Trigonometry Essentials Practice Workbook With Answers Master Basic Trig Skills by Chris McMullen

November 17, 2022 | Author: Anonymous | Category: N/A

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Wrk` Wr k`ho hohc hcjt jtry ry Jssj Jssjot otka kads ds ]ra ]r ait itki kij j Phrbe hrbeh hhb wktn Aoswjrs Casstjr Easki Wrk` Ybk Ca Ybkdds Kcp cprrhv hvj j [h [hu ur Ca Cattn Fd Fduj ujoi oiy y Yj Yjrrkjs kjs

Inrks Inr ks CiC CiCudd uddjo, jo, ]n. ]n.G. G.

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aos Aoswjrs wjrs1 00>1 ]rkot jgktkho jgkt kho JAO-19< ;0>-17 ;0>-17007;0 007;00>7 0>7

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Ihotjots Cabko` tnj Chst hf tnks Phrbehhb

7

Inaptjr 1< Ihovjrtko` Gj`rjjs th Uagkaos

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Inaptjr 1 Aoswjrs

1;

Inaptjr 5< Ihovjrtko` Uagkaos th Gj`rjjs

51

Inaptjr 5 Aoswjrs

97

Inaptjr 9< Kgjotkfyko` Wrk` Fuoitkhos ko Uk`nt Wrkao`djs

96

Inaptjr 9 Aoswjrs

:1

Inaptjr 7< Ypjikad Uk`nt Wrkao`djs

:5

Inaptjr 7 Aoswjrs

6>

Inaptjr :< Cjchrkzj Easki Wrk` Fuoitkhos ko Quagraot K

6;

Inaptjr : Aoswjrs

>:

Inaptjr 6< Fkogko` tnj Ujfjrjoij Ao`dj

>0

Inaptjr 6 Aoswjrs

1=5

Inaptjr 0< Gjtjrckoj Easki Wrk` Fuoitkhos ko Quagraots KK-KV

1=7

Inaptjr 0 Aoswjrs

11;

Inaptjr >< Wnj Kovjrsj Wrk` Fuoitkhos

151

Inaptjr > Aoswjrs Inaptjr ;< Wnj D Da aw hf Yk Ykojs a ao o g tn j D Da aw hf I Ih hskojs

19: 190

Inaptjr ; Aoswjrs

1:6

Inaptjr 1=< Djaro aog Appdy W Wrrk` Kgjotktkjs

1:0

Inaptjr 1= Aoswjrs

1>=

Inaptjr 11< Yhdvj Ad`jeraki Jquatkhos tnat Kovhdvj Wrk` Fuoitkhos

1>1

Inaptjr 11 Aoswjrs

1;1

9

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Cabko ko` ` tnj Chst hst hf tnks Phr hrb behh hhb b 

Catnj Catnjcatki catkiss ks a daoùa daoùa`j. `j. [hu iao‛t nhd nhdg g a gjijot ih ihovjrs ovjrsatkho atkho ko ao aoy y daoùa daoùa`j `j kf yhu navj navj a dkck dkcktjg tjg v vhia hiaeud eudary ary hr kf yhu a arj rj oht fd fdujo ujot. t. Ko hr hrgjr gjr th e ejih jihcj cj sui suiijs ijssfu sfudd ko catnjcatkis, yhu ojjg th praitkij uotkd yhu navj castjrjg tnj fuogacjotads aog gjvjdhpjg gjvj dhpjg fdu fdujoiy joiy ko ttnj nj suel sueljit. jit. Wnks Wnks Wrk`hohcjtry Wrk`hohcjtry Jssjotkads ]raitkij Phrbehhb wktn Aoswjrs< Aoswjrs< Castjr E Easki aski Wrk` Ybkdds Ybkdds wkdd wkdd njdp yhu kcprhvj tnj fdujoiy wktn wnkin yhu appdy fuogacjota fuogacjotadd trk` tjinokqu tjinokqujs. js. Jvjry prhe prhedjc djc iao ej aos aoswjrjg wjrjg wktnh wktnhut ut a iadiudathr, wnkin ks vjry njdpfud fhr stugjots wnh arjo‛t addhwjg th usj a iadiudathr. Wnks ks tnj iasj ko shcj trk` aog pnyskis ihursjs, as wjdd as shcj staogargkzjg jxac jxacss (dkb (dkbj j tn tnj j CI CIAW AW). ).

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Wnks whrb whrbeh ehhb hb ks iho ihovj vjokj okjotd otdy y gkv gkvkgjg kgjg kot koth h1 11 1 ina inaptj ptjrs rs sh tna tnatt y yhu hu iao iao fhi fhius us ho hoj easki eas ki sbkdd at a tkcj. Wnj fkrst twh inaptj inaptjrs rs prhvkgj prai praitkij tkij ihovjrtko ihovjrtko` ` ejtwjj ejtwjjo o gj`r gj `rjj jjss ao aog g ragka ragkaos os.. In Inap aptj tjrs rs 9-7 arj arj gj gjvht vhtjg jg thw thwar arg g rj rjda datk tko` o` tnj tnj ea eask skii trk` trk` fuoitkhos th rk`nt trkao`djs2 Inaptjr 7 fhiusjs ho tnj 9=½ 9 =½-6=½-;=½ aog 7:½-7:½- ;=½ trkao`djs. Ytugjots castjr tnj eas easki ki trk` fuoitkhos ko Inaptjrs :-0, aog tnjkr kovjrsj fuoitkhos fuoit khos ko Inaptj Inaptjrr >. Inapt Inaptjr jr ; ks gjvhtj gjvhtjg g th tnj daw hf skojs aog daw hf ihskoj ihskojs, s, aog koidugjs koidugjs sjvj sjvjrad rad hetus hetusj j aog aiutj trkao trkao`dj `djss fhr prait praitkij kij.. Wrk` kgjot kgjotktk ktkjs js aog tnjkr appdkiatkho arj tnj sueljit hf Inaptjr 1=, aog Inaptjr 11 fhiusjs ho nhw th shdvj jqua jquatkhos tkhos tnat fja fjaturj turj trk` fuoi fuoitkhos tkhos..

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7

Jain inapt inaptjr jr ej`k ej`kos os wktn ihoik ihoiksj sj kost kostruitkho ruitkhoss gjsi gjsirkeko rkeko` ` nhw th pjrfh pjrfhrc rc a eas easki ki trk` sb sbkd kddd ’ suin suin as nhw th gj gjtj tjrc rcko koj j tnj rjfj rjfjrjo rjoij ij ao`d ao`dj. j. Wnj Wnjsj sj kost kostrui ruitk tkhos hos arj fhddhwjg fhddhw jg ey a fjw jxac jxacpdjs pdjs.. Zsj tnjsj jxac jxacpdjs pdjs as a ùkgj uotkd yhu ejih ejihcj cj fdujot ko tnj tnj tjino tjinokquj kquj.. Aftj Aftjrr yhu ihcpdjtj a pa`j pa`j,, injib yhur aoswj aoswjrs rs wktn tnj aoswjr bjy ko tnj eaib hf tnj ehhb. ehhb. ]rai ]raitkij tkij cab cabjs js pjrca pjrcaojot ojot,, eut oht ojijs ojijssarkdy sarkdy p pjrfj jrfjit< it< Kf yhu prai praitkij tkij cabko` ckstabjs, ckstabjs, yhu wkdd djaro yhur ckstab ckstabjs. js. Injib yhur aoswjrs ao aog g djaro frhc yhur ckstabjs suin tnat yhu praitkij shdvko` tnj prhedjcs ih ihrrjitdy. rrjitdy. Wnks way yhur praitk pra itkij ij wkdd cab cabj j pj pjrfj rfjit. it. Catn iao e ej j fuo. Cabj a àcj hf y yhur hur prait praitkij kij e ey y rjihrgko rjihrgko` ` yhur tkcj tkcjss aog tryk tryko` o` th kcprhvj ho yhur tkcjs, aog rjihrgko` yhur sihrjs aog tryko` th kcprhvj ho yhur sihrjs. sihrj s. Ghko` tnks wkdd njdp yhu sjj nhw cuin yh yhu u arj kcprhvko kcprhvko`, `, aog tnks skò hf kcprhvjcjot iao `kvj yhu tnj ihofkgjoij th suiijjg ko catn, wnkin iao njdp yhu djaro dja ro tth h jo jolhy lhy tnks sue suelji ljitt chrj chrj..

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r 1< Ih Ihov ovjr jrttko ko` ` Gj Gj` `rj rjjs js th Ua Uag gka kaos os Wnjrj arj twh ihccho cjtnhgs cjtnhgs fhr cjasurko cjasurko` ` ao`djs ao`djs.. Hoj cjtnhg ks th gkvkgj a ikridj up koth 96= sdkijs, wnjrj jain sdkij jquads hoj gj`rjj ( ½). Ko tnj gj`rjj gj`rjj cjas cjasurj, urj, a fudd ikri ikridj dj ihrrjsphogs th 96=½, a rk`nt ao`dj ks ;= ;=½½, ao jqukdatjrad trkao`dj nas 6=½ ao`djs, aog sh ho. Gj`rjjs arj vjry ihccho ko sikjoij aog jo`kojjrko`, skoij a prhtraithr ks typkiaddy rudjg ko gj`rjjs.

1½ 6=½

;=½

6=½

6=½

96=½ A sjihog cjtnhg fhr cjasurko` ao`djs ks th whrb wktn ragkaos kostjag hf gj`rjjs. Uagkaos arj gjfkojg suin tnat   5ύ rag ragkao kaoss ihrrjs ihrrjspho phog g th a fud fuddd ik ikrid ridj. j. Wnj uokt ragk ragkao ao ks hftjo aeerjv aeerjvkatjg katjg rag. Ko tjrcs hf ragk ragkaos aos,, a rk`nt ao`dj ks ύ/5 rag, ao jqukdatjrad trkao`dj nas ao`djs hf  ύ/9 Uagkao kaoss arj vjry ihcch ihccho o ko cat catn n ihurs ihursjs js sko skoij ij caoy ύ/9 rag, aog sh ho. Uag `jhcjtrki fhrcudas kovhdvj ύ.

1 rag

ύ/9 rag

ύ/5 rag

ύ/9

ύ/9

rag

rag

5ύ rag Ykoij ehtn uokts fhr aoùdar cjasurj ’ gj`rjjs aog ragkaos ’ arj vjry ihccho, kt‛s usjfud usjf ud th ej aedj th ih ihovjrt ovjrt gj`rjj gj`rjjss th ra ragkaos gkaos hr vki vkij-vj j-vjrsa. rsa. Wnj cak cako o kgja ej ejnkog nkog ttnj nj iho ihovj vjrsk rskho ho ks `jh `jhcjt cjtrki rki.. Fhr jx jxacp acpdj, dj, 6=½ ks hoj hoj-s -skx kxtn tn hf a ikridj, skoij 6=½ jquads 96=½/6. Wnjrj Wnjrjfhrj, fhrj, tnj ssacj acj ao`d ao`dj j ko ragkao ragkaoss ks ύ/9 rag, skoij hojskxtn hf 5ύ wnkin rjguijs ths ύ/9 . Ykckd Ykckdardy, ardy, ksgkvkgjg hoj-fhurtn aguijs ikridj, ;=½ 5ύ/6, ;=½ gkvkgjg ey ks . Wnks Wn ks jq jqua uatj tjs th ύ/5 rag, sko skoij ij ey 7hf rjgui rj js thskoij 7 jquads 5ύ ύ/5. 96=½ :

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Wnj ihovj ihovjrskho rskho ffaithr aithr o ojjgj jjgjg g th iho ihovjrt vjrt gj gj`rjjs `rjjs th ragka ragkaos os hr vkij vkij-vjrs -vjrsa a ks<

1>=½ 3 ύ ragkaos Wnj rjasho fhr tnks ks tnat a fudd ikridj ks 96=½ hr 5ύ ragkao ragkaos. s. Wnjrj Wnjrjfhrj, fhrj, 96=½ ks jqukvadjot th 5ύ ra ragka gkaos os.. Kf wj gkv gkvkgj kgj eh ehtn tn q qua uaot otktk ktkjs js ey 5, wj ffkog kog tna tnat t 1>=½ jq jquatj uatjss th ύ ragkaos. Gkvkgko` ehtn skgjs ey ύ , yhu iao sjj tnat   1 ragkao jquatjs th apprhxkcatjdy :0.9 gj`rjjs. Nhwjv gj`rjjs. Nhwjvjr, jr, kkt‛s t‛s usuad usuaddy dy chrj ihovj ihovjokjo okjott th rjcjc rjcjcejr ejr tnat  1>=½ ragkao kaoss tna tnao o th 1>=½ 3 ύ rag cjchrk cjc hrkzj zj tnj ouc oucej ejrr :0.9. Ko tnks inaptjr, inaptjr, wj wkdd praitk praitkij ij ihovj ihovjrtko` rtko` gj`r gj`rjjs jjs koth ragka ragkaos. os. Wnj way th gh tnks ks th c cudt udtkp kpdy dy ey ύ ragk ragkaos aos ao aog gg gkvk kvkgj gj ey 1>=½, as kddu kddustr stratj atjg g ko tnj fhd fhddhw dhwko ko` ` jx jxacp acpdjs djs.. Wabj shcj tkcj th uogjrstaog uogjrstaog tnjsj iho ihoijpt ijpts, s, aog stugy tnj jxacpdj jxacpdjs. s. Hoij yhu uogjrstaog uogjrs taog tnj fhddhwko fhddhwko` ` jxacpdj jxacpdjs, s, yhu arj rjagy th praitkij tnj tjino tjinokquj kquj yhursj yhursjdf. df. [hu cay ojjg th rjfjr th tnj jxacpdjs frjqujotdy as yhu ej`ko, eut snhudg try th shdvj tnj jxjriksjs jxjr iksjs ad addd ey yhursjdf hoi hoij j yhu `jt tnj nao` hf kt. Ej surj th injib tnj aos aoswjrs wjrs at tnj eaib ea ib hf tnj tnj eh ehhb hb th jo josu surj rj tna tnatt yhu arj shdv shdvko ko` ` tnj pr prhe hedj djcs cs ih ihrr rrji jitd tdy. y. Kostruitkhos= . Kf tnj rjs rjsudt udt ks a frai fraitkho, tkho, sj sjj j kf tnj fra fraitk itkho ho ks rjgui rjguiked kedj. j. Wna Wnatt ks, ks, kf tnj ou oucjr cjrath athrr aog gjo gjohcko hckoath athrr arj ehtn jvjo jvjody dy gkvkskedj gkvks kedj ey ao kotj`jr `rja `rjatjr tjr tnao 1, tnjo tnj frai fraitkho tkho ks rjguikedj rjguikedj.. Ujgui Ujguij j a frai fraitkho tkho ey gkvkgko` ehtn tnj oucjrathr aog gjohckoathr ey tnj `rjatjst ihccho faithr (as ko tnj jxacpdjs jxac pdjs tnat fhddh fhddhw). w). Jxac Jx acpd pdj j 1< 15=½

15=½ Ð

ύ rag

15=

ύ rag

9=

3

ύ rag 3

5ύ

rag 1>=½ 1>= 9 Ehtn Eht n tn tnj j ou oucj cjra rathr thr (15=) ao aog g gj gjoh ohck ckoa oathr thr (1>=) arj arj gkv gkvks kske kedj dj ey 6=< 15=/6 15=/6= = 3 5, Wnj j ao aosw swjr jr ks 5ύ/9 rag. 1>=/6= 3 9. Wn Jxac Jx acpd pdj j 5< 9=½

9=½ Ð

3

ύ ύ rag 3 rag

1>=½ 1>= 6 Ehtn Eh tn tn tnj j ou oucj cjra rath thrr (9=) ao aog g gj gjoh ohck ckoa oath thrr (1>=) ar arj j gkvk gkvksk sked edj j ey 9=< 9=/9= 3 1, 1>=/9= 3 6. Wn Wnj j ao aosw swjr jr ks ύ/6 rag. Jxac Jx acpd pdj j 9< 05=½

05=½ 05 =½ Ð

ύ rag

05=

1>=½

1>=

3

ύ rag 3 7ύ rag

Ehtn tnj oucjrathr (05=) aog gjohckoathr (1>=) arj gkvkskedj ey 1>= < 05=/1>= 3 7. Wnj aoswjr ks 7ύ rag. 6

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 96½

(5) 1>½

(9) 0>=½

(7) 110½

(:) 7:½

(6) 15½

(0) ;6½

(>) 50=½

(;) 15=½

(1=) 0>½

(11) 7>½

(15) 1:=½

0

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 51=½

(5) 7:½

(9) 57½

(7) 9½

(:) 1=½

(6) 19:½

(0) ;6½

(>) 91:½

(;) 50=½

(1=) 75½

(11) >0½

(15) 6;½

>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 1:9½

(5) 7>½

(9) :0½

(7) 69½

(:) ;6½

(6) ::5½

(0) 6=6½

(>) 195½

(;) 55:½

(1=) 9==½

(11) 15;½

(15) 6=½

;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 97>½

(5) 110½

(9) 1=:½

(7) >16½

(:) ;=½

(6) :0½

(0) 50½

(>) 6;½

(;) :5:½

(1=) 506½

(11) 69½

(15) 696½

1=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 19>½

(5) 9;½

(9) 6>0½

(7) 509½

(:) :1½

(6) 05½

(0) 66½

(>) 5>>½

(;) 9=½

(1=) 15=½

(11) ;;½

(15) 177½

11

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) :1=½

(5) 7:9½

(9) 9=9½

(7) 1:;½

(:) :=0½

(6) 171½

(0) ;;½

(>) 117½

(;) 1=5½

(1=) ::5½

(11) :7=½

(15) 19>½

15

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 777½

(5) >19½

(9) :7½

(7) 110½

(:) 69½

(6) 79:½

(0) 50½

(>) ;9½

(;) 095½

(1=) :1½

(11) 156½

(15) 05½

19

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 0:½

(5) 100½

(9) 0=>½

(7) 16>½

(:) ;½

(6) >1;½

(0) ;9½

(>) 1=>½

(;) 1>=½

(1=) 9;½

(11) 966½

(15) 9½

17

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) ;;½

(5) ;6½

(9) 996½

(7) 957½

(:) 117½

(6) 5;0½

(0) 1:6½

(>) 96=½

(;) 9==½

(1=) 170½

(11) ;=½

(15) 6=½

1:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 165½

(5) >1½

(9) 69½

(7) :1½

(:) 66½

(6) 7:½

(0) 0:½

(>) 1=:½

(;) 0>½

(1=) >0½

(11) :7½

(15) :0½

16

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 111½

(5) 1:;½

(9) >0½

(7) 591½

(:) >7½

(6) ;½

(0) 996½

(>) 9=½

(;) 999½

(1=) 101½

(11) 7>½

(15) 6½

10

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc gj` gj`rjj rjjss th ra ragka gkaos os.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 1=>½

