mA0 mI0 ko pauMDa phuTa meM uttara: 7.23 pauMDa phuTa (iii) bI.TI.yU. ko kigrA0mI0 meM uttara: 107.54 kigrA0mI0 (iv) phuTa pauMDa ko kilo vATa meM uttara: 3.77x10-7 kilo vATa -

Page #31
karmazAlA parikalana / 23 guNanakhaNDa: jaba do yA adhika saMkhyAyeM Apasa meM guNA hotI hai, saMkhyAoM ko guNanakhaNDa hai aura pariNAma ko ghAta kahate haiN| ghAta aura mUla adhyAya 3 jaba guNanakhaNDa eka jaise ho, to guNanakhaNDa ko AdhAra kahate hai aura pariNAma ko ghAta kahate haiN| | 2x4 x 8 = 64 1 guNA guNanakhaNDa 4x4x4ml 64 guNanakhaNDa - AdhAra ghAta yadi AdhAra ko guNanakhaNDa kA dugunA prayoga kiyA jAe, guNA varga hai, yadi 3 bAra kiyA jAe to ghana hai| agara AdhAra guNanakhaNDa ke rUpa meM tIna se adhika bAra prayoga ho to guNA ko cauthI ghAta kahate hai pAMcavI bAta chaTI pAta aura isI prakAra / 4X4 = 16, 16 varga hai 4 kA 4x4X4 64 dhana hai 4 kA 64 samaya kI saMkhyA jJAta karane ke lie AdhAra guNanakhaNDa ke rUpa meM prayoga kiyA jAtA hai eka choTI AkRti AdhAra ke dAMI aura Upara sthita hotI ho jisa ko ghAtAMka kahate haiN| 4X4 ko aise likhA jAyegA 42 (4 kA varga) = 16 4 x 4 x 4 = 64 yA 48 (4 kA ghana) 4X4 x 4X4 - 256 yA 44 (4 kI zakti 4) dazamalava kI apanI zaktiyAM hotI haiM, jitanI zakti jyAdA hogI utanA mAna kama hogA 1 udAharaNataH 0.22 yA 0.2X0.2 = 0.04 jo ki 0.2 se kama hai / ghAta kI ghAta : jaba koI AdhAra kisI ghAtAMka ke sAtha eka zakti taka bar3hAyA jAtA hai, do ghAtAMka Apasa meM guNA hokara nayA ghAtAMka ko banAte haiM jo ki samaya kI saMkhyA ko batAtA hai / AdhAra eka guNanakhaNDa ke rUpa meM prayoga hotA hai / (43)443 x4 412 48 =

Page #32
karmazAlA parikalana/24 zaktiyoM kI guNA: yaha vAstavika ka) 43x42x4 ghAtAMka kA jor3a hai aura kevala tabhI =43+2+1 saMbhava hai jaba AdhAra barAbara hote hai| ___kha) (2.5)3x (2.5) =46 zaktiyoM kI bhAga: yaha ghAtAMka kA (2.5)3+5 = 2.58 RNAtmaka hai ka) =1077:104-107-4-103 kha) = (1.25) : (1.25)? __= 1.259-7 = 1.252 saMketa sabhI dazAoM meM AdhAra eka jaisA honA caahie| mUla :-kisI saMkhyA kA mUla eka barAbara guNanakhaNDa hotA hai, jo ki jaba Apasa meM guNA hote haiM, naI saMkhyA banAte haiN| isa prakAra kisI saMkhyA kA mUla ghAta se viparIta hotA hai| 16 ke barAbara guNanakhaNDa 4 aura 4 hai (16 =4x4) isalie 4, 16 kA mUla hai| kyoMki vahAM para do barAbara guNanakhaNDa yA mUla haiM, ina meM se kisI eka ko vargamUla kaheMge / kisI saMkhyA kA ghanamUla tIna barAbara guNanakhaNDa hotA hai| usI sakhyA kA cartumala cAra guNanakhaNDoM kA hotA hai, aura isI prakAra adhika mUla ke lie hotA hai| AmUla cinha aura mUla kA sAMketaka : / yaha cihna mUla ko batAtA haiM aura isako AmUla cinha kahate haiN| eka choTI AkRti jo ki mUla kA saMketaka kahalAtI hai jo AmUla cihna ko kholane ke liye lagatI hai aura kisI mUla ko batAne ke liye prayoga hotI hai| isa prakAra 3/64, 64 kA ghanamUla batAtA hai, choTA 3 mUla kA saMketaka hai| vargamUla kA saMketaka 2 hai jo ki vahAM se haTAyA huA hai aura sAdhAraNatayA isako aise likheMge /625, aise nahIM likheMge 24/6251 adhika (UMce) mUla aise likhe jAyeMge 41243, 7/128 aMkagaNita dvArA varga mUla : udAharaNa: 1236.618 kA mAna dazamalava ke tIna sthAna taka jJAta karanA hai| pahale saMkhyA likha lete haiM aura do AkRti ke pIriyaDa meM unake jor3e banA lete haiM jo ki pratyeka dAIM ora se zurU hogaa| (jor3e banAne ke lie damazalava ke bAda bAIM ora se zurU karate haiM) +-1- ka kha ga gha ca 25) ja ga 303) jha gha 3068) 2 36.61 8000(1 5.382 1 / / / 135.1 / / 1 25+ / / 1161 / / 9 09 / / 2 52 80 | 2 45 44 73600 61524 12076 tIna sthAna taka uttara =15.382 Na ca 30762)

Page #33
karmazAlA parikalana/25 vyAkhyA : ka para bar3e se bar3A nambara rakheM jisakA varga barAbara hai yA kama hai| pahale pIriyaDa (2) se aura pahale pIriyaDa se ghttaao| agale pIriyaDa ko nIce laao| ka ko Davala karo aura cha meM lgaao| aba eka AkRti kha cuno jo ki jaba kisI saMkhyA se guNA ho aura cha aura kha Apasa meM 136 se bar3e nahIM hai| unake dvArA dikhayA jaae| uttara meM kha ko likho aura dUsarI tarapha gha, banAvaTa cha kha ko kha se guNA karo (25x5 = 125) aura 136 meM se ghttaaeN| dubArA agale pIriyaDa (61) ko nIce lAo, banAvaTa ka kha ko Dabala karo (15x2 = 30) aura ja meM isako lgaao| ga ko cuno isalie ki jaba yaha ga dvArA guNA ho to banAvaTa ja ga (303x3-909) pariNAma 1161, se jyAdA nahI AtA, pahale kI bhAnti guNA karo aura ghaTA kro| isa vidhi ko agalA pIriyaDa lAne ke lie lagAtAra calAeM jaba taka ki pariNAma nahIM aataa| nimnalikhita pariNAmoM ko yAda ke lie pakkA kara leM sAriNI 1 /2 13 15- =1.414 1.732 2.236 V6 -2.449 17--2.6458 18 =2.8284 dhana aura mUla ko laghu guNA dvArA hala kiyA jAtA hai : hala kI huI udAharaNa 1. vargamUla jJAta karo: 21025, 18, 97.8121 (i) 21025 2 10 25(145 24)110 96 (ii) 18 18000000(4.242 16 82)200 164 844)3600 3376 8482) 22400 16964 5436 uttara : 4.242 - 285)1425 1425 uttara: 145 (iii) 97.8121 97.81 21(9.89 81 188)1681 1504 1969)17721 17721 uttara 9.89

Page #34
karmazAlA parikalana/26 3. jJAta karo (ka) 27, (kha) 125 (ka) isa prakAra 27 =V9x3-3/3 (sAraNI se 1, 13 = 1.732) =3x1.732 = 5.196 (kha) isa prakAra 125 = 125 x 5 =5/5 (sAraNI se 1, 15 = 2.236) -5x2.2362311.180 nimnalikhita kI vyAkhyA karo 10 kI ghAta ke rUpa meM : 10,000; 10,00,000; 100,00,000 isa prakAra 10,000-10x10x10x10-104 10,00,000=10x10x10x10x10x10=106 100,00,000 %3D10x10x10x10x10x10x10-107 noTa : dasa kI ghAta ko sarala nambara meM badalanA (Upara kI udAharaNa ke viparIta vidhi) dasa ke pazcAta jIro kA ghAta se eka nambara kama lagAye 107=10,000.000 abhyAma : 1. nimnalikhita kA vargabhUla jJAta karo : (i) 961 uttara 31 (iv) 58081 uttara 241 (ii) 2401 , 49 (v) 101761 , 319 (iii) 22201 , 149 (vi) 281961 531 (2) nimnalikhita kA vargamUla nikAlie : (i) 0.01 uttara 0.1 (v) 665.1241 uttara 25.79 (ii) 2.89 uttara 1.7 (vi) 27 uttara 5.196 (iii) 1481.4801 uttara 38.49 (vii) 7.25 uttara 2.69258 (iv) 0.9216 uttara 0.96 (viii) 0.001225 uttara 0.035 nimnalikhita kA mAna jJAta kareM : (i) 32 uttara 5.6568 (iv) 30 uttara 5 475964 (ii) 200 uttara 14.14 (v) 320 uttara 17.888 (ili) 108 uttara 10.392 (vii) 600 uttara 24.49 DI.sau. zanTa jainereTara meM Aramecara kI tAmbe kI hAni 800 vATsa hai| Aramecara kA pratirodha 0.02 oham hai, Aramecara kA karanTa jJAta kreN| (Aramecara kI kApara hAni kA sUtra AI. e.xAra.e. jahAM.ki Ai.e - Aramecara karanTa tathA Ara.e. Aramecara kA prtirodh)| uttara : 200 empIyarasa rasisaTara kI adhika se adhika karanTa lene kI kSamatA kyA hogI, jisa para ki 1000 Ahamaz2a tathA 10 vATsa likhe hoN| (yaha sUtra prayoga kareM : pAvara, vATsa meM-karanTa kA varga empIyara meMx pratirodha ohamaz2a meM uttara : 0.1 empiyara (6) 240 vATasa kI moTara kI phIlDa kAyalaz2a kA kula pratirodha 60 oham hai| moTara ko calAne ke lie Avazyaka volTeja jJAta kreN| (yaha sUtra lagAyeM : pAvara vATasa meM volTeja kA varga volTa meM pratirodha ohama meM uttara : 120 volTaz2a

Page #35
karmazAlA parikalana/27 adhyAya 4 pratizata pratizata : pratizata dazamalava bhinna kI eka kisma hai| jisakA hara 100 hai| (1%=ro) pratizata ko dazamalava rUpa meM badalanA tathA isake viparIta : niyama 1. pratizata ko dazamalava meM badalanA : pratizata cihna ko haTA kara aura dazamalava bindu ko do sthAna bAI ora sarakA do| 5%-0.05 121%-12.5% = 0.125 niyama 2. pratizata ko bhinna meM badalanA : pahale dazamalava meM badala lo phira usako nazamalava bhinna vanA lo| 34% = 0.34 =18-18 niyama 3. dazamalava ko pratizata meM badalanA : dazamalava kA cihna dAIM ora do sthAna aura sarakA do| taba pratizata kA cihna lgaao| udAharaNatayA : 0.56 = 56% niyama 4. bhinna ko pratizata meM badalanA : bhinna ko dazamalava me badala lo aura taba dazamalava ko pratizata meM badala lo| udAharaNatayAH : 1-0.25=25% udAharaNa: 1. 125 eka Dhera meM 7500 vAzara thiiN| usameM se 125 kharAba niklii| kharAba vAzaroM kA pratizata jJAta kro| yahAM 125 kharAba vAzareM 7500 bAzaroM meM se haiN| isalie pratizata-120x100 -I-1%% 600 Dhalate lohe ke pUrje mazIna zApa meM mazIniMga ke liye lAye gye| unameM se 8% kharAba nikle| kitane purje kharAba nikale, kitane pUrje ThIka nikale ? 8%-.08 (niyama 1) .:. kharAba Dhale hue purjI kI saMkhyA = 0.08 x 600 = 552 .:. ThIka Dhale hue puoM kI saMkhyA-600-48-48 - -

Page #36
karmazAlA parikalana/28 - -2% 3. eka emITara kI rIDiMga TaisTa karane para 4.65 empiyarasa pAI gii| bAstavika mAna 45 empiyara hai| pratizata truTi jJAta kro| grupa 5 2 varSa prArambhika julAI, 1972 kula truTi-465--450 0.15 empiyara .:. 1 = 0.0333-3.33 . (niyama 3) 4 pola inaDakzana moTara kI gati 2000 cakra prati minaTa hai| jaba moTara khAlI cala rahI ho, 1960 cakra prati minaTa jaba AdhA bhAra (load) DAlA gayA aura 1920 cakra prati mintt| jaba pUrA bhAra DAlA gyaa| spIDa kA pratizata DrApa Adhe aura pUre loDa (load) para jJAta kro| Adhe loDa para spIDa DrApa-2000-1960-40 40X100 isalie pratizata DrApasAla 2000 -10 pUre loDa para spIDa DrApa = 2000-1920-80 isalie pratizata DrApa-80X100_an 2000 5. kisI dhAtu ke 75 kilo bhAra ko vizleSaNa karane para isameM 10% lohA pAyA gyaa| 15% TaMgasTana, 500/. kromiyama pAyA gyaa| pratyeka dhAtu kI pratizata ajJAta dhAtu meM kitanI hai ? lohA : 75 ki. grA. meM 10 ki. grA.-18-0 1333 isalie pratizata-13.33% (niyama 3) TaMgasTana : 75 ki. grA. meM 15 ki. grA. ::. I--0.20 isalie pratizata =20% kromiyama : 75 ki. grA. meM 50 ki.grA. .:.=0.6666 isalie pratizata = 66.66% 6. eka gana maiTala kI kAsTiga meM 85.5% tAMbA, 10.5% Tina aura bAkI jasta hai| yadi kAsTiga kA bhAra 70 kilo hai to pratyeka dhAtu kA kAsTiMga meM bhAra btaao| _(grupa 1 aparenTisazipa kI parIkSA mArca 1971) hamAre pAsa hai 85.5%+10.5% =96% tAMbA aura Tina 85.5% tAMbA .:. 100-96-4% jasta 10.5% Tina ... tAMbe kA bhAra-70 kilo kA 85.5% -85.5x70 = 59.85 ki. grA. 100 .:. Tina kA bhAra = 70 kA 10.5% -10.5 x 70-7.35 ki. grA. .:. jasta kA bhAra-70 kA 4% -4x70= 2.80 ki. mA.

Page #37
karmazAlA parikalana/29 abhyAsa 1. eka vizeSa abhyAsa ke kucha samaya pazcAt eka apareTara apanI kArya kuzalato 120 puoM se 145 purje prati ghaNTA bar3hA letA hai| pratizata bar3hautarI jJAta kro| uttara 20.8% 2. eka Tala kA nayA DijAina badalate samaya Aparezana kI spIDa 150 se 250 cakkara prati minaTa bar3hAI jA sakatI hai| lekina isI kaTa se phIDa 0.020 DesImITara se 0.015 DesImITara ghaTAI jA sakatI hai dhAtu kATate samaya pratizata tabadIlI jJAta kreN| uttara : 25% 3. eka vyakti apanI Aya kA 15% khetIbAr3I ke lie, 21% apane parivAra aura 24% baccoM kI zikSA ke lie kharca karatA yadi usake pAsa 360 rupaye baca rahe / batAo kula kitanA dhana thA? (grupa 4, 2 varSa, julAI, 1970) uttara : 900 rupaye 4. volTeja kI saplAI eka lambe phIDara ke anta meM 220 volTa hai| volTeja DisTrIbyUzana painala para 250 volTa hai| lAIna meM pratizata kA giranA jJAta kro| uttara : 12% 5. eka phaikTarI meM paidAvAra kA 8% bhAga mAtrA niyantraNa ke lie sthagita kara diyA jAtA hai| yadi sthagita kI huI mAtrA ke 64 Tukar3e hoM to kula kitane Tukar3e paidA kie gaye / uttara : 800 Tukar3e 6. eka baibiTa kA banA huA sandUka, jisakA vajana 125 ki0grA0 hai| isameM 80% TIna kI mAtrA 12% tAMbA aura 8% aiMTImanI hai| baibiTa kA bane hue sandUka meM TIna, tAMbA aura eMTImanI ko ki0grA0 kI saMkhyA meM jJAta kro| uttara : TIna=100 ki0grA0 kApara-15 ki0grA0 eMTImanI-10 ki0mA0 7. eka phaikTarI, jo ki chApane kI mazIneM banAtI hai, usakI nimnalikhita mUlyAMka kro| padArtha 38% majadUrI 41% ovarahaiDa 6% aura lAbha 15% hai| pratyeka kI kImata jJAta karo jabaki chApane kI mazIna 5445 rupaye meM bikatI hai| uttara : padArtha -2069.10 rupaye ovarahaiDa-326.70 rupaye majadUrI-2232.45 rupaye lAbha-816.75 rupaye 8. eka nizcita lohe kI khAna 9% lohA utpAdita karatI hai| 43 mITrika Tana lohe kI khAnoM ko kitane Tana AvazyakatA hai| uttara : 50 mITrika Tana -

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karmazAlA parikalana/30 adhyAya 5 anupAta aura samAnupAta anupAta : do vyaMjakoM ke bIca ke sambandha (saMkhyAoM kI mAtrA) jaba ve eka hI prakAra ke hoM, ko anupAta kahate hai| sambandha kA artha hai, do vyaMjakoM ke bIca meM tulanA / jaise 10 aura 5 ke sambandha ko pradarzita karane ke lie hama kaheMge 10 se 5 yAni 19-2. anupAta ko hama aise bhI kaha sakate haiM : anupAta 10 se 5 yA 10 : 5 (aura ise 'se' (to) uccAraNa karege) jaisA ki bhinna, do vyaMjakoM ko eka sAmAnya saMkhyA se gaNA karane para anupAta nahIM bdltaa| anupAta 1 : 2 ko aisA bhI kaha sakate haiM 2 : 4 yA 12 : 24 yA 48 : 96 ityAdi / anupAta aura vyaMjaka jJAta karanA niyama 1. anupAta ko jJAta karane ke lie pahale vyaMjaka ko dUsare vyaMjaka se bhAga denaa| udAharaNa ke taura para 6:2-? 6:2-3 jo ki anupAta hai| niyama 2. pahalI saMkhyA jJAta karane ke lie dUsarI saMkhyA ko anupAta se guNA kro| udAharaNa ke lie ?: 2-3 naM02 niyama kI sahAyatA se hama 2X3-6 prApta karate haiN| isalie pahalI saMkhyA 6 hai| niyama 3. dUsarI saMkhyA jJAta karane ke lie pahalI saMkhyA ko anupAta se bhAga kro| udAharaNa: 6:?-3 niyama 3 kI sahAyatA se, hama 6:3-2 prApta karate haiN| 2 dUsarI saMkhyA hai / samAnupAta ko do anupAtoM kI samAnatA pradarzita karanA bhI vaha kaha sakate haiM / samAnupAta: 688600Dimina@isa 00000 (-)0000000000 - 12 9 3 udAharaNa ke lie, 1 barAbara hai 3 ke aura 12 varAbara hai 3 ke hama yahAM para donoM anupAta ke lie saMkhyA 3 hI prApta karate haiM, hama isako aise bhI kaha sakate haiM / barAbara hai 12 ke yA 9 : 3-12 : 4 isako aise bhI likhA jA sakatA hai 9:3 :: 12:4 jabaki [::] & isakA artha barAbara hai (isako 'As to' uccAraNa kiyA jAtA hai) cAra saMkhyAoM ke samAnupAta meM, anta kI do saMkhyAoM ko 'bAharI' aura madhya vAlI ko 'bIca' vAlI saMkhyA jAnA jAtA hai|

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AT, karmazAlA parikalana/31 bAharI 9:3 - 12:4 niyama 4. bIca vAlI kisI bhI samAnupAta meM bAharI makhyAoM kA gaNanaphala vIca vAlo saMkhyAoM ke barAbara hotA hai| yA 9X4-3x12 yadi cAra saMkhyAoM meM se eka nahIM dI gaI to Upara vAle niyama kI sahAyatA se isa saMkhyA ko jJAta kiyA jA sakatA hai| 9x4 udAharaNa : 1. 9 : a =12x4 .:a = -3 3x12 2. 9:3=12: .. a sIdhA samAnupAta : sIdhA samAnupAta vaha vastu hai jisameM anupAta eka hI paddhati meM badalatI hai| udAharaNa ke lie aisA mAnA jAtA hai ki vatoM kA gherA unake vyAsa ke vargoM ke sIdhA samAna pAta hotA hai| isakA artha yA bar3hatA hai vaise vaise varga kA vyAsa bhI bar3hatA hai eka vRta jisakA vyAsa 2 seMmI0 hai usakA kSetraphala 3.1416 varga se mI0 hai, jaba ki eka vRta jisakA vyAsa 4 semI hai| usa kA kSetraphala 12.5664 varga se mI0 hai isa kathana ko hama vata kA kSetraphala ke niyamita sUtra se pramANita kara sakate haiN| kSetraphala - --vyAsa mawater-ms jaisA ki sIdhe samAnupAta, ke sambandha ko aise bhI kahA jA sakatA hai| (2) : (3)=3.1416 : 12.5664 (choTA vyAsa) - : (bar3A vyAsa) : choTA kSetraphala bar3A kSetraphala jabaki choTA vyAsa-choTe vRta kA vyAsa bar3A vyAsa-bar3e vRta kA vyAsa choTA kSetraphala-choTe vRta kA kSetraphala var3A kSetraphala=bar3e vRta kA kSetraphala indiasishrmstournearanamuma asamAna anupAtI: eka asamAna anupAtI aura viloma samAnupAta vaha hai jisameM anupAta eka hI praNAlI meM nahIM badalate / gatiyoM aura pulI ke vyAsoM ke bIca kA sambandha asamAna anupAtI kA eka acchA udAharaNa hai| isako acchI / prakAra se jAnA jA sakatA hai jaba do vibhinna prakAra kI puliyoM para jaba eka sAtha peTI caDhAI jAe to choTe vAlI pUlI bar3I vAlI pulI se jyAdA teja clegii|

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karmazAlA parikalana/32 ina samasyAoM ko hama nimnalikhita tarIke se le sakate haiM: choTI kI gati : baDI kI gati :: bar3e kA vyAsa : choTe kA vyAsa yA sa : sA :: bar3A vyAsa : choTA vyAsa jabaki sa-choTI pulI kI gati sA-bar3I pulI kI gati bar3A vyAsa=bar3I pulI kA vyAsa choTA vyAsa- choTI pulI kA vyAsa kama se kama cakra prati minaTa - adhika se adhika cakra prati minaTa udAharaNa (ka) jaisA ki citra meM samakoNa tribhuja ko dikhAyA gayA hai aba : basa-aya : yala F18.3 yadi sar3aka tala kI UMcAI 100 mITara meM 'ha' mITara hai, taba sar3aka kA greDa hai hai yA horIjeMTala dUrI ke anupAta kA bar3hAva hai| yadi sar3aka 100 mITara meM 3 mITara Upara uThI hai to greDa hogA 10-3% prazna : usa sar3aka kA greDa nikAlo jisameM uThAva 1.2 mITara hai, horIjeTala dUrI 40 mITara hai| hala : mAna lo 'ha' mITara 100 mITara meM uThAva ko darzAtA hai| isakA artha hai ha : 100-1.2 : 40 .: greDa-12 = 0.3 -3% (kha) khar3e hue vRkSa kI UMcAI nApanA nirIkSaNa karane vAlA eka vyakti jamIna para paidala cala kara eka nizcita dUrI ada bindu ase per3a taka pUrI karatA hai| taba vaha apanI pITha ke bala leTa jAtA hai jaisA ki citra meM dikhAyA gayA hai| usakA sahAyaka usake pAMva ke pAsa khar3e khambe ke Upara bindu sa se dekhatA hai jahAM usakI najara kI sarala rekhA vRkSa ke UparI hisse ja se kATatI hai| khambe basa kI UMcAI mApI jAtI hai tathA usakI apanI UMcAI aba usake pairoM se lekara usakI AMkhoM taka taba nimnalikhita anupAta aba: basa-ada:da ja yamkarahasya

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karmazAlA parikalana/33 2. usa carca sTIpala kI UMcAI nikAlo jisakA chAyA vAlA bhAga 115 mITara hai| jaba eka khambhA 8 mITara lambA hai usakI chAyA vAlA bhAga 5 mITara hai| hala : mAna lo 'a' sTIpala' kI UMcAI hai| 115x8 .:.5:8-115: a yA a -184 mITara N - 8 L- -5--- -115 ---- (ga) uttolaka eka sakhta char3a jo kisI kendra bindu para sthita ho, jo ki AsAnI se ghama sakatI ho, ko uttolaka kahate haiN| kendra hindu ko (akSa) Alamba kahate haiN| uttolaka vibhinna prakAra se yAntrika praNAlI meM prayoga meM layA jAtA hai| Fig 5 meM, 'pha' Alamba hai 'va' vajana hai aura 'ca' bala hai joki isako Upara uThAtA hai. 'la' dUrI bala ke bindu se Alamba taka hai aura 'ma' dUrI Alamba ke bindu se hai, jahAM ki vajana ko sAtha rakhA gayA hai| vibhinna prakAra ke sambandhoM se akSa vajana va bala ko nimnalikhita samAnupAta meM jor3A jA sakatA hai : ca : va-ma : la lagAyA gayA bala vajana ke Alamba se unakI dUriyoM ke viparIta samAnupAta hotA hai| isakA matalaba eka choTA mA bala adhika vajana ko tabhI baileMsa kara sakatA hai jaba bhAra Alamba ke bala se adhika pAsa ho / 3. eka tAra kATane vAle kaTara me tAra ko Alamba se 0.5 seM. mI. kI dUrI para rakhA gayA hai aura hAtha kA davAba Alamba se 7 sai. mI. kI dUrI para hai / tAra kA pratirodha jJAta karo yadi hAtha 40 nyUTana kA davAba DAlatA hai| hala : mAna lo tAra kA pratirodha 'ca' hai (cinna naM05 meM) __40 : ca-.5 : 7 yA ca =40x7 = 560 nyUTana (da) hAiDrolika mazIneM eka niyama jo ki pAsakaeNla niyama ke nAma se jAnA jAtA hai vaha kahatA hai ki yadi kisI baMda bartana meM par3e hae tarala padArtha para davAba DAlA jAye to saba dizAoM meM kama kiye binA eka jaisA davAba par3atA hai| citra naM06 meM yadi 'a' kA kSetraphala 1 varga se. mI. hai, taba 'a' para eka ki.grA. davAba, sa ke hara varga iMca tala para

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karmazAlA parikalana/34 eka ki. grA. davAba DAlatA hai| yadi sa ke Upara vAle bhAga kA kSetraphala 100 varga se. mI. hai, taba 1 ki. grA. davAba 'a' para 100 ki. grA. bhAra 'A' para utthaayegaa| yadi a, A, da aura dA kramazaH kSetraphala aura davAba hoM to samAnupAta ke niyama se a : A =da : dA yA dA - Ada 100ki. grAma Fig.6 abhyAsa eka hAIDrolika yantra (liphaTara) jo ki bhAra uThAne ke lie istemAla hotA hai usakA davAba jo ki pisTana para paDatA hai usakA kSetraphala uttolaka dvArA 0.5 varga se. mI. hai| Alamba kI dUrI choTe pisTana ke sAtha jur3e hue bindu se 4 se. mI. hai aura usa bindu se jahAM ki 100 ki. grA kA bala lagatA hai 22 seM. mI. hai| taba vo bhAra jJAta karo ji pisTana ko Upara uThAyA jA sakatA hai, jisakA kSetraphala 75.6 varga seMmI. hai| hala : mAna lo 'va' = dabAba ki0grA0 meM jo choTe pisTana para par3atA hai taba 100 : ba-4 : 22 taba bhAra-550 ca =100 ki0grA0 dA-22 se0mI0 da-4 se0mI0 bhAra-ba aura 0.5: 75.6-550: ca (citra naH 6 ko dekheM) va ki0grA-dabAva jaba ki 1 ki0grA0 a-0.5 varga se. mI.. A--75.6 varga se. mI. isalie ca-550X75.6 = 83.160 0.5 isalie isase 83, 160 ki. grA. kA bhAra uThAyA jA sakatA haiN|--uttr / (la) sIdhA mizrita samAnupAta hameM aksara aisI parezAnI hotI una praznoM 3 jinameM tIna mAtrAoM ikaTThI dI hoM usako nIce dikhAyA gayA hai| udAharaNa : 100 pItala ke bane hue bolTa jisakI lambAI 10 seM. mI. hai, kA mUlya 60 rupaye hai / taba 200 bolToM kA mUlya jinakI lambAI 7.5 se. mI. ho| cetAvanI: bolTa ke mUlya ko lambAI ke samAnupAta rakhanA hai| tIna mizrita rAziyoM meM bolToM kI saMkhyA, pratyeka bolTa kI lambAI va mUlya hai / isalie jo ki anupAta isake bIca meM hai, use hama nikaaleNge|

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100 200 600 a 10 : 7.5 : : 60 : va eka sire para 100, 10 aura ba hai / madhya meM 60. 200 aura 7.5 hai| isalie 10 x 100 X 200 x 7.5 X 60 4. 1. 2. yA hala : 3 anupAta isa prakAra hai 40 20 AdamI 8 : 5 ghaNTe abhyAsa 1. cha. mizrita viparIta samAnupAta: 40 AdamI 8 ghaNTe pratidina kAma kara ke pAnI kA gaDDA sApha karate hai 3 dina meM 20 AdamI 5 ghaNTe pratidina kAma karake kitane dinoM meM gaDDhA sApha kareMge / pahalA bhAga lete hue 40 : 20 : : a : 3 8 : 5 : : a : 3 isalie 40 20 8:5 abhISTa guNanaphala ba - 200 x 7.5 x 60 10x100 yA ) a - karmazAlA parikalana / 35 mazIna kI dakSatA - 3 dina a dina kyoMki kama AdamI jyAdA dina lagAeMge aura anupAta viparIta hai / bilkula isI kAraNa se kama ghaNTe kAma karane se kAma samApta karane meM jyAdA dina lgeNge| > - 20 x 5 x a - 40 x 8 x 3 : : a dina 3 dina nimnalikhita anupAta (ka) 144 24 uttara : f (kha) 9 ghaNTe 30 minaTa uttara : 40 x 8 x 3 20 x 5 va = 90 rupaye uttara ma 3 4-M = = 48 5 ------ - ko sarala bhinnoM meM badaleM jahAM va aura ma pUrNa saMkhyA haiM dina (ga) 2.5 3 uttara 5 (gha) 5 ki0 mI0 : 50 mITara uttara: 120 mazIna kI dakSatA AUTa puTa aura ina puTa ke anupAta ko kahate haiM aura ye prAya: pratizata ke rUpa meM prakaTa kI jAtI hai AUTa puTa ina puTa eka moTara meM inapuTa 6000 vArasa hai aura AUTa puTa 5300 vATsa hai dakSatA ke pratizata jJAta karo uttara 883% 3. eka pItala ke Tukar3e kA bhAra 10 ki0 grAma hai jisa meM tAMbA ora jasta 3.2 anupAta meM hai yaha 12 ki0 grAma pItala ke sAtha pighalAyA jAtA hai jisameM tAMbA ora jasta 5 : 3 ke anupAta meM hai naye alAya meM tAMbA aura jasta kA anupAta nikAlo. uttara : tAMbA : jasta = 27 : 17 halave lohe ke lie prayoga meM lAI jAne vAlI reta kA mizraNa, 10 bhAga silikA seMDa (Silica Sand), 1.4 bhAga miTTI aura 0.6 bhAga pAnI hai pratyeka kI banAvaTa jJAta karo jabaki reta kA mizraNa 600 kilo diyA uttara: silikA seMDa 500 kilo miTTI 70 kilo pAnI 30 kilo huA hai

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karmazAlA parikalana/36 15. agara do tribhujoM kI bhujAyeM isa citra meM samAnupAtI (Corresponding) haiM to choTI tribhuja kA nApa nikAlo jo nahI diyA gyaa| uttara :9.8 sai. mI., 4.2 se. mI. og in Joch 14 cr | 6. do tribhujoM meM jaisA ki citra meM dikhAyA gayA hai ki UcAIyAM AdhAra ke samAnupAtI hai choTe tribhuja kI UcAI uttara : 1.23 sai .mI. jJAta karo 18mI 3.25cm . 75cm __ do garAriyoM ke cakkaroM ke nambara jahA ve maiza (mesh) kara rahe hai garAriyoM ke dAMtoM ke nambaroM ke viparIta samAnupAtI hai agara dAMtoM ke nambara garAriyoM meM 15 aura 48, kramaza: hai aura cakkara prati minTa choTe kA 40 haiM to prati minTa bar3I kA jJAta karo uttara : 121 cakkara prati minTa eka borDa para 5 mAikrona (micron) moTI nikkala kI parata caDhAne kA kharca 15 rupaye hai dUsare borDa kI 12.5 mAikrona moTI parata kA kharca jJAta karo jaba ki vaha pahale se 4 gunA hai uttara : ru. 150/ 8.