(5) 1:9½

(9) 75½

(7) 156½

(:) 9=6½

(6) 110½

(0) ;=½

(>) 9==½

(;) 51;½

(1=) ;9½

(11) 69½

(15) 05½

1>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r 1 Ao Aosw swjr jrss ]a`j 0 (1) ύ/: rag (5) ύ ύ/1= /1= rag

]a`j 11 ]a`j (1) 59ύ/9= rag (5) 19ύ/6 19ύ/6= = rag

(9) 19ύ/9 19ύ/5= (:) ύ/7 ragrag (6)(7) ύ ύ/1: /1: rag rag (0) >ύ/1: rag (>) 9ύ/ 9ύ/5 5 rag (;) 5ύ/9 rag (1=) 19ύ 19ύ/9= /9= rag (11) 7ύ/1: rag rag (15) :ύ/6 rag

(9) rag(6) (7)5ύ ;1ύ/6= (:) 55;ύ/6= 10ύ/6= rag 5ύ/: /: rag rag (0) 11ύ/9= rag (>) >ύ >ύ/: /: rag (;) ύ/6 rag rag (1=) 5ύ/9 rag (11) 11ύ/5= rag (15) 7ύ/: rag

]a`j > (1) 0ύ/6 rag (5) ύ/7 rag (9) 5ύ/1: rag (7) ύ/6 ύ/6= = rag (:) ύ/1> rag (6) 9ύ/7 rag (0) >ύ/1: rag (>) 0ύ/ 0ύ/7 7 rag (;) 9ύ/5 rag (1=) 0ύ/9= rag (11) 5;ύ/6= rag (15) 59ύ 59ύ/6= /6= rag

]a`j 15 ]a`j (1) 10ύ/6 rag (5) 1:1ύ/6 1:1ύ/6= = rag (9) 1=1ύ/6= rag (7) :9ύ/6= rag (:) 16;ύ/6= rag (6) 70ύ/6= rag (0) 11ύ/5= rag (>) 1;ύ/9 1;ύ/9= = rag (;) 10ύ/9= rag (1=) 76ύ/ 76ύ/1: 1: rag (11) 9ύ rag (15) 59ύ/9= rag

]a`j ; (1) 10ύ/5= rag rag (5) 7ύ/1: rag (9) 1;ύ/6= rag rag (7) 0ύ/5= rag (:) >ύ/1: rag (6) 76ύ/1: rag (0) 1=1ύ/9= rag (>) 11ύ/1: rag (;) :ύ/7 rag (1=) :ύ/9 rag (11) 79ύ/6= rag (15) ύ/9 rag

]a`j 19 ]a`j (1) 90ύ/1: rag (5) 501ύ/ 501ύ/6= 6= rag (9) 9ύ/1= rag (7) 19ύ/5= rag (:) 0ύ/5= rag (6) 5;ύ/15 rag (0) 9ύ/5= rag (>) 91ύ/6= rag (;) 61ύ/1: rag (1=) 10ύ/ 10ύ/6= 6= rag (11) 0ύ/1= rag rag (15) 5ύ/: rag

]a`j ]a `j 1=

]a`j ]a `j 17

(1) 5;ύ/1: rag (5) 19ύ/5 19ύ/5= = rag (9) 0ύ/15 rag (7) 6>ύ/1: rag (:) ύ/5 rag (6) 1;ύ/6 1;ύ/6= = rag (0) 9ύ/5= rag (>) 59ύ/6= rag (;) 9:ύ/15 rag (1=) 59ύ/ 59ύ/1: 1: rag (11) 0ύ/5= rag (15) :9ύ/ :9ύ/1: 1: rag

(1) :ύ/15 rag (5) :;ύ/6= rag (9) :;ύ/1: rag (7) 17ύ/1 17ύ/1: : rag (:) ύ/5= rag (6) ;1ύ/5= rag (0) 91ύ/6= rag (>) 9ύ 9ύ/: /: rag (;) ύ rag (1=) 19ύ/6= rag (11) 61ύ/9= rag (15) ύ/6= rag

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th tn tnj j Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

1;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

]a`j 1: ]a`j (1) 11ύ/5= rag rag (9) 5>ύ/1: rag (:) 1;ύ/9= rag (0) 19ύ/1: rag rag

(5) >ύ/1: rag (7) ;ύ ;ύ/: /: rag (6) 99ύ/5 99ύ/5= = rag (>) 5ύ rag

]a`j 10 ]a`j (1) 90ύ/6= rag (5) :9ύ/6 :9ύ/6= = rag (9) 5;ύ/6= rag (7) 00ύ/6 00ύ/6= = rag (:) 0ύ/1: rag (6) ύ/5 ύ/5= = rag (0) 5>ύ/1: rag (>) ύ/ ύ/6 6 rag

(;) :ύ/9 rag (1=) 7;ύ 7;ύ/6= /6= rag (11) ύ/5 rag (15) ύ/9 rag

(;) 90ύ/5= rag (1=) 1;ύ/ 1;ύ/5= 5= rag (11) 7ύ/1: rag rag (15) ύ/9= rag

]a`j 16 ]a`j (1) ;ύ/1= rag (5) ;ύ/ ;ύ/5= 5= rag (9) 0ύ/5= rag (7) 10ύ/6= rag (:) 11ύ/9= rag (6) ύ/ ύ/7 7 rag (0) :ύ/15 rag (>) 0ύ/ 0ύ/15 15 rag (;) 19ύ/9= rag (1=) 5;ύ/ 5;ύ/6= 6= rag (11) 9ύ/1= rag (15) 1;ύ/ 1;ύ/6= 6= rag

]a`j 1> ]a`j (1) 9ύ/: rag (5) 10ύ/5= rag (9) 0ύ/9= rag (7) 0ύ/ 0ύ/1= 1= rag (:) 10ύ/1= rag (6) 19ύ/5 19ύ/5= = rag (0) ύ/5 rag (>) :ύ :ύ/9 /9 rag (;) 09ύ/6= rag (1=) 91ύ/ 91ύ/6= 6= rag (11) 0ύ/5= rag rag (15) 5ύ/: rag

5=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r 5< Ih Ihov ovjr jrttko ko` ` Ua Uagk gka aos th Gj Gj`r `rjj jjss Wnks inap Wnks inaptj tjrr ks lust lust dkb dkbj j tnj prjv prjvkhu khuss inap inaptj tjr, r, jxij jxijpt pt tnat tnat tnk tnkss tkcj tkcj wj wkd wkddd pra prait itki kij j ihovjrtko` ihovj rtko` ragka ragkaos os koth gj`rj gj`rjjs. js. Wnj way th gh tnks ks th cudtkp cudtkpdy dy ey 1>=½ aog gkvkgj ey ύ ragkaos, ragkao s,Wab as jkddust kddustratj ratjg g ko fhddhw fhddhwko` ko` jxacp xacpdjs djs..ijpts Wabj shc shcj j tkc tkcj j tnj th uogj uogjrst rstaog aogj tnj iho ihoij pts,, ao aog g stugy stugy tnj jxacp jxacpdjs djs.. Hoi Hoij j yhu uogjrstaog uogjrs taog tnj fhddhwko fhddhwko` ` jxacpdj jxacpdjs, s, yhu arj rjagy th praitkij tnj tjino tjinokquj kquj yhursj yhursjdf. df. [hu cay ojjg th rjfjr th tnj jxacpdjs frjqujotdy as yhu ej`ko, eut snhudg try th shdvj tnj jxjriksjs jxjr iksjs ad addd ey yhursjdf hoi hoij j yhu `jt tnj nao` hf kt. Ej surj th injib tnj aos aoswjrs wjrs at tnj eaib ea ib hf tnj tnj eh ehhb hb th jo josu surj rj tna tnatt yhu arj shdv shdvko ko` ` tnj pr prhe hedj djcs cs ih ihrr rrji jitd tdy. y. Kostruitkhos aoswjr oswjr ko tnks ina inaptjr ptjr 1>= = aog gkvkgj ey ύ . Jain a wkdd ej ao kotj`jr ko gj`rjjs2 gj`rjjs2 ohoj hf tnj aos aoswjrs wjrs ko tnks inaptjr ks a fraitkho fraitkho.. Nhwj Nhwjvjr, vjr, tnj `kvj `kvjo o ao ao`dj `dj ko ragka ragkaos os ca cay y ej a fr frai aitk tkho2 ho2 cu cudtk dtkpd pdy y tnj tnj fr frai aitkh tkho o ey tnj sp spji jikf kfkj kjg g ihovj iho vjrsk rskho ho fai faithr, thr, as kddu kddustr stratj atjg g ko tnj jxacp jxacpdjs djs ej ejdhw. dhw. Ohtj=½

ύ rag

3

1>=½ 3 ;=½ 5

Wnj aos aoswjr wjr kkss ;=½. Jxac Jx acpd pdj j 5< 9ύ/7 rag

9ύ

1>=½

7

ύ rag

rag Ð

Wnj aos aoswjr wjr kkss 19:½. Jxac Jx acpd pdj j 9< :ύ/9 rag

:ύ

1>=½

9

ύ rag

rag Ð

3

9 Ð 1>=½ 3 19:½ 7

3

: Ð 1>=½ 3 9==½ 9

Wnj aos aoswjr wjr kkss 9==½. Jxac Jx acpd pdj j 7< 9ύ rag

9ύ rag Ð

1>=½

ύ rag

3 9 Ð 1>=½ 3 :7=½

Wnj aos aoswjr wjr kkss :7=½.

51

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) ;ύ/5= rag

(5) ύ/5= rag

(9) 10ύ/9= rag

(7) 0ύ/5= rag

(:) 5;ύ/9= rag

(6) ύ/15 rag

(0) 19ύ/1: rag

(>) 70ύ/5= rag

(;) ύ rag

(1=) ύ/7 rag

(11) 19;ύ/9= rag

(15) ύ/5 rag

55

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 510ύ/6= rag

(5) :ύ/15 rag

(9) 10ύ/5= rag

(7) 1;ύ/9= rag

(:) 5ύ/9 rag

(6) 7;ύ/1: rag

(0) 1=0ύ/6= rag

(>) 151ύ/6= rag

(;) 10ύ/9= rag

(1=) 0ύ/6= rag

(11) ύ/: rag

(15) 0ύ/5= rag

59

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) ύ/6= rag

(5) 10ύ/9= rag

(9) ύ/5= rag

(7) ;ύ/5 rag

(:) ύ/5 rag

(6) 79ύ/6= rag

(0) 1;ύ/6= rag

(>) 7ύ/: rag

(;) 9ύ/1= rag

(1=) 0;ύ/9= rag

(11) >ύ/1: rag

(15) 11ύ/15 rag

57

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 11ύ/9= rag

(5) ύ/7 rag

(9) >ύ/1: rag

(7) 5;ύ/6= rag

(:) 1;ύ/6= rag

(6) 11ύ/5= rag

(0) 9;ύ/5= rag

(>) 5ύ/1: rag

(;) ύ/15 rag

(1=) ;ύ/1= rag

(11) ;ύ/5= rag

(15) 9ύ/1= rag

5:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) >ύ/: rag

(5) 19ύ/6= rag

(9) 59ύ/: rag

(7) 91ύ/1= rag

(:) 71ύ/5= rag

(6) 17ύ/1: rag

(0) ύ/1: rag

(>) ;ύ/5= rag

(;) 70ύ/6= rag

(1=) 7;ύ/6= rag

(11) 5;ύ/9= rag

(15) 5;ύ/6= rag

56

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 0ύ/5= rag

(5) 11;ύ/9= rag

(9) 19ύ/6= rag

(7) 19ύ/9= rag

(:) 90ύ/6= rag

(6) :ύ/15 rag

(0) 70ύ/6= rag

(>) 71ύ/6= rag

(;) 9ύ/5= rag

(1=) 19ύ/1: rag

(11) 1;ύ/9= rag

(15) 19ύ/5= rag

50

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 550ύ/6= rag

(5) ;ύ/1= rag

(9) 70ύ/6= rag

(7) 9ύ/5= rag

(:) 11ύ/1: rag

(6) ύ/9= rag

(0) 119ύ/9= rag

(>) 19ύ/5= rag

(;) 5ύ/1: rag

(1=) 19ύ/1: rag

(11) 01ύ/9= rag

(15) 0ύ/6= rag

5>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 91ύ/5= rag

(5) ύ rag

(9) 91ύ/6= rag

(7) 19ύ/15 rag

(:) 9ύ rag

(6) :ύ/6 rag

(0) 7;ύ/6= rag

(>) 0;ύ/9= rag

(;) 9ύ/1= rag

(1=) 90ύ/6= rag

(11) 7ύ/: rag

(15) 5;ύ/6= rag

5;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 7;ύ/15 rag

(5) 1;ύ/9= rag

(9) 9ύ/5= rag

(7) >ύ/1: rag

(:) ύ/1: rag

(6) >ύ/9 rag

(0) 7ύ/1: rag

(>) 11ύ/9= rag

(;) 5ύ/9 rag

(1=) 9ύ/1= rag

(11) 9ύ/: rag

(15) 65ύ/1: rag

9=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 0ύ/15 rag

(5) 51ύ/1= rag

(9) 0ύ/6 rag

(7) 0ύ/6= rag

(:) 6;ύ/5= rag

(6) 510ύ/6= rag

(0) :ύ/6 rag

(>) 550ύ/6= rag

(;) 70ύ/15 rag

(1=) ύ/6 rag

(11) 0ύ/5= rag

(15) ;ύ/5= rag

91

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 11ύ/1: rag

(5) 11ύ/15 rag

(9) ;ύ/1= rag

(7) >;ύ/9= rag

(:) 1;ύ/6= rag

(6) ύ/9 rag

(0) 71ύ/6= rag

(>) :ύ/5 rag

(;) >ύ/1: rag

(1=) 71ύ/9= rag

(11) 70ύ/6= rag

(15) 0ύ/1: rag

95

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Iho Kostruitkhos< Ihovj vjrt rt ttnj nj `kv `kvjo jo ao` ao`dj dj frhc rag ragkao kaoss th gj gj`rj `rjjs js.. Inj Injib ib yhu yhurr ao aoswj swjrs rs ko ttnj nj eaib ea ib hf tn tnj j eh ehhb hb.. (1) 5;ύ/6 rag

(5) 11ύ/15 rag

(9) 169ύ/6= rag

(7) 0ύ/6= rag

(:) 5;ύ/1= rag

(6) >ύ/1: rag

(0) ύ/9 rag

(>) 90ύ/6= rag

(;) 70ύ/6= rag

(1=) 1;ύ/6= rag

(11) 0ύ/1= rag

(15) 7ύ/1: rag

99

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Inap In aptj tjr r 5 Ao Aosw swjr jrss ]a`j 55 ]a`j (1 (1)) >1 >1½½ ((5) 5) ;½

]a`j 56 ]a`j (1) (1) 5> 5>>½ >½ ((5) 5) 9; 9;½½

(9 (9)) 1= 1=5½ 5½ ((7) 7) 69 69½½ (: (:)) 10 107½ 7½ ((6) 6) 1: 1:½½ (0) 1:6 1:6½½ (> (>)) 759 759½½ (;) 1>= 1>=½½ (1 (1=) =) 7: 7:½½ (11)) >97 (11 >97½½ (15) (15) ;= ;=½½

(9) >5> >5>½½ (7 (7)) ::> ::>½½ (:) 96; 96;½½ (6 (6)) 16> 16>½½ (0) (0) 15 15½½ ((>) >) >1 >1½½ (;) 171 171½½ (1=) (1=) 17 170½ 0½ (11)) 107 (11 107½½ (15) (15) >0 >0½½

]a`j 59 ]a`j (1 (1)) 6: 6:1½ 1½ ((5) 5) 0: 0:½½ (9) 1:9 1:9½½ (7 (7)) 117 117½½ (:) 15= 15=½½ (6 (6)) :>> :>>½½ (0) 951 951½½ (> (>)) 969 969½½ (;) 1=5 1=5½½ (1 (1=) =) 51 51½½ (11)) 96½ (1 (11 (15) 5) 69 69½½

]a`j 50 ]a`j (1) (1) 69 69½½ (5 (5)) 01 017½ 7½ (9) (9) 9; 9;½½ ((7) 7) 0> 0>½½ (:) (:) 11 111½ 1½ ((6) 6) 0: 0:½½ (0) 171 171½½ (> (>)) 159 159½½ (;) 50½ (1 (1=) =) 1:6 1:6½½ (11)) 117 (11 117½½ (1 (15) 5) 11 110½ 0½

]a`j 57 ]a`j (1 (1)) 9½ (5 (5)) 1= 1=5½ 5½ (9 (9)) ;½ (7 (7)) >1 >1=½ =½ (: (:)) ;= ;=½½ (6 (6)) 15 15;½ ;½ (0 (0)) :0 :0½½ (> (>)) 17 177½ 7½ (;) :7½ (1 (1=) =) 707 707½½ (11)) ;6½ (1 (11 (15) 5) 16 16:½ :½

]a`j 5> ]a`j (1) 6>1 6>1½½ (5 (5)) 165 165½½ (9) (9) 17 171½ 1½ ((7) 7) 50 50½½ (:) (:) 19 195½ 5½ (6) 6½ (0) 60> 60>½½ (> (>)) 110 110½½ (;) 57½ (1 (1=) =) 1:6 1:6½½ (11)) 756 (11 756½½ (15) (15) 51 51½½

]a`j ]a `j 5:

]a`j ]a `j 5;

(1 (1)) 66 66½½ ((5) 5) 7: 7:½½ (9 (9)) ;6 ;6½½ ((7) 7) >0 >0½½ (: (:)) :0 :0½½ ((6) 6) ;; ;;½½ (0 (0)) 9: 9:1½ 1½ ((>) >) 57 57½½ (;) 1:½ (1 (1=) =) 165 165½½ (11)) >1½ (1 (11 (15) 5) :7 :7½½