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karmazAlA parikalana/37 adhyAya-6 bIja gaNita cinha prArambhika bIja-gaNita Aparezana bIja gaNita ke viSaya meM saMsthAoM kI bajAya akSaroM tathA cihnoM kA prayoga hotA hai| aura yaha aMkagaNita ko jArI rakhatA hai| aura sarala tathA adhika zaktizAlI gaNita Aparezana kI vidhiyoM ko bar3hAvA dene meM lAbhaprada hai| bIja gaNita meM prayoga hone vAle cihna artha artha barAbara ke lie se adhika yA barAbara haiM barAbara nahIM ke lie VIE | + | | jamA bilkula barAbara hai ke lie ghaTAnA anurUpa, samatulya ke lie aXba,aba a ko ba se guNA kiyA lagabhaga barAbara hai aba,aba;aba-1 a ko ba se bhAga diyA samAnupAta ke lie a pariNAma, mAtrA ke lie jisakA anta na ho ke lie a ki ghAta na " se kama ke lie jor3a ke lie W | 4 | 8 | V | A | ::| :: se adhika ke lie rekhA koSThaka isalie laghu koSTaka kyoMki ghanu koSThaka se kama ke lie yA barAbara ke lie gurU koSThaka vl,

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karmazAlA parikalana/38 guNAMka : hamAre pAsa 4 a ba eka bIja gaNita kI vyaMjaka hai jisa meM 4, a, ba isake guNana khaNDa haiM / inameM se kisI eka guNana khaNDa thA 2 yA 2 se adhika guNana khaNDoM kI guNA ko bAkI guNana khaNDa kA guNAMka kahate hai / pada, sajAtIya pada, vijAtIya pada : pada : yaha bIja gaNita dvArA batAI jAne vAlI vidhi hai jo ki guNanaphala aura bhAgaphala kI sAmAnya saMkhyA aura akSara hai isa prakAra 4 abara, 2 aba', a--pada hai| bIja gaNita ke vyaMjaka jo alaga pada rakhate hoN| 4 a+3 a+5 a; aba+sa-basara sajAtIya pada : jina padoM meM akSara aura unake ghAta samAna hoM tathA guNAMka kevala saMkhyAtmaka ho, unako sajAtIya pada kahA jAtA hai| vijAtIya pada : jina padoM meM akSara yA unake ghAta bhinna ho to unheM vijAtIya pada kahate haiN| udAharaNa ke lie: sajAtIya pada : 1. 2 aba, 3 baa', 5 a'ba' 2. -4 ka kha, ga ka, --9 ka ga vijAtIya pada : 1. aba, 5 a sa, 9 basa jor3anA (Addition) : bIja gaNita meM bhI jor3a aMka gaNita kI hI bhAMti kiyA jAtA hai| lekina dhyAna meM rakhane vAlI kucha mahatvapUrNa bAteM hai| kevala sajAtIya padoM ko jo ki eka hI prakAra ke pada haiM inheM jor3A yA ghaTAyA jA sakatA hai| tuma sajAtIya padoM ke maMkhyA sUcaka guNAMka ko jamA yA ghaTA sakate ho| 7 a+5ba ko 3 a-2ba meM joDo 7+5ba 3a - 2ba 10a+3ba 5aba+8basa ko 9asa2 - 10 meM jor3o 5aba+8basa 9asa. 10 5a'ba'+8 +9asa-10 ghaTAnA (Substraction) : bIja gaNita meM sajAtIya pada hI ghaTAye jA sakate haiN| mAnA ke cihnoM ke bAda jo ki ghaTAyA jAnA hai taba dUsare vyaMjaka meM jamA kro| cihnoM kA badalanA socakara kiyA jAtA hai| udAharaNa : a-24-2sa ko 48-5ba+6sa meM se ghaTAo 42-5ba+6sa a2-2ba-2sa 332-34+8sa

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karmazAlA parikalana/39 - ghAta aura ghAtAMka : jaba koI rAzi 'a' apane Apa se 'ba' vAra guNA hotI hai to guNA a.a.a..""a (ba bAra) ko 'a1 cihna dvArA likhA jAyegA jo ki isa prakAra liyA jAtA hai 'ba ghAta a kI' yA 'a kI ghAta ba' yA 'a se b'| yahAM rAzi a AdhAra kahalAegI aura ba, pUrNa saMkhyA, ghAtAMka khlaaegii| ghAtAMka ke niyama : jaba la aura va ghanAtmaka pUrNa saMkhyAyeM hoM to nimnalikhita pariNAma prApta kie jAte haiN| 1. ala aba - ala+va 2. ala ala-ba 1 la-va jahAM ki a#0 3. (ala )va =ala va 4. (ava)la - sajana . ( ) - 5, jahAM ki ba0 udAharaNaH (i) a.a =a2+3= 5 a6 a - ==a2-3 -a5-7 -a-2... / (iii) (a)5-30 adegkA mAna: pahalI bAra dekhane meM hI yaha zUnya hogaa| parantu jaba hama isakI kImata mAvA dvArA nikAleMge jisase ki hama jAna kara haiN| hamAre pAsa isa prakAra haiM: a22 a2-2 =a0 (ghAtAMka ke niyama dvArA) parantu a2 a2 = .:. adeg -1 isI prakAra 20 = 1, 1000 =1, (abasa) +1 aura anya kaI cihnoM ke niyama udAharaNa +guNA yA bhAga jamA dvArA hameM+ kA cihna detI hai a.ba = a ba, aba = 4 -guNA yA bhAga ghaTAne para hameM+kA cihna milatA hai--a-ba-aba,-a (-ba) = a + guNA yA bhAga-dvArA hameM-kA cihna detI hai-a.(ba) =-a ba, a (-ba) -guNA yA bhAga+ dvArA hameM-kA cihna detI hai ---a.(ba)- -aba, -a (ba) = -a yaha jarUrI nahIM hai ki jamA kA cihna kisI saMkhyA ke Age lagAe / isa kA matalaba hI jamA hotA hai guNA : eka sI aneka saMkhyAoM ke jor3a nikAlane kI sarala vidhi ko guNA kahate haiM /

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karmazAlA parikalana/40 udAharaNa: Apasa meM guNA karane para 14 a sa-3 aba+2 aura a sa-a ba+1 14 a sa 3 aba+2 asa-aba+1 14 asa2-3aba sa+2a sa -14 aba sa +3abara-2aba +14 asa -3 aba+2 14asa2-17aba sa+16a sa+3 aba25-a ba+2 bhAga : bhAga guNA se ulTa hotA hai / eka saMkhyA dUsarI sakhyA meM kitanI bAra sammilita hai ko jJAta karane kI vidhi ko bhAga kahate hai ! a+3 ke dvArA udAharaNa: bhAga karo aba a+12, a+3) a2+4 +12 (a+4 a+3a 4 +12 4+12 sarala karanA koSThaka ko haTAnA : koSThaka kucha padoM ko vyaMjaka ke rUpa meM banAne ke liye prayoga kI jAtI hai| koSThakoM kA khAsa artha hai| jaba jarUrI pada koSThaka ke andara banda hote haiM pahale hama padoM ko saMkSipta karate hai aura pariNAma padoM ko agale sthAna para prayoga karaMga ! guNA, bhAga, jor3a yA ghaTAne ke cihna koSThaka ke sAmane pAye jAte hai ! aura kucha niyama lagAye jAte hai koSThaka ko haTAte samaya / koSThaka ko haTAne ke niyama : 1. jaba jor3a kA cihna kisI koSThaka ke sAmane lagA ho to koSThaka ke andara ke vyaMjaka meM koI parivartana kiye binA koSThaka ko kholA jA sakatA hai| udAharaNa : a+ (ba+sa)-a+ba+sa 2. jaba koSThaka ke sAmane ghaTAoM kA cihna lagA ho to koSThaka ko haTA kara usake andara se cihna badala dene caahie| udAharaNa : ka-(kha+ga) = ka-kha-ga 3. eka se adhika koSThaka kholate samaya hameM saba se pahale choTe koSThaka ko kholanA cAhie aura anta meM saba se | bar3A koSThaka kholanA caahie| sarala karane ke kucha udAharaNa 1. sarala karo jaba ki a-2 aura ba-3,3aba2-6aba --aba-3a+ aba - aba+aba

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karmazAlA parikalana/41 sajAtIya padoM kA jor3a: 3aba abara-6aba- aba aba+4aba-392 =4242-7aba+3a ba-332 =4.22.32-7.22.3+3.2-3.22 =4.4.9-7.4.313.2.3-3.4 =144-84+18-1266 uttara 2. sarala kage: (ka-2kha) (5ka+7kha)-(2ka-3kha)2 grupa 5, 2 varSa prArambhika julAI, 1972 =50+7ka kha--10ka kha-14kha2-(402-12ka kha+9kha') --52+7ka kha-10ka kha-142-4+12ka kha-9kha =ka+9ka kha-232 uttara 3. sarala karo : [{2ka-(4ka-2ka-- 3ka)}--{6ka+ (5ka+3ka-4ka)}] -[{2ka-4ka-2ka-3ka}-{6ka+5+3 -4ka}] =2ka-40+20-32-61-52-3+4--13ka uttara sarala karo : 3/ka-khaka2x4/ka 4. ka + + vargamUla ke cihnoM ko ghAtAMka bhinnoM meM badalane me ka' x ka , ka x ka - 1 haroM ko Upara lekara jAne se tathA ghAtAMka bhinnoM ke cihna badalane se hameM prApta hotA hai = ka x kazx ka + ka x ka x ka-1 pratyeka grupa kI yuktiyAM (Indices) jamA kro| 421-+ +3-1 = 1+ 21 uttara. 5. sarala karo : [(1) (ka) .') [ (kakhayx d'x') -xx ka.) (kakha'xhix"] abhyAsa nimnalikhita kA mAna nikAlo : (1) (2ka+kha-3 ga), jaba ki ka = 1, kha = 2, ga =-3 = 13 2ka-5kha-7ga - jaba ki ka =3, kha- -6, 6ga-1-32 4ka-2kha+10ga uttara. uttara.

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karmazAlA parikalana, 42 2, jabaki ma, = 214, ma=186, ja = 5.64, ja, = 3.27-11.8 uttara. 3ka-kha+2ga ., jabaki ka-1, ga= -2, ga- --1 =ka+5kha 4ga' (5) ka+4 +6ka-2-4kakha+kha, jabaki ka == 1, kha =3==40 uttara. (6) V(ka+ga) V(gha+ ca) ka = 1, ga-3 gha-4, ca=5 uttara: 6 2, nimnalikhita samUhoM kI bIjagaNita uktiyoM dvArA Apasa meM jamA kge| (1) 22+ba a+ba, 34+a-a, a-2ba+a-44 uttara : 292+a-ba (2) ka -ka kha+2kha ga+3ga, 2ka kha +kha2-3kha ga-4ga, ka kha -4kha ga+ga-ka, ka+22+kha ga-2ka kha uttara : ka+kha+2ga 3) 2kakha ga-2kaga kha+5gaka kha, 4khaka ga+4kha ga ka2-7ka gakha. 4ka kha2-3kakha ga-3ka khaga, khaka ga-ka kha ga2-3kakha ga uttara : ka kha ga2 (4) a+2-sa+2aba-2ba sa, ba+ma -a+2ba sa-2sa a, sa+a2-42+2ma a -29 ba, 1-2 -ba-sa2 uttara: / . nimnalikhita meM dUsarI uktiyoM ko pahalI meM se ghttaao| (1) 3aba 2ba sa+4sa a, 3sa a+basa-2aba uttara : a ba-3ba sa+sa a (2) 4a+ 342-6a+4ba -2, 2a--ba+ a+4ba+3 uttara: a2+4ba---8a+8ba -5 (3) ya: 3yara-44ya ra2 ra, 2+3raya -2ra ya:-34deg uttara : 4ya-yara+ya ra-323 4) 4aba -3ka kha+222-ava, 4aba+ ka kha 30+2ka kha uttara : 4aba-5ka kha+522-5aba-ka kha2 4. nimnalikhita samhoM kA bIjagaNita uktiyoM dvArA guNanaphala nikaalo| (1) ba-4ba+16, ba+4 uttara : ba+ 64 (21 ba-4, ba+3 uttara : ba-ba-12 (3) 3ya -ra-la. 2ra+ya+302 uttara : 31+5yara+8772 - 212-5rala-304 (4) 3-a-ba, 2a-ba+1, a ba uttara : ba3 - 242-3ba+3a---5a.-3aba 2a - aba+2aba (5) a - a ba- ba, a+aba+ba uttara : a+aba+ba (6) a +aba+aba+aba+ba, a - ba uttara : a-ba

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karmazAlA parikalana/43 5. bhAga do| 51 4kakha+16kakha-422 uttara : 2ka kha - - -2kakha 294+393-92-1 uttara : 2a+72+13a+26+a-2 a -2 1644-1 uttara : 843+4ba+2ba+1 2ba-1 273-64 uttara : 91+12sa+16 3sa -4 4aba+5aba+a+2aba uttara : a2+aba a+2 +3aba (4) grupoM ke cihnoM ko dUra kiijie| (1) (a+3ba-sa)-(2ba a+3sa) + (4sa-3a+2ba) uttara : 3ba-a (2) 3 (a-2ba sa+ba)-4(a -ba2-3ba sa)+a+ba uttara : 84+ 6ba sa (3) 3a+4ba+3 {a-2 (ba -a)-ba} uttara : 12a-5ba (4) 3-[2a-{1- (a+ba)}+ {a-2ba}] uttara : ba-4a+4 7. sarala kiijie| (1) kakha+kha 2ka kakha+ ka uttara : 3-ca 1 uttara: 1 1+aka-kha + 1+ aba kha-ka jabaki, a- -6 uttara: / - -

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karmazAlA parikalana/44 adhyAya-7 guNana khaNDa aura samIkaraNa bIjagaNita aura sTaiNDarDa phArmUle : ina pariNAmoM ko guNA kI vidhi dvArA pramANita karo : 1. ka (ga+dha) =ka ga+ka gha 2. (ka+kha) (ka-kha)-(ka -kha) 3. (ka+kha) (ka+kha) =(ka+kha) = ka+2ka kha+kha (ka-kha) (ka -kha)-ka-kha) =ka2-2ka kha+kha 5. (a+ka) (a+kha)-a+ (ka+kha) a+ ka kha 6. (ka+kha) (ga+gha)-ka ga+kha ga+ka gha+kha gha 7. (ka+kha) (ka+kha) (ka+kha)- (ka+kha) = ka +32 + 3ka kha+kha. 8. (ka-kha) (ka kha) (ka-kha)-(ka-kha) = ka:-3kakha+3ka -kha 9. (ka-kha) (ka+ka kha+kha2) =ka3.-kha ____10. (ka+kha) (ka -ka kha+kha)-ka+kha: 11. (ka+kha+ga) -ka+kha+ga2+2ka kha+2kha ga+2ka ga guNanakhaNDa : ye bIjagaNita kI baha ukti hai jisa me do yA do se adhika bIjagaNita kI uktiyAM hotI hai, jinako ki yadi guNA kiyA jA to dI huI ukti bana jAtI hai guNanakhaNDa kI lAbhadAyaka vidhiyAM nimna likhita hai 1. sAdhAraNa tarIkA : ka ga+ka gha-ka (ga+gha) udAharaNa : (i) 4ka+8kha +12ga -4(ka+2kha + 3ga) (ii) 342+643.4124 = 342(1+29+ 4ba) 2. do vargoM kA antara tarIkA-ka -kha -(ka+kha) (ka+kha) udAharaNa : (i) ka -9-22 32 (i) azva 36ba = ba (a-3692) = (ka+3) (ka -3) -ba{a + (ba)2} = ba*(a+6ba) (a-6ba)

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3. 4. 5. 6. samIkaraNa udAharaNa: (i) 1 + 4 + 4 ba 2 =1+2.2+(2)2 =(1+2a)2 udAharaNa: (i) ka2 + 6ka + 8 = ka + 4ka + 2ka + 8 udAharaNa : udAharaNa: (i) a + 27 = a + 33 = (a+3) (a2 - ( a + 3 ) ( a2 karmazAlA parikalana / 45 = ka ( ka + 4 ) + 2 (ka + 4 ) - ( ka + 4 ) ( ka + 2) 3a + 32 ) 3a + 9 ) (ii) ma2 - 4 ma +4 kakha + kaga +kha + ga -ka(kha+ga) + (kha+ga) - (kha+ga) (ka+1) ka2 + 2ka kha + kha+- ( ka + kha ) 2 ka' - 2 ka kha + kha' = ( ka -- kha ) 2 = ma+---2.2ma + (2)2 = ( ma - 2 ) 2 (ii) a2-2a-8 a+- + (ka+kha) a + ka kha (a + ka ) ( a + kha) - a2 - 4a + 2a - 8 = a ( - 4) + 2 ( a - 4) - ( a - 4 ) ( a + 2) (ii) ka - 8 sarala samIkaraNa: samIkaraNa eka tarAjU kI bhAnti hai / donoM tarapha samAna mAtrA meM bar3hAI jA sakatI hai yA ghaTAI jA sakatI hai / ka+kha' (ka+ kha) (ka2 - ka kha + ga 2 ) ka--kha = (kakha) (ka2 + ka kha + ga 2) ka - 28 - ( ka - 2) (ka2 + ka. 2+22) - (ka- 2) (ka2 + 2ka + 4 ) ka ga+kha ga+ka gha+kha ghaga (ka+kha) + ka (ka+kha) -- (ka+kha) (ga+gha) (ii) a ba ba ' + 8a - 8 =a(a+--1) + 8 (a - 1 ) = ( a - 1 ) (ba + 8) (iii) (a + 2 ) ( a + 4 ) ( a + 8 ) ( a + 10 ) +20 -- (3T+2) (3+ 10) (+4) (+8) + 20 = (a2+12+20) (2+12+32)+20 mAnA a + 12a ka taba (a' +12a + 20 ) ( a + 12a + 32 ) + 20 = ( ka + 20 ) ( ka + 32 ) + 20 252+640+20=2+52 +560 - ka ( ka + 30 ) +22 (ka +30) 'ka' kA mAna Upara rakhate hue : (a +12 a + 22 ) ( a 2 + 12a + 30 ) isa prakAra guNanakhaNDa (a 2 + 12a + 22) aura ( a + 12a + 30 ) banate hai / athavA, donoM tarapha samAna mAtrA se guNA kI jA sakatI hai yA bhAga kI jA sakatI hai /

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karmazAlA parikalana/46 A 29-6 a+3 -7 a+3 | -3 | -7 | -3 | jjogeul a-4 a-3 kaI bAra eka hI prakAra ke padoM ko eka tarapha lAne ke lie sAIDa badalI jAtI hai| isa dazA meM sAIDa badalate samaya unake cihna bhI badala jAte haiN| udAharaNa : (i) 18-74+4 yA, 18-4 = 74 (4 kA cihna badala jAtA hai) ____yA, a-14 ... a =2 (i) 17a-3-12+2a yA, 17a- 24--12+3 yA, 158-15 yA a-1 (iii) 3(15a-2) = 13a+-10.5 yA, 45-6-12a+10.5 yA, 45a-12a-10.5+6 yA, 332-16.5 : a-0.5 2 guNA karane para 4-5-20 donoM tarapha 20 a +20.9 - 2x20 yA 5a+ 4a--40 (v) a -5 yA, a-5(a-4) yA, a= 5a-20 a-40 yA, 20-4a .:. a =5 (vi) 2a-214 yA V2-17 a =7 donoM tarapha vargamUla lene para .:. a-17 -2 828 yugapata samIkaraNa: 40Kg 50Kg 140*5)Kg SOKS SOKg VIIIIIIIIIIIIIIM -xm---- - m-Im tarAja kI santuSTi ke liye hama do samIkaraNa citroM dvArA banA sakate hai| 40-50ba......(i) (40+5)a-50(ba+ )....... .....(ii) aba ke mAna donoM samIkaraNoM ko sAtha-sAtha santuSTa karate hai, jina samIkaraNoM meM do yA do se adhika ajJAta rAziyAM hoM use yugapata samIkaraNa kahate hai|

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karmazAlA parikalana/47 hala do samIkaraNoM kA do ajJAta ke sAtha : 1. jor3ane dvArA 2. ghaTAne dvArA 3. pratisthApana dvArA 4. tulanA dvArA jor3ane kI rIti dvArA vilopana udAharaNa-1 : jJAta karo a+ba-15.........(i) 3a-ba-21.........(ii) hala: samIkaraNa (1) aura (2) ko jor3ane para a+ba-15 3a-ba-21 a kI ye kImata samIkaraNa (ii) meM rakhe yA, agara samIkaraNa (i) meM isa se AsAna hai| 4. .. ba-36 a-9 9+va-15 yA, ba-15-9-6 ... hala a-9 ba-6 a kI kImata jJAta karane ke liye va kI kImata ko samIkaraNa (i) meM rkhe| ghaTAne kI rIti dvArA vilopana udAharaNa - 2 : jJAta karo a-ba-9......(i) a+3ba-1......(ii) donoM samIkaraNoM ko ghaTAne para (i) aura (ii) a-ba-9 a+3ba-1 .:.ba--2 a-ba-9 a-(-2)-9 a=9-27 -4ba=8 udAharaNa 3. diyA hai a+3ba =5 a-ba-3 8aba kI kImata nikAlane ke lie (a+ba2) grupa-4, 2 varSa, julAI 1970 varga karane para a+2aba+ 25...."(i) 82-23 ba+ba' =9...... (ii) 4aba -16 .:. aba-4 2(a+ba)-34 - ghaTAne para jor3ane para % 3D (i) aura (ii) .:. a+bara-17 8a ba (a+ba)-8x4x17-544

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karmazAlA parikalana/48 pratisthApana rIti dvArA vilopana udAharaNa 4. jJAta karo ba+7442...... (i) a -ba =8....... (ii) ba+7-42 .:. ba=42-7a ba kI yaha kImata samIkaraNa (ii) meM rakhane para a-(42+7a)-8 3a-42+7=8 10a-8+42-50 ___ a=5 ba kI kImata nikAlane ke lie a kI kImata samIkaraNa (ii) meM rakhate hae 3a-ba-8 yA, 15-8-ba yA, 3.5-va-8 yA, ba ? tulanA rIti dvArA vilopana udAharaNa 5. ka+4kha =21 3ka-kha 311 hala ka+4kha =21... ......(i) 3ka-kha-11........... (i) ka+4kha = 21 yA, ka = 21-4kha......."(iii) 3ka-va-11 yA, 3ka-11kha yA ka- 11+kha ......(iv) 3 kyoMki ka =ka, samIkaraNa (iii) aura (iv) ke dAhine tarapha ke maimbaroM ko barAbara karanA sambhava hai isa lie ajJAta 'ka' kA vilopana karate hue 11+kha "kha" kA mAna samIkaraNa (i) meM rakhane se 'ka' kA mAna nikalatA hai yA, 11+kha-63-12kha ka+4kha-21 yA, 13kha-63-11 = 52 yA, ka+4.4-21 yA, kha=4 yA, ka-21-16-5 3 -21-4kha 2 TS udAharaNa 6: a aura ba ko hala karo 8a-4ba =58 a ba -0.7 grupa, 5, 2 varSa., julAI 1971 84-4ba-58 .....(1) 3 + 5 = 0.7.....(i) samIkaraNa (ii) ko 10 se guNA karane para 5 a+- 2ba = 7......(iii) samIkaraNa (iii) ko 2 se guNA karane para aura jamA karane para

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karmazAlA parikalana/49 72 8a-4ba-58 10a+4ba-14 18a -72- yA, a- a kA mAna samIkaraNa (ii) meM rakhane para 4 ++ -0.7 yA, bu +0.7-2- --1.3 yA, Y = -6.5 dvighAta samIkaraNa (Quadratic Equations): yaha vaha samIkaraNa hai jimameM adhika se adhika ajJAta ghAta do hotA hai dvighAta samIkaraNa dvArA vargamUla nikAlA jAtA hai jaba ki mUla vyaMjaka kisI samIkaraNa ko nikAlane ke lie upayoga kiye jAte hai dvighAta samIkaraNa hala karane ke DhaMga : udAharaNa 1. zuddha dvighAta samIkaraNa :-- udAharaNa : a2-3 yA aE/3 a-1.73 yA, -1.73 aura mUla hai a = +1.73, -1.73. 2. guNanakhaNDa dvArA hala :udAharaNa-1 : a-4a, a2-4aD0, a (a-4)-0 yahAM para do guNanakhaNDoM kI guNA jIro hai, eka guNanakhaNDa yA donoM guNanakhaNDa jIro hai agara donoM jIro haiM taba a- 0, aura (a-4) 30, yA, a%3D4 isa prakAra a%30 a -4 2. 32+25-5 guNanakhaNDa ke dvArA (3ka+5) (ka-1)=0 taba 3ka+5-0, 32- -5, ka- - yA, ka-1-0, ka=1 isa prakAra ka = -3, 1 do mUla hai 3. varga karane para hala : udAharaNa-1 : ka-62-220 yA, ka-6 -2 yA, ka-6ka+9-2+9%3D11 yA, ka2-2 3. ka+ (3)2 = 11 yA, (ka-3)-11 isalie ka-3-t/il, ka=3+/11

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2. ta2 + ta 0 yA ta+ta+- M yA (+) 2 (9) 8 = yA ta+-+8 yA, ta-1+1-0 isalie 1-0 ta 4. dvighAta sUtra dvArA hala : udAharaNa : ka a 2 + kha a + ga = 0 isa samIkaraNa dvArA prAya: dvighAta samIkaraNa ko isa prakAra darzAyA jAtA hai| yA, yA, a kA mAna nimnalikhita DhaMga se nikAla sakate haiM : ka a 2 + khaa + ga 0 ka a + kha a = vA thA, yA a a+ taba 372+ a + a + a kha ---- 2 ka a (:-)-3+2 ka 42 vargamUla nikAlate hue kha kha a = B 2.ka 2 ka 2 + ga ka kha - 4ka ga 4 ka Vkha 24 kaga 8 ka Vkha 2 4ka ga kha+ V24ka ga 2 ka isa sUtra kI sahAyatA hama dvighAta samIkaraNa (Quadrtic Equations) nikAla sakate hai / yAta ------- 35 + 10 yahAM ka = 3, kha- 5, ga = 1 5deg/13 6 karmazAlA parikalana / 50 2 ka 5+25-12 6 = _ _ (-5) deg V (- S) 24.3.1 2.3 5

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karmazAlA parikalana/51 samIkaraNoM dvArA banAvaTa, praznoM kA hala aura epalIkezana udAharaNa 1. - - (ka) kula lambAI ke lie sAmAnya sUtra jJAta karo (kha) ajJAta karo jaba la-750 mi0mI0 (ka) la=a+3 ka+kha+ga+a -2a+3ka+kha+ga (kha) ka kA mAna rakhate hae 360 kha- 120, ga-400 aura la-750 samIkaraNa meM rakhate hue hameM prApta hotA hai 750-2+3.60+120+400 ___=2a+180+120+400 yA, 29 350 .. a=25 udAharaNa 2. opana bailTa jo ki barAbara pulisa para daur3a rahI hai ki lambAI la dI gaI hai - va+2ga, jahAM va-pulI vyAsa, ga-pulI sa ko madhya dUrI ga ke lie sUtra batAo jaba ki la-136 sai0mI0 aura va-8.5 sai0mo0 la- va+2ga yA 2ga-la-va ... ga= la-pava la aura va kA mAna Upara ke mUtra meM rakhate hue . 136-3 14x8.5 :- (ga kA mAna rakhate hue 2 __ 136-26.7 3.14) - 2 -54.65 sai0mI0 udAharaNa 3. jaba diye hue varga kI pratyeka bhujA 4 saM0mI0 hai to usa kA kSetraphala 64 sai0mI0 bar3ha jAegA pahale varga kA / mApa jJAta kiijie| agara a varga kI bhujA hai isakA kSetraphala a diyA gayA hai : aba mAnA a-diye gaye varga kI bhujA taba a+4 naye varga kI bhujA nayA kSetraphala -purAnA kSetraphala+ 64 a+4)2-a2+64 yA, a2+8 +16=2+64 yA, 8a =48 .:. a-6 sai0mI0 udAharaNa 4 vITa sTona brija dvArA vidyuta pratirodha mApane ke lie, 3 jJAta pratirodha ajJAta pratirodha ke sAtha joDane ke lie prayoga kie gae haiM ajJAta pratirodha meM se nar, aura jaisA ki citra meM dikhAye gae hai 3 jJAta pratirodhoM + 11 anukUla banAne ke lie lagAye gae hai isa sUtra se ajJAta pratirodha jJAta kro|