(1) 50; 50;½½ (5 (5)) 1>= 1>=½½ (9) (9) ;9 ;9½½ (7 (7)) 1; 1;:½ :½ (:) :7= :7=½½ (6 (6)) 1:= 1:=½½ (0) 170 170½½ (> (>)) 707 707½½ (;) :7½ (1 (1=) =) 111 111½½ (11)) 177 (11 177½½ (15) (15) >0 >0½½ Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th tn tnj j Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

97

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

]a`j 9= ]a`j (1) 09: 09:½½ (5 (5)) 117 117½½ (9 (9)) 50 50½½ ((7) 7) ;6 ;6½½ (: (:)) 15 15½½ (6 (6)) 7> 7>=½ =½ (0 (0)) 7> 7>½½ ((>) >) 66 66½½ (;) 15= 15=½½ (1 (1=) =) :7 :7½½ (11)) 1=> (11 1=>½½ (1 (15) 5) 07 077½ 7½

]a`j 95 ]a`j (1) 195 195½½ (5 (5)) 16: 16:½½ (9) 165 165½½ (7 (7)) :97 :97½½ (:) (:) :0 :0½½ ((6) 6) 6= 6=½½ (0) 159 159½½ (> (>)) 7:= 7:=½½ (;) ;6½ (1 (1=) =) 576 576½½ (11)) 171 (11 171½½ (15) (15) >7 >7½½

]a`j 91 ]a`j (1) 1=: 1=:½½ (5 (5)) 90> 90>½½ (9 (9)) 51 51=½ =½ ((7) 7) 51 51½½ (:) 651 651½½ (6 (6)) 6:1 6:1½½ (0) 1:= 1:=½½ (> (>)) 6>1 6>1½½ (;) 0=: 0=:½½ (1 (1=) =) 9= 9=½½ (11)) 69½ (1 (11 (15) 5) >1 >1½½

]a`j 99 ]a`j (1) >0= >0=½½ (5 (5)) 16: 16:½½ (9) (9) 7> 7>;½ ;½ ((7) 7) 51 51½½ (:) (:) :5 :55½ 5½ ((6) 6) ;6 ;6½½ (0) (0) 6= 6=½½ (> (>)) 11 111½ 1½ (;) 171 171½½ (1 (1=) =) :0 :0½½ (11)) 156 (11 156½½ (15) (15) 7> 7>½½

9:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Inap In aptj tjr r 9< KKgj gjot otkf kfyk yko` o` Wr Wrk` k` Fuo uoit itkh khos os ko Uk` Uk`nt Wr Wrka kao` o`dj djss Wnj easki trk` fuoitkhos ’ skoj (sko), ihskoj (ihs), aog tao`jot (tao) ’ arj gjfkojg as tnj ratkhs hf skgjs skgjs hf rk`nt trkao`dj trkao`djs. s. Ko a rk`nt trkao`dj trkao`dj,, tnj skoj hf ao ao`dj jquads tnj ratkh ratkh hf tnj hpphsktj skgj th tnj nyphtjousj, tnj ihskoj hf ao ao`dj jquads tnj ratkh hf tnj aglaijot skgj th tnj nyphtjousj, aog tnj tao`jot jquads tnj ratkh hf tnj hpphsktj skgj th tnj aglaijot skgj. A rk`n rk`ntt trkao trkao`dj `dj nas hoj ;=½ ao` ao`dj. dj. Wnj hpp hpphsk hsktj tj aog agl aglaij aijot ot skgjs cab cabj j tnj ;=½ ao`dj.. Wnj tnkrg skgj ao`dj skgj,, wnkin ks tnj dho dho`jst `jst sskgj, kgj, ks ia iaddjg ddjg tnj nyp nyphtjous htjousj. j. Wnj ao`d ao`dj j ko tnj arùcjot hf tnj trk` fuoitkho fuoitkho dkjs ej ejtwjjo twjjo tnj aglaijot skgj aog tnj ny nyphtjousj. phtjousj. Ytugy tnj trkao`dj trkao` dj ejdhw. Adsh st stugy ugy tnj gjfkok gjfkoktkhos tkhos hf tnj skoj, ihs ihskoj, koj, aog tao`j tao`jot. ot. @kvj @kvjo o gkffjrj gkffjrjot ot snap snapjs js ao aog g hrk hrkjo jota tatk tkhos hos hf rk rk`nt `nt tr trka kao` o`dj djs, s, kt ks ir irui uika kadd ko trk` trk`ho hohc hcjt jtry ry tn tnat at yh yhu u ia iao o ihrrjitdy ihrrji tdy kgjotkf kgjotkfy y tnj skoj skoj,, ihskoj, aog tao`jot hf a spjikfk spjikfkjg jg ao`dj. Wnks inaptj inaptjrr prhvkgjs jxtjos jxt joskvj kvj pra praitk itkij ij ko hrgjr th njdp yhu gjvj gjvjdhp dhp tnks sb sbkdd. kdd.

nyphtjousj

hpphsktj

aglaijot

sko

3

hpphsktj nyphtjousj

,

ih s

3

aglaijot nyphtjousj

,

tao

3

hpphsktj aglaijot

Kt cay ej njd njdpfu d thj-aglaijo cjc cjchrk hrkzj zj shn shn-ia -ian-t n-tha, ha,tao`j wnkin ks aosktj-agla ae aeerj erjvka vkatkho tkho sko skojjhpphsktj-nyphtj hpphsktj-ny phtjousj ousj2 2pfud ihsko ihskoj-agl aijot-nyph t-nyphtjo tjousj2 usj2 tao`jot-hpph ot-hpphsktj -aglaijot ijot. . fhr Ytugjo Ytugjots ts wnh iao wrktj ghwo sshn-ia hn-ian-tha n-tha iao hftjo ihrrj ihrrjitdy itdy kgjotk kgjotkfy fy tnj skoj skoj,, ihsko ihskoj, j, aog ttao`j ao`jot ot hf ao ao`dj wnjo wnjo dhhbko` at a rk`nt trka trkao`dj. o`dj. Ohtj tna tnat t   ks tnj dhwjriasj @rjjb djttjr tnjta, aog ks vj vjry ry ihc ihccho chody dy usj usjg ga ass tnj va varkae rkaedj dj fhr ao u uob obohwo ohwo ao` ao`dj. dj. Wnjrj Wnj rj arj tnrjj agg aggktkh ktkhoad oad trk trk` ` fuo fuoitk itkhos hos ’ tnj ihs ihsji jiaot aot (isi), sj sjiao iaott (ihs (ihs), ), aog ihtao` iht ao`jot jot (ih (iht) t) ’ wnki wnkin na arj rj rji rjikpr kprhia hiads ds hf tnj sko skoj, j, ihs ihskoj koj,, aog tao tao`jo `jott fuoi fuoitkho tkhos< s<

isi

3

nyphtjousj hpphsktj

,

sji

3

nyphtjousj aglaijot

,

iht 3

aglaijot hpphsktj

Kt ks kcp kcphrta hrtaot ot th oht ohtj j ks tna tnatt ttnj nj ihs ihsji jiaot aot ks tnj rji rjikprh kprhiad iad hf sko skoj j fuo fuoitk itkho ho,, wnk wnkdj dj tnj sj sjia iaot ot ks tnj rjikprhiad hf tnj ihskoj fuoitkho2 caoy stugjots gh oht fkog tnks asshikatkho th ej kotuktkvj. 96

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Ko tnks inaptjr, jain prhedjc `kvjs `kvjs yhu a rk`nt trkao`dj wktn twh hf tnj skgjs bohwo aog hoj uobohwo ao`dj kgjotkfkjg as . Fhr jain trkao trkao`dj, `dj, yhu ojj ojjg g th gjtjrckoj tw twh h easki trk` fuoitkhos fuoitkhos ’ k.j. skoj, ihsk ihskoj, oj, tao`j tao`jot, ot, ihsjia ihsjiaot, ot, sjia sjiaot, ot, aog ihtao ihtao`jot `jot.. Ko hrgjr th gh tnks, yhu wkdd ojjg th ej aedj th gjtjrckoj wnkin skgj ks aglaijot th , wnkin skgj ks hpphsk hpp hsktj tj th , ao aog g wn wnki kin n skgj kgj ks tnj ny nyph phtj tjou ousj sj.. [h [hu u wk wkdd dd ads adsh oj ojjg jg th ap appd pdy y tn tnj j ]ytna`hrja ]ytn a`hrjao o tnjhrjc ko hrgjr th gjtj gjtjrckoj rckoj tnj uobohw uobohwo o skgj. Aiih Ai ihrgk rgko` o` th tn tnj j ]y ]ytn tna` a`hrj hrjao ao tnj tnjhr hrjc jc,, tn tnj j hp hpph phsk sktj tj ( ), aglai glaij jot ( ), aog nyphtj nyp htjous ousj j (ℏ ) arj rjd rjdatj atjg g ey tnj fhd fhddhwk dhwko` o` jq jqua uatkho tkho

1= ∜ 1=

(7) sko ,iht 3 8

(:) ihs , is isii

38

(6) isi ,tao

>

7

7

51 ∜ 51 6

∜ 0

77

38

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Fhr jain rk`nt trkao`d Kostruitkhos< trkao`dj, j, jxprj jxprjss ss tnj twh spj spjikfkj ikfkjg g trk` fuoitkhos as rjgui rjguijg jg fr frai aitk tkho hos. s. In Inji jib b yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. Ohtj< Wnj trka Ohtj< trkao`d o`djs js arj oh ohtt grawo th sia siadj. dj. Wnj skg skgj j tnat dhhb dhhbss dho` dho`jr jr (jx (jxijp ijptt fhr tnj nyphtjousj, wnkin ks adways dho`jst) cay aituaddy ej snhrtjr, aog tnj ao`dj tnat dhhbs dar`jr dar `jr (jx (jxijp ijptt fhr ;=½, wnk wnkin in ks idj idjard ardy y car carbj bjg g wktn a ehx ehx)) cay ait aituad uaddy dy ej sca scaddj ddjr. r. (1) sko ,tao

38

(5) sko ,ihs

38

5

1:

9

;

38

∜ 0

1=

(7) ihs ,iht 3 8

(:) sko , sji

38

7∜ 5

∜ 9

(9) sji , tao tao

5∜ 9

(6) isi ,ihs

38

; 5 6

7:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Fhr jain rk`nt trkao`d Kostruitkhos< trkao`dj, j, jxprj jxprjss ss tnj twh spj spjikfkj ikfkjg g trk` fuoitkhos as rjgui rjguijg jg fr frai aitk tkho hos. s. In Inji jib b yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. Ohtj< Wnj trka Ohtj< trkao`d o`djs js arj oh ohtt grawo th sia siadj. dj. Wnj skg skgj j tnat dhhb dhhbss dho` dho`jr jr (jx (jxijp ijptt fhr tnj nyphtjousj, wnkin ks adways dho`jst) cay aituaddy ej snhrtjr, aog tnj ao`dj tnat dhhbs dar`jr dar `jr (jx (jxijp ijptt fhr ;=½, wnk wnkin in ks idj idjard ardy y car carbj bjg g wktn a ehx ehx)) cay ait aituad uaddy dy ej sca scaddj ddjr. r. (1) sko ,tao

38

(5) sko , ta tao o

38

(9) ihs ,iht 3 8

5 5= ∜ 5=

1= ∜ 1=

1

15

16

(7) sji , tao tao

38

(:) isi ,sji

38

(6) isi ,iht 3 8

:

∜ 5 ∜ 5

76

:

19 1=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Fhr jain rk`nt trkao`d Kostruitkhos< trkao`dj, j, jxprj jxprjss ss tnj twh spj spjikfkj ikfkjg g trk` fuoitkhos as rjgui rjguijg jg fr frai aitk tkho hos. s. In Inji jib b yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. Ohtj< Wnj trka Ohtj< trkao`d o`djs js arj oh ohtt grawo th sia siadj. dj. Wnj skg skgj j tnat dhhb dhhbss dho` dho`jr jr (jx (jxijp ijptt fhr tnj nyphtjousj, wnkin ks adways dho`jst) cay aituaddy ej snhrtjr, aog tnj ao`dj tnat dhhbs dar`jr dar `jr (jx (jxijp ijptt fhr ;=½, wnk wnkin in ks idj idjard ardy y car carbj bjg g wktn a ehx ehx)) cay ait aituad uaddy dy ej sca scaddj ddjr. r. (1) isi ,ihs

38

(5) sko , sji

17

38

56 ∜ 56

19 ∜ 19

(9) ihs ,tao

38

∜ 5

1= ∜ 1=

6

(7) ihs , tao tao

38

(:) sko , sji

38

(6) sko ,ihs

38

∜ 9 5=

5 5

1:

1 5

∜ 9

70

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Fhr jain rk`nt trkao`d Kostruitkhos< trkao`dj, j, jxprj jxprjss ss tnj twh spj spjikfkj ikfkjg g trk` fuoitkhos as rjgui rjguijg jg fr frai aitk tkho hos. s. In Inji jib b yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. Ohtj< Wnj trka Ohtj< trkao`d o`djs js arj oh ohtt grawo th sia siadj. dj. Wnj skg skgj j tnat dhhb dhhbss dho` dho`jr jr (jx (jxijp ijptt fhr tnj nyphtjousj, wnkin ks adways dho`jst) cay aituaddy ej snhrtjr, aog tnj ao`dj tnat dhhbs dar`jr dar `jr (jx (jxijp ijptt fhr ;=½, wnk wnkin in ks idj idjard ardy y car carbj bjg g wktn a ehx ehx)) cay ait aituad uaddy dy ej sca scaddj ddjr. r. (1) ihs ,iht 3 8

(5) sko , ta tao o

38

(9) sko ,sji 1

38

5

1 9 :

1

:

1

(7) ihs ,iht 3 8

∜ :

5

19

(:) sko ,ihs

38

(6) sji ,iht 3 8

9

:

5 9∜ 9

5 :

7>

5∜ 5

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Fhr jain rk`nt trkao`d Kostruitkhos< trkao`dj, j, jxprj jxprjss ss tnj twh spj spjikfkj ikfkjg g trk` fuoitkhos as rjgui rjguijg jg fr frai aitk tkho hos. s. In Inji jib b yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. Ohtj< Wnj trka Ohtj< trkao`d o`djs js arj oh ohtt grawo th sia siadj. dj. Wnj skg skgj j tnat dhhb dhhbss dho` dho`jr jr (jx (jxijp ijptt fhr tnj nyphtjousj, wnkin ks adways dho`jst) cay aituaddy ej snhrtjr, aog tnj ao`dj tnat dhhbs dar`jr dar `jr (jx (jxijp ijptt fhr ;=½, wnk wnkin in ks idj idjard ardy y car carbj bjg g wktn a ehx ehx)) cay ait aituad uaddy dy ej sca scaddj ddjr. r. (1) sko ,ihs

38

(5) sji ,tao

38

(9) isi ,tao

38

∜ :

9∜ 5

0

9

:

∜ 6

(7) sko , tao

38

(:) sko , sji

38

(6) ihs ,iht 3 8

5= 5

>

1>

1=

57

7;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Fhr jain rk`nt trkao`d Kostruitkhos< trkao`dj, j, jxprj jxprjss ss tnj twh spj spjikfkj ikfkjg g trk` fuoitkhos as rjgui rjguijg jg fr frai aitk tkho hos. s. In Inji jib b yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. Ohtj< Wnj trka Ohtj< trkao`d o`djs js arj oh ohtt grawo th sia siadj. dj. Wnj skg skgj j tnat dhhb dhhbss dho` dho`jr jr (jx (jxijp ijptt fhr tnj nyphtjousj, wnkin ks adways dho`jst) cay aituaddy ej snhrtjr, aog tnj ao`dj tnat dhhbs dar`jr dar `jr (jx (jxijp ijptt fhr ;=½, wnk wnkin in ks idj idjard ardy y car carbj bjg g wktn a ehx ehx)) cay ait aituad uaddy dy ej sca scaddj ddjr. r. (1) sji , isi

38

(5) sji ,iht 3 8

(9) isi ,iht 3 8

> 7

;

10

5

11

(7) sko ,iht 3 8

(:) ihs , is isii

38

(6) sko ,ihs

16

>

>

15 15 :

:=

38

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r 9 Ao Aosw swjr jrss ]a`j 9; ]a`j (1 (1)) 7/ 7/:, :, 9/: (5 (5)) :/ :/19 19,, :/ :/15 15

]a`j 7: ]a`j (1) 9∜ 1=/1= 5) ∜ :/9 :/9, 5/9 1=/1=, 9 ((5)

(9) 5∜ :/: 1/5 5 ((7) 7) ∜ 9/5 :/:, 1/ 9/5, ∜ 9/9 9/9 (: (:)) 7/ 7/:, :, :/9 ((6) 6) ∜ 5, ∜ 5/5 5/5

(9) ∜ 51/9 51/9, 5∜ 9/9 9/9 (7) ∜ 9/5 9/5, ∜ 9 (:) 5∜ 5/9 6) 9/5 /5,, ∜ :/9 5/9, 9 ((6 :/9

]a`j 7= ]a`j (1) 9∜ 19/19 5/9 9 ((5) 5) ∜ 5/5 19/19, 5/ 5/5, ∜ 5/5 5/5 (9 (9)) 1/ 1/5, 5, ∜ 9 (7) 5∜ :/: :/:, 5 (:) ∜ 6/5 (6)) :/ :/7, 7, 7/9 6/5, ∜ 9 (6

]a`j 76 ]a`j (1) ∜ 5/5 5) 7/ 7/: :, 7/9 5/5, 1 ((5) (9) ∜ 9/5 9/5, ∜ 9 (7) ∜ 5, 1 (:) 5∜ 9/9 6) 19 19/ /:, 15 15/: /: 9/9, 5 ((6)

]a`j 71 ]a`j (1 (1)) 9/ 9/:, :, 7/: ((5) 5) ∜ 55/11 55/11, ∜ 5/9 5/9 (9) ∜ 5/5 5/5, 1 ((7 7) ∜ 6/9 6/9, ∜ 5/5 5/5 (: (:)) 9/ 9/:, :, :/7 ((6) 6) 5∜ 9/9 9/9, 1/5

]a`j 70 ]a`j (1) (1) 0/ 0/9, 9, 5∜ 1=/0 1=/0 (5) ∜ 5/5 5/5, ∜ 5 (9) 5 :/:, 1/ 1/5 5 ((7) 7) 9/: /:,, 7/9 ∜ 5, 5∜ 9/9 (:) (:) 1/ 1/5, (6) 1/ 1/5, 5, ∜ 9/5 9/9 (6) 9/5

]a`j 75 ]a`j (1) >/1 >/10, 0, 1:/ 1:/> > ((5) 5) 0∜ 5/1= 5/1=, 1/0 (9 (9)) 7/ 7/:, :, :/9 ((7) 7) 5∜ 19/19 19/19, 9/5 (:) 5∜ :/: :/:, ∜ :/: :/: (6) ∜ 1=/9 1=/9, 1/9

]a`j 7> ]a`j (1) (1) 7/ 7/:, :, 7/ 7/9 9 (5 (5)) 15 15/1 /19, 9, 15 15/: /: (9) ∜ 5/5 5/5, ∜ 5 (7) 5∜ :/: :/:, 5 (:) (:) 1/ 1/5, 5, ∜ 9/5 9/5 (6) ∜ 6/5 6/5, ∜ 5

]a`j 79 ]a`j (1) 15/ 15/19, 19, :/ :/19 19 ((5) 5) ∜ 5, 1 (9) ∜ 9, ∜ 5/5 5/5 (7) (7) 9/ 9/:, :, 9/7

]a`j 7; ]a`j (1) 5∜ 6/0 6/0, :/ :/0 0 ((5) 5) ∜ 9, ∜ 5 (9) 9∜ :/: :/:, ∜ :/5 :/5 (7) ∜ 1:/7 1:/7, ∜ 1: 1:

(:) 9∜ 19/19 19/19, ∜ 19/5 19/5 (6) ∜ :/: :/:, 1/5

(:) (:) 9/ 9/:, :, :/ :/7 7 (6 (6)) ∜ 9/5 9/5, ∜ 9

]a`j 77 ]a`j (1) 10/ 10/1:, 1:, 10 10/> /> ((5) 5) ∜ 5, 1 (9 (9)) :/ :/9, 9, 7/9 ((7) 7) ∜ :/: :/:, 5 (: (:)) 5/ 5/9, 9, 9∜ :/: :/: (6) 5, ∜ 9/9 9/9

]a`j := ]a`j (1) ∜ :/5 :/5, ∜ : (5) 11∜ 1=/5= 1=/5=, 5∜ 1=/; 1=/; (9) 10/ 10/1:, 1:, >/ >/1: 1: ((7) 7) ∜ :/: :/:, 5 (:) (:) 5/ 5/9, 9, 9∜ :/: :/: (6) (6) 15 15/1 /19, 9, :/ :/19 19

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th ttnj nj Bko Bkogdj gdj jgkt jgktkho kho (oht tnj prkot j jgktkho gktkho). ).