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karmazAlA parikalana/52 (i) diyA hai, 7-50 oham, ra.-300 oham rA-125 oham 20 jJAta kro| ra -1 500 300 125 yA 300 ra3-500x125 500X1256 .. 0-300 --208 oham ba-baiTarI udAharaNa-5 : ___ AghUrNa (moment) : DijAina ke praznoM me AghUrNa kA sUtra, jo bala bIma para laga rahe hoM unakI dazA jJAta karane ke lie yA bala kA bhAra jJAta karane ke lie upayogI hai| isa niyama kI isa prakAra vyAkhyA kI jAtI hai / ApUrNa kA joDa baloM ke sisTama ke girda baileMsa meM zUnya hogaa| sUtra isa prakAra likhA jAtA hai 2m = 0, jabaki 2 jor3a ko darzAtA hai aura m AghUrNa ko darzAtA hai / baloM kA sisTama nIce citra meM dikhAyA hai tathA varNita kiyA gayA hai / aura AghUrNa ke sUtra ko udAharaNa ke taura para dikhAyA gayA hai Upara citra meM bIma ke donoM ora do bala lagAye gaye haiN| bIma phalakrama pha para bailensa kI huI hai| bala ga phalakrama se ma mi0 mI0 kI dUrI para hai : aura bala na phalakrama me ba mi. mI. kI dUrI para hai / dUrI a aura ba ko AghUrNa kI bhujAyeM kArA jAtA hai / kyoMki yaha praNAlI vaileMsa meM hai, 2m=0 eka bIma kI lambAI 10 sai0mI0 hai usake eka sire para 1000 ki0grA0 kA bhAra lagA huA hai aura dUsare sire ra 250 ki. grAma kA bhAra lagA haA hai (jaisA ki nIce citra meM diyA hai)| phalakrama ko kahAM rakhA jAye ki bIma baileMsa ho naaye| (bIma ke bhAra ko na lete hue) 1000 Kg 250Kg la : kRpayA citra dekheN| adhArNa (moment = 0 a(1,000)-250(10-a)-0 1000-2500+250 a-0 1250 -2500 =2 seMTImITara, 1000 kigrA bhAra se

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karmazAlA parikalana/53 abhyAsa 1. nimnalikhita ke guNana khaNDa banAyeM / (ka) 4902-16kha uttara : (7ka+4kha) (7ka-4kha) (kha) a-(ba-sa) uttara :(a+ba+sa) (a-ba-sa) (ga) a6-6 uttara - (a+ba)(a2-a ba+ba) (a-ba) (a+aba+ba) ___ aba uttara : (a + ba)(a+ ba)(a+ba) (Ga) 22+ka-6 uttara : (ka+2)(2ka-3) (ca) 4kha2-3kha-10 uttara : (4kha+ 5)(kha-2) (cha) 42. 2a ba-6ka a .. 3ka ba uttara .(2a+ba) (2a-3ka) (apraiTisa parIkSA grupa 3, sitambara, 1973) (ja) 8a +2:ba uttara : (2a+ 3ba)(49-6a ba+9ba) (jha) (ka+5ka) (ka+5+7)+12 uttara : (ka+1)(ka+4)(ka+5+3) (Ja) a-2-6a ka + 2ba ka+82 uttara : (a+ba-4ka)(a-ba-2ka) 2. mAna jJAta kreN| (ka) ka-+ jabaki ka-1-6 uttara : 38 (kha) a + 1jabaki a---- (ga) (ka-kha) jaba ki ka+kha = 5 tathA ka kha - -14 uttara : 81 uttara : 14 3. nimna likhita samIkaraNoM ko hala kIjie / (ka) 2a = a+6 uttara : a = -12 (kha) 542-6va uttara : va=0, 6/5 a+a =12 uttara : a-3-4 a2-a-20-0 uttara : a--4,5 332+4a =4 uttara : a-.-2 (ca, 292-5a -3 uttara : a-3, 4a= 4+11 uttara : a =t/3 a+8-4 uttara : a-2+1-1 (jha) 6a = 12+a uttara : a-, (Ja) 8a+3 = 4a uttara : a= __-3+121-1 uttara : ma-4 4, nimnalikhita samIkaraNoM se aba kA mAna jJAta kre| (ka) 6a-12ba-1 uttara : a } ba-3 8a+9ba=18 grupa 4, 2 varSa julAI, 1972

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(kha) 3a + 4ba 29 7a + 336 ! saMketa : (ga) (4) 38+28-8 (gha) 2a - ba 3 2ka kha 5ka + 4kha - 12 (ca) 2a - ba - 4 a + ba= 5 (cha) 5ba + 2-3 a- 3ba+ 2 a- ba 6 (na) (ja) 2a + 3ba = 3 2a + 3ba 1 (jha) 5 ba = 3 - 1 a 3 a = 3ba + 1 (1) 6 ba 6 a -1 (2) 37-2 3 a+3 4 + ba+1 6 (pa) (pha) 34 + 2Rs = 7 la+kha - 24-7-34 2ba - 1 2 aba 2 ka 2+5 ka a+2 ba +1 2 =1 karmazAlA parikalana / 54 bhinna uttara : a = 3, ba= 5 a 1 2+2 -3/5 a ko hala karate hue a-2, ba7 aura bhinna uttara : ka = 0, kha - 3 grupa 4 2 varSa prArambhika julAI, 1972 uttara : a = 2, uttara : a - 8, grupa 11 uttara : a = 3, unara : a mAnA a = aMza ba = hara ba - 1/2 yA 2a - = -3 ba - 1 grupa 5, 2 varSa prArambhika julAI, 1968 uttara : a- 1, a hai, ba uttara: ava uttara : a. 5. do rAziyoM kA jor3a 28 hai aura una kA antara 12 hai| rAziyAM jJAta karo uttara : 6. yadi kisI bhinna kA aMta 2 bar3he aura hara eka bar3e to jo bhinna banatI hai vaha 1/2 ke barAbara aMza 1 bar3hA diyA jAe aura hara 2 ghaTA diyA jAye aura jo bhinna banatI hai 3/5 ke jJAta karo / uttara : ba- 2 varSa prArambhika, julAI, 1972 ba - 2 ba- 1 59 x-1,-17 ba 9 uttara : a 17 ka 175.0-5 ba uttara : yala+kha, ra* 2la - kha yA 5 a - 3 ba 5 a - 3ba 11 = ka 20,8 hotI hai| yadi phira bhI barAbara hotI hai| bhinna

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karmazAlA parikalana/55 (7) do varSa pahale eka vyakti kI Ayu apane beTe se chaH guNI thii| 18 varSoM meM usakI Ayu apane beTe se doguNI ho jAnI caahie| unakI vartamAna Ayu jJAta kro| uttara : vyakti 32, beTA 7 (8) eka die hue mizraNa meM 20% tAMbA aura 50% Tina hai| kitane kilogrAma tAMbA aura Tina pighalA kara usa 100 kilogrAma die hae mizraNa meM DAleM ki anya mizraNa vizleSaNa meM 30% tAMvA aura 10 pratizata Tina ? sabhI pratizata bhAra dvArA haiN| uttara : tAmbA=17.500 ki0mA0 Tina = 7.500 ki0 grA0 9. miliMga mazIna : a tathA ba para bala kA mAna jJAta kro| uttara : a-245.61 ki0 grA0 ba=154.39 ki.grA. L-20 - - TF-400Kg -398 -220 16.50Kg 10. pampa asambalI: a aura ba para vala kA mAna jJAna kro| uttara : a-586.53 ki0grA0 ba=363.47 ki0grA0 | + wIF Kgn - c ommaranemamaamanand F10200kg VA_mMA 11. biyariMga : a aura ba para bala kA mAna jJAta kro| uttara : a-4606.451 ki0grA0 ba=5593.549 ki.grA. -10-----20 musmanna..MRA 12. jaba gola char3a ko miliMga mazIna para samatala kara rahe hoM to siddha kro| 2ra U-la- +U isalie U kA mAna jJAta kareM jabaki ra%2.4 sai0mI0, la-30.9 sai0mI0 uttara : .042 sai0mI0 saMketa : pahale bhAga ke lie pAI thA gorasa thiyorima AraTIkala 33, peja 74, vAlI lagAyeM ra aura la ke isa mAna ko rakhakara dvighAta samIkaraNa hala kro| hala karate samaya peja 56 kA sUtra lgaayeN| Heamin

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karmazAlA parikalana/56 - - - - adhyAya 9 laghuguNaka aura laghuguNaka sAraNI ke lAbha laghugaNaka eka ghAtAMka hai : kyoMki laghuguNaka eka ghAtAMka hai, kucha saMkhyAeM ghAtAMka ho sakate haiM jo ki AdhAra kahalAte hai, koI bhI sakhyA jo ki AdhAra ke lie prayoga kI jAtI hai parantu adhikatara laghuguNaka kI sAraNI 10 kI saMkhyA ko AdhAra mAnakara banAI jAtI hai (ghAtAMka, ghAta aura AdhAra pahale se hI adhyAya 3 ke peja 22 meM varNana kiye gae hai) 1000 saMkhyA rakho. 1000 isa prakAra pradarzita kiyA jAtA hai =103 yahAM 10=AdhAra 3-ghAtAMka 1000-saMkhyA ::: 3 paribhASA mAnakara Upara ladhuguNaka kI saMkhyA 1000 hai jo ki AdhAra 10 se lI gaI hai aura likhI jAtI hai lAga 1000-- 3. prAyaH AdhAra 10 ko haTAyA jAtA hai aura sAdhAraNatayaH aise likhA jAtA hai lAga 1000-3. laghuguNaka : pratyeka laghuguNaka kI saMkhyA do bhAga meM banA hai mamyA laghugaNaka 453 3.6561 rekTarasTika (pUrNa bhAga) maiTIsA (dazamalava bhAga) 1. pUrNa bhAga-raikTarasTika kahA jAtA hai jo ki (a) jamA hogI agara saMkhyA eka se adhika hogii| (ba) ghaTA hogI agara sakhyA eka se kama hogii| | 2. dazamalava bhAga-mainTIsA kahA jAtA hai laghugaNaka sAraNI kevala maiMTIsA batAtI hai| mainTIsA hamezA hareka saMkhyA ke lie jamA hotA hai raikTarasTika kI saMkhyA eka se jyAdA hotI hai| akSara kI saMkhyA dazamalava bindu ke bAMI ora se ghaTA eka (---1) hai kraikTarasTika jamA hai

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karmazAlA parikalana / 57 karaikTarisTika eka vaha saMkhyA hai jo ikAI se kama hai / dazamalava se dAMI aura saMkhyAyoM kI mAtrA zUnya hone para +1 bana jAtA hai / karaikTarisTika RNAtmaka ho to usako abhyAsa - 1.6561 ko aise likheMge dvArA likhate hai. 1.6561 karaikTarisTika dazamala bindu ke bAMI aura vartamAna digits meM eka kama ho jAtA hai| isa taraha laghuguNaka hai 4530 kA 3.6561 453 kA 26561 45.30 T1.6561 4530 kA 0.6561 0.4530 kA 16561 0.0453 kA 2.5561] 0.00453 T 3.6561 (561) aura ityAdi ityAdi ! laghuguNaka sAraNI : kisI saMkhyA kA laghuguNaka dekhane ke liye hameM usase sambandhita cAra dazAoM kA adhyana karanA par3atA hai jo isa prakAra hai / isI prakAra enTIlAga bAra bindu eka dazamalava se dAI aura zUnya kI saMkhyA +1 hotI hai 3.6561 kA 4530 2.6561 kA 453 1.6561 kA 45.30 0.6561 kA 4.530. 1.6561 kA 0.4530 2.6561 kA 0.0453 3.6561 kA 0.00453J aura antara jor3ane para - 9 karaikTarisTika dazamalava se bAMI aura ko saMkhyA se eka jyAdA abhyAsa 1: jJAta karo lAga 3768 sabase pahale 37 saMkhyA vAlI sAraNI meM dekho taba sAraNI meM 6 ke nIce dekho tAki lAga kA menTIsA 37605752 ho / lAga kA menTosA diyA jAtA hai| sAraNI ke antima sire para eka kaoNlama banA honA cAhie jisase antara kA patA calatA hai isa prakAra AkRti 8 ke nIce dekhane para 9 milegaa| jisako kI pahale prApta menTIsA meM jor3a denA hogaa| isa vidhi ko inTarapolaieena kahate hai| isa prakAra lAga 376 = 5752 ho jAtA ho / vAra dazamalava bindu eka zUnya kama hotI hai jitane kisI saMkhyA kA viparIta laghuguNaka dekhanA yA usa kA eNTIlAga dekhanA kI dazamalava bindu ke bAda bAra ke nIce jo maMkhyA hotI hai usame / agara diyA gayA laghuguNaka 2.4725 to 02968, ityAdi saMkhyA cAhie aMka gaNita Aparezana jisameM laghuguNaka AMkalana meM hai ax b kI guNA jamA meM badala jAtI hai| ataH lAga 37683.5761 aura bhI 0.003768- 3.5761 lAga 0.3768-1.5761 ityAdi 3768-5761 abhyAsa 2 lAga 2.4725 diyA hai saMkhyA jJAta karo / menTIsA ke viparIta eNTIlAga kI sAraNI se 472 hamAre pAsa 2967, antara kaoNlama 5 ke nIce aura horIjenTala rekhA meM 47 hamAre pAsa 3 AtA hai isa prakAra menTIsA 295532968, aura saMkhyA 296.8 A jAtI hai / - gahana

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karmazAlA parikalana/58 lAga (axb)= lAga a+lAga b 1-menTIsA, 2314 udAharaNa : lAga 49.1-1.6911 .231 :.491x347 +lAga 3.47-05403 2.2314 :- 1702 1704 49.1x3.47-170.38 49.1x3.47=170.4 ab kI bhAga ghaTA meM badala jAtI hai 1-menTIsA .8492, eNTI lAga sAraNI meM dekhakara | lAga ( ab)= lAga a-lAga b. udAharaNa : lAga 3.47--0.5403 .849 :3.47:49.1 -lAga 49.1 - 1.691 / 2.8492 - antara ke kAlama me 3 lekara 7063 :- 3 7066 3.47:49.1 = 0.07066 yahAM para 28492 karaikTarisTika 2 hai| isalie dazamalava bindU bAra ke nIce jo 7066 likhA huA hai, .07066 likhA jAyegA an kimI saMkhyA kI zakti ko bar3hAne se saMkhyA jamA meM badala jAyegI lAga an -n lAga a |--menTIsA .6123 enTolAga sAraNI meM dekhakara .612 : antara ke kAlama se 3 lekara - 4093 udAharaNa 168 lAga 16-1.2041 3. log 16-3.6123 4096 163 =4096 yahAM para 3 6123 kI karaikTarisTika 3 hai, isalie dazamalava bindu 4 sthAna ke bAda lagegA 4096 nv kisI maMkhyA ke mUla ko nikAlane se bhAga badala jAtI hai| |-menTIsA 7205 lAga sAraNI lAe nva --lAga a meM dekhakara .720 :- 5248 - udAharaNa : lAga 145-2.1614 antara ke kAlama 5se lekara 6 3/145lAga 145-0.72047 n 5254 31145 -5.2534 yahAM karaikTarisTika vazamalava bindu se Arambha hotI hai isa lie dazamalava bindu eka sthAna ke bAda lgegaa| udAharaNa hala : mAna jJAta karo-1. 2563x1.861x0.155 . laghugaNaka kI sahAyatA se 18.75

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UparI paMkti saMkhyA 1625 3.142 jamA karane para 2. laghuguNaka kI sahAyatA se mAna jJAna karI : ghaTAne para .0643 saMkhyA (ba) 10.762 saMpA - 0 762 2563 1,861 0.155 jamA karane para karmazAlA parikalana / 59 18.75 ghaTAne para lAga 3. laghuguNaka dvArA jJAta karo (a) 100643 (a) V0.0643 (0.0643)+ saMkhyA lAga 0 2108 0 4972 0.7080 1.8883 28197 1 2.8082 (0.762) lAga lAga I 8820 3.4087 0.2697 1.1903 2.8687 1.2750 1.5957 J 1.625 x 3.142 1.713x9-561 4 722 'o nicalI paMkti saMkhyA 1.713 9 561 4.722 jamA karane para - eMTIlAga (ba) 10.762 lAga isalie pariNAma = 39.42 0.2337 0.9805 0.6741 eMTIlAga6603 1 8883 isalie pariNAma - 0.06603 2 para bhAga kiyA gayA 1.4041 (dekhie peja 65, aMkagaNita Aparezana jisame ki laghuguNaka diyA huA hai) eMTIlAga kA 40.41- 2536 isalie pariNAma =.2536 --3942 ##

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2. abhyAsa 1. nimnalikhita kA mAna nikAlo : likha sakate haiM : jJAta karo 2+1,8820 eMTIlAga kA 9410-8730 2 para bhAga kiyA gayA hai 1.9410 isalie pariNAma - 8730 (a) 2.6153-2 1437+3.8613 (a) 4.5622-2624+2 9143 uttara 3,2141 ( sa ) ( lAga 752 + lAga 16.37 ) - ( lAga 375 + lAga 24 25 ) uttara : 3.1415 (ra) lAga 1000 - ( lAga 37.32+ loga 6.752 ) + lAga 0.0065 uttara: 2.4116 3x T.3010 ()(2 5771-3.1637) uttara 3.9030 (a) 3 (2.4771+2.1152-T.6521) ()(T.6286-1.8123) (ba) 3. laghuguNaka dvArA mAna nikAlo (ar) 23.8 x 3.029 0.0129 x 35,27 karmazAlA parikalana / 60 8.28 x 34.68 x 0.216 87.39 X 2.013 uttara : 4.3329 () (3.567) (.029) hai (*) (-659) +22 (la) / 10.32.785 grupa 5 julAI 68. uttara : 1.7769 uttara : 2.7067 uttara : 2.9082 uttara : 1595. grUpa. 9 sitambara 68. uttara : 0.3527 uttara : 4.473. uttara : 1.2104 uttara : 1.57.

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maulika paribhASAeM : 1. bindu (ca) rekhA (ga) sIdhI rekhA (ca) vakra rekhA (ca) TUTI rekhA (cha) samAntara rekhA 8 90deg .C ( 90deg A. A A. B A - C B pd - B -D karmazAlA parikalana | 61 adhyAya 9 jyAmitI koNa :- jaba do sIdhI rekhAe~ kisI dizA meM eka sAtha jhukI ho / jisa kI koI lambAI, caur3AI, UMcAI na ho / do binduoM ko milAne vAlI rekhA jisakI lambAI ho / cor3AI nahIM eka aisI rekhA jo samAna dizA meM lambAI kI tarapha se bar3hatI hai / eka rekhA jo lagAtAra apanA dizA badalatI rahe / jaba kaI sIdhI rekhAeM eka sIrIja meM jur3I ho / samAntara rekhAeM ve rekhAeM hotI haiM joki eka sIdhI sAmane kI tarapha hotI haiN| jaisA ki a usako aise likheMge aba || sa ya eka koNa kI pahacAna aise kI jAtI hai jaise kI pahacAna ke liye yaha cihna prayoga kiyA jAtA hai| 2. koNa aura rekhA kI vizeSatAeM 2.1 samakoNa, adhika koNa aura nyUna koNa dUsare se samAna dUrI para ba sa ya ke samAntara hai 1 avasa yA 8ba yA 0 kimI koNa

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karmazAlA parikalana/62 samakoNa taba hotA hai jaba eka rekhA Obfuse angle dUsarI rekhA para lamba ho Aurange 2sa baya-1800 =ga reDIyana adhika koNa 900 se bar3A hotA hai| nyUna koNa 900 se choTA hotA hai| a+8 =1800- reDIyana .:. 1800-8 2. kATatI huI sIdhI rekhAeM agara do sIdhI rekhAeM Apasa meM eka dUsare ko kATeM to cAra koNa banate hai jinakA jor3a 360deg ke barAbara hotA hai| aura viparIta koNa barAbara hote hai ___ do sIdhI rekhA a ba aura sa ya eka dUsare ko kATa rahI hai ___a+8+0+0-360deg -2 reDIyana aura a-0,P= 2.3 sIdhI rekhAeM do samAntara rekhAoM ko kATatI haiN| ra la do samAntara rekhAoM aba aura sa ya ko kATatI haiN| koNa eka dUsare ke barAbara hai aura isI prakAra koNa B bhI barAbara hai| 3. tribhuja kI vizeSatAeM: 3.1 tribhujeM :-tIna bhujAoM vAlI AkRti ko tribhuja kahate hai aura isakA cihna A hai| tribhuja ke tIno koNoM kA jor3a 180deg hotA hai| Upara diye gaye 2.38-e 8-0 parantu + +e-180deg :: +8+7-180deg viSamabAhu tribhuja, samadvibAhu tribhuja, samakoNIya tribhuja aura samakoNa tribhuja viSamabAhu tribhuja :-jisa tribhuja kI tInoM bhujAeM aura . tInoM koNa asamAna hoN| aba #ba sa#sa a Za+/ba#Lsa samadvibAhu tribhuja :-jisakI do bhujAeM aura do koNa barAbara hote haiN| aba-asa 2ba = Lsa samakoNIya tribhuja :-jisa tribhuja kI tInoM bhujAeM aura tInoM koNa barAbara hote haiN| aba-ba sa-sa a -a- ba-2sa

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karmazAlA parikalana/63 samakoNa tribhuja Lba=90deg so A Base B / 3.3 prameya paribhASA :-samatribhuja meM, AdhAra para banA varga tribhuja kI anya bhujAoM para bane vargoM ke / jor3a ke barAbara hotA hai| asa2 = aba+basa yAni kSetra a sa ya za-kSatra a ba na ma+kSetraphala va sa ra la / / 3.4 bAharI koNa -(a+P) do bhItarI koNoM kA jor3a 3.5 samAna tribhujoM kI vizepatAeM : jaba do tribhujeM AdhAra meM eka jaisI hoM lekina nApa alaga-2 hoM to ve samAna hotI hai| A a ba sa aura A a sa la samAna haiN| samAna tribhujoM meM aba- aba aba aya asa ala | 4. Ayata, varga, samAntara cartubhuja aura rombasa kI vizeSatAeM : ( 4.1 Ayata cAra bhujAoM vAlI aisI AkRti hai jisa ke sabhI koNa 90deg ke hote hai| 0 42 vaha Ayata jisa kI sabhI bhujAeM barAbara hoM to usa ko varga kahA jAtA hai| 0 4.3 samAntara cartubhuja cAra bhujAoM vAlI aisI AkRti hai jisa kI viparIta bhujAeM samAntara hotI haiM aba sa ya eka samAntara cartubhuja a ba || ya sa aura aya // basa rekhA asa aura ya ba do vikarNa haiN| + - - - - / 0

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karmazAlA parikalana/64 4.4 vaha samAntara cartubhuja jisa kI cAroM bhujAeM barAbara hoM rombasa kahalAtI hai / rombasa meM ya la-ya ba 4.5 samalamba cartubhuja cAra bhujAoM vAlI eka aisI AkRti hai jisameM do viparIta bhajAeM samAntara hotI haiM a ba sa ya eka samalamba cartubhuja hai aba // ya sahotA hai| 4.6 kisI bhI AkRti meM cAra bhujAoM ke bAharI koNoM kA jor3a 360deghotA hai| a+B+l+V= 360 5. vRta kI vizeSatAeM 5.1 vRta binduoM kA eka vaha samaha hai jo ki eka sthira bindu jise kendra kahate haiM se samAna dUrI para sthita hotI hai| -cApa vRta ke mahatvapUrNa bhAga sAtha vAlI AkRti meM batAye gaye haiN| SE. segamenTa jIyA - saMkTara vyAsa khiy| 52 5.2 jaba eka trijyA kisI jIvA ko samakoNa para kATatI hai yaha jIvA ko samadvibhAjita karatI hai aura jIvA koNa do bhAgoM meM parivartita ho jAtI hai vijyA pasa jIvA a ba samakoNa ya para samadvibhAjita karatI hai| 4k 5.3 (ka) vRta kA TenajenTa trijyA para lamba hai| aba TenajenTa vRta ko ba para chUtA hai aura paba eka trijyA hai| Lpaba a-90deg (kha) vRta meM do TenajenTa eka hI bindu se khIMcanA / (i) samAna hai a ba a sa (ii) rekhA apa se samAna koNa banAo, koNa a barAbara hai aura (iii) A paba a aura A pa sa a sabhI dazAoM meM Apasa meM milatI hai| 6. samabAhu bAhubhuja : bahabhuja eka aisI AkRti hai jo ki 4 yA jyAdA sarala rekhAoM se ghirI ho| yadi isakI sabhI bhajAeM tathA koNa barAbara hoM to ise regulara kahate haiM /

Page #73
karmazAlA parikalana/65 cAra bhujAoM vAlI bahubhuja ko caturbhuja kahate hai| pAMca bhujAoM vAlI bahubhuja ko paMcabhuja kahate haiM / , " " , SaTabhuja , , sAta " saptabhuja , aSTabhuja nau , , , , nau bhuja , , dasa , , , , dasabhuja , , gyAraha ,, ,, , gyArahabhuja , , bAraha , , , , bArahabhuja , , ATha yaha sApha hai ki samabAhu bahubhuja kA madhya bindu donoM vRtoM kA bhI madhya bindu hogA jo ki bahubhuja ke bAhara tathA andara lagAe jAte hai| yaha bhI sApha hai ki samabAhu bahubhuja ke madhya bindu se bhujA taka girAyA gayA lamba, adara lagAe gae vrata kI trijyA hai tathA bahubhuja ke madhya vindu tathA kone vAle bindu ko milAne vAlI sarala rekhA, bAhara lagAe gae vata kI trijyA hai| ka la, vRta ya ra la kI trijyA hai tathA ka a, vata aba sa kI trijyA hai| AB aSTa bhuja paMca bhuja udAharaNa 1. mApa ya ke lie, ra tathA va ke rUpa me samIkaraNa banAo (citra dekhie)| ya kA mAna jJAta kIjie jabaki ra-6.25 sai0 mI0 tathA va-1.00 sai0 mI0 citra meM, Lsa-90deg h O PLUG DIA KE PUG DIA aba-ra+ basa- ya-va saa =ra sa a =ra dvArA 3.3, basa+sa a2-aba (pa-) + ( 2-6.) -(ra+4) -

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karmazAlA parikalana/66 -50deg F (ya-va)+ (2ra-va) = (2ra-va)2 ya2-2ya va+va+4ra2-4ra va+va-42+4ra va+va (ya - ba)=8 rava ya-- -18ra va -2.828/ra va .: ya-2.828/ra va -va samIkaraNa hai ra-6.25 sai0 mI0 tathA va-1 sai0 mI0 kI kImata Upara likhe samIkaraNa meM rakhane se ___ya-2.82x16.25X1-1 -8.070 sai0 mI0 uttara citra meM dikhAye gaye kampAUMDa vI blAka meM koNa jJAta kIjiye -120 nimnalikhita banAie :ra ya lamba khIMco ba sa para la ra lamba khIMco ya ra para para ko ka taka bar3hAo ::.va ra ya--1 (50deg)-25deg Lya ra la-90deg, tribhuja ka phapa ko [pha ka pa-60deg, Lpa pha ka-90deg ::.[pha pa ka-30deg .:. pa ra la == 30deg aba L-[pa ra la+Lla ra ya+va ra ya -300+ 90deg+ 250 -1450 uttara 3. aba sa da ja eka blaoNka hai jaisA ki citra meM dikhAyA gayA hai| madhya rekhA ya ra para eka chidra karanA hai tAki ya ra, koNa ja a ba ko barAbara hisse meM bAMTatA hai| koNa e jJAta kiijie| dvArA 2.3 peja 73 se Lpha aba-70deg Lja apha-40deg .:.ja aba-1100 Lra aba-55deg (ya ra, [ja a ba ko barAbara hissoM meM kATatA hai) e-Lpha a ba-ra aba --70deg-55deg-15deg uttara 4. eka SaTbhuja peca, mITrika 16, ke do bhujAoM meM adhikatama dUrI 24 mi.mI. hai| isa prakAra kA eka peca banAne ke lie kisa vyAsa kI gola char3a caahie| (cina dekheM) 2011 Fig.II citra 1 citra 2 citra 3

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karmazAlA parikalana/67 hameM usa vRta kA mApa cAhie jo ki SaTbhuja ke sabhI konoM ko chue jisakI Amane sAmane kI bhujA 24 mi0mI0 dUrI para hoN| 2 citra meM dikhAI gaI tribhuja, gola char3a ke madhya bindu ko peMca ke konoM se milAne se banI huI tribhujoM meM se eka hai| ka char3a kA madhya bindu hai tathA kaba-char3a kI trijyA (dvArA 6, peja 76) ka sa ba eka samabAhu tribhuja hai tathA ka a use do barAbara 90deg-60deg-30deg nibhujoM me bAMTatA hai / ka a- Amane sAmane kI bhujA meM dUrI-2-12 mi0mI0 Upara diye gae citra 3 se, 900-600-30deg tribhuja kaba-03 aura ka ba-a ba-23 ka kaa-12 mi0mI0 kA mAna rakhane para, hame prApta hotA hai| - 12x224 kaba -13.85 V3 1.732 char3a kA vyAsa isase duganA hogA -2x13.85-27.7 mi0mI0 amaan eka zAphTa meM kI-ve kATanA hai jaisA ki citra meM dikhAyA gayA hai| kI-ve kI gaharAI va mAlama kIjie / citra meM s ka kha-ka a-25 asa-7 ka sa-ka a-a sa-25-7-18 va kha-4-8 (dvArA 5.2, pez2a 75) kaba-ka kha-bakhara -252-82 -561 ::. ka ba=1561 -23.68 va-ba sa=ka ba-ka sa 500 -23.68-18 5.68 mi0 mI0 uttara 6 eka vI-grUva (jhirI) jisakA kula koNa 90deg hai tathA Upara se 30 mi0 mI0 caur3A hai| yadi 20 mi0 mI. vyAsa vAlA plaMga grUva meM rakhA jAe to dUrI 3 jJAta kiijie| (cina dekhie) dvArA 5.3, peja 72 hama jAnate haiM (1) plaga kA madhya bindu vI ke koNa kI samadvIbhAjaka rekhA para rahatA hai yAni ki ka ba a-45deg (ka, plaga kA madhya bindu hai tathA a bindu vI se sAtha milane vAlA bindu hai|) (2) Lka aba-90deg yadi hama sa da khIMcate haiM taba sa da-1 (30mi. mI.) 80 -91 -20 -