:1

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Inap In aptj tjr r 7< Ypji Ypjika kadd Uk Uk`n `ntt Wrk rka ao`dj o`djss Wwh spjikad rk`nt trkao`djs tnat arj vjry ihccho arj tnj 9=½-6=½-;=½ aog 7:½-7:½-;=½ trkao trk ao`d `djs js.. Wnj Wnjsj sj rk rk`nt `nt tr trka kao` o`dj djss arj arj jo joih ihuot uotjr jrjg jg ko ca catn tn ao aog g si sikj kjoi oij j ihu ihurs rsjs js ’ ao aog g staogargkzjg catn jxacs ’ sh frjqujotdy tnat kt ks agvaota`jhus th ej aedj th rjihòkzj tnjsj trkao`djs aog th ej aedj th fdujotdy shdvj fhr aoy uobohwo ao`dj hr skgj ko tnjsj trkao`djs. Wnj 9=½-6=½-;=½ 9=½-6=½-;=½ trkao`dj ks hoj-nadf hf ao jqukdatj jqukdatjrad rad trkao`dj trkao`dj.. Wnjrj Wnjrjfhrj fhrj,, tnj skgj hpphs hpp hsktj ktj th 9= 9=½½ ks nadf as dho` as tnj ny nyph phtjo tjous usj. j. Kf tnj skgj skgj hp hpph phsk sktj tj th 9=½ ks 1, tnj nyphtjousj nyphtj ousj ks 5. Wnj rjcakok rjcakoko` o` skgj, wnkin ks aglai aglaijot jot th 9=½ (eut hpp hpphsktj hsktj th 6=½), iao ej fhuo fhuog g frhc frhc tnj ]y ]ytn tna` a`hr hrja jao o tn tnjh jhrj rjc< c< 3 ∜ ℏ ∕ 3 ∜ 5 ∕ 1 3 ∜ 7 ∕ 1 3 ∜ 9. Ko `j `joj ojra rad, d, wj iao iao sa say y tna tnatt ttnj nj ra ratkh tkh hf tn tnj j skgjs skgjs hf a 9=½ 9=½-6= -6=½½-;= ;=½½ trka trkao` o`dj dj ks 1< ∜ 9 wnjr jrj j 1 ks 9∜ 9 (9) (9) 15 15,, 15∜ 9 (7) 1= 1=,, 1= (:) (:) 9= 9=½, ½, 7∜ 9 (6) 7: 7:½½, 16

]a`j :0 ]a`j (1 (1)) 6= 6=½, ½, 17∜ 9 (5) 9∜ 5, 9 (9) 6, 9∜ 9 (7 (7)) 9= 9=½, ½, ;∜ 9 (:) (:) 7: 7:½, ½, : (6) 6, 6∜ 9

]a`j 69 ]a`j (1 (1)) 6= 6=½, ½, 51 ((5) 5) 1> 1>,, ;∜ 5 (9) 7= 7=,, 5= ((7) 7) 6=½ =½,, > (: (:)) 6= 6=½, ½, : (6 (6)) 57∜ 5, 57∜ 5

]a`j :> ]a`j (1) 5∜ 5, 7 ((5 5) 9∜ 9, ;

]a`j 67 ]a`j (1) 5∜ 17 17, 7∜ 0 (5) 9∜ 51 51, ;∜ 0

(9)) 9= 16½, 95/9 9∜ /9 ∜ 9/9 ∜ 9/9 (: (:) 9=½, 6,(7) ∜ 5, >(6) ∜ 9 ∜ 6, 5∜ 5

(9 (9))) 9= 1> 1>,½, , ;5((7) 7) 11, 5 11 5∜ 11 11 1, ∜ 55 ∜ 11 (:) (: 9=½, 19∜ (6) 19 1 55 ∜

]a`j :; ]a`j (1) 9∜ 6, 9∜ 5 (5) ∜ 6, 5∜ 9 (9 (9)) 9= 9=½, ½, ∜ 5 ( (7) 7) 1, ∜ 9/5 9/5 (: (:)) 1/ 1/5, 5, ∜ 5/5 5/5 (6) ∜ 5, ∜ 5/5 5/5

]a`j 6: ]a`j (1) 1>∜ 9, 1> (5) :, : (9) (9) 6= 6=½, ½, 1>∜ 5 (7) 5∜ 9/9 9/9, 1 (:) ∜ 5/5 5/5, 1 ((6) 6) ∜ 5/9 5/9, ∜ 5/6

]a`j 6= ]a`j (1 (1)) 7: 7:½, ½, ∜ : (5) 6= 6=½, ½, ∜ 0 (9) >∜ 6, 7∜ 6 (7) 7∜ 6, 7∜ 6

]a`j 66 ]a`j (1) (1) 9= 9=½, ½, 5∜ 10 10 (5) (5) 7: 7:½, ½, ∜ 1; 1; (9) 5∜ 17 17, ∜ 17 17 (7) (7) 7: 7:,, 1:∜ 9

(: (:)) 6= 6=½, ½, ∜ 1: 9=½, ½, 17 1: (6) 9=

(:) (:) 7: 7:½, ½, ∜ 1= (6) 9= 9=½, ½, 15∜ 5 1= (6)

]a`j 61 ]a`j (1 (1)) 9= 9=½, ½, 5∜ : (5) (5) 7: 7:½, ½, ∜ 0 (9 (9)) 95 95,, 16∜ 9 (7 (7)) 6= 6=½, ½, 7∜ 9 (: (:)) 9= 9=½, ½, 15∜ 9 (6) >∜ 9/9 9/9, 16∜ 9/9 9/9

]a`j 60 ]a`j (1) (1) 7: 7:½, ½, 5∜ : (5) (5) 9= 9=½, ½, ∜ : (9) 5∜ 9= 9=, 9∜ 1= 1= (7) (7) 6= 6=½, ½, :∜ 9= 9= (:) (:) 9= 9=½, ½, 7:∜ 1= 1= (6) 0=∜ 51=/9 51=/9, 17=∜ 51=/9 51=/9

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th tnj Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

6>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Ina In apt ptjr jr :< Cjchr jchrkz kzj j Ea Easski Wrk rk` ` Fuo uoit itkh kho os ko Qu Qua agr gra aot K Kt ks vjry usjfud usjfud th bohw tnj skoj, ihsko ihskoj, j, aog tao`jo tao`jott hf =½, 9=½, 7:½, 6=½, aog ;=½. Wnjsj ao`djs arj usjg frjqujotdy ko caoy catn, pnyskis, aog staogargkzjg tjst prhedjcs skoij tnjy gho‛t rjqukrj rjqukrj usj hf a iadiudathr iadiudathr.. Caoy trk`ho trk`hohcjtry hcjtry ao aog g pnyskis tjai tjainjrs njrs rjqukrj tnjkr stugjots stugjots th cjchrkzj tnks. Wnj jxjri jxjriksjs ksjs hf tnks inap inaptjr tjr prhvkgj acp acpdj dj praitkij th gjvjdhp gjvj dhp fdujoiy wktn tnj eas easki ki trk` fuoitkhos jv jvaduat aduatjg jg at tnjsj ao`djs ao`djs.. Ejfhrj wj ej`ko wktn tnj cjchrkzatkho jxjriksjs, wj wkdd gjrkvj jain trk` fuoitkho‛s vaduj at jain hf tnjsj ao`djs. Ko tnj 7:½-7:½-;=½ trkao`dj kddustratjg ejdhw, tnj hpphsktj aog aglaijot th jktnjr 7:½ ao`dj arj ehtn jquad th 1, wnkdj tnj nyphtjousj ks ∜ 5. Wnj Wnjrjf rjfhrj hrj,, tnj skoj skoj,, ihsk ihskoj, oj, aog tao`jot tao`j ot hf 7:½ ar arj< j<

1 ∜ 5 ∜ 5 1 3 3 3 5 nyphtjousj ∜ 5 ∜ 5 ∜ 5 aglaijot 1 ∜ 5 ∜ 5 1 3 3 3 ih ihss 7:½ 3 5 nyphtjousj ∜ 5 ∜ 5 ∜ 5 hpphsktj 1 ta tao o 7: 7:½½ 3 3 3 1 aglaijot 1 sko sko 7:½ 3

hpphsktj

∜ 5 7:½ 1

6=½

5

1

9=½

7:½

∜ 9

1

Ko tnj 9=½-6=½-;=½ trkao`dj kddustratjg aehvj, tnj skgj hpphsktj th 9=½ ks 1, tnj skgj aglaijot th 9=½ 9=½ ks ∜ 9, ao aog g tnj tnj ny nyph phtj tjou ousj sj ks 5. Wnj Wnjrjf rjfhrj hrj,, tnj sko skoj, j, ihs ihskoj koj,, ao aog g ta tao`j o`jot ot hf 9=½ arj arj) sko 9=½

(1;) ihs 7:½

(5=) sji =½

(51) isi ;=½

(55) sji 6=½

(59) ihs ;=½

(57) ihs =½

09

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) isi 7:½

(5) sji(ύ/9)

(9) isi(ύ/6)

(7) sko(ύ/5)

(:) isi(ύ/7)

(6) isi 7:½

(0) tao ;=½

(>) sji 7:½

(;) sko(ύ/6)

(1=) isi =½

(11) ihs(ύ/5)

(15) tao ;=½

(19) iht 7:½

(17) sji =½

(1:) ihs =½

(16) ihs 6=½

(10) tao ;=½

(1>) ihs(ύ/9)

(1;) tao =½

(5=) iht =½

(51) sko 9=½

(55) sko(ύ/6)

(59) ihs 7:½

(57) ihs ;=½

07

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) ihs =½

(5) tao(ύ/5)

(9) iht 7:½

(7) sji =½

(:) sji 9=½

(6) iht =½

(0) isi(ύ/7)

(>) iht ;=½

(;) sji ;=½

(1=) sko(ύ/9)

(11) isi 9=½

(15) sko 6=½

(19) ihs(ύ/9)

(17) iht =½

(1:) iht 9=½

(16) iht 6=½

(10) isi(ύ/9)

(1>) sji 6=½

(1;) sko(ύ/5)

(5=) iht =½

(51) sji =½

(55) sji(ύ/6)

(59) ihs(ύ/5)

(57) sji 9=½

0:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) sko 9=½

(5) sji =½

(9) tao(ύ/6)

(7) ihs 6=½

(:) isi ;=½

(6) iht(ύ/5)

(0) tao 7:½

(>) sji 9=½

(;) sji(ύ/9)

(1=) isi 9=½

(11) iht 7:½

(15) ihs(ύ/7)

(19) sko =½

(17) tao(ύ/5)

(1:) isi(ύ/7)

(16) iht ;=½

(10) tao ;=½

(1>) sji =½

(1;) tao =½

(5=) tao 9=½

(51) isi(ύ/5)

(55) iht(ύ/7)

(59) ihs 9=½

(57) iht 9=½

06

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) isi =½

(5) iht 7:½

(9) tao =½

(7) iht(ύ/5)

(:) sji ;=½

(6) ihs =½

(0) iht =½

(>) sji(ύ/5)

(;) iht 7:½

(1=) tao(ύ/5)

(11) sji(ύ/6)

(15) sko 9=½

(19) sji ;=½

(17) iht(ύ/6)

(1:) isi(ύ/9)

(16) sko(ύ/5)

(10) tao(ύ/5)

(1>) sji 9=½

(1;) sji =½

(5=) ihs ;=½

(51) sji 6=½

(55) isi ;=½

(59) ihs(ύ/6)

(57) ihs(ύ/5)

00

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) isi ;=½

(5) tao 6=½

(9) sko =½

(7) ihs 6=½

(:) ihs (ύ/9)

(6) isi(ύ/7)

(0) tao(ύ/6)

(>) isi 7:½

(;) iht(ύ/9)

(1=) ihs(ύ/7)

(11) isi ;=½

(15) sji(ύ/7)

(19) iht 9=½

(17) iht(ύ/6)

(1:) tao(ύ/9)

(16) ihs 6=½

(10) sji ;=½

(1>) isi(ύ/6)

(1;) isi(ύ/9)

(5=) sji(ύ/5)

(51) ihs(ύ/5)

(55) iht(ύ/5)

(59) ihs ;=½

(57) sko 6=½

0>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) sji 9=½

(5) sko 7:½

(9) isi =½

(7) sko(ύ/5)

(:) ihs(ύ/7)

(6) sko 7:½

(0) isi 7:½

(>) ihs 7:½

(;) iht(ύ/7)

(1=) sji =½

(11) iht 6=½

(15) ihs =½

(19) tao =½

(17) isi(ύ/9)

(1:) isi 9=½

(16) tao(ύ/7)

(10) sji(ύ/5)

(1>) iht(ύ/5)

(1;) iht =½

(5=) isi(ύ/7)

(51) tao(ύ/7)

(55) isi 7:½

(59) isi =½

(57) sji(ύ/9)

0;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) isi(ύ/6)

(5) sji ;=½

(9) ihs(ύ/7)

(7) isi =½

(:) isi 7:½

(6) iht(ύ/7)

(0) ihs 9=½

(>) iht(ύ/9)

(;) ihs(ύ/9)

(1=) tao(ύ/5)

(11) ihs =½

(15) isi 6=½

(19) ihs =½

(17) sko 9=½

(1:) tao(ύ/9)

(16) isi(ύ/6)

(10) iht 9=½

(1>) sji(ύ/7)

(1;) tao ;=½

(5=) isi(ύ/5)

(51) sji =½

(55) ihs 7:½

(59) ihs ;=½

(57) ihs(ύ/5)

>=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) sko(ύ/6)

(5) sko 6=½

(9) iht 9=½

(7) isi =½

(:) isi(ύ/5)

(6) sji(ύ/5)

(0) tao(ύ/5)

(>) isi(ύ/7)

(;) ihs(ύ/9)

(1=) isi =½

(11) sji(ύ/7)

(15) iht(ύ/7)

(19) sji ;=½

(17) isi(ύ/5)

(1:) sji 7:½

(16) tao(ύ/7)

(10) iht =½

(1>) isi 9=½

(1;) iht(ύ/6)

(5=) tao(ύ/6)

(51) ihs ;=½

(55) iht(ύ/7)

(59) isi 6=½

(57) ihs 9=½

>1

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) iht(ύ/9)

(5) iht 6=½

(9) sji =½

(7) sko(ύ/6)

(:) ihs =½

(6) ihs ;=½

(0) sji =½

(>) sko =½

(;) tao =½

(1=) sko(ύ/6)

(11) isi(ύ/6)

(15) isi =½

(19) iht 7:½

(17) ihs(ύ/6)

(1:) tao ;=½

(16) ihs ;=½

(10) tao(ύ/7)

(1>) iht(ύ/6)

(1;) ihs =½

(5=) tao(ύ/6)

(51) sji(ύ/7)

(55) sko ;=½

(59) tao ;=½

(57) isi ;=½

>5

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) sko(ύ/7)

(5) sko(ύ/6)

(9) isi =½

(7) sko 9=½

(:) sji(ύ/5)

(6) isi ;=½

(0) tao 9=½

(>) ihs 6=½

(;) tao(ύ/6)

(1=) isi =½

(11) tao ;=½

(15) ihs =½

(19) sji(ύ/5)

(17) sko(ύ/5)

(1:) sko 6=½

(16) tao 6=½

(10) tao 7:½

(1>) ihs(ύ/6)

(1;) isi ;=½

(5=) tao(ύ/6)

(51) tao 9=½

(55) sko 7:½

(59) tao(ύ/7)

(57) sko =½

>9

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) isi(ύ/6)

(5) isi 9=½

(9) isi(ύ/6)

(7) isi =½

(:) sko ;=½

(6) sji(ύ/9)

(0) sko(ύ/7)

(>) sji =½

(;) isi(ύ/9)

(1=) sko(ύ/6)

(11) sji 7:½

(15) isi(ύ/6)

(19) tao =½

(17) ihs(ύ/5)

(1:) isi(ύ/7)

(16) isi(ύ/6)

(10) sji(ύ/6)

(1>) sko 6=½

(1;) sko 7:½

(5=) isi 6=½

(51) sji 9=½

(55) iht ;=½

(59) tao(ύ/9)

(57) ihs(ύ/6)

>7

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r : Ao Aosw swjr jrss ]a`j 09 ]a`j (1) 5∜ 9/9 (5) (5) 1/5 (9) ∜ 5/5 (7) uogj uogjfko fkojg jg ((:) :) 1/5 (6) ∜ 9 (0) (0) = ((>) >) 1/ 1/5 5 ((;) ;) = (1=) ∜ 5 (11) ∜ 9/9 (15) uogj uogjfko fkojg jg (19) uog uogjfk jfkojg ojg (17) 5∜ 9/9 (1: (1:)) 5 (16) ∜ 9/5 (10) ∜ 5 (1 (1>) >) 1/ 1/5 5 (1;) ∜ 5/5 (5= (5=)) 1 ((51 51)) 1 (55) (55) 5 ((59 59)) = ((57 57)) 1

]a`j 06 ]a`j (1) (1) 1/ 1/5 5 (5 (5)) 1 (9 (9)) ∜ 9/9 (7 (7)) 1/ 1/5 5 ((:) :) 1 ((6) 6) = (0) 1 (>) 5∜ 9/9 (;) (;) 5 (1=) (1=) 5 (1 (11) 1) 1 (1 (15) 5) ∜ 5/5 (19) = (17 (17)) uogj uogjfko fkojg jg ((1:) 1:) ∜ 5 (16)) = (1 (16 (10) 0) uog uogjf jfko kojg jg ((1>) 1>) 1 (1;)) = (5 (1; (5=) =) ∜ 9/9 (51 (51)) 1 (55)) 1 (5 (55 (59) 9) ∜ 9/5 (57) ∜ 9

]a`j 07 ]a`j (1) ∜ 5 ( (5) 5) 5 ((9) 9) 5

]a`j 00 ]a`j (1) uo uogj gjfk fkoj ojg g ((5) 5) 1 ((9) 9) =

(7 (7)) 1 ((:) :) ∜ 5 (6) ∜ 5 (0) uogj uogjfko fkojg jg (>) ∜ 5 ( (;) ;) 1/ 1/5 5 (1=) uog uogjfk jfkojg ojg ((11) 11) = (15) uo uogjf gjfkoj kojg g (19) (19) 1 ((17 17)) 1 ((1: 1:)) 1 (16) 1/5 (10) uo uogjf gjfkoj kojg g (1>) 1/5 (1;)) = (5=) uog (1; uogjf jfko kojg jg (5 (51) 1) 1/ 1/5 5 (55) 1/5 (59) ∜ 5/5 (57 (57)) =

(7) ((:) :) fkojg uo uogj gjfk fkoj ojg g ((6) 6) fkojg 1 jg (;) 1 (0) = uogj uogjfko jg (>) uogj uogjfko (1=) uogj uogjfko fkojg jg (11) 5∜ 9/9 (15) (15) 1/ 1/5 5 (19) uogjf uogjfkojg kojg (17) ∜ 9 ( (1: 1:)) 5∜ 9/9 (16)) 1 (1 (16 (10) 0) uog uogjf jfko kojg jg ((1>) 1>) 5∜ 9/9 (1 (1;) ;) 1 ((5= 5=)) = ((51 51)) 5 (55)) 1 (5 (55 (59) 9) ∜ 9/5 (57 (57)) =

]a`j 0: ]a`j (1) 1 ((5) 5) uo uogj gjfk fkoj ojg g ((9) 9) 1 (7) 1 (:) 5∜ 9/9 (6) uog uogjfk jfkojg ojg

]a`j 0> ]a`j (1) (1) 1 ((5) 5) ∜ 9 ( (9 9) = (7) 1/5 (: (:)) 1/ 1/5 5 ((6) 6) ∜ 5

(0) ∜ 5 (>) = (;) uo uogj gjfk fkoj ojg g (1=) ∜ 9/5 (11) (11) 5 (1 (15) 5) ∜ 9/5 (19) 1/5 ((17) 17) uo uogjf gjfkoj kojg g (1:) ∜ 9 (16) ∜ 9/9 (10 (10)) 5∜ 9/9 (1> (1>)) 5 (1;)) 1 (5 (1; (5=) =) uog uogjf jfko kojg jg ((51) 51) 1 (59) 9) = ((57 57)) 5∜ 9/9 (55 55)) 5∜ 9/9 (5

(0) ∜ 9/9 (>) ∜ 5 (;) ∜ 9/9 (1=) ∜ 5/5 (11) (11) 1 (1 (15) 5) ∜ 5 (19) ∜ 9 (17) ∜ 9 (1:) ∜ 9 (16)) 1/ (16 1/5 5 (10) uo uogj gjfk fkoj ojg g (1>) 5 (5=) uo uogjf gjfkoj kojg g (5 (51) 1) = (1; 1;)) 5∜ 9/9 (5=) (55) (55) = (5 (59) 9) = (5 (57) 7) ∜ 9/5

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th ttnj nj Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

>:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

]a`j 0; ]a`j (1) 5∜ 9/9 (5) ∜ 5/5 (9) uogj uogjfko fkojg jg (7 (7)) 1 ((:) :) ∜ 5/5 (6) ∜ 5/5 (0) ∜ 5 (>) ∜ 5/5 (; (;)) 1

]a`j >5 ]a`j (1) ∜ 9/9 (5) ∜ 9/9 (9) (9) 1 (7 (7)) 1/ 1/5 5 ((:) :) 1 ((6) 6) = (0) 1 ((>) >) = ((;) ;) =

(1=) 1 (1 (1=) (11) 1) ∜ 9/9 (15 (15)) 1 (19) (19) = ((17 17)) 5∜ 9/9 (1: (1:)) 5 (16)) 1 (1 (16 (10) 0) uog uogjf jfko kojg jg ((1>) 1>) = (1;) uogjf uogjfkojg kojg (5=) ∜ 5 ( (51 51)) 1 (55) ∜ 5 (5 (59) 9) uog uogjf jfkoj kojg g (5 (57) 7) 5

(1=)) 1/ (1= 1/5 5 (11) 5 (15 (15)) uo uogj gjfk fkoj ojg g (19) 1 (1 (19) (17) 7) ∜ 9/5 (1: (1:)) uogj uogjfko fkojg jg (16) (16) = (1 (10) 0) 1 (1 (1>) >) ∜ 9 (1;)) 1 (5 (1; (5=) =) ∜ 9/9 (51) ∜ 5 (55)) 1 (5 (55 (59) 9) uog uogjf jfko kojg jg ((57) 57) 1

]a`j >= ]a`j (1) 5 (5) uo uogj gjfk fkoj ojg g (9) ∜ 5/5 (7) uogj uogjfko fkojg jg (:) ∜ 5 ( (6 6) 1 (0) ∜ 9/5 (>) ∜ 9/9 (;) (;) 1/ 1/5 5

]a`j >9 ]a`j (1) ∜ 5/5 (5) (5) 1/5 (9) uog uogjfk jfkojg ojg (7) 1/5 (: (:)) uo uogj gjfk fkoj ojg g (6 (6)) 1 (0) ∜ 9/9 (>) (>) 1/ 1/5 5 (;) ∜ 9/9 (1=) uogj uogjfko fkojg jg ((11) 11) uog uogjfk jfkojg ojg (15) 1

(1=)) uo (1= uogj gjfk fkoj ojg g (1 (11) 1) 1 (15 (15)) 5∜ 9/9 (19) 1 (1 (19) (17) 7) 1/5 ((1:) 1:) ∜ 9 (16)) 5 (1 (16 (10) 0) ∜ 9 (1>) ∜ 5 (1;)) uo (1; uogj gjfk fkoj ojg g (5 (5=) =) 1 (51 (51)) 1 (55) ∜ 5/5 (59 (59)) = ((57 57)) =

(19) uogj uogjfko fkojg jg ((17) 17) 1 (1: (1:)) ∜ 9/5 (16) ∜ 9 (10 (10)) 1 (1 (1>) >) ∜ 9/5 (1;)) 1 (5 (1; (5=) =) ∜ 9/9 (51) ∜ 9/9 (55) ∜ 5/5 (59 (59)) 1 ((57 57)) =

]a`j >1 ]a`j (1) 1/5 (5 (5)) ∜ 9/5 (9) ∜ 9 (7) uogj uogjfko fkojg jg (:) 1 (6 (6)) uo uogjf gjfkoj kojg g (0) uogj uogjfko fkojg jg (>) ∜ 5 ( (;) ;) 1/ 1/5 5 (1=) uogjf uogjfkojg kojg (11) ∜ 5 ( (15 15)) 1 (19) uog uogjfk jfkojg ojg (17) 1 (1:) ∜ 5 (16)) 1 (1 (16 (10) 0) uog uogjf jfko kojg jg ((1>) 1>) 5 (1;) ∜ 9 (5=) ∜ 9/9 (5 (51) 1) = (55) (55) 1 ((59 59)) 5∜ 9/9 (57) ∜ 9/5

]a`j >7 ]a`j (1) 5 ((5) 5) 5 ((9) 9) 5 (7) uo uogj gjfk fkoj ojg g ((:) :) 1 ((6) 6) 5 (0) ∜ 5/5 (> (>)) 1 ((;) ;) 5∜ 9/9 (1=) 1/5 (11) ∜ 5 (1 (15 5) 5 (19) (19) = (1 (17) 7) = (1 (1:) :) 5 (1>) ∜ 9/5 (1 (16) 6) 5 ((10 10)) 5∜ 9/9 ∜ (1;) ∜ 5/5 (5= (5=)) 5∜ 9/9 (51 (51)) 5∜ 9/9 (55)) = (5 (55 (59) 9) ∜ 9 (57) ∜ 9/5

>6

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In apttjr 6< Fko Fkogk gko` o` tnj Uj Ujfj fjr rjoij joij Ao`d Ao`dj j Kf yhu ojjg th jvaduatj a trk` fuoitkho at ao ao`dj ejtwjjo ;=½ aog 96=½, kt ks usjfud th fkrst gjtjrckoj gjtjrc koj tnj rjfjrj rjfjrjoij oij ao`dj. Wnj rjfjrjo rjfjrjoij ij ao`dj ks ao ao`dj ejt ejtwjjo wjjo =½ aog ;=½, wnkin `kvjs tnj sacj vaduj vaduj fhr tnj trk` fuoitkho apart frhc a phsskedj phsskedj ckous skò. Ko tnks inaptjr, wj wkdd fhius ho nhw th gjtjrckoj tnj rjfjrjoij ao`dj, aog ko Inaptjr 0 wj wkdd sjj nhw tnks rjdat rjdatjs js th jva jvaduatko duatko` ` a trk` fuo fuoitkho itkho a att ao a ao`dj o`dj ejt ejtwjjo wjjo ;=½ aog 96=½. Wnj staogarg ihovjotkho fhr cjasurko` ao`djs ko trk`hohcjtry ks ihuotjridhibwksj frhc tnj +‫ ݗ‬-ax -axks, ks, as kddu kddust strat ratjg jg ej ejdhw. dhw. Pkt Pktn n tnks sys systjc tjc,, =½ ihr ihrrjs rjspho phogs gs th tnj +‫ݗ‬-ax -axks ks,, ;=½ ihrrjsphogs th tnj +‫ݚ‬-axks, 1>=½ ihrrjsphogs th tnj ∕‫ݗ‬-axks -axks,, 50=½ ihrrjsphogs th tnj ∕‫ݚ‬axks, axk s, ao aog g 96=½ kkss ea eaib ib th tnj +‫ ݗ‬-axks.

;=½ ‫ݚ‬ ;=½ ‫ݚ‬

Quagraot KK Quagraot K ‫½= ݗ‬, 96= 96=½½

1>=½ 1>=½

‫½= ݗ‬

Quagraot KKK Quagraot KV

50=½ Ao`djs ejt Ao`djs ejtwjj wjjo o =½ aog 96= 96=½½ iao iao ej gkv gkvkgj kgjg g kot koth h fh fhur ur quagr quagrao aots. ts. Wnj sta staoga ogarg rg ihovjotkho fhr oucejrko` tnj fhur quagraots ks th usj Uhcao oucjrads K, KK, KKK, aog KV as kddustratjg kddust ratjg aehv aehvj. j. Ao ao`dj ejt ejtwjjo wjjo =½ aog ;=½ ks ko Quagra Quagraot ot K, ao ao`dj ejtwj ejtwjjo jo ;=½ aog 1>=½ ks ko Quagraot KK, ao ao`dj ejtwjjo 1>=½ aog 50=½ ks ko Quagraot KKK, aog ao ao`dj ejtwjjo ejtw jjo 50=½ aog 96=½ ks ko Quagra Quagraot ot KV. Ohtj tnat tnj ao`dj ks uoinao`jg, uoinao`jg, `jhcjt `jhcjtrkiadd rkiaddy, y, kf yhu agg 96=½ th kt. Fhr jxacp jxacpdj, dj, 7:½, 7=:½, 06:½, aog ∕91:½ arj add tnj sacj ao`dj. ao`dj. Wnjrjf Wnjrjfhrj, hrj, ao ao`dj ejtwj ejtwjjo jo ∕;=½ aog =½ dkjs dkjs ko Qua Quagrao graott KV aog a ao o ao` ao`dj dj ej ejtwj twjjo jo ∕1>=½ aog ∕;=½ dkjs ko Quagr Quagraot aot KKKK. KK. Ko trk`hohcjt trk`hohcjtry, ry, kt ks hftjo usjfud th rjfj rjfjrr th tnj uokt ikrid ikridj. j. Wnj uokt ikrid ikridj j dkjs ko tnj ‫ ݚݗ‬pd pdao aoj, j, ijot ijotjr jrjg jg ae aehut hut tnj hrk` hrk`ko ko,, ao aog g na nass a ra ragku gkuss hf 1 uo uokt, kt, as kd kddus dustra tratj tjg g ho tnj fhddhwko fhdd hwko` ` pa` pa`j. j. Fhr aoy ao`dj ejt ejtwjj wjjo o =½ aog 96=½ 96=½,, wj iao gra graw w a ihrr ihrrjs jspho phogko gko` ` rk` rk`nt nt trkao`dj ko tnj uokt ikridj wktn a nyphtjousj hf hoj uokt aog dj`s tnat arj paraddjd th tnj ‫ݗ‬aog ‫ݚ‬-axjs -axjs,, adsh as kddustrat kddustratjg jg ho tnj fhdd fhddhwko` hwko` pa pa`j. `j. Ko Inapt Inaptjr jr 0, wj wkdd sjj nhw suin a uokt ikridj iaofhius njdp us gjtjr tnj skò hf tnj easki trk` fuoitkhos fuoitkho s ko jain quagr quagraot. Fhr ohw, wj wkdd hogjtjrckoj nhwckoj grawko` a rk`nt trkao`dj ko tnj uokt ikridj njdps us aot. fkog tnj rjfjrjoij rjfj rjoij ao`dj ao`dj..

>0

Kcprhvj [hur Catn Fdujoiy Yjrkjs

;=½ ‫ݚ‬

1 ‫½= ݗ‬, 96= 96=½½

1>=½

50=½ Ihoskgj Ihosk gjrr tnj rk rk`nt `nt tr trka kao` o`dj dj fh fhrc rcjg jg ko tn tnj j uo uokt kt ik ikri ridj dj ey tnj tnj Qua Quagra graot ot KK ao ao`dj `dj kddustratjg ejdhw. Wnj rjfjrjoij ao`dj ks tnj ihrrjsphogko` Quagraot K ao`dj fhr wnkin tnj hpphsktj hpphs ktj aog aglaij aglaijot ot skgjs navj tnj sacj djo`tns as tnjy navj fhr tnj hrk`koad hrk`koad ao`dj. Ko Quagraot KK, tnj rjfjrjoij ao`dj iao ej fhuog ey suetraitko` tnj Quagraot KK ao`dj frhc 1>=½. 1>= ½. Fh Fhrr jx jxac acpd pdj, j, tnj rj rjfj fjrj rjoi oij j ao ao`d `dj j fh fhrr 15= 15=½½ ks 1>=½ ∕ 15=½ 15=½ 3 6=½.

;=½ ‫ݚ‬

;=½ ‫ݚ‬

1>=½

‫½= ݗ‬

1>=½

rjfjrjoij ao`dj

‫½= ݗ‬

Ihoskgj Ihosk gjrr tnj rk` rk`nt nt trk trkao ao`d `dj j fh fhrcj rcjg g ko tn tnj j uo uokt kt ik ikri ridj dj ey tnj tnj Qu Quag agra raot ot KK KKKK ao ao`dj `dj kddust kddu strat ratjg jg ho tnj fhdd fhddhwko hwko` ` pa pa`j. `j. Ko Quag Quagrao raott KK KKK, K, tnj rjf rjfjrj jrjoij oij ao`d ao`dj j iao iao ej fhuog ey suetraitk suet raitko` o` 1>=½ frhc tnj Quagra Quagraot ot KKK ao`dj. Fhr jxacpdj jxacpdj,, tnj rjfj rjfjrjoi rjoij j ao`dj fhr 51=½ ks 51=½ 51 =½ ∕ 1>=½ 1>=½ 3 9= 9=½½. Oh Ohw w ihos ihoskg kgjr jr tnj tnj rk`n rk`ntt trkao rkao`d `dj j fh fhrc rcjg jg ko tnj tnj uo uokt kt ik ikri ridj dj ey tn tnj j Quagraot Quagra ot KV ao`dj kddust kddustratjg ratjg ho tnj fhddhwko fhddhwko` ` pa`j. Ko Quagrao Quagraott KV, tnj rjfjrjoij ao` ao`dj dj iao ej fhuog ey suetraitko` suetraitko` tnj Quagrao Quagraott KV ao`dj frhc 96=½. Fhr jxacp jxacpdj, dj, tnj rjfjrjo rjfjrjoij ij ao`dj ao` dj fhr 97 97:½ :½ ks 96 96=½ =½ ∕ 97 97:½ :½ 3 1:½ 1:½. Wnj rjfjrjoij ao`dj ks gjfkojg as tnj Quagraot K ao`dj fhr wnkin tnj rk`nt trkao`dj fhrcjg ko tnj uokt ikridj nas hpphsktj aog aglaijot skgjs hf tnj sacj djo`tn as tnj rk`nt trkao`dj trkao` dj fhrcj fhrcjg g ko tnj uokt ikrid ikridj j fhr tnj hrk`koad Quag Quagraot raot KK, KKK KKK,, hr KV ao`dj ao`dj.. Ko tnks way, tnj skoj, ihskoj, aog tao`jot wkdd navj tnj sacj ratkh fhr ehtn rk`nt trkao`djs (eut cay oht navj tnj sa navj sacj cj sskò kò,, as wj wkdd sjj ko I Inap naptjr tjr 0). Wnj Wnjrjf rjfhrj hrj,, as wj wkdd jx jxpdh pdhrj rj ko Ina Inaptj ptjrr 0, tnj rj rjfj fjrj rjoi oij j ao ao`d `dj j sjrv sjrvjs js th nj njdp dp us jvad jvaduat uatj j tnj ea eask skii trk` trk` fu fuoi oitk tkhos hos at ao ao`dj `djss ko Quagra Qua graots ots KK KK,, KK KKK, K, aog KV KV..