Page #76
karmazAlA parikalana/68 sa da= da ba tathA da ba-15 mi0 mI0 450 samadvIbAha tribhuja ka a ba me :ka a- a ba plaga vyAsa-10 mi0 mI0 ka ba=ka a+ a ba102+102-200 kaba-/200-14.14 mi0 mI0 uttara yadi ka ba-14.14 taba plaga kA madhya bindu ka, vI blAka ke UparI hisse se 15 mi0mI0-14.14 mi0mI0-0.86 mi0 mI0 nIce hogaa| :.3=plaga kI trijyA-0.86 -10-0.86 =9.14 mi0mI0 uttara 7. citra meM phormiga paMca ko AkRti dikhAI gaI haiN| gaharAI va jJAta kro| samakoNa tribhuja a ba sa meM basa- (28.5-16)--12.5 mi0 mI0 a ba-(41-16) -25 mi0 mI0 asa-/252-12.52 --/625-156.25 -/468 75 -21.65 mi0 mI0 .:. sada-ada-a sa-41-21.65 =19.35 mi. mI0 uttara abhyAsa 1. nimna tribhujoM meM tIsare koNa kA mAna jJAta karo hodeg_ Kirti1025AM Ans.1050 Ans.400 uttara 105deg uttara 40deg uttara 107deg--34'-35" 12 cm citra meM dikhAI gaI samadvIbAhu tribhuja ke AdhAra kI lambAI jJAta kiijie| uttara : 15.872 sai0 mI0 9cm citra meM dikhAI gaI puliyoM a tathA ba meM dUrI jJAta kIjiye / uttara : 9.229 mITara --6m -7m . citra meM tIkhI V cUr3iyoM kA hissA dikhAyA gayA hai jo ki samabAhu tribhuja hai| yadi cUr3I kI gaharAI a barAbara 15 mi0 mI0 ho to pica pa jJAta kiijie| pa-a/3 uttara : 10/3

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5. sIr3hI kA eka konA bhUmi para dIvAra se 10 mITara ( eka hI plena meM) sIr3hI kI lambAI jJAta kIjie / 9. RAKE 10. 13R chenI kA koNa CLEARANCE 10 26R greNI kA mukAva 40 1677 1200 -26 karmazAlA parikalana / 69 41. dUra hai tathA dUsarA konA bhUmi se dIvAra para 15 mITara UMcA hai (grupa 1 1 varSa julAI, 1971) " uttara : 18.01 mITara miliga kI gaharAI 'ga' jJAta kIjie javaki 6. 1 8. 2 va 80 60 ba 40 28 uttara :- - 5.35 5.03 7. eka samatala cheNI se dhAtu ko kATane ke lie chaMNI kAma para 40deg jhukI huI hai / yadi kaTiMga reka, kalIyaresa se duganA ho to chaMNI kA koNa jJAta kIjie / uttara : 600 eka Tukar3A jisakA koNa 100 hai, ko mazIna ke meja ke sAtha bAMdhanA hai tathA a ba kI tarapha se kATanA hai| tAki koNa sa a ba 1620 kA ho jAe (citra dekheM) ki Tukar3e kI bhujA ko uttara : $ = 80 koNa jJAta kIjie jo bAMdhane ke lie jarUrI haiM / 9. eka 90deg vI blaka, bI ke UparI hisse se 26 mi0 mI0 caur3A hai| plaga kA vyAsa jJAta kIjie jo ki jaba vI meM DAlA jAe to usakA Upara kA dharAtala vI blAka ke UparI hissA eka sIdha me ho / uttara : 10.77 mi0mI0 vyAsa 10. citra meM dikhAye gae TaimpaleTa meM caur3AI ca jJAta kIjie / 14.34 mi0mI0 uttara :

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karmazAlA parikalana/70 adhyAya 10 mainasurezana 1. samatala AkRtiyAM : 1.1 tribhuja : kSetraphala -lambAI-caur3AI -aba 1.4 samAnAntara cartubhuja : (i) kSetraphala = AdhAra X UMcAI __ = x baX u = bau kSetraphala-AdhAra 4 UMcAI -aXu 1.5 viSamakoNa cartubhuja (ii) yadi ka-(a+ba+sa), taba kSetraphala = 1ka(ka-a) (ka-ba) (ka-sa) 1.2 varga : - D u kSetraphala=1x samAnAntara bhujAoM kA jor3a X una ke bIca kI dUrI-1 (a+ba) x u (TrapIjoiDa) 1.6 kSetraphala = bhujA- bhujA -ka-ka =ka Ayata: 1.3 b - a ----- - . (H+ha+bh+cH

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1.7 samabAhu bhuja kSetraphala bhujAoM kI saMkhyA 2 = samaSaTabhuja ke lie ya a 1.8 vRta na 2 ra- 0.866 ya kSetraphala - 2.598 = 3.464 2 kSetraphala - - T 4 X a x ra - (vyAsa) paridhI x vyAsa va 2 ra 1.9 butAkAra challA aMtaH vRta kI vijyA -*2-0.785 2 ra+- [ .. va= 2ra] 2 x bhujA X - 2.598 a kSetraphala = bar3e vRta kA kSetraphala - choTe vRtta kA kSetraphala karmazAlA parikalana / 71 kSetraphala T 1.11 vRttakhaNDa 4 77 = = 1.10 vRtta kA dvitrijyA sekTara -- (2--32) - S T S sekTara kA koNa 360 X mara 360 kSetraphala - 21/2 saikTara kI lambAI X trijyA = 1/2ya ra To 2 kSetraphala sekTara kA kSetraphalavibhuja kA kSetraphala ba 360 jabaki sa- 2ra sin tan (2 - 2) 2 - - 23 (2ra - u ) x= (farar) x 4 2 (ii) lagabhaga zuddha phArmUlA kSetraphala - sa u a 2

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karmazAlA parikalana/72 1.12 aNDAkRti (ilipsa) 1.13 phileTa kSetraphala - - para kSetraphala = " x bar3A akSa x choTA akSa - A a Thosa AkRtiyAM: 2.1 prijma 1- - -- AO Ayatana-AdhAra kA kSetraphala x UMcAI = a ba sa (yadi AdhAra Ayatana haiM / ) -asa (yadi AdhAra varga hai|) =a (yadi prijma ghana ho dhana meM lambAI, caur3AI tathA UMcAI sabhI barAvara hote haiN|) - - sa (yadi AdhAra tribhuja hai) (iv) (v) =bahubhuja kA kSetraphala X UMcAI (yadi AdhAra bahubhuja hai) * jaba hama kahate haiM ki eka prijma hai, usakA AdhAra nahIM batAte, to AdhAra ko trimuja mAnanA cAhie / - -A-2 8 Prism - a paraphesa kSetraphala kSe0 ku. =kula saraphesa kSetraphala

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karmazAlA parikalana/73 kSe0 ku. = 2kSe0 - +4 kSe0 - (vargAkAra AdhAra ke lie) =2kSe0 - +2 kSe0 = 1+2kSe0 = 2 (AyatAkAra AdhAra ke lie) prijma ke lie kSe0 ku | kula saraphesa kSetraphala --2 kSa. A + 3 kSe0 - (samabAhu tribhuja AdhAra ke lie) 2 kSe0 A + kSe0 -1+ - 2 +kSe0- 3 (viSamabhuja tribhuja AdhAra ke lie) A1 viSamabhuja tribhuja AdhAra vAlA prijma -A3 Ao kSe00Ayatana-kSetraphala XUMcAI kSe04 sa saraphesa kSetraphala = va sa 2.3 pirAmiDa - - - ". 1 111/ HIXI/ VIIILLIUNT - ~ AyatAkAra AdhAra tribhujAkAra AdhAra Ayatana = 1 (AdhAra kA kSetraphala) x UMcAI asa (yadi AdhAra vargAkAra hai) =aba sa (yadi AdhAra AyatAkAra hai) -aba su aba sa (yadi AdhAra tribhujAkAra hai) - - -

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karmazAlA parikalana/74 saraphesa kSetraphala kSe0 ku0 = kSe0 + 4 kSe0 A (vargAkAra AdhAra ke lie) = kSe0 + 2 kSe0 A1 + 2 kSe0 A. (tribhujAkAra AdhAra ke lie) -A + 3 kSe0 A. (samabAhu tribhujAkAra AdhAra ke lie) 2.4 zaMku : - D kSe0 0.sa Ayatana gavaTa.sa 3 gavasa 12 3 saraphesa kSetraphala kSenu- va (va+2ra) triryaka pRSTha = gavara 2.5 pirAmiDa kA chitraka (phrasTama) : Ayatana- (kSe0 2+ V kSe0kSe0, + kSe.) kSeta-kSetraphala AdhAra kA kSeta -Upara ke hisse kA kSetraphala saraphesa kSetraphala kSekazaMku kA chitraka phrasTama) :Ayatana = TM (A+ A a+ a) niryaka kSetraphalakSe.ni.-+ja jabaki ra-vsa* + (A.- a) saraphesa kSetraphala =kSe0 + kSe0+ kSetri0

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3 2.7 golA Ayatana = 3 6 saraphesa kA kSetraphala kSetra = "va ai ku0 yadi golA khAlI ho 4p 4p 73 3 3 Ayatana rA = bAharI saraphesa kI trijyA ra = andarUnI saraphesa kI trijyA 2.9 Torasa - ( rA ra 3 ) V - karmazAlA parikalana / 75 Ds mot * TT Ds 2.8 golAkAra khaNDa LR Ayatana = U ku0 52( saraphesa kSetraphala kSe0. yA = U = 2 ra U Ayatana = ( ba va saraphesa kSetraphala kSe0ku0 8 U 313533 gavagavA + 32) gavA padArtha kA bhAra : jaba hameM kisI Thosa kA Ayatana patA ho to hame isakA bhAra nikAlane ke lie isake Ayatana ko padArtha ke ekAMka Ayatana ke bhAra se guNA kiyA jAtA hai athavA ghanatva se Thosa kA bhAra = Ayatana X ekAMka Ayatana kA bhAra mITrika praNAlI meM prAya: ekAMka Ayatana ke bhAra ko bhAra/se0mI03 se likhA jAtA hai| bhinna-bhinna padArthoM kA bhAra se0mI0 pariziSTa peja para diyA huA hai| 4 aMgabhUta kamponenTa kA padArtha mUlya aMgabhUta kA padArtha mUlya hama isake bhAra ko padArtha ke ekAMka bhAra mUlya se guNA karake prApta kiyA jA sakatA hai| mUlya kula bhAra x padArtha ke ekAMka bhAra kA mUlya L padArthoM kA mUlya yahAM para nahIM diyA jA sakatA kyoMki ye bAjArI hAlata ke anusAra badalate rahate haiN|

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karmazAlA parikalana/76 maharaNa -1 eka gola Tukar3e, jisakA vyAsa 112 sai0mI0 hai, se bar3e se bar3A sambhAvita varga kATA gayA hai / bekAra kSetraphala [lUma kiijie| (grupa 5, sitambara 1969) mAnA ka sai0 mI0- varga kI bhujA taba ka+ka-(112)2 ____ 22-(112) kara 112x112 - 6272 varga se0mI0 112cm parantu varga kA kSetraphala- bhujA X bhujA-ka -ka-ka :: bar3e se bar3A sambhAvita varga-6272 varga me0 mI. __ vRta kA kSetraphala - va 22 (112) 4 7x4 -9856 varga se0 mI0 bekAra kSetraphala - vRta kA kSetraphala - varga kA kSetraphala -9856 -6272-3584 varga sa0 mI0 uttara bAharaNa-2 tribhuja kA kSetraphala mAlUma kIjie jisakI bhujAeM 32 mI0, 38 mI0 haiM tathA 45 mI0 haiN| (grupa 4,2 varSa prArambhika 1972) 0.38 1971) kSetraphala-/ka (ka-a) (ka-ba) (ka-sa) yahAM ka-145+38+32) =57.5 mI0 aura ka a%357.5-45 = 12.5 mI0 ka-ba-57.5-38=195 mI0 ka-sa-57.5-32 =25.5 mI0 .:. kSetra phala-V57.5x12.5x19.5x25.5 =598 mI0 uttara C.32m a:45m bAharaNa - 3 relagAr3I ke pahiyoM kA vyAsa 150 sai0 mI0 hai / eka minaTa meM ve kitane cakkara lagAeMge jaba ki iMjana kI ti 75 ki mI prati ghaNTA ho| (grupa 3 mArca, 1971) paridhi-7 vyAsa =2 x 150 gati-75 ki0mI0/ghaNTA = 75X1000X 100 #OmI./fr: 60 -sa0mI0/minaTa cakkara prati minaTa-75X1000X100 . 22x150 60 D265 cakkara prati minaTa uttara bAharaNa 4 - eka esITIlIna siliNDara kA vyAsa 30 sai0mI0tathA lambAI 100 sai0mI0 hai / isameM gaisa dabAva se bharA gaI tAki isake pratyeka ghana sai0mI0 meM gaisa ke 105 ghana sai0mI0 A jAeM / isameM kitane ghana sai0 mI0 esITIlIna hai| (grupa 1, 1 varSa julAI 1971)

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karmazAlA parikalana/77 Ayatana = AdhAra kA kSetraphala X UMcAI = (vyAsa)2xUMcAI -100 == "(30)2x 100 ___22x900X100 7x4 = 70714.28 ghana sai0mI0 : gaisa kI mAtrA =-70714.28X 105-7424999.4 ghana ma0mI0 L. 1-3001 uttara udAharaNa 5-eka mAilDa sTIla kI gola chaDa, jisakA vyAsa 200 mi0mI0 tathA lambAI 300 mi. mI0 hai, ko phorja karake AyatAkAra saikzana 50 mi0mI0x30 mi0mI0 banAyA gyaa| mAnA ki dhAtu kA koI nukasAna nahI hai| phorjaDa AyatAkAra char3a kI lambAI jJAta kro| (grupa 4, 2 varSa julAI, 1971) gola mAilDa sTIla char3a kA Ayatana = AyatAkAra char3a kA Ayatana gra (vyAsa)2 x lambAI = lambAIx caur3AI 4 lambAI x (200)2 x 300 - 50 x 30x lambAI lambAI_22X200x200x300 7x4x50x30 44000_6285.71 mi.mo. 7 uttara udAharaNa 6. eka gole kA bhAra jJAta kIjie, jisakA vyAsa 80 mi0mI0 tathA moTAI 10 mi0mI0 hai. yadi sTIla kA bhAra 7 grAma prati ghana sai0mI0 ho| (grupa 3,2 varSa julAI, 1971) khAlI gole kA Ayatana--80 (rA--ra3) [2.7, peja 87] yahAM rA-bAharI trijyA-4 sai0mI0 ra-andarUnI trijyA-3 sai0mI0 :: Ayatana-2x3.14 (43-33) -4X3.14x37 = 154.9 3 :: gole kA bhAra -154.9x7[3, peNa 87] __=1084.3 grAma-1.084 kilogrAma uttara udAharaNa 7. eka SaTa bhujAkAra madu ispAta char3a kA bhAra jJAta karo, jabaki SaTabhuja kI bhajA 10 mi0mI0 tathA char3a kI lambAI 1.75 mI0 hai| (mRdu ispAta kA bhAra-7.75 grAma prati ghana sai0mI0) (grupa 5, 2 varSa, julAI, 1972)

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karmazAlA parikalana/78 -175m a:17cm 6:12cm 6. 15 --- bhujA kI lambAI =10 mi0mI0-1 semI SaTabhuja kA kSetraphala-2.598X12 [1.7, peja 82] -2..98 mai0 mI. char3a kA Ayatana = 2.598x175 =454.6 ghana se.mI0 .:. char3a kA bhAra-454.6x7.75 --+-0mm -3524 grAma -3.524 kilogrAma uttara udAharaNa-8 : eka prijma jisakA AdhAra tribhajAkAra hai jisakI bhujAeM 12,15 tathA 17 saM0 mI0 hai aura UMcAI / 8.5 se mI. hai| prijma kA kula saraphesa kSetraphala tathA Ayatana jJAta kiijie| prijma kA kula kSetraphala -do tribhajoM kA kSetraphala+tIna AyatAkAra Tukar3oM kA kSetraphala tribhuja kA kSetraphala-Vka (ka-a) (ka-va) (ka-sa) [1.1, peja 82] 17+12+15 22 ka-a = 22-12 = 10 ka-ba-22-15-7 ka-sa 322 --12 =5 :: tribhuja kA kSetra phala-22x10x7x5 -87.7 pahale AyatAkAra Tukar3e kA kSetra phala = 15 x 8.5-1275 dUsare AyatAkAra Tukar3e kA kSetra phala-12 x 8.5 =102 tIsare AyatAkAra Tukar3e kA kSetraphala-17x8.5-144.5 kUla saraphesa kSetra phala = 2x87.7+127.5+ 102+144.5 -549.4 varga saM.mI0 uttara - - - --22 prijma kA Ayatana =AdhAra kA kSetraphala - UMcAI -87.7x8.5-744.45 ghana mI. uttara udAharaNa 9 : pirAmiDa kA AdhAra eka sama SaTabhuja jisakI eka bhujA 6 sai0mI0 tathA lamba UMcAI 16 sai0 mI. hai| jJAta kiijie| (ka) Ayatana (kha) kula tirachA saraphesa kSetraphala (ga) tirache kone kI lambAI (gha) tirache mukha tathA AdhAra ke bIca kA koNa (Ga) tirache kone tathA AdhAra ke bIca kA koNa -16cm

Page #87
(kha) (ST) karmazAlA parikalana / 79 a ba sa da kha ga SaTabhujAkAra AdhAra hai tathA ja pirAmiDa kA zIrSa hai jaisA ki citra me dikhAyA gayA hai / mAna loka AdhAra kA kendra hai aura gha, rekhA kha ga kA madhya bindu hai, ka ga ka kha tathA ka dha ko milAo / vibhuja ka kha ga kA kSa etraphala aba ka kha = kha ga = 6 se0mI0 tathA khagha kagha - V ka kha kha .. kagha = 5.196 saM0mI0 .. tribhuja ka kha ga kA kSetraphala = AdhAra X UMcAI -1x6x5.196 = 15.588 varga saM0mI0 (ka) = '62 3- - pirAmiDa kA Ayatana - isa prakAra paTabhuja a ba sa da va ga ko kSetra phala = 61538 = 93.528 varga saM0mI0 SaTabhuja a ba sa da kha ga ko kSetraphala 1.7, peja 82 dvArA bhI nikAlA jA sakatA hai / -2.598 x 62 = 93.53 varga saM0mI0 93.528 x 16 3 31.176 X 16 = 498.8 ghana se mI. = aba jagha = / ka ja + ka gha da kha 2 v'36-9 =V AdhAra kA kSetraphala X UMcAI 3 V (16) 2 + (5.196) 2 V256+27 = 2 = 3 maM0mI0 = V283 .. tribhuja ja kha ga kA kSetraphala = kha ga Xja gha isa prakAra tirache saraphesa kA kSetraphala = uttara 19.82 seM. mI. 27 - 1/2 x 6 x 16.82 - 50.46 varga saM.mo. aba ja kha eka tirachA konA hai / hama jakha samakoNa tribhuja ja ka kha me prApta kara sakate haiM / isalie, jakha * Vka ja+-+ka kha+-=V162+62 = 256+36 - 6 tribhujoM, ja kha ga jaisI, kA kSetraphala = 6 x 50.46 = 302.76 varga se.mI. uttara -292-17.09 se, bhI. uttara ...... 7

Page #88
karmazAlA parikalana/80 (gha) tirachA mukha kha ja ga lo aba ja gha, kha ga para lamba hai tathA ka gha, kha ga para lamba hai| :: mukha kha ja ga tathA AdhAra aba sa da kha ga ke bIca Lja gha ka hai / ja ka 16 aba, tan Lja gha ka = ka gha 5.196 Lja ghaka-7200 --tan 72deg0' isa prakAra tirache mukha tathA AdhAra ke bIca kA koNa -720 uttara (Ga) tirachA konA ja kha lo jabaki Lja ka kha eka samakoNa hai, taba tirache kone ja kha tathA AdhAra aba sa da kha ga ke bIca Lja kha ka hai| aba tan Lja kha ka = jakha-=10-2.6667 kha ka 6 =tan 690 27 :. Lja kha ka =69027' uttara udAharaNa-10 bartana meM tela kA bhAra mAlUma kIjie, jaisA ki citra meM dikhAyA gayA, yadi ghanatva = 0.8 grAma/ma.mI. Ayatana= esa (A+ A a+ a2) [2.6, peja 86] 12 2420 jabaki sa =UMcAI-245 A-bar3A vyAsa-242 a-choTA vyAsa-188 3.14 -1221000x 245 ( (242)2+ 242x188+ (18812) se.mI.73 | 011 ...._3.14 x 245 [ (242)2+ 242+188+ (188)2] x 0.8 tela kA bhAra-- 12 x 1000 3 14x245(58564+45500+35344)0.8 12X1000 3.14X245x139408x0.8 --7150 grAma 1 12 x 1000 -7.15 ki. grA. uttara udAharaNa-11 challe kA bhAra jJAta kIjie. jaisA ki citra meM dikhAyA gayA hai / yadi ghanatva-1.8 grAma/se.mI. Ayatana=va, gavA kA vyAsa-8 vA = challe kA ausata vyAsa-24+8 -32

Page #89
karmazAlA parikalana/81 76 .:. Ayatana = (8)2xT X 32 mi mI. 3.14x64x3.14x338 4x1000 314x64x3.14x32x1.8 .:.challe kA bhAra 4x1000 =9.084 grAma uttara abhyAsa 1. eka jika pleTa kI samAnAntara cartubhuja kA kSetraphala nikAlo, jisakA eka vikarNa 65 seM. mI. hai tathA jisakI do sAtha kI bhujAe kramaza: 70 se. mI. aura 75 seM. mI. hai| uttara : 4200 varga se. mI. bindu a tathA ba, eka vRta kI paridhI para sthita hai| sarala rekhAyeM ka a tathA ka kha dvArA banAyA gayA koNa a ka ba 60deg ke barAbara hai jabaki ka madhya bindu hai| cApa tathA jIvA kI lambAI me anupAta jJAta kiijie| (grupa 5, 2 varSa prArambhika, julAI, 1972) uttara : ga 3. samabAha vibhujAkAra prijma kA Ayatana jJAta karo jisakI eka bhujA 2 seM. mI. tathA UMcAI 6 se. mI hai| (grupa 4, 2 varSa, julAI 1971) uttara : 10.393 sai.mI. 4. eka AyatAkAra TukaDe, jisakI lambAI 11 se. mI., caur3AI 8 se. mI. tathA UMcAI 5 se. mI. hai, se kitanI golAkAra goliyAM, jinakA vyAsa 1 se. mI. hai, banAI jA sakatI haiN| uttara : 840 goliyA 5. eka patalI khAlI nAlI (Tayuba) kA Ayatana jJAta karo jisakI lambAI 10 seM. mI. ausata vyAsa 5 sai mI.. tathA moTAI 1 mi. mI. hai| (grupa 5, 2 varSa julAI, 1970) uttara 15.70 sai. mI. 6. citra meM jIvA aba dvArA haTAe gae khaMDa kA kSetraphala mAlUma kiijie| IOR uttara : 28.27 se.mI. 7. eka khokhalI DhalaveM lohe kI zAphTa kA bAharI vyAsa 18 se mI. hai tathA isakA andara kA vyAsa 10 seM. mI. hai, isakA Ayatana jJAta karo yadi isakI lambAI 20 seM. mI. ho / uttara : 3520 se. mI. 8. eka svimiMga pUla 50 mITara lambA tathA 15 mITara caur3A hai| isake pharza meM eka jaisI DhalAna hai jisakA ochA kinArA 1 mITara gaharA hai tathA gaharA kinArA 5 mITara hai, pAnI kA bhAra jJAta kIjie jabaki pAnI kA stara oche kinAre se 1 mITara ho| (pAnI kA ghanatva = 1 ki. grA. prati liTara) (grupa 3, 2 varSa julAI, 1970) uttara : 2062500 ki. grA.

Page #90
karmazAlA parikalana/82 9. eka golA, jisakI trijyA 8 sai. mI. hai, ko do samAnAntara pleToM se kATA gayA hai, eka kendra se 2 sai. mI. tathA dUsarI kendra se 6 seM. mI. dUra se gajaratI hai| do pleToM ke bIca ke hisse kA kSetraphala tathA khaNDa kA Ayatana jJAta kIjie yadi donoM pleTeM kendra ke eka hI tarapha hoN| uttara : 201.14 varga se. mI. 603.42 ghana se. mI. . 10. eka dhAtu ke ghana, jisakI pratyeka bhujA 50 mi. mI. hai, kA bhAra jJAta kIjie isake madhya me eka chidra, jisakA vyAsa 20 mi. mI. hai, Drila kiyA huA hai| dhAtu kA ghanatva 100 grAma prati ghana seM. mI. hai| (grupa 4, 2 varSa prArambhika julAI, 1968) 11. 100 DhalaveM lohe kI phlaineM kA bhAra jJAta karo jaisA ki citra meM dikhAyA gayA hai, yadi DhalaveM lohe kA ghanatva = 7.85 grAma/se. mI. ho. uttara : 47.42 ki. grA.

Page #91
karmazAlA parikalana/83 adhyAya 11 trikoNamiti tribhujoM ke nApa kA adhyayana hI trikoNamiti hai / trikoNamitI meM tribhuja ke koNoM ko bhujAoM ke anupAta se pradarzita kiyA jAtA hai| 1 trikoNamiti anupAta : PERPENDICULAR iP) a ba sa eka samakoNa tribhuja hai| L.asa ba= 90deg tathA (thITA) eka nyUna koNa hai| karNa aba, 90deg se viparita dizA me hai AdhAra ba sa, nyUna koNI ke sAtha vAlI bhujA hai tathA lamba a, sa nyUna koNa ke viparIta bhujA hai Upara likhita hAlata meM nimnalikhita nikoNamitI anupAta lAgU hote hai| HYPOTENUSE (H) 900 __ ___Asts) BASE (B) lamba asa -- --- isa anupAta ko Sinee (soIna thITA) kahate haiN| karNa aba (2) AdhAra- ba ma isa anupAta ko Cosine o (kosAina thITA) kahate haiM / kaNaM aba lamba ama AdhAra vasa anupAta ko Tangent O (TenajeMTa thITA) kahate haiN| karNa aba AdhAra asa aba isa anupAta ko Cosecant (kosIkaiMTa thITA) kahate haiM / karNa aba AdhAra basa isa anupAta ko Secante (sIkaiTa thITA) kahate haiN| AdhAra basa -= -isa anupAta ko Cotangent 8 (koTenajeMTa thITA) kahate haiN| lamba asa

Page #92
ina anupAtoM ko sakSipta meM Sin 8, Cos 8, tan 8, Cosec 8, Sec 0 tathA Cot 0 likhate haiM / likhe anupAta tabhI lAgU hoMge jabaki tribhuja samakoNa tribhuja hogI / yaha bhI noTa kareM Sin 0' 2.1 sAraNiyoM se koNoM kA mAna jJAta karanA : udAharaNa A = 50deg50 , sin 0 ? 6' 0' 12' 6' - ausata antara 2' - ( jamA karanA hai) 50deg50' udAharaNa 8 - 27deg14' cost? 12' karmazAlA parikalana / 84 7.8910 .8902 .8894 | naicurala kosAina sAraNI se 1 Cosec 2. trikoNamitI sAraNiyAM : 0 se 90deg ke koNoM ke sAIna, kosAina tathA TenajeMTaDa ke mAna, naicurala sAInasa, naicurala kosAinasa tathA necurala TainarjeMTasa sAraNiyoM meM diye gaye haiM / mAraNI ke bAI tarapha DigrI kA khAnA hai tathA sAtha hI Upara 6 ke guNAMka meM minaTa haiM / trikoNamitI koNoM kA mAna jJAta karane ke lie jisake minaTa kI kImata Upara die hue kisI se milatI ho to DigrI vAlI rekhA para calo aura anupAta kI kImata minaTa ke anurUpa hisse ke nIce milatI hai / minaToM ke hara 6 bhAgoM ke bIca ke mAna ke lie ausata antara kA hissA sAraNI ke sAtha jor3A gayA hai| sAina tathA TenajeMTa ke lie mukhya sAraNI se par3hI gaI kImata meM ausata antara jor3A jAtA hai / tathA kosAina ke lie aumata antara ghaTAyA jAtA hai / ausata antara (ghaTAnA hai ) 0.7660 .7672.7683 .7694 7705 .7716 7727 .7738 naicurala sAina sAraNI se 50deg 48' O 18' 24' 30' 36' 0 7749 ,Cos @ 4 18' 24' 1 Sec - tan 8 27deg 12' 0 8894 2' 3 0.7753. sin 50deg 50'-0.7753 42' 1 Cot 8 ' 48' sin O Cost 30' 36' 42' 48' 54' 2deg 14' 0.8891. Cos 27deg 14' 0.8891 7749 .7760 2 -tano 54' yn ausata antara 1' 2' 3' 4' 5' Upara 4 .8886 .8878 .8870 .8862 8854 .8846 .8838 2 3 4 6 7 ausata antara 2' 3' 4' 5' 9 5 6

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karmazAlA parikalana/85 udAharaNa : 0-42deg20', tan 8--? ausata | 24' | 30' _ 36 42' | 48' | 54' antara .ke. 36 14 2 9004.9036/9067| 9099 1913/9163.919592289260.9293 / 5 11 16 21| tan sAraNI se 42deg 18'-09099 ausata antara - :tan 42deg 20' -- 0.9110 42" 20 7.9110 2.3 mukhya trikoNamiti koraNoM kI sAraNI : koNa s.n COS tan - - 300 hai (0.5) (0.5774) 450 V(0.707) | 600 | V (0.866) 3 (1.7321) 900 13. tribhujoM ko hala karane ke lie phArmUle (1) sAIna phArmUlA ___ a . ba . sa sin A sin bA sin sA kosAina phArmUlA a ba +sa-2ba sa cos A ba sa +-2sa a cos bA sa-a+2-2a ba cos sA (3) TenajaiTa phArmUlA .... A bA tan 2 A+bA - tan a -ba a+ba 2 - -