>>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs ‫ݚ‬

‫ݚ‬ ‫ ݗ‬96=½

1>=½

50=½

‫ ݗ‬96=½

1>=½

50=½

Wabj shcj tkcj th uogjrstaog uogjrstaog tnjsj iho ihoijpt ijpts, s, aog stugy tnj jxacpdj jxacpdjs. s. Hoij yhu uogjrstaog uogjrs taog tnj fhddhwko fhddhwko` ` jxacpdj jxacpdjs, s, yhu arj rjagy th praitkij tnj tjino tjinokquj kquj yhursj yhursjdf. df. [hu cay ojjg th rjfjr th tnj jxacpdjs frjqujotdy as yhu ej`ko, eut snhudg try th shdvj tnj jxjriksjs jxjr iksjs ad addd ey yhursjdf hoi hoij j yhu `jt tnj nao` hf kt. Ej surj th injib tnj aos aoswjrs wjrs at tnj eaib ea ib hf tnj tnj eh ehhb hb th jo josu surj rj tna tnatt yhu arj shdv shdvko ko` ` tnj pr prhe hedj djcs cs ih ihrr rrji jitd tdy. y. Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Adsh, graw a uokt ikridj, graw tnj rk`nt trkao`dj trkao`dj fhrcjg ko tnj uokt ikrid ikridj j fhr tnj `kvjo ao ao`dj, `dj, graw tnj rk`nt trkao`dj fhrcjg ko tnj uokt ikridj fhr tnj rjfjrjoij ao`dj, daejd tnj `kvjo ao`dj,, aog da ao`dj daejd ejd ttnj nj rjfj rjfjrjoij rjoij a ao`dj. o`dj. ]rhijgurj< Kf tnj `kv ]rhijgurj< `kvjo jo ao ao`dj `dj ks ojà ojàtkv tkvj, j, fkrst agg agg 96=½ th kt. Ojx Ojxt, t, gjtj gjtjrcko rckoj j ko wnkin quagraot quagra ot tnj `kvj `kvjo o ao`dj dkjs dkjs.. Ao ao`dj ejt ejtwjjo wjjo ;=½ a aog og 1 1>=½ >=½ kkss ko Q Quagra uagraot ot KK. Ao ao`dj ejt ejtwjjo wjjo 1>=½ aog 50=½ ks ko Qua Quagraot graot KKK KKK.. Ao a ao`d o`dj j ej ejtwj twjjo jo 50=½ aog 96=½ ks ko Q Quag uagrao raott KV KV.. Fk Fkoa oaddy ddy,, us usj j tnj ihrrj ihrrjit it fh fhrc rcud uda a th fk fkog og tn tnj j rjfj rjfjrj rjoi oij j ao ao`d `dj< j< Kf tnj `kv `kvjo jo ao ao`d `dj j dkjs dkjs ko Qua Quagra graot ot KK, KK, su suet etra rait it tnj `kvj `kvjo oa ao` o`dj dj fr frhc hc 1 1>= >=½. ½. 







 

Kf tnj `kv `kvjo jo ao` ao`dj dj dkj dkjss ko Qua Quagra graot ot KKK KKK,, sue suetra trait it 1>=½ fr frhc hc tnj `kv `kvjo jo ao ao`dj `dj.. Kf tnj `kv `kvjo jo ao ao`d `dj j dkjs dkjs ko Qua Quagra graot ot KV, KV, su suet etra rait it tnj `kvj `kvjo oa ao` o`dj dj fr frhc hc 96 96=½ =½..

Ohtj< Wnj jxa Ohtj< jxacp cpdj djss tna tnatt fhdd hddhw hw aog tn tnj j ao aosswj wjrs rs ko tn tnj j ea eaib ib hf tnj tnj eh ehhb hb lus lustt `kvj `kvj tnj rjfjrj rjf jrjoij oij ao`d ao`djs js (aog oht tnj gka gka`ra `racs cs). ). Nhw Nhwjvj jvjr, r, kt ks nk` nk`ndy ndy rjihc rjihccjo cjogjg gjg tnat yhu graw tnj gka`racs ejiausj tnks wkdd njdp yhu th vksuadkzj tnj ihoijpts aog th uogjrstaog tnj ihoij ihoijpts pts `jhcj `jhcjtrkia trkiaddy. ddy. Jxac Jx acpd pdj j 1< 1= 1==½. =½. Wn Wnks ks ao ao`d `dj j ks ko Qua Quagra graot ot KK< KK< Wnj rj rjfj fjrj rjoi oij j ao ao`d `dj j ks 1> 1>=½ =½ ∕ 1==½ 1==½ 3

>=½ >=½.

Jxac Jx acpd pdj j 5< 5; 5;=½. =½. Wn Wnks ks ao ao`d `dj j ks ko Qua Quagra graot ot KV KV=½ 1>=½ 3 5:½ 5:½.

>;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 5=9½

(5) 991½

(9) 1>>½

(7) 1;:½

(:) 971½

(6) ∕;>½

(0) 1=;½

(>) 5=>½

(;) 91:½

(1=) 116½

(11) 55=½

(15) ∕10;½

(19) ∕1=7½

(17) 57;½

(1:) 19:½

(16) 111½

(10) 5>>½

(1>) ∕5>½

;=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 996½

(5) ∕11½

(9) ∕16=½

(7) 950½

(:) 511½

(6) ;5½

(0) ∕17:½

(>) ∕1:½

(;) 59=½

(1=) 1=;½

(11) ∕96½

(15) 976½

(19) ∕0;½

(17) ;6½

(1:) 5;0½

(16) 5:=½

(10) 106½

(1>) 595½

;1

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) ∕7;½

(5) 99>½

(9) 5==½

(7) ;>½

(:) 915½

(6) 17:½

(0) ;;½

(>) 1;:½

(;) ∕15=½

(1=) 911½

(11) ∕:5½

(15) 5=;½

(19) 17=½

(17) 517½

(1:) 995½

(16) 99=½

(10) ;>½

(1>) 16:½

;5

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 550½

(5) 9=5½

(9) 161½

(7) ∕0½

(:) 1:;½

(6) 59=½

(0) ∕169½

(>) 55>½

(;) 196½

(1=) 106½

(11) 1:7½

(15) 1=9½

(19) 55=½

(17) ∕176½

(1:) 1;:½

(16) 591½

(10) 97:½

(1>) 15=½

;9

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 5:9½

(5) 16=½

(9) 9=7½

(7) 15=½

(:) 1;6½

(6) 5=>½

(0) ∕7:½

(>) 567½

(;) ∕7½

(1=) 9=;½

(11) 116½

(15) 17:½

(19) 955½

(17) 10:½

(1:) 17=½

(16) ∕19½

(10) 155½

(1>) 517½

;7

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 16;½

(5) 15>½

(9) 9==½

(7) 117½

(:) 175½

(6) 10>½

(0) 5;=½

(>) ∕17=½

(;) ∕5:½

(1=) 1>;½

(11) 116½

(15) 167½

(19) 5>7½

(17) ∕16;½

(1:) 1:0½

(16) 9=:½

(10) 57=½

(1>) ∕;5½

;:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 5=;½

(5) 175½

(9) 9=6½

(7) ∕5;½

(:) ∕17>½

(6) 59=½

(0) 51=½

(>) 176½

(;) 9:9½

(1=) 5:;½

(11) ;7½

(15) ∕>:½

(19) 5;0½

(17) ∕9½

(1:) 9:;½

(16) 1>:½

(10) 55>½

(1>) ∕190½

;6

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 5>9½

(5) ∕1:9½

(9) 5=5½

(7) 917½

(:) ∕:>½

(6) 1:0½

(0) 1:9½

(>) 110½

(;) 1=>½

(1=) 97:½

(11) ∕11½

(15) 997½

(19) 571½

(17) 159½

(1:) 1;:½

(16) 5=;½

(10) ∕>7½

(1>) 99:½

;0

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 55=½

(5) ∕1=>½

(9) 1:1½

(7) 169½

(:) 5>7½

(6) ∕:1½

(0) 5=;½

(>) 9=5½

(;) 151½

(1=) 19=½

(11) 9::½

(15) 59=½

(19) 970½

(17) 59=½

(1:) 91:½

(16) ∕;6½

(10) 5>9½

(1>) 1:7½

;>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 97:½

(5) 19>½

(9) 1:=½

(7) 10;½

(:) 97;½

(6) 191½

(0) 151½

(>) 1:1½

(;) 191½

(1=) 11>½

(11) 150½

(15) 996½

(19) 1>9½

(17) ∕1=½

(1:) 51:½

(16) 569½

(10) ∕;7½

(1>) 9:;½

;;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 951½

(5) 50;½

(9) 911½

(7) ∕5½

(:) ;0½

(6) 1=9½

(0) 5:1½

(>) 5=:½

(;) 19=½

(1=) 56:½

(11) ∕119½

(15) 977½

(19) 5:1½

(17) 990½

(1:) 5:7½

(16) ∕70½

(10) 5;>½

(1>) 1:9½

1==

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj rjf rjfjrj jrjoij oij ao` ao`dj dj fhr tnj `kv `kvjo jo Quagr Quagraot aot KK, KKK KKK,, hr KV ao` ao`dj. dj. Ad Adsh sh,, gra graw w ao aog g da daej ejdd a gka gka`r `rac ac.. Inj Injib ib yh yhur ur a aos oswj wjrs rs ko ttnj nj ea eaib ib hf tnj eh ehhb hb.. (1) 59;½

(5) 95:½

(9) 169½

(7) 17:½

(:) 555½

(6) ∕165½

(0) 99=½

(>) ∕::½

(;) ;1½

(1=) 5:0½

(11) 9=6½

(15) 156½

(19) 176½

(17) 5;6½

(1:) 1=5½

(16) 111½

(10) 9=>½

(1>) 1=;½

1=1

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Inap In aptj tjr r 6 Ao Aosw swjr jrss ]a`j ;= ]a`j (1 (1)) 59 59½½ ((5) 5) 5; 5;½½ ((9) 9) >½ (7 (7)) 1: 1:½½ (: (:)) 1; 1;½½ (6 (6)) >5½ (0 (0)) 01 01½½ (> (>)) 5> 5>½½ (; (;)) 7:½ (1=)) 67½ (1 (1= (11) 1) 7= 7=½½ ((15) 15) 1½ (19)) 06½ (1 (19 (17) 7) 6; 6;½½ (1:) (1:) 7: 7:½½ (16)) 6;½ (1 (16 (10) 0) 05 05½½ (1>) (1>) 5> 5>½½

]a`j ;7 ]a`j (1) (1) 09 09½½ (5 (5)) 5= 5=½½ (9 (9)) :6 :6½½ (7) (7) 6= 6=½½ (: (:)) 16 16½½ (6 (6)) 5> 5>½½ (0) (0) 7: 7:½½ ((>) >) >7 >7½½ (;) (;) 7½ (1=)) :1½ (1 (1= (11) 1) 67 67½½ (15) (15) 9: 9:½½ (19)) 9>½ (1 (19 (17) 7) :½ (1 (1:) :) 7= 7=½½ (16)) 19½ (1 (16 (10) 0) :> :>½½ (1>) (1>) 97 97½½

]a`j ;1 ]a`j (1 (1)) 57 57½½ (5 (5)) 11 11½½ (9 (9)) 5=½ (7 (7)) 99 99½½ (: (:)) 91 91½½ (6 (6)) >>½ (0 (0)) 9: 9:½½ (> (>)) 1: 1:½½ (; (;)) :=½ (1=)) 01½ (1 (1= (11) 1) 96 96½½ (15) (15) 17 17½½

]a`j ;: ]a`j (1) (1) 11 11½½ (5 (5)) :5 :5½½ (9 (9)) 6= 6=½½ (7) (7) 66 66½½ ((:) :) 9> 9>½½ (6) (6) 5½ (0) (0) 0= 0=½½ (> (>)) 7= 7=½½ (; (;)) 5: 5:½½ (1=)) ;½ (1 (1= (11) 1) 67½ (1 (15) 5) 16 16½½

(19) 0;½ (1 (19) (17) 7) >7 >7½½ (1:) (1:) 69 69½½ (16)) 0=½ (1 (16 (10) 0) 7½ (1>) :5 :5½½

(19) 06½ (1 (19) (17) 7) 11 11½½ (1:) (1:) 59 59½½ (16)) ::½ (1 (16 (10) 0) 6= 6=½½ (1>) (1>) >> >>½½

]a`j ;5 ]a`j (1 (1)) 7; 7;½½ (5 (5)) 55 55½½ (9 (9)) 5=½ (7 (7)) >5 >5½½ (: (:)) 7> 7>½½ (6 (6)) 9:½ (0 (0)) >1 >1½½ (> (>)) 1: 1:½½ (; (;)) 6=½ (1=)) 7;½ (1 (1= (11) 1) :5 :5½½ (15) (15) 5; 5;½½ (19)) 7=½ (1 (19 (17) 7) 97 97½½ (1:) (1:) 5> 5>½½ (16)) 9=½ (1 (16 (10) 0) >5 >5½½ (1>) (1>) 1: 1:½½

]a`j ;6 ]a`j (1) (1) 5; 5;½½ (5 (5)) 9> 9>½½ (9 (9)) :7 :7½½ (7) (7) 5; 5;½½ (: (:)) 95 95½½ (6 (6)) := :=½½ (0) (0) 9= 9=½½ ((>) >) 97 97½½ (;) (;) 0½ (1=)) 0;½ (1 (1= (11) 1) >6 >6½½ (15) (15) >: >:½½ (19) (19) 69 69½½ (17 (17)) 9½ ((1: 1:)) 1½ (16)) :½ (1 (16 (10) 0) 7>½ (1 (1>) >) 79 79½½

]a ]a`j ;9 (1 (1))`j 70 70½ ½ (5 (5)) :> :>½½ (9 (9)) 1;½ (7 (7)) 0½ (: (:)) 51 51½½ (6) (6) := :=½½ (0 (0)) 10 10½½ (> (>)) 7> 7>½½ (; (;)) 77½ (1=)) 7½ (1 (1= (11) 1) 56½ (15) 00 00½½ (19)) 7=½ (1 (19 (17) 7) 97 97½½ (1:) (1:) 1: 1:½½ (16)) :1½ (1 (16 (10) 0) 1: 1:½½ (1>) (1>) 6= 6=½½

]a`j ]a ;0 (1) (1)`j 00 00½ ½ (5 (5)) 50 50½½ (9 (9)) 55 55½½ (7) (7) 76 76½½ (: (:)) :> :>½½ (6 (6)) 59 59½½ (0) (0) 50 50½½ (> (>)) 69 69½½ (; (;)) 05 05½½ (1=)) 1:½ (1 (1= (11) 1) 11 11½½ (15) (15) 56 56½½ (19)) 61½ (1 (19 (17) 7) :0 :0½½ (1:) (1:) 1: 1:½½ (16)) 5;½ (1 (16 (10) 0) >7 >7½½ (1>) (1>) 5: 5:½½

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th ttnj nj Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

1=5

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

]a`j ;> ]a`j (1 (1)) 7= 7=½½ (5 (5)) 05 05½½ (9 (9)) 5;½ (7 (7)) 10 10½½ (: (:)) 06 06½½ (6 (6)) :1½ (0 (0)) 5; 5;½½ (> (>)) :> :>½½ (; (;)) :;½

]a`j 1== ]a`j (1) (1) 9; 9;½½ (5 (5)) >1 >1½½ (9 (9)) 7; 7;½½ (7) (7) 5½ (:) (:) >9 >9½½ (6) (6) 00 00½½ (0) (0) 01 01½½ (> (>)) 5: 5:½½ (; (;)) := :=½½

(1=) :=½ (1 (1=) (11) 1) :½ (15) := :=½½ (19)) 19½ (1 (19 (17) 7) := :=½½ (1:) (1:) 7: 7:½½ (16)) >7½ (1 (16 (10) 0) 00 00½½ (1>) (1>) 56 56½½

(1=)) >:½ (1 (1= (11) 1) 60 60½½ (15) (15) 16 16½½ (19) 01½ (1 (19) (17) 7) 59 59½½ (1:) (1:) 07 07½½ (16)) 70½ (1 (16 (10) 0) 65 65½½ (1>) (1>) 50 50½½

]a`j ;; ]a`j (1 (1)) 1: 1:½½ (5 (5)) 75 75½½ (9 (9)) 9=½ (7 (7)) 1½ (: (:)) 11 11½½ (6) (6) 7; 7;½½ (0 (0)) :; :;½½ (> (>)) 5; 5;½½ (; (;)) 7;½ (1=)) 65½ (1 (1= (11) 1) :9 :9½½ (15) (15) 57 57½½ (19)) 9½ (1 (19 (17) 7) 1=½ (1:) 9: 9:½½ (16)) >9½ (1 (16 (10) 0) >6 >6½½ ((1>) 1>) 1½

]a`j 1=1 ]a`j (1) (1) :; :;½½ (5 (5)) 9: 9:½½ (9 (9)) 10 10½½ (7) (7) 9: 9:½½ (: (:)) 75 75½½ (6 (6)) 1> 1>½½ (0) (0) 9= 9=½½ (> (>)) :: ::½½ (; (;)) >; >;½½ (1=)) 00½ (1 (1= (11) 1) :7 :7½½ (15) (15) :7 :7½½ (19)) 97½ (1 (19 (17) 7) 67 67½½ (1:) (1:) 0> 0>½½ (16)) 6;½ (1 (16 (10) 0) :5 :5½½ (1>) (1>) 01 01½½

1=9

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Inap In apttjr 0< Gj Gjtj tjrc rcko koj j Ea Eask ski i Wrk` rk` Fuoi Fuoitk tkho hoss ko Qu Quag agra raot otss KK KK-K -KV V Ihoskgjr Ihoskg jr tnj rk`n rk`ntt trkao trkao`d `dj j fhr fhrcjg cjg ko tnj uokt ik ikrid ridj, j, wnki wnkin n wj gjs gjsirk irkej ejg g ko tnj kot kotrhgui rhguitkho tkho th Ina Inaptj ptjrr 6, aog wnki wnkin n ks kddus kddustra tratjg tjg ko Qua Quagra graot ot K ej ejdhw. dhw. Wnj nyp nyphtj htjous ousj j hf tnj rk`nt trkao`dj trkao` dj jquad jquadss tnj ragkus hf tnj ikri ikridj, dj, aog skoi skoij j kt ks a uokt ikrid ikridj, j, tnj ragkus ks hoj. Wnj skoj fuoitkho jquads tnj hpphsktj hvjr tnj nyphtjousj, wnkdj tnj ihskoj fuoitkho jquads tnj aglaijot aglai jot hvjr tnj nyphtjou nyphtjousj. sj. Ykoij tnj nyphtj nyphtjousj ousj ks hoj, fhr tnj rk`nt trkao` trkao`dj dj fhrcjg ko tnj uokt ikridj, tnj skoj fuoitkho jquads tnj hpphsktj skgj aog tnj ihskoj fuoitkho jquads tnj aglaijot aglai jot skgj skgj.. Wnj agla aglaijot ijot sk skgj gj ks ‫ݗ‬, wnkdj tnj hpphsktj skgj ks ‫ݚ‬. Wnjrjf Wnjrjfhrj hrj,, fhr tnj rk rk`nt `nt trkao`dj trkao` dj fhrc fhrcjg jg ko tnj uokt ikri ikridj, dj, ‫ ݗ‬3 ihs aog ‫ ݚ‬3 sko .

;=½ ‫ݚ‬

1 ‫½= ݗ‬, 96= 96=½½

1>=½

50=½

1

‫ݚ‬

‫ݗ‬

Ujiadd Ujia dd nhw wj gjfkojg tnj rjfjrj rjfjrjoij oij ao`dj ko Inaptj Inaptjrr 6< Wnj rjfjr rjfjrjoij joij ao` ao`dj dj ks tnj Quagraot K ao`dj tnj rk`nt ko fhrcjg tnj uoktko ikridj nas hpphsktj aglaijot skgjs hf fhr tnj wnkin sacj djo`tn as trkao`dj tnj rk`ntfhrcjg trkao`dj tnj uokt ikridj fhraog tnj hrk`koa hrk` koadd Quagra Quagraot ot KK, KKK, hr KV ao`d ao`dj. j. Wnks cj cjaos aos tna tnat t  ‫ ݗ‬aog ‫ ݚ‬navj tnj sacj djo`tn, eut phsskedy gkffjrjot skò, ko tnj hrk`koad rk`nt trkao`dj as tnjy gh fhr tnj Quagraot K rk`nt trkao`dj trkao` dj kovhdv kovhdvko` ko` tnj rjfjrj rjfjrjoij oij ao`dj ao`dj.. Ykoij ‫ ݗ‬3 ihs aog ‫ ݚ‬3 sko , tnks cjaos tnat add hf tnj trk` fuoitkhos jvaduatjg ko Quagraots KK, KKK, aog KV arj tnj sacj as tnj sacj trk` fuoitk fuo itkho ho j jvad vaduat uatjg jg a att tnj rjf rjfjrj jrjoij oij ao` ao`dj dj ’ ap apart art ffrhc rhc a phs phsske skedj dj cko ckous us sk` skò. o. Wnjrjfhrj, kf yhu waot th jvaduatj a trk` fuoitkho ko Quagraots KK, KKK, hr KV, yhu ojjg gh twh tnko` tnko`s< s< Fkrst Fkrst,, gjtjrckoj tnj rjfj rjfjrjoi rjoij j ao`dj2 aog, ojxt, gjtjrcko gjtjrckoj j kf tnj aoswjr ks phsktkvj phskt kvj hr ojàtkv ojàtkvj. j. Fhr jxa jxacpdj, cpdj, kf yhu waot th fkog ihs 1:= 1:=½½, fkrst yhu ojjg th gjtjrckoj tnatt tnj rjfj tna rjfjrj rjoij oij ao ao`d `dj j ks 1>=½ ∕ 1:=½ 3 9=½ (sjj (sjj In Inap aptj tjrr 6), ao aog g tn tnjo jo yh yhu u oj ojjg jg th gjtjrckoj kf ihs ihs 1:= 1:=½½ ks phsktkvj hr ojàtkvj. [hu snhudg adrjagy b bohw ohw tnat  ihs9=½ ihs9=½ 3 ∜ 9/5 9/5 (s (sjj jj Ina Inapt ptjr jr :). :). Ch Chcj cjot otar arkd kdy, y, wj wkd wkddd djar djaro o tn tnat at tnj ihs ihsko koj j fu fuoi oitk tkho ho ks oj ojà àtk tkvj vj ko Quagra Qua graot ot KK, wnki wnkin n cja cjaos os tna tnat t  ihs1:=½ ihs1:=½ 3 ∕∜ 9/5 9/5.

1=7

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

;=½ ‫ݚ‬

;=½ ‫ݚ‬

‫½= ݗ‬

1>=½

1>=½

rjfjrjoij ao`dj

‫ݚ‬

‫½= ݗ‬

‫ݚ‬ ‫ ݗ‬96=½

1>=½

‫ ݗ‬96=½

1>=½

50=½

50=½

Ujiadd tnat  sko sko jquads ‫ ݚ‬fhr tnj rk`nt trkao`dj trkao`dj fhrcj fhrcjg g ko tnj uokt ikridj ikridj.. Wnks cjao cjaoss tnat tnj skoj fuoitkho nas tnj sacj skò as ‫ = snhudg dg bo bohw hw tna tnat t sko 15= 15=½½. Wnj rjfj 1>=½½ ∕ 15=½ 15=½ 3 6=½ 6=½. [hu snhu sk sko o 6= 6=½½ 3 ∜ 9/5 9/5. Wnj `kvjo ao` ao`dj, dj, 15=½, dkjs ko Quag Quagraot raot KK2 tn tnj j skoj fuoit fuoitkho kho ks phsktkv phsktkvj j ko Quagraot Quagra ot KK. Wnjrj Wnjrjfhrj, fhrj, sko sko 15= 15=½½ 3 sk sko o 6=½ 3 ∜ 9/5 9/5. Jxacpdj 5< 5< sji rjfjrjo rjoij ij ao ao`dj `dj ks 51=½ ∕ sji 51= 51=½½. Wnj rjfj

sji sji 9=½ 3

ୡୣୱରଷ଺ ର଺ ଶ ଶର ଶର ରର ଶରର ½

3

∜ /

3

∜

3

snhudg dg bo bohw hw tn tnat at 1>=½ 1>=½ 3 9=½ 9=½. [hu snhu

∜ ∜ 3 . Wnj `kvjo `kvjo ao` ao`dj, dj, 51= 51=½, ½, dkjs ko Qua Quagra graot ot KKK KKK22 tnj ∜ ∜

sj sjia iaot ot fuo fuoitk itkho ho ks oj` ojàtk atkvj vj ko Qua Quagra graot ot KKK KKK (skoi (skoij j ihs ihskoj koj ks oj ojàt àtkvj kvj ko Qua Quagra graot ot KK KKK). K). Wnjrjfhrj, sj sjii 51= 51=½½ 3 ∕ sj sjii 9=½ 3 ∕5∜ 9/9 9/9.

ୱୠୡୣୱଷ୤ ଷ ଷ଺ ୱୠ୤଺ଳଷ ଺଺

Jxacpdj 9< 9< tao tao 1>= 1>=½½. Wnj rj rjfj fjrj rjoi oij j ao` ao`dj dj ks 1>= 1>=½½ ∕ 1>=½ 1>=½ 3 =½. [hu ssnhu nhudg dg b boh ohw w tna tnat t

ta tao o =½ 3

½

½

aosw swjr jr kkss =, sh ttnj nj skò skò gh ghjs jso‛ o‛tt ca catt ttjr jr= 1>=½½ 3 ttao ao =½ 3 =.

Jxacpdj 7< 7< isi rjfjrjo rjoij ij ao ao`dj `dj ks 96=½ ∕ isi 50= 50=½½. Wnj rjfj

is isii ;=½ 3

½

snhudg dg bo bohw hw tn tnat at 50=½ 50=½ 3 ;=½. [hu snhu

3 3 1. Wnj `kvj `kvjo o ao`dj, 50=½ 50=½,, dkjs ho tnj ehrgjr hf Qua Quagraots graots KK KKKK aog KV2

tnj ihsjiaot fuoitkho ks ojàtkvj ko ehtn hf tnjsj quagraots (skoij skoj ks ojàtkvj ko Quagra Qua graots ots KK KKKK aog KKV). V). Wnj Wnjrjf rjfhrj hrj,, is isii 50=½ 50=½ 3 ∕ isi isi ;=½ 3 ∕1. Jxacpdj :< :< iht 99= 99=½½. Wnj rjfj rjfjrjo rjoij ij ao ao`dj `dj ks 96= 96=½½ ∕ 99=½ 99=½ 3 ½

∜ /

9=½ 9=½. [hu snhu snhudg dg bo bohw hw tn tnat at

∜

gkvkgj gj tw twh h fr frai aitk tkho hoss, cu cudt dtkp kpdy dy tn tnj j fk fkrs rst t 3 ∜ 9. Wh gkvk ih ihtt 9=½ 9=½ 3 ½ 3 / 3 ½ 3 fraitkho ey tnj rjikprhiad hf tnj sjihog fraitkho. fraitkho. Wnj `kvjo ao`dj, 99=½, dkjs ko Quagraot KV2

୵ ୘୤ରଷ଺ ୡୱୠୣୱରଷ୤ରଷ ଺ର ଶ ଶର ଶ଺

tnj iht ihtao ao`jo `jott fuoi fuoitkh tkho o ks oj` ojàtk atkvj vj ko Qua Quagrao graott KV. Wnjr Wnjrjf jfhrj, hrj, ih ihtt 99=½ 99=½ 3 ∕ ih ihtt 9=½ 9=½ 3 ∕∜ 9. 1=6

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) isi 1:=½

(5) sji(:ύ/7)

(9) iht 91:½

(7) tao 19:½

(:) sko 99=½

(6) isi(:ύ/9)

(0) ihs 55:½

(>) sko(:ύ/6)

(;) ihs 51=½

(1=) isi(9ύ/7)

(11) iht(5ύ/9)

(15) sji(7ύ/9)

(19) iht 1:=½

(17) sji(5ύ)

(1:) ihs(:ύ/6)

(16) isi(9ύ/5)

(10) isi 1>=½

(1>) isi 55:½

(1;) isi 57=½

(5=) isi 55:½

(51) ihs(ύ)

(55) sji 1>=½

(59) tao(:ύ/9)

(57) tao(:ύ/7)

1=0

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) iht(11ύ/6)

(5) sko 50=½

(9) sji 1>=½

(7) sji 96=½

(:) isi 15=½

(6) ihs(9ύ/7)

(0) ihs(5ύ/9)

(>) ihs 9==½

(;) iht(:ύ/9)

(1=) iht 91:½

(11) iht(ύ)

(15) sji(5ύ)

(19) sko 9==½

(17) sji(0ύ/6)

(1:) isi 51=½

(16) isi(9ύ/5)

(10) sji(:ύ/6)

(1>) sko(:ύ/9)

(1;) sji 50=½

(5=) sji 1:=½

(51) sji 9==½

(55) ihs(9ύ/5)

(59) iht 91:½

(57) tao(0ύ/7)

1=>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) tao 50=½

(5) iht(5ύ/9)

(9) sko 1:=½

(7) iht(9ύ/7)

(:) isi 55:½

(6) isi(:ύ/9)

(0) sko(7ύ/9)

(>) ihs 99=½

(;) sko(:ύ/6)

(1=) iht 9==½

(11) sji 15=½

(15) tao 1:=½

(19) sko(11ύ/6)

(17) ihs(0ύ/6)

(1:) sji 19:½

(16) tao 15=½

(10) sko 99=½

(1>) iht(ύ)

(1;) iht 96=½

(5=) sko 57=½

(51) ihs(0ύ/7)

(55) isi(:ύ/7)

(59) iht 19:½

(57) sko(7ύ/9)

1=;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) iht 1>=½

(5) sko(ύ)

(9) tao(:ύ/6)

(7) isi(0ύ/6)

(:) tao 51=½

(6) tao 99=½

(0) isi 51=½

(>) sji 50=½

(;) sji(5ύ)

(1=) isi 96=½

(11) sji(:ύ/7)

(15) sko 1:=½

(19) isi(:ύ/6)

(17) ihs(ύ)

(1:) sji (5ύ/9)

(16) sko(11ύ/6)

(10) isi(9ύ/7)

(1>) sko 1>=½

(1;) iht(9ύ/5)

(5=) iht(ύ)

(51) tao 19:½

(55) ihs 55:½

(59) ihs(:ύ/9)

(57) tao(0ύ/7)

11=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) iht(:ύ/7)

(5) sko(:ύ/9)

(9) tao 1:=½

(7) ihs 96=½

(:) tao 57=½

(6) sko 1>=½

(0) ihs 91:½

(>) ihs(0ύ/7)

(;) iht 9==½

(1=) sko(ύ)

(11) isi 51=½

(15) tao 55:½

(19) ihs 96=½

(17) sko 19:½

(1:) ihs 99=½

(16) isi(0ύ/7)

(10) ihs(5ύ)

(1>) sji 1>=½

(1;) sko(:ύ/6)

(5=) isi(9ύ/7)

(51) isi 1:=½

(55) isi(0ύ/7)

(59) tao(:ύ/7)

(57) sji(0ύ/6)

111

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) iht 9==½

(5) tao 91:½

(9) sji 19:½

(7) sji 96=½

(:) tao 99=½

(6) ihs(9ύ/5)

(0) isi(:ύ/6)

(>) ihs 19:½

(;) sko 51=½

(1=) tao 57=½

(11) ihs(5ύ)

(15) sji 96=½

(19) sji(:ύ/9)

(17) iht(:ύ/7)

(1:) ihs 1:=½

(16) sko 9==½

(10) ihs 15=½

(1>) sji 99=½

(1;) isi 50=½

(5=) tao(9ύ/7)

(51) isi(:ύ/9)

(55) sko(9ύ/5)

(59) sji 51=½

(57) ihs(5ύ/9)

115

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) sji 99=½

(5) isi(0ύ/6)

(9) ihs 1>=½

(7) sko(:ύ/9)

(:) ihs 51=½

(6) iht 96=½

(0) sji(5ύ)

(>) sji 96=½

(;) iht 19:½

(1=) iht 15=½

(11) sji 9==½

(15) iht(ύ)

(19) sji 55:½

(17) ihs(11ύ/6)

(1:) iht 19:½

(16) sko 1:=½

(10) sko 99=½

(1>) tao(5ύ/9)

(1;) iht(:ύ/7)

(5=) sji 15=½

(51) tao(0ύ/6)

(55) ihs(0ύ/7)

(59) ihs 9==½

(57) iht 1:=½

119

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) sji 1:=½

(5) iht(0ύ/6)

(9) isi 55:½

(7) ihs 51=½

(:) isi(9ύ/7)

(6) iht(:ύ/6)

(0) sji(5ύ)

(>) iht 1>=½

(;) ihs 96=½

(1=) sji 1>=½

(11) tao(ύ)

(15) sko 55:½

(19) sko(0ύ/6)

(17) iht 99=½

(1:) iht(:ύ/6)

(16) sko 1:=½

(10) tao(:ύ/9)

(1>) sji 57=½

(1;) sji 1>=½

(5=) isi(0ύ/6)

(51) isi 51=½

(55) tao(0ύ/6)

(59) isi(:ύ/7)

(57) iht 1>=½

117

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) iht(5ύ)

(5) iht 57=½

(9) isi 96=½

(7) tao(11ύ/6)

(:) sji 99=½

(6) ihs(11ύ/6)

(0) sko 55:½

(>) tao 91:½

(;) ihs 1>=½

(1=) ihs(ύ)

(11) sko(0ύ/7)

(15) sko(0ύ/6)

(19) tao(0ύ/6)

(17) ihs 51=½

(1:) sji 15=½

(16) ihs 1:=½

(10) ihs(0ύ/7)

(1>) sko (:ύ/7)

(1;) isi(5ύ)

(5=) ihs 99=½

(51) ihs 50=½

(55) isi 96=½

(59) tao(9ύ/5)

(57) tao 55:½

11:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) tao 1>=½

(5) tao 51=½

(9) tao(ύ)

(7) sji(5ύ/9)

(:) sko(0ύ/7)

(6) isi 96=½

(0) isi(7ύ/9)

(>) isi(ύ)

(;) sji 1>=½

(1=) sji 57=½

(11) ihs 99=½

(15) tao 19:½

(19) tao(:ύ/9)

(17) iht(ύ)

(1:) tao(11ύ/6)

(16) sko(9ύ/5)

(10) ihs 99=½

(1>) sji 96=½

(1;) tao 19:½

(5=) sko 57=½

(51) isi 96=½

(55) sji 55:½

(59) isi 91:½

(57) sji(7ύ/9)

116

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) iht(:ύ/7)

(5) sko 15=½

(9) sji 50=½

(7) sko(:ύ/6)

(:) tao(5ύ/9)

(6) iht 51=½

(0) iht 1:=½

(>) isi(0ύ/6)

(;) isi(:ύ/6)

(1=) sko 51=½

(11) sji 96=½

(15) isi 91:½

(19) tao(0ύ/7)

(17) iht 55:½

(1:) iht 9==½

(16) iht 91:½

(10) isi(:ύ/7)

(1>) sko(0ύ/6)

(1;) sko(5ύ)

(5=) iht(9ύ/5)

(51) ihs 50=½

(55) iht 1:=½

(59) ihs 57=½

(57) tao(:ύ/9)

110

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gjtj Kostruitkhos< Gjtjrckoj rckoj tnj a aoswj oswjrr th jain prhed prhedjc. jc. Inji Injib b yhur ao aoswjrs swjrs ko tnj eai eaib b hf tnj eh ehhb hb.. (1) sji 19:½

(5) isi(9ύ/5)