Page #94
karmazAlA parikalana/86 - bhujA a, LA ke viparIta bhujA hai bhujA ba, LbA ke viparIta bhujA hai bhujA sa, LsA ke viparIta bhujA hai : tribhuja kA kSetraphala (dvArA 01.1, peja 82) tribhuja kA kSetraphala- AdhAra tribhuja kI UMcAI -2 bA sA A dA A dA = A bA sin bA yA A sA sin mA =sa sin bA yA ba sin sA .:. tribhuja kA kSetraphala = a sa sin bA ___ aba sin sA isI taraha, tribhuja kA kSetraphala pramANita kiyA jA sakatA hai-1 ba sa sin A 15. UMcAI tathA dUrI yaha prAya: jarUrI yA sambhava nahIM ki kisI vastu kI UMcAI sIdhI mApI jA sake yA do vastuoM ke bIca kI dUrI mApa skeN| mApa daDa ke upakaraNoM kI sahAyatA se, koI do sarala rekhAoM, jo ki dekhane vAle kI AMkha meM milatI hai. ke bIca kA koNa nApA jA sakatA hai| isa kAma ke lie "saiksaTaiTaDa' tathA 'thiyoDolAiTaDa' kA prayoga kiyA jAtA hai| isa tarIke se dUrabIna kI Ar3I tAroM ko bahata ThIka banAyA jA sakatA hai tAki mAne huI vastu kA pratibimba unase mila sake aura sAtha meM / lage baniyara kI sahAyatA se nirIkSita koNa ko minaTa ke aza taka bhI paDhA jA sake / sIdhI rekhA tathA diye hue vastu ko milane vAlI rekhA ke bIca ke koNa ko elIvezana koNa kahate hai jabaki vastu nirIkSaNa bindu se Upara ho aura DIparezana koNa jabaki vastu nIce ho| isalie, yadi ba nirIkSaNa bindu ho tathA a, diyA huA bindu ho taba sarala rekhA ba tathA a ko milAne vAlI tathA sarala rekhA ba sa ke bIca ke koNa ko elIvezana koNa kahate haiN| isI prakAra yadi a nirIkSaNa vindu ho tathA ba eka vastu ho taba sarala rekhA (a da, jo a se khIMcI gaI hai) tathA rekhA aba ke bIca ke koNa ko DIparaizana koNa kahate hai| udAharaNa 1 eka mInAra ke AdhAra se, 100 mI0 kI dUrI para mInAra ke Upara ke hisse kA elIvezana koNa 600 hai| mInAra kI UMcAI jJAta kiijie| samakoNa tribhuja kA AdhAra aba, 100 mI0 kisI skela para bnaao| asa eka rekhA khIMco joki aba ke sAtha 600 kA koNa banAe tathA basa ko sa para kATe / taba ba sa mInAra kI UMcAI hai| hala karane para, basa = tan 600 aba parantu tan 60deg--V -100ml ... basa - 13 :. ba sa-1003 -173 mI. uttara

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karmazAlA parikalana/87 udAharaNa 2-samabAhu tribhuja kI bhujA jJAta kIjie yadi a da =10 mi0mI0 ada-UMcAI ada, tribhuja ko do barAbara samakoNa tribhujoM meM bAMTatA hai| -ba-60deg tathA Lba ada-300 sin ba- da, aba- ada10 aba' sin ba-0.866 -11.55 mi0 mI0 uttara udAharaNa 3-citra meM dikhAI gaI tribhuja kA kSetraphala mAlUma kiijie| _9deg50' 8 c:10 a:10:36 kSetraphala-1ba sa sin A ___ - (15) (10)(0.6884) -51.6 varga mi.mI. uttara yA dvArA 4, peja 82 kSetraphala-Vka (ka-a)(ka-ba) (ka-sa) 10:15 +ba+sa 35.36_-17.68 jabaki ka-a+ba+sa 35.36 22 kSetraphala = /17.68 (17.68-10.36)(17.68 -15)(17.68-10) -/17.68X7.32x2.68x7.68 -51.6 varga mi.mI. uttara udAharaNa 4 -DiliMga jiga kI Tepara pina kA 'ka tathA jJAta kiijie| Tepara 1:12 kA matalaba hai ki 12 mi.mI. lambAI meM 1 mi.mI. uThAva hai| yAni ki tan e-1 = 0.0833 tan kI sAraNI se.-4042 uttara ka -14_tan 40 42' = 0.0833 180yA ka-14 =14.99 yA ka -29 mi.mI. uttara udAharaNa 5-phalaiMja ke chidra 4 kI akSIya dUrI jJAta kIjie / vRta ke kendra se zurU kiijie| chidra 1 kI x akSa se kendra taka kI dUrI =0 mi mI. Y akSa se-42 mi.mI chidra 2 ke lie ka ba 1-42, 2 akaba-300 ka a1 _cos30 ka bA -0.866 yA ka a=42x0.866-36.37 tathA 1-1=sin 30deg30.5 kaba yA aba =42x0.5-21 -

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karmazAlA parikalana/88 yadi kendra ka ko bAI tarapha X akSa kI RNa bhajA leM tathA kendra ka ke nIce kI dizA ke Y akSa kI RNa bhujA leM to chidra kI akSIya dUrI X akSa kI tarapha -36.37 mi.mI. hai, -21 mi.mI. Y akSa kI tarapha hai / chidra na0 4 ke lie kavaH =42 tathA / aka va 30deg kaba = cos 30deg-0.866 yA ka-42x0.866-36.37 = sin 30deg=0.5 yA aba.-42x0.5-21 : kaba mi.mI tathA Y akSa kI tarapha 21 mi.mI hai| chidra 4 kI akSIya dUrI X akSa kI tarapha 36 37 udAharaNa 6: eka 26 mi.mI. TesTa plaga eka enAlara va meM rakhA gayA hai jaisA ki citra meM dikhAyA gayA hai| dUrI da mAlama kIjie / yadi ka plaga kA kendra ho, ka a ko milAo tathA ka aba vibhuja bnaao| [dvArA 5.3, peja 75] Lka ba a -90deg tathA Lka aba-00 ava ... kaba-tan 30deg yA 15-0.5774 aba 13 :.a ba -1574 05 -22.36 isa prakAra da - aba + plaga kA vyAsa -22.36+13-35.36 mi mI. (uttara) udAharaNa 7 : parophAila geja kI lambAI 'la' jJAta kIjie jaisA ki citra meM dikhAyA gayA hai| mAna lo a eka aisA bindu hai jahAM sarala rekhA asa tathA 26 trijyA milate haiN| aura a se aba tathA a da lamba khiico| jabaki ka a lamba hai a sa para tathA ka ba lamba hai sa da para, isalie do rekhAoM ke bIca kA koNa, unake lamboM ke koNa ke barAbara hotA hai' guNa dvArA hameM prApta hotA hai : La ka ba-36deg citra se, la=26+aba+sa da F6RT 81-7 - Sin 360 : aba-26xSin 360 kaa : aba =26x0.5878 = 15.28 kaba-cos 360 = 6.8090 :: kaba =26x0.8090-21.03 ada-52-26+ ka ba=-52-26+21.03-47.03 ada 17.03 4-tan 36deg-.727:.sada- 164.7 .727 la-- 26+15 28+ 64.7 = 105.98mi.mI. uttara

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karmazAlA parikalana / 89 udAharaNa 8 : tribhuja A bA sA kI bhujAeM, koNa jJAta kIjie, bhujA a = 5 se.mI., bhujA ba = 6 se.mI., sin A - 075 a sa sin a sin ar sin sA 5 6 0.75 sin ar .. Lar-64deg 9' sin ar 0.75.. L= 48deg 35' jabaki A + LbA + L sA = 180deg .. LsA = 80deg-6409-48deg35' - 67016 sa Upara likhita phArmUle kI sahAyatA se sin sA 5 0.75 = ... sin ar-0.9 sa sin 67deg16' 4. A sin A sa 0.9224 .. sa 6.15 saM.mI. isa prakAra pariNAma : a-5 se.mI. ba = 6 se.mI. sa - 6.15 saM.mI. LA = 48deg35' L bA = 64deg 9' LsA - 67deg16' abhyAsa : 1. trikoNamitI sAraNiyoM se sin 38deg 14deg; tan 64deg 36deg kA mAna jJAta karo tathA vo koNa jisakA kosAina 0.3803 hai / B uttara : 6186, 2.1060, 67deg39' 2. eka pleTa meM Tepara chidra ThokanA hai jaisA ki citra meM dikhAyA gayA hai va jJAta kIjie / uttara :- 16.36 A b =6cm a = 5 cm 3. do barAbara UMcAI vAle khambe eka sar3aka ke donoM ora khar3e haiM jo ki 40 mITara caur3I hai, donoM eka dUsare ke viparIta haiM / khamboM ke bIca sar3aka para eka bindu a se khamboM ke UparI hissoM se elIvezana kramaza 60deg tathA 30deg pAyA gayA / khamboM kI UcAI tathA bindu a kI sthiti jJAta kIjie / uttara :- 17.32 mITara, eka khambe se 10 mITara 272 mi0mI0 vyAsa ke vRta meM 9 barAbara kI dUrI para chidra karane haiM / chidroM a tathA ba aura a tathA sa meM jIvIya dUrI jJAta karo / uttara :- a ba 93 mi0mI0 a sa 175 mi0mI0 5. tribhuja kI bhujAe 25 se0mI0 tathA 6 se0 mI0 haiM yadi unake bIca kA koNa 35deg kA ho to tribhuja kA kSetraphala jJAta kIjie / uttara : - 4.302 varga saM0mI0 6. eka bI bailTa DrAIva meM bar3I tathA choTI pulI meM kSetija (Horizontal) dUrI 750 mi0mI0 hai / do puliyoM ke bIca kI dUrI 750 mi0mI0 hai / DrAIva 4751 .3deg

Page #98
karmazAlA parikalana/90 kA koNa jJAta kiijie| uttara :-33deg34 7. eka sTIla kI geda jisakA vyAsa 20 mi0 mI0 ko vI. blAka meM rakhA gayA hai, jaisA ki citra meM dikhAyA gayA hai| vI kA koNa jJAta kIjie jhirI kI UparI cor3AI bhI jJAta kiijie| uttara:-vI kA koNa 45deg46' jhirI kI caur3AI 21.105 8. eka 40 mi0mI0 TaisTa plaga ko Dhalave dharAtala aba para rakhA gayA hai| yadi ba sa = 54.38 mi0mI0 ho aura TesTa plaga tathA sada ke bIca kI dUrI slipa geja dvArA nApI gaI 22.24 mi0mI0 hai, a ba kA urdhvAdhara (Vertical) rekhA se jhukAva jJAta kiijie| uttara :-27deg 30 SLIP GAUGES D PARALLEL STRID

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karmazAlA parikalana/91 - adhyAya 12 rekhAcitra rekhAcitra:-rekhAcina do parivartanIya saMkhyAoM ke sambandha kI AkRti hai| Xox'-X akSa YOY' -Y 727 0-mUla bindu ra.b.O -9/a.b) grApha para koI bindu, binduoM ke eka jor3e se pradarzita kiyA jAtA hai / jor3e meM pahalI saMkhyA ko bhujAkSa kahate haiM tathA x yaha usa bindu kI Y akSa se dUrI ko pradarzita karatA hai / O/-a-D) dUsarI saMkhyA koTi akSa hai tathA yaha usa bindu kI X akSa se dUrI ko pradarzita karatA hai| skela : Upara ke citra se yaha sApha hai ki rekhAcitra para kisI bhI bindu ko aMkita karane ke lie, koI mApa cunanA cAhie tathA rekhAcitra banAne se pahale darzAnI cAhie / mApa ko aisA cunanA cAhie jisase rekhAcina kA AkAra bar3e se bar3A ho (jitanA sambhava ho) pAda cinha : pAda | 1 | 2 | 3 | 4 | bhujAkSa | + | - | - | + | koTi akSa | + | + | - | - udAharaNa udAharaNa 1. diyA haiY-2x-1,Y kI kImateM jJAta kIjie jo ki x- -3,-2,-1,0, 1,2,3 ke anukUla hoM tathA isa prakAra prApta kie gae bindu xY ko rekhAcina para aMkita kiijie| nIce dI gaI sAraNI meM Y ke mAnoM ko X ke anukUla darzAyA gayA hai|

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karmazAlA parikalana/92 diyA hai Y =2x-1 jaba X--3 ___Y-2(-3)-1 =-6-1=-7 aura isI prakAra sAraNI kI zeSa kImate nikAlI jA sakatI hai (-3,-7), (-2,--5), (-1,-3), (0,-1), (1,1), (2,3,), (3,5) binduoM ko cinA meM aMkita kiyA gyaa| hai| yAda rahe ki sabhI bindu Y-2x 1, ko saMtuSTa karate haiM tathA eka sIdhI rekhA para rahate haiN| Velocity udAharaNa 2 kisI vastu ke lie gati-samaya rekhAcitra aMkita kIjie jo isa prakAra calatI hai : samaya (sakiNDa meM) a ba sa da ya ra la 0 1 2 3 4 5 6 gati 6 7 8 9 10 / / 12 rekhAcina se jJAta kIjie :3.5 saikiNDa para antima gati (sitambara 69) cinna meM X -akSa samaya hai tathA eka hissA samaya ke / saikiNDa ko darzAtA hai| gati ko Y -akSa meM aMkita kiyA gayA hai aura pratyeka himsA 2 mI0sai0 darzAtA hai| 3.5 saikiNDa ke anukUla, X tathA Y akSa para lamba girAye jAte haiM aura gati 9.75 mI0sai0 jJAta kI jAtI hai| udAharaNa 3 nimnalikhita rIDiMgasa TaimpaleTa ko banAne meM 123456789x Time lage samaya ko darzAtI hai| TempaleTa liyA gayA samaya 1 ghaMTA 20 minaTa 2 ghaMTe 40 minaTa 3 ghaMTe 20 minaTa 5 ghaMTe 40 minaTa 25 9 ghaMTe 20 minaTa Upara diye gae sAraNI ko rekhA cina para aMkita kIjie tathA rekhAcina se 18 TaimpaleTa ko banAne meM lage samaya ko jJAta kIjie tathA yaha bindu rekhAcina para drshaao| (grupa 4, 2 varSa, julAI, 1971) isa cina meM X akSa samaya darzAtA hai tathA Y akSa kA hara eka hissA eka TempaleTa ko darzAtA hai| TIME - 18 TempaleTa ko banAne meM lage samaya ko x akSa para lamba girAne se jJAta kiyA jA sakatA hai| tathA yaha 460 minaTa hai yAni ki 7 ghaMTe 40 minaTa / .. 1600 TEMPLATES 160 M200 1240 280 320 098 007 077 087 520 560 abhyAsa 1. (i) y=2x+3 (ii) y-2x--3 kA rekhAcitra bnaaiye| rekhAcitrA dvArA, y-2x+3 samIkaraNa meM y kA mAna jJAta karo jabaki x-2 samIkaraNa y-2x-3 meM y kA mAna jJAta karo jabaki x-3 (TreDa TaisTa, agasta, 1967)

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karmazAlA parikalana/93 2. T (kilogrAma meM) 50 110 140 160 175 200 (cauDAI sai0 mI0 meM) 7.5 16.5 20 22.5 25 28.5 binduoM ke bIca sambandha ko dikhAne ke lie rekhAcina bnaaiye| rekhAcitrA se jJAta kIjiye : -. - - -..- 30 40 - ..-. 3. eka ghara ke tAro ke dhArAmaNDala, jo ki samAnAntara meM hai, meM taraha-taraha ke pratirodha tathA dhArA pAe gae jo ki nIce diye gaye haiM : R (om) 20 45 50 60 C (empIyara) 11 7.7 5.5 4.9 4.4 3.67 R, oma meM pratirodha hai tathA C, empIyara me dhArA hai| Upara dI huI sAraNI se rekhAcitra banAie tathA rekhAcitra se jJAta kIjie : (1) R jabaki C = 8.2 (2) C jabaki R==38 uttara : (1) 27 (2) 59 ! 4. dhAtu kI gola char3a ko TaniMga meM, cakkara prati minaTa tathA bhinna-bhinna vyAsoM ke bIca saMbaMdha nimnalikhita hai :D (mi0 mI0) 3530 25 2015 N (cakkara prati minaTa) 227 265 318 398 530 Upara dI huI sAraNI se sApha-sApha rekhAcina banAie tathA nimnalikhita praznoM ke uttara dIjie :(1) jaba vyAma 23 mi0 mI0 ho to cakkara prati minaTa kitane hoge ? (2) jaba cavakara prati minaTa 480 hoM to sambhAvita vyAsa kyA hogA? uttara : (1) 350 cakkara prati minaTa (2) 17 mi0 mI0 5. do lakar3I ke dharAtaloM meM gharSaNa kA gaNAMka nikAlane ke lie eka prayoga meM, bala F tathA khisakane vAle bhAra W meM nimnalikhita sambandha prApta kiye gaye the : w (ki0 grA0 meM) 3 5 8 10 13 15 18 20 (F ki0 grA0 meM) 1.05 1.75 2.8 3.5 4.55 5.25 6.30 7.0 Upara dI huI kImatoM ko rekhAcina para aMkite kIjie tathA isase jJAta karo :(1) 9 tathA 16 ki0 grA0 bhAra ke anukUla bala kA mAna (2) 1.4 tathA 3.58 ki0 grA0 bala ke anukUla bhAra kA mAna uttara : (1) / 3.12 ki0 grA0 tathA 5.6 ki. grA0 (2) 4 ki0 grA0 tathA 10 ki0 prA0 6. kAbale ke vyAsa tathA isakI mITrika cUr3iyoM kI pica meM nimnalikhita sambandha haiM :-- kAbale kA vyAsa (mi0 mI0) 3 4 5 6 8 10 12 14 pica (mi0 mI0) 0.5 0.7 0.8 1 1.25 1.5 1.75 2 rekhAcinna aMkita kIjie tathA isase 7 mi. mI. tathA 11 mi. mI. vyAsa vAle kAbaloM ke lie pica jJAta kiijie| uttara : 1.125 mi0 mI0 tathA 1.625 mi. mI0

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karmazAlA parikalana/94 8. belTa kI gati, jo ki eka jaisI gati se cala rahI pulI ke Upara hai, pulI ke vyAsa ke Upara nirbhara karatI hai| nimnalikhita sAraNI dvArA sambandha diyA jAtA hai :vyAsa (inca) 2 4 6 8 10 12 gati (phuTa/minaTa) 73 147 220 293 3 67 440 rekhAcina aMkita kIjie tathA isase bailTa kI gati jJAta kIjie yadi pulI kA vyAsa 61" ho / (grupa 1, sitambara 1972) 9. nimnalikhita sAraNI meM rolara bIyariMga jaranala, jo ki 1000 cakkara prati minaTa se ghUma rahA hai, kI bhAra sahane kI zakti ko darzAyA gayA hai : bIyariMga kA vyAsa (mi0 mI.) 25 35 455565 surakSita bhAra (ki0 grA0) 1385 2260 3300 48206880 rekhAcitra aMkita kIjie tathA 50 mi0 mI. vyAsa vAlI bIyariMga ke lie surakSita bhAra jJAta kiijie| (grupa 1, sitambara 1970)

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bhAga 2 karmazAlA parikalana pratyeka TreDa ke grupa ke lie prazna (yAMtrika tathA vidyuta) grupa 1. phiTara, Taranara, mazInisTa (milara), mazInisTa (grAiMDara), mazInisTa (sa0sa0pa0), phiTara (sTrakacalara), __ mazInisTa (insTramaiMTa) tathA TUla aura DAI mekara / grupa 3. lohAra, zITa maiTala varkara tathA vailDara (gaisa tathA vidyut) grupa 6. mila rAITa mazInisTa, TaiksaTAila mazInarI mazInisTa, DerI dekhabhAla / grupa 9. DrAphTasamaina (mazInisTa)

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karmazAlA parikalana/97 - adhyAya 13 -D%3D14 gavana 1. saraphesa gati: ghamate hae vastu kI saraphesa gati sa- mI0 minaTa se dI jAtI hai| 1000 jabaki sa-garaphema gati mI0/minaTa meM va-vyAsa mi0mI0 meM na-nakkara prati minaTa Upara diye gaye sUna se DriliMga, TaniMga tathA miliMga kI kaTiMga spIDa jJAta kI jA sakatI haiN| udAharaNa1 DriliMga yadi vyAsa-14 tathA sa-22 mI0/minaTa (40 ki0 grA0/mi.mI. ispAta ke lie) cakkara prati minaTa (na) jJAta kIjie / 1000 sa 22x1000 gava 3.14X14 -501 cakkara prati minaTa uttara udAharaNa 2. Taniga yadi va-38 tathA na--140 cakkara prati minaTa kaTiMga spIDa sa jJAta kiijie| gavana kaTiMga spIDa sa::." 1000 ..3 14x140x38 na - - ---- -D338 H IN=140 1000 -16.7 mI0/minaTa uttara udAharaNa 3. eka kArbana sTIla ko, eka plena miliMga kaTara, jisakA vyAsa 75 hai, se karanA hai| kArbana sTIla kI kaTiMga spIDa 17 mI0 / minaTa hai tathA miliMga mazIna ko nimnalikhita cakkara prati minaTa para calA sakate haiM : 37-49-64-86-113-147-197--260-338-455-600-700 kaTara ke cakkara prati minaTa jJAta kiijie|

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1000 sa 1000 x 17 72 cakkara prati minaTa va 3.14 x 75 isa udAharaNa meM na 64 cakkara prati minaTa cunA gayA hai / uttara abhyAsa : 1. yadi eka DriliMga mazIna ko 20 mi0mI0 se 8 mi0 mI0 Drila taka, 16 mI0 / minaTa kaTiMga spIDa se calAyA jAe to isakI uccatama tathA nyUnatama spIDa jJAta kIjie ? na uttara : 2. ( 1 ) 25 pItala kIjie / kaTiMga spIDa : (1) ( 2 ) ( 3 ) uttara : 637 tathA 215 cakkara prati minaTa (2) 40 mRdu ispAta ( 3 ) 250 / Dhalave lohe kI TarniMga ke lie kharAda kI spIDa jJAta uttara : pItala 50 mI0 / minaTa mRdu ispAta 22 mI0 / minaTa DhalavAM lohA 20 mI0 / minaTa ( 1 ) (2) ( 3 ) 3. zaila aiNDa mila kaTara kA vyAsa, va = 80 DhalaveM lohe kI kaTiMga spIDa sa - 20 mI0 / minaTa kaTara kI spIDa jJAta kIjie / 80 cakkara prati minaTa Drila vyAsa mi0mI0 phIDa (100 mimI 0 prati cakkara 638 cakkara prati minaTa 175 cakkara prati minaTa 25.5 cakkara prati minaTa 2. Drila ko phIDa karanA : viSTa Drila hara cakkara kI tAkata ke anusAra phoDa kA cayana kiyA jAtA hai mazIna kI tAkata tathA zakti taka sImita hai / 13 7 1/2 5 karmazAlA parikalana / 98 -chidra kI gaharAI + Drila bindU lAla +03x va va - Drila kA vyAsa mi0mI0 meM na = cakkara prati minaTa Drila ke phIDa dUrI phIDa / minaTa sa- Drila kI phIDa mi0mI0 / ca0pra0mi0 phIDa / minaTa phIDa / ca . pra mi. X ca . pra mi. == sa X na mazIniMga samaya - 3. DriliMga ke lie mazIniMga samaya : mazIna kA mazIniMga samaya kAma karane meM lage samaya ko kahate haiM / yAni ki vaha samaya jisameM Drila kA kATane vAlA konA cipsa ( burAdA ) utAratA hai / yadi la -chidra kI gaharAI lA - Drila kI gaharAI meM kucha mAtrA meM kAma ke andara dha~sa jAtI hai| choTe DriloM meM, Drila kyoMki jyAdA phIDa dene se Drila TUTa jAtI hai| bar3e DriloM meM phIDa nimna likhita Drila phIDa ke lie sahAyaka siddha hoMge / 5167 10 | 13 | 16 10 12 18 22 25 28 30 la sa X na minaTa | 19 24 1-01

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karmazAlA parikalana/99 udAharaNa 1. eka 52 mi.mI. chidra ko, 0.23 mi.mI. phIDa aura gati 320 ca.pra.miDila karane ke lie samaya kA anumAna lgaaie| (grupa 1, sitambara, 1970) Upara se dvArA 3, 0.3 va hisse nakAra kara, lAla lA52 mazIniga samaya -- --0.7 minaTa uttara saXna 0.23x320 abhyAsa: 1. agara Upara die gae citra meM dvArA 3 meM la-303 va=18, sa% 0.2/cakkara tathA na=300 ca.pra.mi. mazIniMga samaya jJAta kro| uttara: 0.59 minaTa mad ispAta meM eka 20 mi. mI. vyAsa, 80 mi. mI. gahare chidra karane ke lie kitanA samaya lagegA (kaTiMga spIDa 15 mI./minaTa tathA phIDa 0.28 mi mI./cakkara lo tathA Drila bindu ke lie 6 mi.mI. lo) uttara: 1.28 minaTa --- 4. TaniMga meM phIDakaTa kI gaharAI tathA utArI gaI dhAtu kA Ayatana : loMgIcyUDInala tathA TrAMsavarsala TaniMga meM TUla kArya (jaoNba) para eka cakkara meM jitanI lambAI para calatA hai use phIDa kahate haiN| phIDa ko TUla kI gaharAI se guNA karane para burAde (cipsa) kA kraoNsa saMkzana patA calatA hai| - in-AALArmaar-Ranawaraar TARRATE saxa-kSetraphala utArI gaI dhAtu kA prati minaTa Ayatana jJAta kiyA jA sakatA hai yadi cipsa krAsa saMkzana ko kaTiMga spIDa se guNA kiyA jaae| utArI gaI dhAtu kA prati minaTa Ayatana-1000xsaxkSe.mi mI. yadi sa mITara meM ho| udAharaNa 1. 24 mI./minaTa se Taniga kI jA rahI hai: kaTa 3 gaharA hai aura phIDa 0.65 hai| dhAtu utarane kI gati jJAta kiijie| dvArA 4, A-1000xsaxkSe. kSe.-3x0.65-1.95 mi.mI.2 sa-1000x24 A-1000x24x1.95 = 46800 mi mI. --46.8 se.mI uttara abhyAsa : 1. utArI gaI dhAtu kA Ayatana jJAta kIjie, jaba kaTiMga spIDa 20 mI./minaTa phIDa 0.8 mi.mI tathA kaTa kI gaharAI 3 hai| uttara : 48 sai. mI. 5. Taniga ke lie mazIniMga samaya : mazIniMga samaya- TaniMga lambAI __ lana saxna phIDa/minaTa minaTa

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karmazAlA parikalana/100 jabaki la = TaniMga lambAI kAma kI lambAI (la.)+ zurU kA alAuMma(la....) + TaniMga ke bAda kA alAuMsa (la ba) :: la-la. + la. + la , sa = phIDa mi.mI/cakkara meM na-ca. pra. mi. .. phIDa prati minaTa = sana - - - udAharaNa : va= 80 mi.mi. la-490 mi.mI. la. = la =5 mi.mI. sA-20 mI./minaTa, sa-0.5 mi.mI./cakkara na-74 ca. pra mi , mazIniMga samaya jJAta karo / la= 490+5+5+ 500 mi mI. la 500 saXna 0.5x74 - 13 5 minaTa uttara la =ra+la. udAharaNa : va= 190 mi.mI., la - 5 mi.mI. sA-20 mI/minaTa, sa-05 mi.mI./cakkara na-37 ca.pra.mi., mIniMga samaya jJAta kro| la-- -+5=100 mi.mI. 2 samaya samaya - la - 100 . sana 0.5x37 35.4 minaTa uttara abhyAsa : 1. 165 mi mI. lambAI, jisakI phIDa 0.38 mi.mI.,kArya kA vyAsa 38 mi.mI., 24 mI./minaTa para hai, ko Tarna karane kA samaya jJAta kiijie| 2. haa| uttara : 2.16 minaTa udAharaNa 1 meM dhAtu utArane kI gati jJAta kIjie jaba kaTa 11 mi.mI. gaharA ho| uttara : 13.7 se.mI3/minaTa Tepara TaraniMga (ka) Tela sTaoNka dvArA Tepara TaraniMga : 6 1. kAma kI lambAI, Tepara lambAI ke barAbara ho / TelasTAka saiTa ovara ka- vAva 2. Tepara lambAI, kArya lambAI kA bhAga hai / sarvAMgasama tribhuja kI bhujAoM kA sambandha isa prakAra hai : vA-va ka : lA = vA-va : la : ka-_2 la jabaki saiTa ovara

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karmazAlA parikalana/101 ka- vA-va x lA 2la UparI slAIDa eDajasmaiMTa dvArA Tepara Taniga : UparI slAIDa ko saiTiMga koNa Tepara koNa ke Adhe ke barAbara hotA hai taper --length 1 -14 work length 12 jJAta karanA caahie| AdhA Tepara - D-d_T la _vA-ba 2Xla yaha koNa = , ke TainajeNTa ke barAbara hai| ANINNI M8 udAharaNa 1. ___saiTiMga koNa jaisA ki udAharaNa meM dikhAyA gayA hai, jJAta kro| TenajeTa 70-500 -=0.165 2 2x60 120 anurUpI koNa ke lie TainajeMTa sAraNI se, jJAta kI gaI TenajeTa kA mAna Avazya hI lenA cAhie, usa saiTiMga koNa 4-9deg 24 -60udAharaNa 2. eka jAba jo ki 310 mi.mI. lambI hai usake Upara Tepara 1 in 15 kATanI hai| TaMla sTAka kI saiTa auvara jJAta kro|| jAva kI lambAI para kula Tepara-18-20.66 mi.mI. Tela sTAka maiTa ovara-20,66--10.33 uttara udAharaNa 3. eka jAba jo ki 185 mi.mI lambI hai usa ke Upara 15% Tepara kATanI hai / saiTa ovara jJAta kro| 185 kA 15%-185X15-27.75 mi. mI. 100 imalie saiTa auvara-27.75-13.9 mi. mI. uttara : 13.9 mi. mI. abhyAsa: 1. eka jAba jisa kI kula lambAI 190 mi.mI hai, usake Upara 10 kA Tepara kATanA hai| Tela sTAka kI saiTa ovara jJAta kro| uttara: 11.63 mi.mI. MIAS

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karmazAlA parikalana/102 kisa koNa para kharAda kI kampAuMDa slAIDa saiTa kI jAe tAki Tepara hola kiyA jA sake. jaisA ki citra meM dikhAyA hai| --075 1097 uttara : 5021 228 13. jJAta karo : ) kampAUMDa kAMgala saiTiMga uttara : (a) 1 in 20 (ba) 5deg 44 --500 AraTIkala 7. kharAda para cUr3iyAM kATanA / nimnalikhita sUtra se aMDa kaTiMga oparezana ke daurAna, gIyara rezo nikAlI jAtI hai| DrAIviMga gIyara ga, ke TItha la zrRMDa kI lIDa Drivana gIyara ga, ke TItha va lIDa strayU kI lIDa Ta siMgala sTArTa zrRMDa ke lie lIDa - pica, lekina bahuta sAre bhaMDa sTArTa ke lie lIDa = pitta x sTArTa kI saMkhyA / cenja gIyaraja ke saiTa 3 aisI gIyaraja, jinameM dAMtoM kI saMkhyA nimnalikhita hai : 20, 25, 30, 35, 40, 45, ! 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110, 120, 125, 127 (hara eka saiTa meM / do saMkhyAe~) lIDa skraya incoM yA milImITaroM meM hotI hai| lIDa kA sTaiMDarDa banAyA jAtA hai / aura inheM mITrika lIDa strayU meM 4 mi mI., 6 mi.mI, 12 mi.mI. tathA 24 mi.mI, taka banAyA jAtA hai| IcoM ke lIDa skrayU meM " aura " kI lIDa hotI hai / udAharaNa : lIDa skrayU kA lIDa milImITara kA hai aura jAba kI lIDa bhI mi.mI. hai / udAharaNa 1. aMDa kI lIDa=2 mi.mI., lIDa skrayU kI lIDa = 6mi. mI. gaH, ---- ( se 3) bhinna ! ko upayukta saMkhyAoM meM badalA jAtA hai tAki upayukta gIyara mile| ga -la-2--20 ors ityAdi ga, va 6 3 60 (20 se 60) ga-20 TItha, ga, -60 TItha yA ga-30 TItha, ga=90 TItha ga eka AiDalara gIyara hai jisake Totha kI saMkhyA upayukta hai udAharaNa 2. aMDa kI lIDa-1 mi.mI., lIDa skrayU kI lIDa- 12 mi.mI. ga1 _la = ga va 12

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karmazAlA parikalana/103 ARMA yahAM para gIyara ke ucita jor3e nahIM hai jo hameM anupAta 1 de ye isalie do vyaMjakoM meM badala jAtA hai aura pratyeka ucita saMkhyA se guNA kiyA jAtA hai / 1 1 1 2030 12 438090 -Imm do giyara saiTa kA badalanA pariNAma hai| (kamapAUMDa giyariMga) Zr _ 20 aura Z_30 Z, 802,90 12mm DrAiviMga gIyara-Z&Z, Z---20 Z3-30 Divana gIyara=Z.&Z. Z= 80Z,-90 abhyAsa : 1. nimnalikhita picisa 6 mi.mI p lIDa skraya para kATane se ceMsa vhIla jJAta karo (ka) 0.8 mi.mI. (kha) 1.75 mi. mI. (ga) 3.5 mi.mI (gha) 10 mi.mI. meM 9 zrRMDa (Ga) 0.8 mi.mI. 3 sTArTa / ArTIkala 8. miliMga ke lie phIDa aura mazIniMga samaya : miliMga Aparezana ke lie, phIDa kA artha hai phIDa kA anupAta mi mI./minaTa ye mi mi. meM darI hai jo miliMga mazIna sAraNI aura imalie varkapIsa kI eka minaTa meM gati karatI hai| miliMga ke lie mazIniMga samaya jJAta karo mazIniMga samaya _ miliMga Tabala kI calane kI dUrI (mi. mI.) (kIDa kA anupAta mi. mI./minaTa), _ - minaTa calane kI dUrI (L) varkapIsa (1) kI lambAI para nirbhara karatI hai phIDa alAyansa aura ovara Trevala (1, aura 1) udAharaNa : eka St 42 kI sTrIpa jisa kI lambAI 250 mi. mI. hai use palena miliMga dvArA eka miliMga kiyA jAnA hai| mazIniMga samaya jJAta kro|| diyA hai : 1 -30 mi.mI., 1 =5 mi.mI., phIDa kA anupAta = 100 mi.mI./minaTa yahA, L-1+1 +1, -250 mi.mI.+30 mi.mI+5 mi.mI. = 285 mi.mI., __ _.._285 mi.mI. " 5 100 mi.mI./minaTa -2.85 minTa uttara abhyAsa 1. a kA mUlya jJAta karo vyAsa mi. mI. | mi. mI. JOB FAM (pAyathayAgorasa premaya kA prayoga karate hue) uttara : 9.8 mi. mI,

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karmazAlA parikalana/104 - 2. kaTara la kI gati prophAIla miliMga se jJAta kI hai| mazIniMga samaya jJAta karo agara phIDa (feed) 100 mi. mI./minaTa hai| la | vyAsa | ka / mi. mI. mi. mI. mi. mI. | mi. mI. | mi. mI. TION | 120 | 50 | 2 | ? | ? uttara : a%9.83; la-139.6; samaya =1.4 minaTa ArTa-9 giyara jJAta kro| thikanasa prApha Tuya hola Ikya sarakavara pica -vakiMga patha araMDama - d V GALIA ____ phalaMka phesa 8pica sarakala giyara ke cihna sapara giyara TIya proporazana ina inDiyana sTaiMDarDa sisTama ina TArmaja Afa moDayUla (m) & nambara Apha TItha (2) AI. ema : 2467-1963 cihna gIyara TUtha proporazanaja (prezana aiMgala 20deg) rm zm m Tutha elimeMTa kA nAma sarakulara pica pica DAyamITara aDaiDama DiDeMDama varakiMga Deptha Tutha Tepya AUTa sAIDa DAyamITara dRtha thikanasa kalIyareMsa 1.25m 2m 2.25 m (2+2) 1.5708 m 0.25m d+2ha hf - ha yuniTa kA mApa mi. mI. hI lekara hala kreN| -

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karmazAlA parikalana/105 sapara gIyara TItha proporazanaja ina amerikana sTaiMDarDa sisTama ina Tarama Afa DAyAmITarala pica (DP) nambara Afa TItha (N) TUtha elimaiMTa kA nAma cihna gIyara Tutha proporazanaja 141deg praizara aiMgala 20deg prezara aiMgala sarakulara pica pica DAyAmITara DP aDeMDama DP DiDaeNDama s+f 1.157 DP varakiMga Deptha DP 1.6 DP 1.8 Tutha Deptha D + f 2.157 DP N+2 DP AUTa sAIDa DAyAmITara PD + 25 DP N+1.6 DP 1.5708 DP Tutha thikanesa 1.5708 DP 0.157 DP 0.2 kalIyareMsa yuniTa kA mApa Ica lekara hala kareM udAharaNa-1 : eka TUTI haI gIyara kA bAhya vyAsa 150 mi. mI. hai| gIyara ke 45 dAnte hai| DAyAmITarala pica tathA ToTala haiptha jJAta kro| apareMTisa parIkSA grupa 1, sitambara, 1970 bAhya vyAsa = 150 mi. mI.-5.9 iMca ArTIkala 9 dvArA: bAhya vyAsa 5.9* = DP ___45+2 (DP= DAyAmITarala pica) 47 : DAyAmITarala pica ---8 uttara 59 kula Deptha ___2.157 _-2.157iMca DAyAmITarala pica 8 2.157... x25.4 mi. mI. 8 = 6.84 mi. mI. uttara noTa yadi eka gIyara ke TItha aura moDayala yA DAyAmITarala pica patA ho to ati Avazyaka gIyara ke nAma patA kiye jA sakate haiN|

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karmazAlA parikalana/106 abhyAsa: eka gIyara kI nimnalikhita paimAIza jJAta kareM, jaba ki moDayUla 2 ho aura gIyara ke dAnte 30 hoN| (i) pica (ii) pica sarakala DAyAmITara (iii) aDeMDama (iv) DiDaeNDama (v) Tutha Deptha (vi) bAhya vyAsa uttara : (i) 6.28; (ii) 60; (iii) 2; (iv) 2.5; (v) 4.5; (vi) 64 vAmavhIla indexing spindle ArTIkala-10 DIvAiDiMga haiDa imakA prayoga vibhinna prakAra ke vibhAjana kArya ke lie kiyA jAtA hai| hAUsiMga meM, eka bArma gIyara anupAta 40.1 se lagAyA jAtA hai| ina DaikasiMga karaika ke samIpa hI. inDekama pleTa meM, surAkhoM kI bahuta sI ginatI vRtoM meM kI hotI hai| lAka pina - Index plate Zsingle thread worm inDeksa ka kyoMki haiDa kI gIyara kA anupAta 40 : 1 hai, kraika ke 40 cakkara spiDala kA eka cakkara banAte hai yA keMka kA eka / cakkara spiDala kA cakkara ghuggatA hai| inDaksa pleTa sahita isa ke surAkhoM kA kArya, kaika ke cakkara ko phira vibhAjita karanA hai| surAkhoM kI reMja jitanI adhika hogI utanA hI adhika vibhAjana hogA, eka khAsa inDaiksiga ke DhaMga meM / inDaksa pleToM kA Adarza saiTa nimnalikhita surAkhoM kI sakhyA rakhatA hai| 16 | 17 | 18 19 | 20 | 21 | 23 | 27, 29 | 31 | 33 37 | 39 41 43 inDaiksiga ke vibhinna DhaMga : (i) sAdhAraNa inDaiksiga (i) kampAUMDa inDaiksiga (iii) Diphrainziyala inDaiksiga (iv) eMgulara inDaiksiga AraTIkala :-10. sAdhAraNa inDaiksiga inDaiksiga ke lie kaiMka ke cakkaroM kI saMkhyA (nk) 40 = vibhAjita sakhyA (N) yadi keMka kI mUvamaiMTa jo ki Upara ke sUtra ke dvArA prApta kI gaI hai eka pUrI saMkhyA nahIM hai to Upara diye gae saiTa se / Avazyaka inDaksa pleTa cuna lenI cAhiye / -

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karmazAlA parikalana/107 abhyAsa : eka SaTa bhaja kI miliMga kI jAnI hai| miliMga ke lie kitane cakkara banAne par3eMge? yahAM para N = 48, Upara diyA gayA sUtra lagAne para nk == 62-61 or old .. 6 pUre cakkara + 14 surAkha 21 vRtta meM) yA 16 surAkha 24 vRtta meM) uttara udAharaNa 2 : 48 vibhAjana ke lie Avazyaka inDaiksiga kare / yahAM para N-48, Upara diyA gayA sUtra lagAne para nk-- 48-5-18 yA 20 , .:. 15 surAkha 18veM vRta meM yA 20 surAkha 24veM vRta meN| uttara abhyAsa: sapara mIyaraja ke nimnalikhita dAnte kATane ke lie DIvAiniga haiDa ko saMTa kro| (ka) 10, (kha) 28, (ga) 30, (gha) 62 / uttara : (ka) 4; (kha) 1 yA 118 (ga) 137 (gha) : yA ! 10.2 kaMpAUMDa iMDaksiga : taba prayoga kI jAtI hai jaba ecchika vibhAjana maujUda chidra vrata kI kSamatA se bAhara hotA hai| Ama taura para iMDeksa pleTa ko bAMdhA jAtA hai tAki vo palaMjara, jo ki chidroM ke kisI eka vrata meM lagA huA hai, se na hila ske| kaMpAUMDa iDeksiga kA siddhAnta ecchika vibhAjana ko do hissoM meM prApta karanA hai: * Amataura se keMka kI cAla se * iMDaiksa pleTa ko ghumA kara agalI cAla jamA karanA yA ghaTAnA tathA palanjara ko bAMdha kara niyantrita karanA / kampAUMDa iDaksiga ke lie sUtra : 140 nA jabaki nA-ecchika vibhAjana nA = kaika pina dvArA prayoga kiyA gayA chidra vRta nA,-laoNka pina dvArA prayoga kiyA gayA chidra vRta na. = ka pina dvArA nA, chidra vRta meM chidroM kI dUrI na-pleTa tathA keMka pina dvArA nA, chidra vRta meM chidroM kI dUrI (1) aicchika vibhAjana ko Tukar3oM meM bAMTiye / (2) koI bhI do chidra vRta cuniye / (3) eka vRta ke chidroM kI saMkhyA ko dUsare meM se ghaTAiye / (4) antara ke Tukar3e bnaao| (5) aicchika vibhAjana ke Thukar3oM ko tathA antara ke Tukar3oM ko eka kSaitija rekhA para rkho| (6) spiDala ke eka cakkara (40) ke lie Avazyaka keMka ke lie cakkaroM ke Tukar3e banAo tathA cune gaye chidra vRtoM ke Tukar3e bnaao| (7) ina naye tIna Tukar3oM ko kSatija rekhA ke nIce rakho / (8) Upara tathA nIce ke eka jaise Tukar3oM ko kATa dIjie / yadi rekhA ke Upara ke sabhI Tukar3e rekhA ke nIce ke Tukar3oM se kaTa jAte haiM to cune gaye do vRtoM ko iMDaiksiga ke lie prayoga kiyA jA sakatA hai| yadi rekhA ke Upara ke sabhI Tukar3e pUrI taraha se nahIM kaTa sakate to prayoga hetu hala karane ke lie do anya vRta cunane caahie| (9) jo Tukar3e rekhA ke nIce bagaira kATe raha jAeMge, vRta chidra meM dUrI mAlUma karane ke lie, unako guNA karane para nikAlI jA sakatI hai jo ki do iMDaiksiga mUyamaiMTasa meM calAnI hai|

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karmazAlA parikalana/108 udAharaNa -1 : kampAUMDa iMDeksiga dvArA 69 hissoM ko iMDaiksa kro| dvArA 10.2, sUtra kA prayoga karake 40 _na na. 69 nA nA na, nA, na, tathA nA, kA mAna jJAta karane ke lie 1) 69-23x3 6) 40-2x2x2x5 2) 23 tathA 33, iMDaiksa vRta 23323x1 cune jAte haiN| 33-3x11 3) 33-23 =10 7, 8) 69-23x3 4) 10-2x5 10 %D2X5 5) 69 =23x3 40=2x2x2x5 10%3D2x5 23 D23X1 33-3x11 jabaki kSatija rekhA ke Upara vAle sabhI Tukar3e kATe jA sakate hai| isaliye 23 tathA 33 chidra vata, iMDaiksiga ke lie prayoga kiye jA sakate haiN| isalie nA, -23 tathA nA-33 9) 2x2x11-44 iMDaksiga ke lie chidroM meM antara kA nambara 44 hai / aba sUna ko dubArA hala kiyA jA sakatA hai : 40 44 44 _ 21_11_21_11 69 28 332333 2333 isalie 69 hissoM kI inDaksiga ke lie iMDeksa keMka ko 23 chidra vRta me 21 chidra Age bar3hAnA cAhie tathA taba pleTa aura kaiMka ko eka sAtha 33 chidra vrata meM 11 chidra pIche karanA caahie| abhyAsa: 1. nimnalikhita hissoM ke lie ucita kampAUMDa inDaiksiga kIjie : (ka) 51 (kha) 63 (ga) 87 uttara : (ka) in +12; (kha) A+ 19 (ga) 22, (bhinnoM ke aMza chidroM ko tathA hara chidra vyAsa ko pradarzita karate haiM) 10.3 DiphareMziyala inDaiksiga :-- IHMINJ 1921 CH KIWAN jo hisse sAdhAraNa yA kampAUMDa inDaiksiga se nahIM kiye jA sakate. vo DiphareMziyala iMDeksiga se, ceMja giyarasa kI sahAyatA se kiye jA sakate haiN| Dipharaiziyala iMDaksiga meM, iMDeksa pleTa DhIlI rakhI jAtI hai| yaha eka samaya Age yA pIche cAla iMDeksa spiDala se ceMja giyarasa ke dvArA prApta karatI hai| ceMja gIyarasa ke dAMta hala karake nikAle jA sakate hai| -NE II-IMEI (i) ceMja giyarasa kA giyara anupAta nimnalikhita sUtra se nikAlA jA sakatA hai : (a-nax40 giyara anupAta a jabaki, na-aicchika vibhAjana saMkhyA a-aicchika saMkhyA jo sAdhAraNa inDaiksiga se inDeksa kiyA jA sakatA hai tathA saMkhyA lagabhaga na ke barAbara hai|

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karmazAlA parikalana / 109 , (ii) Upara nikAlI gaI gIyariMga anupAta meM bhinnoM ke hara ko iMTaiksa haiDaspiTala ke DrAiviMga giyara ko pradarzita karate haiM tathA aMza iMDeksa pleTa ke ulina giyara ko pradarzita karate haiN| 40 (iii) iMDeksa pheMka mUvameMTa jabaki na cunI gaI saMkhyA hai| pUre kArya ke vibhAjana ke lie iMDeksa ka , na ko Upara die hue sUtra meM mAtrA ko na bAra ghumAnA pdd'egaa| abhyAsa : (iv) iMDeksa phaMka tathA iTaiksa pleTa ko eka hI dizA meM yA viparIta dizA meM ghumAnA cAhie jo ki gIriMga anupAta kI kisma tathA cunI gaI saMkhyA a para nirbhara karatA hai| yadi (ana) dhana (+) hai to iMDeksa pleTa ko pheMka kI dizA meM hI ghumAnA cAhie tathA yadi (ana) RNa ( ) hai to iMDeksa pleTa ko pheMke kI dizA ke viparIta ghumAnA caahie| ina zartoM ko pUrA karane ke lie, ucita saMkhyA meM AiTalara giyarasa prayoga kiye jAte haiN| udAharaNa 1 51 hissoM ko iMTeksa kIjie / yahAM cuniye (1) giyara anupAta (2) isalie DrAivara sa72,40 tathA haricana 24, 56 1. a - 56, saMkhyA 53 ke nikaTatama ho tathA plena iMDeksiMga se iMDeksa kI jA sake / (ana) x 40 45 9x5 (56-53) x 40 a 7240 X. 24 56 56 21 3x7 udAharaNa- 1: (3) ka mUvameMTa 40 5 56 7 ke ko 53 bAra, 15 chidra, 21 a uttara : 40 ( ka ) (ka) (kha) sf (4) jabaki (ana) dhana (+) hai tathA gIyariMga anupAta kampAUMDa hai isalie koI bhI AiDala giyara kI AvazyakatA nahIM hai, pleTa ko kraiMka kI dizA me ghumAnA cAhie / Diphareziyala iMDeksiMga dvArA nimnalikhita kI ucita iMDeksiMga tathA giyarasa jJAta kIjie (ka) 97, (kha) 83 5 x 3 7 x 3 aicchika koNa DigriyoM meM 90 aicchika koNa minToM meM 540' 15 21 chidra vRta meM ghumAnA par3egA / / 10.4 eMgulara (koNIya) ksiga yaha taba prayoga kI jAtI hai jaba eka koNa ko iMDeksa karanA ho| ghumAtA hai| kArya ke madhya para koNa phraiMka ke eka cakkara 400 =5deg ke ghUmatI hai : 13 chidra, 33 buta meM; gIyara anupAta 20 chidra, 43 bUta meM gIyara anupAta 2 29020 koNa iMDeksa kiijie| 29deg20'-1760' hai pleTa ko pheMka kI dizA meM ghumAnA hai| hai pleTa ko pheMka kI dizA meM hI ghumAnA hai| kyoMki kraiMka kA eka cakkara spiMDala ko baiTha cakkara barAbara hotA hai, isalie kisI bhI koNa ke lie ka . Uparalikhita ke lie pheMke mUvameMTa 1280323 = - 3 pUre cakkara tathA 7 chidra 27 chidra vRta meM

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abhyAsa 1 nimnalikhita koNo ke lie iMDeksiga jJAta kIjie : (ka) 19deg 40' () 15deg 30' uttara : ( ka ) 2 pUrA cakkara tathA 5 chidra 27 chidra vRta meM (kha) 1 pUrA cakkara tathA 13 chidra 18 chidra vRta meM 11 hailikala ( ghumauvA) slaoNTasa tathA kI ve (key ways) kI miliMga : ghumAvadAra yA pecadAra miliMga meM, kAma ko isake loMgicyUDInala akSa ke sAtha sAtha calAyA jAtA hai jabaki sAtha meM hI eka aura koNiya gati dI jAtI hai, pariNAma svarUpa kaTara ghumAvadAra gaDDhA (slATa ) banAtA hai / donoM taraha kI gatiyAM s Tebala phIDa spiDala se dI jAtI hai / yaha kArya ko isake logIcyUDInala akSa ke sAtha-sAtha calAtA hai jabaki usI samaya eka gIyaroM kA seTa DivAiDiMga haiDa spiDala tathA Tebala phIDa peca ke bIca meM lagAyA jAtA hai tAki koNiya gati dI jA sake / iMDeksa pleTa ko DhIlA kara diyA jAtA hai tAki spiDala ko ghumAyA jA sake / kAma ko cakka meM bAMdhA jAtA hai tathA meja (Tebala) ko hailiksa koNa ke barAbara ghumAyA jAtA hai / 1. hailiksa koNa yA Tebala koNa ke lie sUtra diyA jAtA hai / gava tan8= la jabaki, va kArya kA vyAsa karmazAlA parikalana / 110 la = hailiksa kI lIDa (lead) .. gIyara anupAta - 2. gIyara anupAta ke lie sUtra : DrAIvara_ga1. ga3. gIyara anupAta Dakhina ga. ga Tebala spiDala kI lIDa (la) X kArya ko eka cakkara ghumAne ke lie kraiMka ke cakkara (40) - 7 pitch 6m aicchika hailiksa kI lIDa ( 40 Ta la ha la. eka mukhya ceMja gIyarasa ke saiTa meM 24 24, 28, 32, 36, 40, 44, 48, 56, 64, 72, 86 tathA 100 dAMtoM vAle gIyarasa hote haiM / udAharaNa 1: eka jaoNba 40 4 tathA lIDa 450 para hailikala grUva kATane ke lie gIyara anupAta tathA Tebala seTiMga koNa jJAta kIjie / miliMga mazIna ke spiDala kIM pica 6 mi. mI. hai /

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Tebala seTiMga koNa ke lie, sUtra 1 kI sahAyatA se gva 3.14 X 40 tan B 1 450 gIyara anupAta sUtra 2 kI sahAyatA se 40 tan B. 2. phorjiMga gIyara anupAta .. la gha. ga. gva 3.14 X 42 = udAharaNa 1. kSe. phorja la udAharaNa- 2 : gIyara anupAta tathA hailiksa koNa jJAta kIjie yadi (ka) kArya kA vyAsa 42, (kha) lIDa 263" tathA ( ga ) miliMga mazIna Tebala kI pica " dvArA 11, sUtra 1, hailiksa koNa diyA jAtA hai / (263 * = 667 mi. mI. ) ga ga ga. ga ga. ga gaga 667 0.1977 .. P = 10deg11' (tan sAraNI se ) 40 la mAnA ki lIDa skayU kI pica 6 hai / uttara : ( ka ) 45deg (a) 905.8 (ga) 32 x 24 40x72 karmazAlA parikalana / 111 la. ha ha kSa. sa kSe.pha --- 0.2796 8 15deg31' (tan sAraNI se ) 6 x 40_2x4 450 5 x 3 1x 40 261 uttara 40 8 2x4 -----34 21 3x7 40x32 100x24 abhyAsa : 1. eka hailokala gIyara, jisakA pica vyAsa 288 tathA hailiksa koNa 45deg haiM, kI miliMga ke lie nimnalikhita jJAta kIjie : (ka) Tebala koNa, (kha) lIDa tathA (ga) gIyara anupAta / 24x32 36 x 56 (905.8 ke bajAya 900 lIDa lekara ) sTaoNka kA kSetraphala (kSe. sa) phorjiMga kA kSetraphala (kSe. pha) uttara uttara phojiMga meM ghaTatI guNanakhaMDa ( riDakAra phaikTara) : phorjiMga meM ghaTotI guNanakhaMDa, sTaoNka ke Tukar3e tathA taiyAra phorjiMga, ke kraoNsa saikzanala kSetraphaloM ke anupAta ko samajhA jAtA hai / ghaTotI guNanakhaMDa jitanA jyAdA hogA, kaNa bhI utane acche hoMge tathA phorjiMga kA isalie ghaTautI guNanakhaMDa (gha. ga.) uttara eka phorjiMga kA ghaTautI guNanakhaMDa jJAta karo jaba vo 300x300 se 200 x 200 taka banAI jAe / 200 x 200 = 40000 varga mi.mI.

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karmazAlA parikalana/112 tathA kSe. sTAka =300x300-90000 varga. mi.mI. :: ghaTautI guNanaphala (gha.ga.) = _90000 -2.25 uttara 40000 abhyAsa: 1. ghaTautI guNanakhaMDa jJAta kIjie jabaki eka gola char3a 40 ko 25% meM banAyA jaae| uttara: 2.56 AraTIkala-13 vailDiga AraTIkala 13.1. vailDiga ke daurAna paidA kiyA gayA tApa vailDiga ke samaya paidA kiyA gayA tApa isa prakAra nimnalikhita sUtra dvArA darzAyA jAtA hai| sUtra: H-kIVT kailorI jahAM ki, k eka kAnsaTeMTa hai, tApa ke jJaya hone ke kAraNa sUtra meM rakhA hai aura Amataura para isakA mAna 0.24 hai| I-dhArA empiyara meM / v=volTeja volTaz2a meN| t=samaya saikiMDa meN| udAharaNa-1: eka bijalI kI Araka eka ghaNTe ke lie calAI gaI hai, dhArA-200 empiyara tathA volTeja-20 volTa / kitanA tApa paidA kiyA gayA ? hameM AraTIkala 13.1 se prApta hai / H=kIVT, k%3D0.24 lete hue hameM prApta hai; H-024 x 200 x 20X3600-3456 kilo kailorI (uttara) abhyAsa : yadi eka Araka ko 15 minaTa taka rakhA jAtA hai aura dhArA I-100 empiyara tathA volTeja V-12 volTaja, paidA kiyA gayA tApa jJAta karo (k-024) uttara : 2592 ki. kailorI AraTIkala-13.2 : vIlDaMga kA mUlya jJAta karanA dhAtuoM ko jor3ane ke lie vailDiga hI eka aisA DhaMga jo dUsarI vidhiyoM se sastA hai| vailDiMga ke lie bahuta se DhaMga haiN| vailDiMga kA sahI DhaMga cunane se vailDiga kA kama se kama kharca A sakatA hai| (velDa kI prati mITara kilo DipojiTa)- ilekTroDa kI prati mITara kImata vailDa ke ilaikTroDa kA prati mITara mUlya DipojiTa kI gaI dhAtu kI dakSatA prati ghaMTA kyUbika mITara gaisa kA pravAha gaisa kA mUlya prati kyUbika mITara gaisa kA mUlya cAla kI gati prati ghaNTA mITara meM wimmmmmmymat udAharaNa-1: vailDa ke prati mITara vailDiga kA mUlya jJAta karo jaisA ki citra meM dikhAyA gayA hai| yadi valDa kI kilo meM DipojiTa prati mITara, 0.3. ilaikTroDa kA mUlya prati kilo 16 rupaye hai| DipojIzana maiTala kI dakSatA 0.8.

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ilaikTroDa kA mUlya pratimITara = abhyAsa : 1. 6 phileTa kI jinakI lambAI 5 mI. vailDiMga karane kA mUlya jJAta karo / yadi prati ki. grA. DipojiTa ke prati mITara vailDa 0., kImata / ki. grA ilaikTroDa kI 28 rupaye, dhAtu kI DiposiTa kI dakSatA 0.7. uttara 100 rupaye 2. lohe kI banAvaTa ko aseTalIna dvArA velDa karane kI kImata jJAta karo / yadi gaisa kA pravAha 0.6 mITara / ghaNTA hai yadi gati - 5 mITara / ghaNTA tathA gema kI kImata 40 ru0 / mITara uttara : 48 rupaye : karmazAlA parikalana / 113 0.3 X 16 0.8 zITa dhAtu kA kAma AraTIkala - 14 : khAlI gherA kisI khAlI sthAna kI bar3hI huI lambAI jJAta karane ke lie hameM sIdhe sekzana kI lambAI ko jJAta karanA hotA hai / cApa meM saMkSipta lambAI kI rAzi yA lambAI prAkRtika avasthA ke sAtha / khAlI lambAI 'sa' jJAta kI jA sakatI hai / 90deg beMDa sUtra se kAma ke dvArA / jahAM ma aura ma = kAma kI sIdhe saikzana kI lambAIyAM hai, mi0 mI0 ka - cApa meM blaika kaTauto kA mAna, mi0 mI0 blaika kaTautI kA mAna jJAta karanA mur3e hue reDiyasa aura kAma kI moTAI para nirbhara karatA hai / sama, + ma ka ka udAharaNa- 1 : ra za - 6 rupaye uttara 2 jahAM para ra-mur3I huI trijyA hai mi. mI. meM za - kAma kI moTAI, mi. mI. + za kisI bhI blaika kI lambAI kisI koNa para mur3ate samaya kama yA jyAdA ho sakatI hai taba 90deg sUtra dvArA jJAta kiyA jA sakatA hai / jahAM ma aura ma- bleMka ke sIdhe sekzana kI lambAI hai, mimI. meM khacApa meM prAkRtika akSa yA avasthA kI lambAI, mi. mI. sama1 + ma + kha golAI kI hada meM prAkRtika avasthA kI lambAI jJAta karanA bleMka moTAI para nirbhara hotI hai / mur3I huI trijyA aura mur3A huA koNa yaha diyA huA hai| kha= 0.0175 ( x + 1/2 ) za ra+ jahAM ki ra= mur3I huI vijyA, mi. mI. * blaika moTAI, mi. mI. c - mur3A huA koNa, DigrI nimnalikhita prophAIla paimAIza dvArA eka baleMka kI lambAI P jJAta karo jabaki : ni- 15 mi.mI., ng 15 ac

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karmazAlA parikalana/114 mi. mI., R-2.5 mi. mI., m-0.5 mi. mI. P-ni+n,-A-15+15-(2.5+0.5)-28.25 mi. mI. uttara 2 udAharaNa-2: nimnalikhita prophAIla paimAIza dvArA citra meM blaika kI lambAI jJAta karo : 1-20 mi.mI., n40 mi. mI., R-5 mi. mI., m = 6 mi. mI., 3-30deg P-20+40+0.0175(5+)x30deg ___ =64.2 mi. mI. uttara abhyAsa : 1. nimnalikhita prophAIla paimAIza dvArA citra meM balaiMka kI lambAI jJAta karo : n=20 mi. mI., ng-40 mi. mI., R-10 mi. mI., m=3 mi. mI. a=137deg uttara : 88 mi. mI. 2. nimnalikhita prophAIla praimAIza dvArA kAma kI lamlAI jJAta karo:0-20 mi. mI., n,=40 mi. mI.= 1370, R=10mi. mI, m =3 mi. mI. (abhyAsa 1 kA cinna dekho) uttara : 87.5 mi.mI.

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udAharaNa- 1 : karmazAlA parikalana / 115 grupa- 11 DhalAI ke kArakhAne kA viSaya kisI gubaMda kA AMtarika vyAsa jJAta karo / jo ki ghula jAtA hai 6 Tana prati ghaNTA / mAna lo ki 5 ki0 grA0 lohA milatA hai / prati varga seMTImITara meM pighalAyA jA sakatA hai / adhyAya 14 karmazAlA parikalana se saMbaMdhita prazna udAharaNa-3 : 6 Tana prati ghaNTA - 6 x 1000 6000 ki. grA / ghaNTA gubaMda kA kSetraphala - 0000 1200 seMTImITara varga 1200 .. gubaMda kA AMtarika vyAsa - Vo.433444 seM. mI. uttara (=0.7854) udAharaNa - 2: kisI gubaMda kI 6 Tana / ghaNTA kI kSamatA meM prati minaTa vAyu kA kitanA Ayatana Avazyaka hotA hai, yadi yaha 10: 1 kI anupAta se kAma karatA hai ? ( mAna lo ki 1 ki. grA. kASTha cAhie 9 ghana mITara vAyu kI dahanazIlatA ke lie) 6 Tana / ghaMTA - 6 X 1000 6000 ki. grA./ghaMTA 100ki. grA./ minaTa eka dhAtu kI 100 = yaha hameM diyA huA hai ki kASTa 10: 1 kI anupAta meM hai / isalie jitanA kASTha cAhie usakI rakama = 10 ki.grA./ minaTa pratyeka ki. grA. kASTha cAhiye 9 mITara vAyu kI dahanazIlatA ke lie 10 ki. grA. kASTha cAhiye 9 x 10 = 99 mITara vAyu isalie 90 mITara / minaTa cAhie uttara eka Thosa paiTana kA bhAra 2.5 ki. grA. hai r3halI huI dhAtu kI spIsIphika greviTI paiTrana kI lakar3I se 20 guNA hai / Dhale hue purje kA kyA bhAra hogaa| yadi eka surAkha usa ke andara banA diyA jaae| 4 seMTImITara vyAsa se kendra meM aura 8 seMTImITara lambAI 2 seMTImITara jo ki kendra banAtA hai 1 ( mAna lo ki dhAtu kA ApekSita ghanatva 8 grA./seMTImITara hai) Dhale hue purje kA bhAra 2.5 ki. grA. x 12-30 ki.grA.

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karmazAlA parikalana/116 kendra lambAI = 8 seMTImITara, ora kendra banAne kI lambAI-2 se. mI. .:. surAkha kI lambAI-8-2-6 se.mI. kendra kA Ayatana-- mAyatanagax42 -x6=75.42 se.mI. aura barAbara Ayatana vAlI dhAtu kA bhAra-75.42x8 grA. =603.4 grA. =0.6 ki.grA. isalie Dhale hae purje kA bhAra-30-0.6-29.4 ki. grA. udAharaNa-4: eka 1000 ki. grA. kA inagATa molDa meM 1300degC tApamAna para pighalA huA lohA DhAlA gyaa| inagATa molDa ke samaya prati minaTa 1.5degC tApamAna kama hotA hai| inagATa molDa meM kAsTiga ko 200degc para ThaNDe karane ke lie kitanA samaya lgegaa| girA huA tApamAna-1300degC-200degC-1100degc : yadi ThaNDe karane kI dara / 5degC prati minaTa hai to 1100degC kA tApamAna girAne ke lie jo samaya cAhiye: 1100degC minaTa-1.5x60 1100 1.5degC minaTa- -12.22 ghaMTe uttara abhyAsa kyapalA kA Antarika vyAsa jJAta karo joki 3 Tana prati ghaNTA pighalAtI hai| aisA mAnA jAye ki 3 ki.grA. lohA prati varga seMTImITara krAsa seksana airiyA kA prati ghaNTA pighalAtA hai| uttara : 403 se mI vAya kA Ayatana prati minaTa jJAta karo eka kyUpalA ke lie jo 3 Tana prati ghaNTA pighalAtI hai| yadi yaha 15 : 1 anupAta se kAma kre| mAna lo 1 kilo koyalA jalAne ke lie 12 kyUbika mITara havA cAhiye / / uttara : 40 kyUbika mITara 3. eka kyUpalA ko 8 Tana lohA prati ghaNTA pighalAnA hai, yadi 0.70 ki. grA. lohA prati ghaNTA pighalatA hai eka varga seM.mI meN| kyUpalA kA Antarika vyAsa jJAta kro| grupa 2, apareMTisa parIkSA, sitambara 1973 uttara : 1206 seM. mI. karmazAlA parikalana ke prazna grupa-4 vidyuta zAkhA grupa se saMbandhita adhyAya 15 1. vidyuta ke prazna hala karane se pahale kucha mUla jAnakArI Avazyaka hai : dhArA (I) volTeja (V) tathA pratirodha (R) dhArA: dhArA kI ikAI empIyara hai| yaha vaha dhArA kI mAtrA hai jo ki 1 oma ke pratirodha meM se 1 volTa ke dabAva se bala se pravAhita kiyA jaae|

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karmazAlA parikalana/117 - volTeja: volTeja kI ikAI volTa haiM / yaha vaha vidyuta dabAva hai jo ki eka om ke pratirodha vAle dhArAmaNDala meM se eka empI yara dhArA bala se pravAhita ho ske| jaba hama volTeja ke bAre meM bAta karate haiN| hameM tIna ikAiyoM ke bAre meM sAvadhAna honA hogA: ilekTromoTiva bala (11) poTaiziyala antara (U) tathA volTena meM girAvaTa (v) mAtA ilekTomoTiva bala : ilekTromoTiva bala (E) beTarI yA DAyanamo ke Taminalasa ke vIca mApI gaI volTeja hai jabaki ve gaharI dhArAmaNDala meM dhArA de rahe hoN| poTeMziyala antara : poTeMziyala antara (U) baiTarI yA DAyanabho ke Tarminalasa ke bIca mApI gaI volTeja hai jabaki ve bAharI dhArAmaNDala meM dhArA de rahe hoM yAni ki poTeziyala antara- ilekTromoTiva bala-andara kA pratirodha x baha rahI dhArA kI mAnA bolTeja meM girAvaTa : volTeja meM girAvaTa (V) vAlTeja kI hAni hai jaba dhArAmaMDala meM dhArA baha rahI ho / pratyeka cAlaka ko kucha na kucha pratirodha hotA hai cAhe vaha kitanA hI acchA ho| isalie dhArAmaMDala meM bala pUrvakadhArA bahAne ke lie kucha volTeja Esa kAma ke lie prayoga kI jAtI hai tathA isalie yaha lAbhadAyI kArya ke lie upalabdha nahIM hotii| pratirodha : pratirodha kI ikAI oma (2) hai / yaha vaha pratirodha kI mAtrA hai jisa dhArAmaMDala meM eka empIyara kI dhArA baha sake jaba ki dabAva eka bolTa ho| 2. bhomsa kA niyama : omsa kA niyama tInoM, volTeja, dhArA tathA pratirodha meM sambandha batAtA hai jo sUtra meM isa prakAra diyA jAtA hai : R yahAM ki, I-dhArA empIyara meM VvolTeja volTaz2a meM R-pratirodha oma meM udAharaNa-1: eka kAyala meM pravAhita bijalI kI dhArA jJAta karo jaba ki imapraisaDa volTeja 12 volTa tathA pratirodha 4 oham hai| T V 12 ..- -. R4 -3 empIyara uttara udAharaNa-2: 3empIyara kI dhArA pravAhita karane ke lie kitanI volTeja cAhie jaba ki pratirodha 42 hai? ___v-IR-3x4--12V uttara udAharaNa-3 : jaba 10 omasa kA pratirodha eka baiTarI ke sAtha konekTIDa kiyA jAtA hai 0.6 empIyara kA karaMTa pratirodha meM se pravAhita hotA hai agara baiTarI kA Antarika pratirodha 2 omasa hai, to baiTarI kA I. ema. epha. kyA hai ? poTeMziyala DrApa = pravAhita dhArA 4 pratirodha -0.6 empIyara x 10 omasa -6bolTasa volTeja DrApa =pravAhita dhArA x baiTarI kA AMtarika pratirodha -0.6 omasa-2 omasa --1.2 volTasa

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3. ava I. ema. epha. poTeMziyala DrApa + volTeja DrApa - 6 + 1.2 volTasa - 7.2 volTasa abhyAsa 1. eka laimpa ko jalAne meM kitanI dhArA cAhie agara laimpa kA pratirodha 12 2 aura volTeja 6 hai / uttara : 5 empIyara 2. kucha srakiTa jisa meM 10 empiyara dhArA pravAhita karatI hai jaba prezara 13 volTeja hai / sarkiTa kA pratirodha kyA hai ? AraTIkala - 3 : AraTIkala - 3.1 karmazAlA parikalana / 118 uttara : 1.3 omasa DAyanamoM kA Antarika pratirodha (jisakI I. ema. epha. 12 volTa hai) 0.01 oham hai / jaba 20 aimpiyara karaMTa kI saplAI dI jA rahI ho tI DAyenamo kA TaramInala volTeja jJAta karo ? 1 * uttara sIrIja tathA pairelala meM kunaikzana pratirodha kA sIrIz2a meM kunaikzana R1 www Laiki aad ikvaileTa pratirodha (R) = R1+R2+R3 - aura volTeja DrApa hara eka rassiTara ke viruddha V, - IR1, V2 - IR2, V3 =IRg V 12 R2 wwwww kavyaad R 6 udAharaNa - 1 : tIna pratirodha kramazaH 1, 2 tathA 32 haiM, 12 volTa baiTarI ke sAtha sIrIja meM jor3e gaye haiM / mAna jJAta karo : (ka) pravAhita dhArA (kha) hara eka pratirodha ke viruddha bolTeja kula pratirodha - 1+2+3=62 (ka) pravAhita dhArA I (kha) hara eka pratirodha ke viruddha volTeja baiTarI volTeja X pratyeka pratirodha kula pratirodha 12 pratirodha ke viruddha volTeja 22 pratirodha ke viruddha volTeja = 2 2 x 1 = 2 volTeja - 12 x 2 = 4 volTeja - 32 x 3 - 6 volTeja 3 2 pratirodha ke viruddha volTeja baiTarI kula jor3a - 2+4+6 = 12 volTeja yAni ki baiTarI kI volTeja R1 wwwwwww kavyat do = 2 empIyara uttara : 11.8 volTaja

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karmazAlA parikalana/119 ArTIkala-3.2 pairelala meM pratirodha - R2 2mance 13 -v yahAM para ikvaiveTa pratirodha R diyA gayA hai aura kula dhArA ! ..11+-I+-13 udAharaNa-1: cina me diye gaye sarakaTa kA ikvaileMTa pratirodha jJAta kro| 20 (R) -wwwwwwwww 4n (R2) -wwwwwww6nR) B RL) - 1-1+ + + R R, R,'RG'Re - aura R -- R, 'R, 'R + +1+1+1 (12+9-1.4+3) 24 --12-R -25.2 uttara abhyAsa : 1. balba holDara kA pratirodha jJAta karo jo ki igavIzana vAraniMga lAITa ke 12 volTa sisTama se jur3A huA hai| balba kI spesIphIkezana 2.5 volTa tathA 0.2 empiyara hai| uttara : 47.52 citra meM dikhAye gaye sarakiTa kA ajJAta pratirodha tathA ikvaileMTa pratirodha jJAta, yadi 2.4 empiyara kI dhArA pravAhita kara rahI hai aura volTeja 12 volTa hai| uttara:52 aura 32 2. 2NIRN JAR 201RN A crwwwwwMDE.. wwww+ARY 241RICEw -12 -

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karnazAlA parikalana 120 AraTIkala 3.3 maTailika kanDakTara kA pratirodha kanDakTara kA pratirodha, kanDakTara kI pemAIza tathA padArtha kI pratirodhatA (e) se jJAta kiyA jA sakatA hai| padArtha kI pratirodhatA, kanDakTara ke pratirodha joki eka mITara lambAI aura 1 mi.mI.2 ohama meM hai| kanDakTara ke pratirodha kA sUtra R= PP jahAM ki= R = pratirodha oham meM P-pratirodhatA (2 mI.) meM P-lambAI mITara meM a-kSetraphala mi.mI meM AraTIkala 4. vidyuta zakti vidyuta zakti kI yUniTa vATa (W) hai / yaha vidyuta dhArA I empiyara me aura I.ema.epha. (v) volTa kA guNanaphala hai / isalie W-IV PR (jaisA ki IR=v) TippaNI : peja 20 dekheM, vibhinna prakAra ke zakti ke yUniTasa ko badalane ke lie| uharaNa 1. eka 12 volTa, 36-vATa haiDalaimpa balba dvArA prayoga kI gaI dhArA kI mAtrA jJAta kiijie| vATa =Ixv 36-IX 12 I-3 aimpiIyara uttara udAharaNa 2. eka saikaNDarI saila kI volTeja 2.06 hai java 0.1252 ke pratirodha se jor3A jAtA hai to usakI Tarminala volTeja 1.95 volTa hai| saila ke andara kA pratirodha tathA naSTa hue vAToM ko jJAta kiijie| (grupa 4, mArca 1972) dhArAmaNDala meM dhArA kI ma nA J= 95 15.6 empIyara (dvArA 2, peja 133) volTeja me girAvaTa-2.06-1.95-0.11 volTa 0.11 isalie andara kA pratirodha - --.0072 uttara naSTa hae vATa-12R jabaki R-.007 andara kA pratirodha aura 1-dhArAmaNDala meM bahatI haI dhArA (15.6)3x.007 -1.7 vATa uttara 4.1 DropiMga pratirodhaka : kabhI-kabhI kama volTeja vAle bijalI ke upakaraNoM ko jyAdA volTeja vAle saplAI binduoM se jor3anA par3atA hai| taba jyAdA volTeja, DropiMga pratirodhaka joki sIrija meM lagAyA gayA hai dvArA prayoga kI jAtI hai parantu saplAI binduoM tathA upakaraNa ke lIca meM lagAyA jAtA hai| udAharaNa : eka riphalekTara 500w/255V ko 600 V DI.sI. dhArAmaNDala meM lagAyA hai| (ka) DopiMga pratirodhaka se kitanI jyAdA dhArA bahegI? (kha) DropiMga pratirodhaka kitane om kA ho ?

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karmazAlA parikalana/121 (ga) kitanI vidyuta zakti garmI meM badalI jAtI hai ? DopiMga pratirodha -=-- -------0 500 vATa 255 yolTa ----- - --------- - - 255 - -or 600vojyAdA volTeja1-V-V... 600-2253345 volTa pravAhita dhArA 1-w:V=500 : 255-1.96 aimpIyara pratirodha RE-V:1-345--1.96 =3176 oma 4.2 saplAI lAIna meM volTeja DrApa(girAvaTa) : sabhI lAIneM (le jAne tathA vApisa lAne vAlI) bijalI ke upakaraNa taka, upakaraNa ke sAtha sIrIja sambandha banAtI haiM tathA phIDa lAIna meM volTeja kI girAvaTa hotI hai joki nahI caahie| unheM jitanA sambhava ho sake, kama se kama rakhe tathA lambI lAinoM para ve nirIkSita kiye jAte haiN| udAharaNa: 1500W/220V aMkita kImata vAle bijalI ke hITara ko eka tAMbe kI tAra jisakI lambAI 12 mITara tathA kSetraphala 1.5 mi.mI.hai ke sAtha 220V vAle dhArAmaNDala meM jor3A gayA hai| upakaraNa para volTeja jJAta kro| tAbe kA p lo -6 (52 mI.) [pravAhita dhArA I-W-:-V-1500 - 220 = 6.8 empIyara .12 lAina kA pratirodha R-21 --0.286 oma 56x1x5 - - abhyAsa: 1. eka baiTarI cArajara kI aMkita zakti jJAta kIjie jo ki 8A, sAmAnya volTeja 220V para, kharca karatA hai| uttara : 1.76 kilovATa 2. epha pampa moTara 24 ghaMTe calatI hai| yadi yaha sAmAnya volTeja 220V para 10A kharca karatA ho, kula kharcA mAlUma kIjiga yadi zakti kA mUlya 30 paisA prati ikAI ho / (zakti kI ikAI-1 kilovATa ghaMTA) uttara : 1.65 rupaye 3. eka janareTara 15A, 16.5 volTa poTeMziyala antara para dhArA detA hai yadi janareTara kI dI gaI zakti 0.3 azva zakti ho to mazIna kI dalatA jJAta kiijie| _prApta kI gaI zakti x 100 )uttara : 83% (dakSatA = dI gaI zakti 4. eka laimpa baiMka, meM tIna balba haiM jo ki pratyeka 2 empIyara letA hai, ko 120 volTa se jor3A gayA hai| pratyeka tAra kI lAIna kA pratirodha 0.2 oma hai| lAIna meM volTeja girAvaTa tathA loDa para prApta volTeja jJAta kro| uttara : 2.4 volTa tathA 117.6 volTa

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bhAga 3 N . . pariziSTa

Page #130
FAAT OTS/125 CONVERSIO TABLE: INCHES TO MILLIMETRES TABLE-I INCH FRACTION 04 32 16 8 4 12 DECIM- M/M AL EQU- EQUIIVALENT VALENT INCH DECIM- M/M FRACTION AL EQU- EQUI64 32 16 8 4 2 IVALENT VALENT .0156 .40 .0312 .79 .0468 1.19 .0625 1.59 .0781 1.98 .0937 2.38 .1093 2.78 .125 3.17 . 1406 3.57 . 1562 3.97 . 1718 4.35 .1875 4.76 .2031 5.16 .2187 5.56 .2343 5.95 .250 6.35 .2656 6.75 .2812 7.14 .2968 7.54 .3125 7.94 .3218 8.33 .3437 8.73 .3593 9.13 .375 9.52 .3906 9.92 .4062 10.32 .4218 10.71 .4376 11.11 .4531 | 11.51 .4687 11.91 .4843 12.30 .500 12:70 .5156 13.10 .5312 13.49 .5468 13.89 .5625 14.29 *.5781 14.68 .5937 15.08 .6093 15.48 ..626 115.87 .6406 16.27. .6562 16.67 .6718 17.06 .6875 17.46 .7031 17.86 .7187 18.26' .7343 18.65 .750 19.05 .7656 19.45 .7812 19.84 .7968 20.24 .8125 20.64 .8281 21.03 .8437 21.43 .8593 21.83 .875 22.22 .8906 22.62 .9062 23.02 .9218 23.41 .9375 23.81 .9531 | 24.21 .9687 24.61 .984325.00 CONVERSION TABLE: MILLIMETRES TO IN CHES TABLE-II mt 1 2 1 4 5 6 7 8 9 0,0390,079 0,118 0,157 0,1970,236 0,276 0,315 0,354 10 0,394 0,433 0,472 0,512 0,551 0,591 0,630 0,669 0, 7000, 748 20 0,787 10,82710, 8660, 905 0,945 1,984 1,0241,063 1,102 1,142 30 11,181 1,220 1,259 1,299 1,338 1,378 1,417 1,457 1,496 1,535 40 11,575 (1,614(1.65311.69311.732 1,772/1,811 1,850 1,890|1,929 11,968 2,007 2,047 12,0872,126 12.16512.205 2,244 2,2832.323 60 2,362 12,401 2,441 2,48012,520 12,559 12,598 2,638 / 2,6772,716 70 2,756 2,795/2,835 2,8742,9132,953 2,992 3,031 / 3,071 3,110 80 3,149 3, 1893,2283,268/3, 307 3,346 3,386 3,425 3,464 /3, 504 903, 543 13,5833,622 13,6613, 701 13, 740/3, 7793,819 3,858 3,897 50

Page #131
F ETT /126 TABLE-III DENSITY OF MATERIALS DENSITY ELEMENTS/MATERIALS B/cm3 ELEMENTS/MATERIALS DENSITY g/cm3 Aluminium 2.7 Brass 8.5 11.35 Lead 8.4 Al' bronze Carbon 3 Tin bronze 8.6 Graphite 2.25 Lead bronze 9.5 Diamond 3.52 Al-alloy (Al,Cu, Mg) 2.8 Cobalt 8.8 Babbitt metal 17.5.. 10,1 Chromium 7.1 Plexiglass 1.2 Copper 8.9 Alcohol at 18degC 0.79 Steel 7.85 7.85 Water at 4degC Acetylene at o'c 1.0 1,17kg/m3 Cast Steel Gray cast iron 7.2 1.90kg/m3 Carbon dioxide at 00C Air at ooc High-speed Steel 9.0 1.29kg/m" 2.00kg/m3 Invar (36%Ni) 8.7 Propane at ooc TABLE-IV GREEK ALPHABET a Alpha i Jota r Rho Beta Tk x k Karra 8 Sigma & Gamma Lambda Tau u Ypsilon a Deita e Epsilon Nui ph Phi 2 Zeta Ksi ch chi e Eta ps Psi Tool 0 121 p Omikron Pi V th Theta o Omega

Page #132
224 c s 224 1284 56789 CUST CUT 22 2282 85883 88588 99999 25885 89588 85888 88588 RFRRR RRERA 858** *858 LE 828 28 So c 54,768 3*28* 0401 E00 4833 0158 7460 K C MATHEMATICAL TABLE . 88 101 waa 118 13224 120 14400 ho 123 15129 124 15376 125 15625 126 15876 127 16129 129 16641 10 16900! 122 17424. 133 17689 134 17956 135 18225 1 10201 102 10404 10,0995 320, 103 10609101090 328 738494.3 0,22 104 10610409470 329.87 8659.0 593 2463.01 106 11236 10.2956 333,01 8824, 179,07 2551,76 107 11449 10,3441 336,15 8992,0 182,21 2642,08 109 11664 10,3923 339,29 9160,88 185,35 2733,97 109 11881 10,4403 342,43 9331,32 50 2827.431 110 12100 10,4881 345,58 9503,2 2922,47 111 12321 10,5257 348,72 9676,89 3019,07 to 19750 8301 265.00 100287 14 12996 10,6771 358,14 10207,0 164 183 10386,9 c 4119881 11. 142 20164 20449 39,72 144 2073512,000 (088,22 145 21025 12,041 383 07 138 19044 14 139 19321 11,7898 435,69 15174,1 C dicnd 156 157 158 159 160 161 REPRE 24 Le 65 27225 12,8452 518,36 21382, 66 27556 12,8841 521,50 21642,4 167 27889 12,9228 524,65 21904,0 168 28224 12,900 530.93 22431,8 28 534,07 22698,0 170 29584 13:1149 540.35 23235.2 29929 13.1529 543.50 23506.2 74 30276 13,1909 646,6 23778,7 76 30976 13,2665 552, 6060,6 193 16280,0 194 8104 12,3288 400021010010 23716 12,4097 483,81 8826,5 204 24025 12,4499 486,95 18869,2 24336 12,4900 490,09 19113,4 24849 12,5300 493,23 19359,3 24964 12,5698 496,37 19606,7 25281 12,6095 499,51 19855,7 25600 12,6491 502,65 20106,2 25921 12,6886 505,80 20358,3 26569 12.7671 512.08 20867.2 26896 12,8062 515,22 21124, 35721 13,741 36481 13,62 102 36864 C 471,24 17671,5 200 40000 14,1421 698,32 31415,9 17907,9 201 40401 14,1774 631,46 31730,9 24052,8 24328,5 197 38809 14.035 7542,93 148 21904 12,1655 464,96 17203,4 198 39204 14,0712 622,0 12,2086 468,10|17436,6 199 3960119,1007025, 205 206 207 209 32041 13,3791 562,35 25164,9 25446,9 134782 181 32761 13.4536 568.63 25730.4 231 33124 13,4907 571, 232 33489 13,527 385613,564. 210 211 213 214 215 216 217 219 |nnnn 2 57 K .5 41616 14,2829 640,88 32685,1 42025 14,3178 644,03 33006,4 42436 14,3527 647417 33329,2 42849 14,3875 650,31 33653,5 36817222 653,45 33979,5 19061 14,4568 656,59 34307,0 44100 14.4914 659,73 34636,1 44521 14,5258 662,88 34966,7 45369 14.5945 669.16 3563-7 45796 14,6287 672,30 35968,1 46225 14,6629 675,44 36305,0 46656 14,6969 678,58 36643,5 47089 14,7309 681,73 36983,6 47961 14.7988 888.01 376685 223 48729 14,9332 700,58 39057,1 224 50176 14,9666 703,72139408,1 50625 15,0000 706,86 39760,8 226 51078 15,0383 710,0040115,0 51984 15.0907 2008 200000 229 52441 15,1327 719,42 41187,1 52900 15.1658 722.57 41547.6 53361 15.1987 725 7141909 6 53824 15,2315 728,85 42273,3 54289 15,2643 731,99 42638,5 234 54756 15,2971 735,13 43005,3 55225 15,3297 738,27 43373,6 56169 15.3948 72224457345 56544 15,4272 747,70 44488,1 57121 15,4596 750,84 44862,7 57600 15,4919 753,98 45238,9 58081 15,5242 757,12 45616,7 58564 15,5563 760,27 45996,1 59049 15,5885 763,41 46377,0 15,0205 700,3 772 83 475000 7162 775.97 47916.4 61504 15,7480 779,111 48305,1 62001 15,7797 782,2648695,5 karmazAlA parikalana / 127

Page #133
MATHEMATICAL TABLE n: k * k ] na | In A n| | Pan | - } 35 = = tuung |2o| 15,81785,4o| 49087 | f | goo|i7,309942,48|zo ,a sw 225odia,708a|io,so211,al 0 60090|20,0002s, 12866 200|z,21324,19043 { |63Ooi 15,843 73, 9480, 30i }9060i1,3945,62 5 2320i|f8735o|ii02,16761,8| 40i }6080102 , |f253,8} 136293 G 2034oioo23084ig3375 25? 60 5,8 } 121,68 49975,9} 302 | Golia78,16|Ti615 j 352 z39o4i876n|ii05,3273i4o| 402 |f6020,0499262] 12923 04304|z,26031420,9|j8O60 |0o| 15,9n974,8z|50272,8] 33 ] 187,469|85,ao|2i | 3 260818,788a|iiO8,0p78677| #03 |i62409|20,07912661 27 414 205209|ai,2838:423,1161111 23 |mr ,937975 | SO4 191,459304253] zs88,8i|iiia423,o 404 63216|20,0998|i263 28io, asia|a1,71426,3i483 2 |o2| 15.9 |ni.i51o70,5} 305 | 93021, 42|o68,1780\,} 35 126028,4 15,398979,8| 46 |84025|2,12272a| 122 20702sz,33o429,162597 Ss 636 16,00a0,25547,9| 306 | 93f3f7,2386,33|T3541, 356 1267368,8880| H, 48538,2| 40d fA8362,144275,5| 12462 khJ3Bi342132 i33ia 25. |60| 161a| maa7,39874,8} 907 | 942497,5:116,477403,357 |12798,894|i12,5|i0008| 407 |i656499,172|129,6| 1300 457 |2064923T8135,716403 28g J6G564] 6,024|8i0,3s} 5279a| 308 | 9817,5 961,61743oao 38 ]28148,90|i1241|i0O66o| 400 [16644|20,990|1281,8] 1374i| 8 2097 21,4071438,1 48 259 |6708f| 14,04513,67 2685,3} 30g ,Hei7u|970,75|74996} 39 |i28298 , 9a|ija jol22a| #03 |i8728i|20,223728,9| i3382} 459 121038121,4243442,0|i6468 2 |676ook dig88,8i|382,1| a | sok, des,897 3,8| w |izgfood8,1olvi3i.o| iot789| t |i661(o|20,24s|j288,1] 13102s|4 zio]au7e|1,16680 2df | zi| 1 9, | 12 ,6a|97|o|759 1, 301 30329,0o|i|3i|i02 ] It i689't|20,273 291,2] 132$70|df 12f2i2r, Ts 18,3| i i 282 168 16,1884|8io} 12 382 | 0734,6 98oo|764 9a} 32 |i3i49,06s|ia| 10222 812 |i894|20,278 29,a| 123f7 AU2 213 4|2,92145,4|6739 269 \cdo! 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Page #134
Dui TMTZhong Ke /129 ITPU IEE , 21 11 -- 199471 3948 24.21300 sel | nikorashitsukumikosai. - Powei San Liao . ] Ban Ri Zhi 13 Mei Shi Chang Chang Rong Hui Ke Rong Sheng San , Zheng Ti San Ming Luo Luo Ding Wei Zhu Xue Xue Hui Ci . Chu HE . " "Shi Zai Xi BF: 888 333 MATHEMATICAL TABLE FEEL TEL:04 Yi Yi Yi Yi Yi Yi Yi Nian Zhong , Bu TS, . ] Ruo Shi De Mu De BERRI Ke Neng De . 3825 k _ Jing Guo Jia Bin -- - - --- --

Page #135
Bu Tiam Ke Ke 130 Cha Deng Deng | | 24 LASTES -- Sel 291 Hui CHE PE 10 11111 Liang ] Ke Ke Wan Di 83 MATHEMATICAL TABLE 236 San Ri Yue . Liao Dao Zhi Ding ningtng -- - 13: Ge Xing Hao :Ya Se He Cai Piao |San Li Cheng Du Kong Xi << Wang Yan Yan Qia Tai

Page #136
STAT 131 TABLE - VI LOGARITHMIC AND ANTILOGARITHMIC TABLES LOGARITHMS Ne Da 18 1000000 00432 00860 01284 01703 42 86 127 170 212 254 297 139,381 02119 02531 02998 03342 03743 38 61 121 162 202 242 283 323 064 04139 0453204922 05308 05690 35 77 116 1194 193 232 270 309 348 06070 06446 06819 07188 07565 32 74 111 148 185 222 259 296 338 0791808279 08636 0899109342 30 71 106 142 177 213 248 284 319 09891 I 10037 (10380 10721 / 11059 28 68 102 138 170 2041238 272 107 1139411727 12057 1238512710 26 GB 98 131 164 197 229 262 295 1303313354 13672189B8 14301 32 63 95 126 158 190 221 253 284 1 14613149221522915534 15836 30 67 91 122 152 183 219 244 274 18137 1643518732 17026 17919 29 59 88 118 147 177 206 238 265 1760917898 18184 1846918752 28 67 85 114 142 171 199 228-256 19033 19312 19590 1'9866 20140 28 65 83 10 138 165 193 221 248 20412206832095221210 21484 27 63 80 107 134 160 187 214 240 21743 22011 22272 2253 22789 26 3 18 104 130 150 i82 208 213 23045 233002355321805 24058 26 50 76 101 126 151176 201 227 2430424551 24197 25042 25285 25 40 7398 123 147 171 196 220 25527 25768 26007 2624526482 24 48 7195 119 143167 190 214 26717 26951 27184 27416 27640 73 46 89 83 -116 138 162 185 208 1927875 28103 28330 2855628780 23 75 62 96 114 133 158 180 203 29003 29226 294412966729889 22 44 8888 110 132 154 178 198 20 3070330320 30535 3075030963 31175 3138791597918063201521 43 84 85 106 127 148 170 100 23 3222232428 32634 1 3283833041 3324433445 338463384634044 20 41 81 81 101 121 141 162 182 22 34243 34439 34635 3483035025 3521835411 35603357933598420 39 58 57 97 116 135 154 174 1 361 73 36361 36549 3673636922 3710737291 37475 376583784019 37 56 74 93 111 130 148 167 38021 38202 38382 3856136739 3891739094 3927039445 39620 18 35 53 71 89 106 124 142 159 39794 39967 4014042312 40483 40854 40824 4099341102 413 30 17 34 51 68 85 102119 136 154 41497 41664 4183041996 142160 423254248842051 42813 42975 16 33 66 82 98115 131 148 | 4313C 43297 43457 43616 43775 143933440914424844404 4456016 63 79 95 126 142 447164487145025 45 179 45332 1454844583745788 45939 46090 15 30 81 76 01107 122 139 46240 46389 46538 46687 46835 4698247129 47276 47422 4758715 29 59 74 88103 118 112 4771247857 48001 48144 48287 48430 48572 48714 48855 86 100 114 124 491364927649415 49554 49693 4983149969 50106 50243 50379 97 110 124 5051550651 50786 50920 51055 51188 51322 51455 51587 51720 13 94 107 121 5185151983 52114 52244 52375 52504 52634 52763 528925302013 91 104 111 34 5314853275 53403 53529 53656 5378253908 5403354158 54283 76 88 101 113 4154407 54531 8485434777 54900 5502355145 55267 55388 5550912 24 73 85 48 110 3C6563056751 568715599156110 56229 58348 58467 36585 5670312 24 83 95 107 17 5682056937 57054 57171 57287 5740357519576345774017864 12 23 81 99 104 38579785 B082 68206 58320 58548586595877158883589911 23 79 90 102 395910639218 59329 59439 69650 59860 59770 59679 598795998860097 1960208 60314 60423 60531 60638 80746 60853 8095961086 61 172 81278 61 384 61490 61595 61700 161805 I 1909 62014 1 6211862221 62325 62428 62531 82634 62737 8283982941 63043 6314481246 6334763448 63548 63649 63749 63849 639496404864147 16424b 643450444464542 64640 64738 4836 84933 6503165128 G5225 65321 65418 65514 85610 65706 65801 65896 6599266087 66181 10) 19 67 78 86 66276 663 70 66464 66558 66652 88745 86839 669326702567117 919 87210 6730267394 67486 67578 67669 67761 67852 679491 68034 68124 88215 88305 683956848568574 68664 68753 1 68842 68931 89020 69108 69197 69288 69373 69481 695481 69636 69721 69810 9 18 lngmiiy - 4899614 . 10 18 www

Page #137
tdau (132 LOGARITHMS Me Dllerences * 1 * | z 1 1 nit bt - -- 6s91THAT I I 100 1024 10:28 Indio010586706129 116 154 , ros no82 | 108271011096 25|ly 1$$ |++ + In 1800 ISB in 18093 | 2013 | 2092ia\ 123 123s 1 2 1azija09. | s | ad135 136 136 1997 5018 159 1 ! 1323 3310 1500 | 11903560 1960 1939 188 7391 6 1 036 | de ? |? ? | 0z| 588 7663|14141 # 1 19 97 T028 205 | 182 SE9 I IS 187 156 151 40 1 89) 1 61 | T6042 r#15 16 1$ 1 Tcg 16 T682 ITSTATI5T6Io 16668702 5 12 50 31 170Ah 1232 730$ ? ?? | fn52 173 1197717751 5 12 29 J7 | : 11815 71960 1 Bol8101 Insanl 18391310 |1dz aaa is } 1860A | 1a675 I78146 | T81 \r88889 1979] 10dg 1969 ii 12 19109 19319 1949. 858 $ 98 961 1971 1976 18851 142 19934 80003 0072 | 01 #o | 0209 802/ 096 804 80482 | 055014 20 a : 0686 ap+q #08 #088 50955 023 rr 01021 | 11 3 10 ass! S8! #14 | r : | a 62 8810) a1, #r 82 | u1 8891 | 8854 | 82020 kh088 aai aaair | 82282 | 8238 241 3 218 | 82531 3 10 82o7 8b2 {17 | 8202 286 | 2950 8299sT905T 83 aia | Bai 8321 $335 #3378 | 8342 | 8350$ 85569 / 83632 836$ 89 63822 8$89 538 80 | 801 841 gs I 498 |8a} $23 A386 | 85 H0 1a q53 868 | #1 | H8 8880| q z as003 | 06 | 6 : 85$ 881 8248 | $3097 837 | aSai B5i 52 | 85612 | 8567376 ra. 8$33 85 85 | 8914| d 860$) #60$il 86r | 36213 ] &82116 2 8391 86 865 10 eno 529 | #66 8877 86806 | 86866 a ng23 88982 81040} 81099 lanoss as | 8721 81 332 87390 616 2 a706 915 81622 $79 7731 $1195 | 818a89 0! 8797| #8024 | 88081 888 885 I 8622 88309 | 88667 82 8480 1 888 18A28880 885 | 8856 11 889 88705 88162 | 8888Ia88 88930 | 8898 89a|a9016 | all ll 1 8209 892$ 892j 9378 8932 ] 8987 | BS2 89591} 89 89708 $ 1 1 TS B988 | 8913 89921 3982 190037009 901461 90200 | 025s 1 6 50009 sds63 90s sonalG026 | 080 | 9063|90687 | 1014 | 10 dau 9049 90902 909 10011097 19 1 1.222|iz15 25 rr 131 1r 91 67 905939 65 r1r1 8038516 110 2012 sa0852112169, 222 92732321 375 6 228 $280 923 2583263 2686 | 273 2786 280 $289 visat | 36 ] 46 d2942 92993 9:04 93095 9 6 93 91 933a|93198 | 9339 { $33995 ro sad a gol 5s / ++ 930 93500 93}} 93 ,T99 ) | 53702 | 5372 93802 382 9902 - 0 15 20 15 go| $$ 40 93952 9002 d052 90 $ 201 o 1300939 395 0 0 is sol 5 40 4$ d | #4 195656 3 | 1s|98 890 0 0 188 39 40 988 016 585 $ 95 1 82 | 92 9219] 95328 } 91| ios } 9 a | 3 39 44 m521 9$72 92) $589 5195955 1 9519580995855 10 14 29} 34 35 3 m590 1952 (560 | 095 9612 690 6211} 962 196335 4 29} 1 382 96379 | 26 5613 | 960|96561 ] 1994 1996|#118 | 15 | 96803 4 a sava 9688 19895 1692 | a | 103 | 910819728911 | 1230] $12679 - as| ti 11 13 1759 dau 405 91 ) 911 | 97575819189168191121}+ 1 18| da g7, 1nia dii1r 8 | 97 88 979099955 | 98000 | 99H6] $809. 19r $79883 8 zn| a 36 * 19?? 18212 8839 8408 983 998 983 985 88 | a53a |r: 2n 8811 98722 817 881 | 98s|s890 1989 889 90 901 1 .1 12 99255 00 993 | 99988993a dii 9 | so}, sJ8 { qm 99801 l 996 9995l 99779J 3762 981 89970] 11 |11 1 30 $ $9 -- --- - ---- - 99 9 it -- --- - - - - - - - -- -

Page #138
FRNTENT OR Tat/133 AM ANTILOGARITHMS : : : : 2 Moon Dife 3 4 5 6 7 8 9 835 23 BRO 88 3 S 10023 10046 10069 1009310116 10139 10102 10186 1102092S 7 1 9 12 14 16 19 10257 10280 10304 103281035) 3037510399 10423 (10447 2 5 10 12 14 10495 10520 10544 10568 10593 10817 10641 10658 10691 10 12 15 17 20 10740 10765 10789 1081410839 10864 10889 10914 110940 35 110 is a 20 10990 11015 11041 1106611092 1111711143 11169 11194 3 5 3 110 13 15 118 20 11246 (11272 1129811324 11350 1137611402 11429 1145535 11 13 16 11508 11535 11581 11588 11614 11841 11668 11695 1112235 11 13 16 11774 11 803 11830 11858 N88S 11912 11940 11967 11199) 11 14 16 12050 12078 12106 12134 12162 1219012218 12246 122743 11 14 IT 120 12301 12331 12350 12388 12417 12445 12474 12503 12531 12560 1111 IT 120 12618 (12647 12677 13706 22735 12764 12794 12823 12853 12 15 10 12882 1 2912 12942 12972 1 3002 13032 13062 13092 13122 131523. 15 10 13213 13243 1321413305 13:35 333661339733428 134893 19 13 13490 13521 13552 13583 13614 13646 13877 1370913740 13773 33 16 19 13804 13836 13866 13900 19932 13964 1399614028 14000 140933 14125 14158 1410 142131425614289 14322 14355 1438814421 3 7 10 18 30 14454 14486 14521 14555 1458814622 14655 1468914723 14757 13 7 10 11 17 20 14791 1482514858 14894 1492814962 14907 15031 15086 15101 3 7 10 14 19136 15171 13295 15241 15278 15311 15346 15382 15417 1545314 7 11 14 15480 15524 15580 15596 15631 15668 15704 15740 1 15776 15812 14 7 1114 15849 15885 13922 15959 15990 18032 18069 16106 18144 18181 4 7 11 15 16214 16255 16293 18331 1636816406 18444 18482 18520 165584 11 16596 16634 18672 16731 1674916788 16827 18886 116904 118943 14 12 16982 17022 17061 117100 17140 17179 172) 9 17258 17298 173384 & 12 17378 17418 17458 17498 17539 17579 17660 17701 177424 & 12 17783 17824 17385 17906 17947 17989 I 8030 18072 18113 18155 14 8 12 18197 18239 18281 18323 10365 18408 18450 18493 185 35 1857413 118821 18664 18707 18750 18793 18836 TIRSBO 18923 18967 190114 13 19065 19099 19143 19187 1923 19275 19320 19384 19409 19454 13 19408 19543 195B8 19694 1907 10724 19770 10815 19881 J19807 19053 19999 20045 20091 20137 20184 20230 20277 20334 20370 5 24 19 33 20417 20464 20512 20559 20606 20654 20701 20749 20797 20845 5 10 24 20893 20911 20989 21038 210BG 31135 21134 21332 21281 21330 5 10 15 21571 2140 21478 122528 21627 21127 21671 121777 121827 5 10 15 21928 121979 22029 22080 22131 731 83 23733 2336 22336 5 10 15 22439 22491 122542 22584 22646 23699 22751 22803 22858 5 10 16 22961 23014 23067 33121 23174 23227 23281 123336 233886 11 23496 23550 23605 23659 23714 23768 23823 23878 23933 5 11 24044 24099 124155 24210 24348 24922 24378 24434 0449111 24604 24860 24717 24774 24831 24889 24946 25003 25061811 125236 25293 25351 25410 25468 25527 255BG 25845612 25703 25823 25 882 2512 26002 26062 26122 261 83 2634212 26383 26424 2685 28546 2680 36489 26730 26792 288338 12 18 28977 27040 127102 17164 27227 27290 27353 11416 17479 6 13 19 27606 17869 27733 27797 27861 27915 27990 28054 281106 13 10 28240 (30314 26310 18446 28510 2657620542 28700 287747 13 30 28907 28913 28040 10107 20174 20242 29309 29376 20444 7 13 30 29560 29646 29717 207&s, 10354 28023 29002 30061 301301 14 21 3033 30400 30470 30849 3063030690 30761 30833 7 14 21 30974 M 31117 311005136131333 31405 31477 31650 i 14 22 INMENT 21380 11318 24547 25119 2370/ 26918 27542 23) 83. 3036

Page #139
**Ta oferaa/134 ANTILOGARITHMS Men Difference 113 31623 2359 8113 33.88 35481 3690 37154 98019 38POS 39811 079 16877 265 1652 4466 45709 17363 48978 S0119 59119 13 31696 31 784 31842 31916 31989 32063 32137 32211 32285 7 15 22 29 37 44 32434 32509 32584 32659 32735 32809 32885 32961 133037 8 15 23 33189 33266 33343 33420 33497 33574 33651 33729 33806 8 15 23 33963 34041 34119 34198 34277 34356 34435 34514 34594 8 16 24 34754 34834 34914 34995 35075 35156 35237 35318 35400 8 16 35583.35645 35727 35810 35892 35975 36058 36141 36224 8 16 36392 364,75 36559 36644 36728 36813 36898 36983 37068 3724937325 37411 37497 37584 37670 37757 37844 37931 9 17 3810738194 38282 38371 38459 38548 88637 38726 38815 9 18 5899499084 39174 39284 39335 39446 39537 39828 1397199 18 89902 39994 40087 4017040278 40365 40458 40551 408449 19 40832 40928 41020 41115 41210 41305 141400 41495 141591 41783 41879 141976 72073 421 70 142267 42364 42462 42560 42756 1285542954 4805349152 43251 43851 43451 43551 43752 13853 43954 44055 44157 44259 44361 4446344566 4477 44875 44978 45082 45188 4529045394 45499 45604 4581445920 48026 46132 46238 46345 46452 46559 46666 46881 1 46889 47098 47208 47315 47424 47534 47643-47753 47973 48084 48195 18306 484174852948641 48753 48865 56 67 78 89 100 48091 19204 149317 49431 49545 49659 49774 49888 50003 80 91 103 50284 90350 5046650582 50699 50816 50933 51050 51168 82 99 100 81404 51523 5184251761 51880 52000 52240 52360 84 96, 108 5260252723 52845 52966 53088 53211 59333 53456 53580 67385 98 110 53827 53951 54073 34200 34325 154450 54576 $4702 54828 88 100 113 55081 55208 3533435463 555.90 55719 55847 55976 56105 90 102 113 56364 5844 5662456754 56885 57016 57148 572805741213 92 105 118 57677 67810 8794358076 88210 58345 58479 58614 58749 94 107 121 6.9020 59186 59292 39429-19566 59794 59704 59979 | 60117 96 110 123 60395 60534 60674 60814 60854 61094 6235 61 37661518 14 84 98 102 126 6780381944 62087 62230.62373 62517 82861 62806 82951 86 101 115 130 83241 6334 09533 33680 63626 02973 (44121 64269 8441715 103 118 132 84714 64863 880136516385313 65464 65815 65766 65917 90 105 120 135 6622266374 66527 66681 66834 86988 6714367298 67453 108 123 139 67764 '67920 68077 68314 88391 88549 68707 68865 69024 18 95 110 126 142 69343 89503.49663 6989 19984 70148 70307 70469 70622 97 118 129 145 70958 71121 71285 7145075814 7177971945 72111 72377 99 116 132 149 72611 72773 77946 73114 7322 7451 73621 73790 72961 118 135 152 74302 174473 74645 74817 74989 75162 75338 7550975683 17 104 121 138 156 76033 76208 76584 7856076730, 78913 77990 77268 77446 167 125 142 159 77804 77983 7018378343 78524 78705 788867906879250 18 36 54 72 91 109 121 145 163 79618 | 79799 1799631 00164 1 20353 805 38 10072400010 | 81096 19 74 93 111 130 148 167 31419 8185 8184662038 82224 82414 826040279482985 76 95 117 132 151 170 83368 I 89580 83753 BSKG 140 843 184528 84723 84918 78 97 118 136 158 175 85310858078.570485901 8809 88298 68497 8889EUR 86896 20 99 119 189 15B 178 ezint 47498 67700 87903 88105 88308 88512 68716 a8920 81 102 122 142 162 183 331 89536 09743 89950 10137 90365 90873 907 87 90991 83 104 125 146 166 187 91411 1 DI 622 91833 99257 19470 92083 92897 93111 85 106 127 149 170 191 03141 3780 09972 941891440694824 94842 9506095280 87 109 130 132 174 195 951)9 95640 6181 16383 98805 96828 97061 97373 97499 89 11 133 139 178 200 97840 08175 98401 98628 88855 99083 99312 99541 99770 91 114 137 180 188 208 6230 5754 SHOR 60256 61659 63098 64565 68069 67608 69183 70795 12444 74131 74858 79626 18 8126 83176 85114 BTORS abras haas 1201 92045 16489 04124

Page #140
Degrees C-224 SONU CUER ngk97n & #1 d0 kh Urar qfer/135 TABLE VII TRIGNOMATRICAL TABLES NATURAL SINES 200 48 01047 01222 01396 Mega Differac 12 113 2238 03316 29 58 87 117 145 104885 05059 nast 10279 29 58 87 118 kh 58 87 116 ek dd 1 *** k. brH 166 5 ... 18.5 dittth dung FFFFF #F2 nnn nnng 25999 777 F2335 3333 99999 6 - gng bidhiinooHt ttttt 9mii

Page #141
Degrees 29599 55 38688 RFEFT PRE 4 676 95159 95681 9573285782 96593 9663896682 96727 92072 97113 97155 974 76 97515 97553 97851 97887 97922 98511 98541 98570 99051 99075 99452 99470 99488 99768 99780 99872 99881 99889 99951 99956 karmazAlA parikalana / 136 NATURAL SINES 99978 80000 2200 2222 491020 421 SCS HAD NO 15 1763 97647 97531 CON =a

Page #142
...... - td gyy 00094 0R17 100240 008 01746 01930 02095 rel qexe|1 37 NATURAL TANGENTS maanH : mkt: qngg nphng =- tiii 23 ...... kn: t : ni++3 --- ::::: ' : gn d d 952 5388 F#FFF #38 18 : ....

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swag FREE RN ANTEN CORE SU s 100 5471 karmazAlA parikalana / 138 "Numbers in difference columns to be subitarted tackled 06802 05059 04885 NATURAL COSINES . 08368 08194 20 40000 70091 69966 69842 68962 68815 68709 68587 04742292 02618 48 54 0.0deg 44444 SEE. IN CHENN NANA Men Dillerence #3333 CER CERES PRES - khlHd kh 99 bhnM a` vidhii 8

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F#trent afectat/139 NATURAL COSINES Numbers in difference columns 10 by Subti artet wut adhi Mees Differences O' 16' 0deg. 0deg 1 12' 0deg 2 18' 24 09. 30deg 30 0deg 36' 0deg.6 42' 0deg 7 48' deg 54 6deg 9 28 29 --- 1 000 9999999999 99999999989999699995 99993 99990 99988 1 0 1 1 1 1 99985 9998299978 9997499970999669 9961 99956 99951 99945 11 2 2 3 4 1.99939 1 99933 99926 199919 9991299905 99897 199889 199881 99872 11 3 4 5 6 .99863 99854 99844 99834 9982499813 98803 99792 99780 99768 2 4 5 7 99756 99744 99731 99719 99705 99692 99878 99664 99649 99635 2 5 7 .99619 99604 995 88 9957299556 995 40 99523 99506 99488 99470 I36a 99452 99434 99415 99396 9937799357 99337 99317 89297 99276 3 7 10 99255 99233 99211 9918999167 99144 99122 99098 99075 199051 48 .99027 199002 198978 98953 9R927 98902 198876 98849198823 98796 4 9 13 17 22 . 98769 98741 98714 98686 986579862998600 98570 98641 98513 5 10 14 19 24 . 98481 98450 198420 98388 98357 98725 98294 98281 98229 98196 15 11 16 21 27 98163 98129 198096 98061 98027 97792 97958 9792297887 978516 12 17 . 97815 97778 977421 97705 9766797630 97592 97533 97515 97478 6 13 19 25 32 .97437 97398 197358 97318 9727897237 97196 97135 97113 97072 17 14 20 27 34 .97030 96987 98945 96902 96858 96815 96771 96727 96682 96638 17 16 . 96593 198547 96502 96456 196410 8636396316 96289 98222 98174 18 16 0612896018 96029 95981 95931 9588295832 95 782 195732 95681 18 17 95630 95579 95528 9547695424953729531995266 95213 95159 9 17 . 95106 9505294997 8494394888 9483294777 94721 94665 94609 94552 94495 94438 94380 94322 94264 94206 94147 94088 94029 93969 93909 93849 937899372893667 93606 93544 93483 93420 .93358 93295 93232 93169 9310693042 92978 92313 92849 92784 92718 92653 92587 92521 9245592388 92321 92254 92188 92119 . 92050 91 982 91914 91 845 91775 91 706 91636 91566 91496 191425 .91355 91283 91212 91140 91068 90924 90851 90778 90704 . 90631 90557 90483 90408 90334 9025990183 90108 90032 89956 .89879 89803 89726 8964989571 89493 89415 89337 89259 89180 .89101 89021 1 88942 RAAARS 789 TAY 88820. 88539 88458 88377 88295 88213 881 30 880488796587882 87798 87715 87831 87546 .87462 87877 87292 8720787121 87036 86949 86863 86777 86690 .86603 86515 86427 8634086251 86169 88074. 85985 95896 85806 8.5717 85627 185538 854685365 85364 85173 85081 84989 84897 .84805 84619 8452884433 84339 84245 84151 18405783962 16 31 .83867 83772 18387683581 83485 83389 8329283195 83098 83001 16 32 48 .62904 82806 8270882610 82511 82413 82314 82214 82115 82015 16 33 49 .81915 81 815 81714 81614 81513 81412 81310 81208 81106 81004 17 34 80902 80799 180696 80593 B0489 80386 80282 80178 80073 79968 17 35 52 .79864 179758 7965379547 79441 79335 7922979122 7901678908 18 35 53 .78801 78893 785 8878478 7836978261 7815278043 7793477824 18 36 54 . 77715 77605 77494773B4 77273 77162 7705178940 7682876717 18 37 58 76492 76380 76267 7615478041 75927 75813 7570075585 19 38 75471 75356 75241 75126 75011 74896 74780 74664 74548 74431 19 39 74314 74198 74080 73963 73846 73728 73610 73491 73373 73254 20 39 73135 73018 7289772777 72657 725 37 7241772297 72176 72055 20 40 60 B0100 71934 71813 71891 71589 11447 7132571203 70957 70834 20 41 61 82102 ci NNN 30 . 76804

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43 10355 03915 04279 1-07437 370130479 15037 23 2624 325 323 RENEE REFER 788 88 1:344 1223 HUPAY HARLY BLEED 2017 17 HMS HER TIME Che 1-21490 2303: 24175 13276 13187 33073 137630 33145 38553 3916 1-42815 43147 41881 1 48250 481 49378 1 53987 54576 55170 1*600331 00057 01253 1 425 67055 67752.732098 73000 I am co 1-06261 97124 2:34421 15432 2 47 500 48758 2-74748 76247 7776: 2 90421 karmazAlA parikalana / 140 NATURAL TANGENTS 2 22085 2013031210 3-48741 51053 3-73205 EURETTE CUTE MIST HON 20 ZEN UNA PANU HELLE USER AND 24 TLE DURRE MADE HACER 19200 1900 Jor 11180 GAARK JADA) 29251 2 " Moon Diliarences 1 2 3 4 $118 177 237 137 191 255 112 199255 331 dii29 myyn 8&Z22 8# 8& gyy d19 9 1029 786

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karmazAlA parikalana/141 cunA huA nirdeza adhyAya-1 1. praikTikala maitha-pAlamara, biba, jAravisa tathA bharAnteka pablikezana mekapA-hila kampanI adhyAya 1, 2, aura 3 peja 3-44 2. praikTikala maitha-hovasa, mekone tathA dalajela pablikezana-DA. bI. tArAporevAlA sanja tathA kampanI prAIveTa limiTiDa peja 4-170 mazIna zApa maitha-Arana ekselArDa pablikezana : mekanA-hila buka kampanI peja 1-25 maitha phAra ilaikTrIkala injIniyariMga TaiknIzana romane tathA maiTisa pablikezana : dI iMgaliza hivarisaTI presa peja 1-19 n emamanumaunaam adhyAya-2 1. praikTikala maitha-hAvaja, mekIne tathA dalajela pablikezana : DI. bI. tArAporevAlA sanja tathA kampanI prAIveTa limiTiDa peja 237-254 tathA 260. maitha phAra ilaikTrIkala injIniyariMga TaikanIzana romane tathA maiTisa. pablikezana-dI ingaliza yUnivarsiTI presa. peja 20-23 3. esa. AI. yUniTasa-e sorasa buka-jI. esa rAmA svAmI tathA bI. bI. ela rAo, pablikezana : TATA mekanA-hila pabliziMga kampanI peja 9-13 tathA 30-56 4. kanavarazana phaikTara tathA kanavarazana Tebalasa Ai. esa. 786-1967. Namunda adhyAya-3 1. maitha phAra maikanIkala injIniyariMga TekanIzana grITa tathA.Telara, vAlyUma. / pablikezana : jArja rolana tathA anavina limiTiDa peja 29--36 - -

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karmazAlA parikalana/142 2. praikTikala maitha, hAvasa, mekIne tathA dela jela, pablikezana : DI. bI. tArAporevAlA sanja tathA kampanI prAIveTa limiTeDa, peja 285-299 besika maitha phAra ilaikTrIkala tathA ilekTronikasa siMgara pablikezana : mekagrA-hila buka kampanI peja 150-175 adhyAya-4 1. praikTIkala maitha hAbaja maikone tathA dalajela. pablikezana : DI.bI tArAporevAlA sanja tathA kampanI prAIveTa limiTeDa peja 181 se 205. __2. maitha phAra TaikanIzana sTuDeMTasa e. giyare, eca. vI lorI eca. e. hedana. pablikezana : i. ela. vI. esa lo prAIsaDa TaiksaTa buka peja 24 - 26 ___ 3. praikTIkala maitha-pAlamara, biMba, jAravisa tathA marAceka pablikezana : maikagrA-hila buka kampanI peja 48-56 adhyAya-5 1. mazIna zApa maitha-Arana eksala roDa pablikezana : maikagrA-hila baka kampanI peja 146 = 151 2. praikTikala maiya--pAlamara, biba jAravisa tathA marAnteka pablikezana-maikagrA-hila baka kmpnii| peja 59-66 3. praikTikala maitha-hAvasa, maikane tathA dalajela pablikezana: DI. vI. tArAporevAlA sanja tathA kampanI limiTiDa, peja 307-313 adhyAya 6 tathA 7 __ 1. alajabarA, pArTa-1 zAnti nArAyaNa mohana lAla pablikezana-naizanala kauMsala Apha ejUkezanala risarca tathA TreniMga peja 98-125, 198--234 tathA 250-260 2. kAlija alajaibarA-rIsa tathA spakisa pablikezana : mekagrA-hila buka kampanI peja 145-172 tathA 198-233 3, TeknIkala maitha-DI. parI / pablikezana -hIne maina ejukezanala baksa limiTiDa peja 86-164. adhyAya-8 ___ 1. praikTIkala maitha-hAvasa, maikone tathA dala jela pablikezana DI. vI, tArA pArevAlA sanja tathA kampanI prAIveTa limiTiDa. peja 531-564 2. maitha phAra maikenikala injIniyariMga, TeknIzana grITa aura Telara, buka pablikezana : jArja ailana anavina limiTiDa peja 83-101 3. maitha ilekTrIkala injIniyariMga TeknIzanaja romane aura maurisa

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karmazAlA parikalana/143 pablikezana : dI iMgaliza yUnivarsiTI presa peja 76-85 adhyAya-9 | 1. praikTikala maitha-pAlamara, biba, jAravisa aura merAnteka pablikezana : mekagrA - hila buka kampanI peja 265-274 tathA 309 -340. 2. maitha phAra ilaikTrIkala injIniyariMga TaikanIzana romane tathA morisa pablikezana : dI iMgliza yUnivarsiTI presa / peja 193-215 3. alImainTrI varkazApa kailakulezana esa. AI yUniTasa DablayU ai. je. caipamaina. pablikezana : I.ela.vI. esa lo prAIsaDa eDIzana peja 62-81 1. adhyAya-10 ailamainTrI varkazApa kailakulezana- DablyU. e. je. ceyaramaina pablikezana : I. ela. bI. esa. lo prAIsaDa eDIzana peja 193-222 maizInarI haiMDa buka pablikezana : inDasTriyala presa AI, ena. sI. peja 149-170 maitha aura sAIMsa phAra pArTa-2, moTara vhIkala TekanIzana vAlyUma-1, vI. e. lebara jI. I. sATa pablikezana : dI iMgaliza yUnivarsiTI presa peja 14-22 3. adhyAya-11 | 1. ailImainTrI varkazAga kailakulezana-DablyU e. je caipamaina pablikezana : i. ela. bI. esa. nyUna mUlya eDIzana 2. besika maitha phAra ilekTrIsiTI tathA ilekTroniksa siMgara pablikezana : maikagrA-hila baka kampanI peja 349-365 3. mazIna zApa maitha- Arana aiksala ror3a pablikezana : maikagrA-hila buka kampanI peja 160-182 adhyAya-12 | 1. maitha tathA sAIsa phAra pArTa-2 moTara vhIkala

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karmazAlA parikalana/144 TekanIzana vAlyUma-1-bI.e. lebara tathA jI.I. skATa peja 37-53 2. maitha phAra ilekTrIkala injInIyariMga TeknIzana romane tathA morisa pablikezana : dI iMgliza yUnivarsiTI praisa peja 30-42 3. prekTIkala maitha-pAlamara-biva, jAravisa tathA marAnteka pablikezana mekagrA-hila buka kampanI peja 241-257 sIniyara varkazApa kailakulezana-DablyU. e. je. caipamaina pablikezana orIainTa lAngamaina peja 347-403 adhyAya-13 mazIna zAra maMtha-Arana eksala roDa pablikezana : maikagrA-hila buka kampanI, peja 193-278 2. ailImainTasa oNpha varkazApa TeknolojI-vAlyUma-11-8 esa. ke. hAjarA caudharI tathA esa. ke. bosa pablikezana : eziyA pabliziMga hAusa 3. sIniyara varkazApa kailakulezana-DablyU e.je. caipamaina. pablikezana orIeMTa lAMgamaina pez2a 6-211 4. praikTIkala zApa maitha, vAlyUma-11 jona eca. vulfa aura aivareTa Ara philepasa pablikezana maikagrA-hila buka kampanI, peja 165-263 5. varkazApa kailakulezana-DI. rAye, pablikezana : kalakattA buka hAusa adhyAya-14 1. ailImanTasa Apha varkazApa TeknAlojI vAlyUma-1 esa. ke. hAjarA caudharI pablikezana : eziyA pablikezana hAusa peja 351-430 phAMUDarI ijIniyariMga-hAvarDa epha. TelaTa, mAraTana sI. phalamiMgaja tathA jona vulpha pablikezana : vile IsTrana prAIveTa limiTiDa adhyAya-15 1. baisika maitha phAra ilaikTrIsiTI tathA ilekTroniksa siMgara pablikezana : mekapA-hila buka kampanI prAbalamasa ina ilaikTrIkala iMjIniyariMga esa pArakara smitha pablikezana : eziyA pabliziMga hAusa elImainTrI ilaikTrIkala iMjIniyariMga-ema. ela. guptA pablikezana : nyU hAITasa