(9) iht(11ύ/6)

(7) iht(9ύ/7)

(:) isi 96=½

(6) ihs 50=½

(0) isi(9ύ/5)

(>) ihs 99=½

(;) tao 51=½

(1=) iht(7ύ/9)

(11) sji 91:½

(15) sko(11ύ/6)

(19) iht 1>=½

(17) tao 15=½

(1:) ihs(5ύ)

(16) ihs(5ύ/9)

(10) ihs 96=½

(1>) iht(5ύ/9)

(1;) sji 99=½

(5=) sko 50=½

(51) sji 91:½

(55) sko 1:=½

(59) isi(:ύ/6)

(57) ihs(0ύ/7)

11>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r 0 Ao Aosw swjr jrss ]a`j ]a `j 1=0

]a`j ]a `j 11=

(1 (1)) 5 ((5) 5) ∕∜ 5 (9) ∕1 (7) ∕1 (:) ∕1/5 (6) ∕5∜ 9/9 (0) ∕∜ 5/5 (>) (>) 1/ 1/5 5 (;) ∕∜ 9/5 (1=) ∜ 5 (11) ∕∜ 9/9 (15) ∕5 (19) ∕∜ 9 (17 (17)) 1 (1 (1:) :) ∕∜ 9/5 (16) ∕1 (10) uogjf uogjfkojg kojg (1>) ∕∜ 5 (1;) ∕5∜ 9/9 (5=) ∕∜ 5 (51) ∕1 (55) ∕1 (59) ∕∜ 9 (57 57)) 1

(1) uogj uogjfko fkojg jg (5) = ((9) 9) ∜ 9/9 (7) ∕5 (:) ∜ 9/9 (6) ∕∜ ∕ 9/9 (0) ∕5 (>) uo uogj gjfk fkoj ojg g (;) 1 (1=) uogjf uogjfkojg kojg (11) ∕∜ 5 (15 (15)) 1/ 1/5 5 (19)) 5 (1 (19 (17) 7) ∕1 (1:) ∕5 (16) ∕1/5 (10) ∜ 5 ( (1> 1>)) = (1;) = (5= (5=)) uogj uogjfko fkojg jg ((51) 51) ∕1 (55) ∕∜ 5/5 (59) (59) 1/5 ((57) 57) ∕1

]a`j 1=> ]a`j (1) ∕∜ 9 (5) ∕1 (9) ∕1 (7) 1 (:) 5∜ 9/9 (6) ∕∜ 5/5 (0) ∕1/5 (>) (>) 1/5 ((;) ;) ∕∜ 9/9 (1=) ∕1 (11) (11) uogj uogjfko fkojg jg (15) 1 (19) ∕∜ 9/5 (17) ∕5∜ 9/9 (1:) ∕5 (16) ∕1 (10) ∕5∜ 9/9 (1>) ∕∜ 9/5 (1;) uogjf uogjfkojg kojg (5=) ∕5∜ 9/9 (51 (51)) 5 (55)) = (5 (55 (59) 9) ∕1 (57) ∕1

]a`j 111 ]a`j (1) (1) 1 ((5) 5) ∕∜ 9/5 (9) ∕∜ 9/9

]a`j 1=; ]a`j (1) uogj uogjfko fkojg jg (5) ∕∜ 9/9 (9) (9) 1/ 1/5 5 (7) ∕1 (:) ∕∜ 5 (6) ∕5∜ 9/9 (0) ∕∜ 9/5 (>) ∜ 9/5 (; (;)) 1/ 1/5 5 (1=) ∕∜ 9/9 (11) ∕5 (15) ∕∜ 9/9 (19) ∕1/5 (17) ∕∜ 9/5 (1:) ∕∜ 5 (16) ∕∜ 9 (10) ∕1/5 (1>) uogjf uogjfkojg kojg (1;) uogjf uogjfkojg kojg (5=) ∕∜ 9/5 (51) ∜ 5/5 (55) ∕∜ 5 (59) ∕1 (57) ∕∜ 9/5

(7) (7) 1 ((:) :) ∜ 9 ( (6 6) = (0) ∜ 5/5 (>) ∜ 5/5 (;) ∕∜ 9/9 (1=)) = (1 (1= (11) 1) ∕5 (15 (15)) 1 (19)) 1 (1 (19 (17) 7) ∜ 5/5 (1:) ∜ 9/5 (16) ∕∜ 5 (10 (10)) 1 (1 (1>) >) ∕1 (1;) 1/5 (5=) ∜ 5 (5 (51 1) 5 (55) ∕∜ 5 (59 (59)) 1 (5 (57) 7) ∕5∜ 9/9 ]a`j 115 ]a`j (1) ∕∜ 9/9 (5) ∕1 (9) ∕∜ 5 (7) (7) 1 ((:) :) ∕∜ 9/9 (6) (6) = (0) (0) 5 ((>) >) ∕∜ 5/5 (;) ∕1/5 (1=) ∜ 9 (1 (11) 1) 1 ((1 15) 1 (19) (19) 5 (1 (17) 7) 1 (1 (1:) :) ∕∜ 9/5 (16) ∕∜ 9/5 (10) ∕1/5 (1 (1>) >) 5∜ 9/9 (1;) ∕1 (5=) ∕1 (51) ∕5∜ 9/9 (55) ∕1 (59) ∕5∜ 9/9 (57) ∕1/5

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th ttnj nj Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

11;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

]a`j 119 ]a`j (1) 5∜ 9/9 (5) ∕5 (9) ∕1 (7) ∕∜ 9/5 (:) ∕∜ 9/5 (6) uog uogjfk jfkojg ojg (0) (0) 1 ((>) >) 1 ((;) ;) ∕1 (1=) ∕∜ 9/9 (11) (11) 5 (1 (15) 5) uogj uogjfko fkojg jg (19) ∕∜ 5 (17) ∜ 9/5 (1:) ∕1 (16) 1/5 (10) ∕1/5 (1>) ∕∜ 9 (1;)) 1 (5 (1; (5=) =) ∕5 (51) ∜ 9/9 (55) ∜ 5/5 (59) (59) 1/5 ((57) 57) ∕∜ 9

]a`j 116 ]a`j (1) (1) = ((5) 5) ∜ 9/9 (9) (9) = (7) ∕5 (:) ∕∜ 5/5 (6) uogj uogjfko fkojg jg (0) ∕5∜ 9/9 (>) uogjf uogjfkojg kojg (;) ∕1 (1=) ∕5 (11) ∜ 9/5 (15) ∕1 (19) ∕∜ 9 (17) uogj uogjfkoj fkojg g (1:) ∕∜ 9/9 (16) ∕1 (10) ∜ 9/5 (1 (1>) 1 (1;) ∕1 (5=) ∕∜ 9/5 (51 (51)) uogj uogjfko fkojg jg (55) ∕∜ 5 (59) ∕∜ 5 (57) ∕5

]a`j 117 ]a`j (1) ∕5∜ 9/9 (5) ∜ 9 (9) ∕∜ 5 (7) ∕∜ 9/5 (:) ∜ 5 (6) ∕∜ 9 (0) 1 ((>) >) uo uogj gjfk fkoj ojg g ((;) ;) 1

]a`j 110 ]a`j (1) (1) 1 ((5) 5) ∜ 9/5 (9) uogj uogjfko fkojg jg (7) 1/5 (: (:)) ∕∜ 9 (6) ∜ 9 (0) ∕∜ 9 (>) ∕5 (;) (;) 5

(1=) ∕1 (11) (11) = (1 (15) 5) ∕∜ 5/5 (19) ∕1/5 (17) ∕∜ 9 (1:) ∕∜ 9 (16) 1/5 (10) ∕∜ 9 (1>) ∕5 (1;) ∕1 (5=) ∕5 (51) ∕5 (55) ∜ 9/9 (59) ∕∜ 5 (57) uogj uogjfko fkojg jg

(1=) ∕1/5 (11) (11) 1 (1 (15) 5) ∕∜ 5 (19) ∕1 (17) (17) 1 (1: (1:)) ∕∜ 9/9 (16) ∕1 (10) ∕∜ 5 (1 (1>) >) ’1/ ’1/5 5 (1 (1;) ;) = ((5= 5=)) = ((51 51)) = (55) ∕∜ 9 (59) ∕1/5 (57) ∕∜ 9

]a`j 11: ]a`j (1) uogj uogjfko fkojg jg (5) ∜ 9/9 (9) uogj uogjfko fkojg jg (7) ∕∜ 9/9 (:) (:) 5∜ 9/9 (6) ∜ 9/5 (0) ∕∜ 5/5 (>) ∕1 (;) ∕1 (1=) ∕1 (11) ∕∜ 5/5 (15) ∕1/5 (19) ∜ 9/9 (17) ∕∜ 9/5 (1:) ∕5 (16) ∕∜ 9/5 (10) ∜ 5/5 (1>) ∕∜ 5/5 (1;) uogjf uogjfkojg kojg (5=) ∜ 9/5 (51 (51)) = (55) uog uogjfk jfkojg ojg (59) uogj uogjfko fkojg jg ((57) 57) 1

]a`j 11> ]a`j (1) ∕∜ 5 (5) ∕1 (9) ∕∜ 9 (7) ∕1 (:) uo uogj gjfk fkoj ojg g (6) = (0) ∕1 (>) ∜ 9/5 (;) ∜ 9/9 (1=) 9/9 (11) 5 (15) ∕1/5 ∜ ∕∜ 9 (1 ∜ kojg (17) (19) uogjf uogjfkojg (1: :) 1 (16) ∕1/5 (10) (10) 1 (1 (1>) >) ∕∜ 9/9 (1; 1;)) 5∜ 9/9 (5=) ∕1 (51) ∜ 5 (55)) 1/ (55 1/5 5 (5 (59) 9) 5 ((57) 57) ∜ 5/5

15=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In apttjr >< Wn Wnj j Ko Kovj vjrs rsj j Wrk rk` ` Fuo uoit itkh kho os Wnj fuoitkho sko sko 9=½ jquads hoj-nadf ejiausj tnj skgj hpphsktj th 9=½ ks adways hoj-nadf as dho` as tnj nyphtjousj nyphtjousj ko a 9=½-6=½-;=½ trkao trkao`dj `dj.. Wnj skoj fuoitk fuoitkho ho tjdds us wnat tnj ratkh hf tn tnj j hpp hpphs hskt ktj j sk skgj gj th tnj ny nyph phtj tjous ousj j ks fh fhrr a `kvj `kvjo oa ao` o`dj dj.. Wnjrj adsh jxksts ao kovjrsj skoj fuoitkho (sko ), wnkin tjdds us wnat ao`dj cabjs

ସ଺

ସ଺ ቍ଺ଶቁ

ସ଺ ቍ଺ଶቁ

tnj hpphsktj hpphsktj skgj hvjr tnj nyphtjo nyphtjousj usj jqua jquadd th a spjikf spjikfkjg kjg ratkh. Fhr jxac jxacpdj, pdj, sko jquads jqua ds 9=½ hr 1:=½. Wnj kovjr kovjrsj sj skoj hf hoj-nad hoj-nadf, f, wnkin wj jxprjss as sko

ସ଺

, asbs wnat

ao`dj yhu ihudg ihudg tabj tnj skoj hf aog `jt ao aoswjr hf hoj-nadf. (Kt ks kcphrtaot kcphrtaot th ohtj tnat sko ghjs oht oht cja cjao o th fko fkog g hoj hvj hvjrr tn tnj j sko skoj j fuo fuoitk itkho ho ’ kt kkss oht a cudt cudtkpd kpdkia kiatkv tkvj j kov kovjrs jrsj.) j.) Pnjo Pn jo wj us usj j tn tnj j sko skoj j fu fuoi oitk tkho ho,, tn tnj j arù arùcj cjot ot ks ao a ao` o`dj dj ao aog g tnj aos aoswj wjrr ks a fr frai aitk tkho ho ejtwjjo ∕1 aog +1. Pnjo Pnjo wj usj tnj kov kovjrs jrsj j skoj fuoit fuoitkho kho,, tnj arù arùcjo cjott ks a fra fraitk itkho ho ejtwjjo ∕1 aog +1 aog tnj tnj ao aoswj swjrr ks ao ao ao`dj `dj.. h shdvj fhr ko tnks jqua jquatkho, tkho, tabj tnj Ihoskgjr tnj jquatkho ‫ ݗ‬3 sko . Kf yhu waot tth ko kovj vjrs rsj j sk skoj oj hf eh ehtn tn skgjs kgjs= 1>=½, ½, hr 50 50=½ =½.. Jxacpdj 1< 1< ihs whudg jquad

ରଶ

∜

ସ଺ ቍ ଶର ቁ ∜

. Wnj Quagra Quagraot ot K rjfjrjo rjfjrjoij ij ao`dj fhr wnki wnkin n tnj ihskoj hf tnj ao`d ao`dj j

ks 9=½< Wna Wnatt ks ks,, ih ihss 9= 9=½½ 3

ରଶ

∜

. Wnj ihskoj fuoit fuoitkho kho ks phsktkv phsktkvj j ko Quagraot Quagraotss K

aog KV. Wnj Quagrao Quagraott KV ao`dj ihrrjs ihrrjsphogko` phogko` tth h 9=½ ks 96= oswjr wjrss th 96=½½ ∕ 9=½ 9=½ 3 99=½. Wnj aaos tnkss jxac tnk jxacpd pdj j ar arj j 9=½ a aog og 99= 99=½. ½.

ସ଺

Jxacpd Jxac pdj j 5< isi (∕1). Wnj Q Quagrao uagraott K rjfj rjfjrjoi rjoij j ao`dj fhr wnki wnkin n tnj iihsji hsjiaot aot hf tnj ao`dj whudg jquad 1 ks tnj sacj as tnj Quagraot K rjfjrjoij ao`dj fhr wnkin tnj skoj hf tnj ao`dj whudg jq whudg jqua uadd 1 (sko (skoij ij isi 3 ;= =½< Wnat kkss, sko aog 3 1). Wnks kkss ; sko ;=½ 3 1 aog is isii ;=½ 3 1. Eut wj ojj ojjg g ∕1, oht  +1 +1. Ykoi Ykoij j sko50=½ 3 ∕1 aog isi50=½ 3 ∕1, tnjrj ks lust hoj aos aoswjr wjr th tn tnks ks prhe prhedjc djc,, 50=½ (w (wnki nkin n dkj dkjss ho tn tnj j eh ehrgj rgjrr hf Qu Quag agra raot otss KK KKKK ao aog g KV KV). ).

ୱୠ଺୤ఈ ଺

ସ଺

Jxacpdj 9< 9< tao

(∕1). Wnj Quagra Quagraot ot K rjfjrjo rjfjrjoij ij ao`dj fhr wnkin tnj tao tao`jot `jot hf tnj ao`dj

whudg whu dg jq jquad uad 1 ks 7: 7:½½ (sko (skoij ij ta tao o 7:½ 3

ୱୠୡୣୱା଻୤ ା଻

½ ½

aog sko sko 7:½ 3 iihs hs 7:½ 3

ଶଶ

∜

)<

Wnat kkss,

ta tao o 7: 7:½½ 3 1 . Wnj tao` tao`jot jot fuoi fuoitkho tkho ks oj` ojàtkv atkvj j ko Quagra Quagraots ots KKKK aog KV. Wnj Quagra Quagraot ot KK aog KV ao ao`d `djs js ihrrj ihrrjsp sphog hogko ko` ` th 7: 7:½½ arj arj 1>=½ ∕ 7:½ 3 1 19:½ 9:½ aog 96=½ 96=½ ∕ 7:½ 7:½ 3 991: 1:½½. Wnj aoswjr aos wjrss th ttnks nks jxacp jxacpdj dj arj 19:½ aog 91:½ 91:½.. Jxacpdj 7< sji 7< Quagrao t K rjfj rjfjrjoij ao`d ao`dj jao`dj fhr wnkin tnj sjiao sjiaot t hf tnjhf ao`dj (∕5 ). Wnj whudg jquad 5 ks tnj sacj as Quagraot tnj Quagraot Krjoij rjfjrjoij fhr wnkin tnj ihskoj tnj

ସ଺

ao`dj ao` dj whud whudg g jq jquad uad 1/5 (skoi (skoij j sji

3

ୡୣୱఈ଺

).

Wnks kkss 6 6= =½<

Wnat kkss, ihs ihs 6=½ 3 1/ 1/5 5 aog

sji sji 6=½ 3 5. Wnj sj sjiao iaott aog ihs ihskoj koj fuo fuoitk itkhos hos ar arj j ojà ojàtkvj tkvj ko Qu Quagr agraot aotss KK aog KKK. Wnj Quagraot KK aog KKK ao`djs ihrrjsphogko` th 6=½ arj 1>=½ ∕ 6=½ 6=½ 3 15=½ 15=½ aog 1>=½ + 6=½ 3 57=½. Wnj ao aosw swjr jrss th tnk tnkss jxac jxacpd pdj j arj arj 15= 15=½½ a aog og 57= 57=½. ½.

ସ଺

Quagraott K rjfjrjoi rjfjrjoij j ao`dj fhr wnkin tnj ihtao` ihtao`jot jot hf tnj ao`dj Jxacpdj :< :< iht (=). Wnj Quagrao whudg jquad = ks tnj sacj as tnj Quagraot K rjfjrjoij ao`dj fhr wnkin tnj tao`jot hf tnj ao`dj whudg ej uogjfkojg (skoij iht 3

୵୘୤ఈ଺

)< Wn Wnks ks ks ;= ;=½< ½< Wn Wnat at ks, ks, ta tao o ;=½ ks uogjfkojg

aog iht ;=½ 3 =. Wnj adt adtjro jroatj atj a ao`d o`dj j ks 50=½. Wnj ao aoswj swjrs rs th tnks j jxac xacpdj pdj ar arj j ;=½ aog 50=½.

155

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺ ଺ ቍସ଺ ଶቁ ∕

(1) ihs

(7) sji

(0) isi

(5)

ସ଺

(∕5)

ସ଺

(1=) iht (∕1)

(19) ihs

(16) sji

∕ ∜

(1;) ihs

൨

∜ 5

ସ଺

(1)

(55) iht (∕1)

ସ଺

ൢସ଺ൢ ൨ ൨ ସ଺ൢ ൨ ସ଺ ቍ ଺ଶቁ

(:) sji

∜ 5

(>) isi

∕∜ 5

∕

(17) sji

(59) sko

ସ଺

(9) sko

(=)

ସ଺ ቍ ଶଶ ቁ

(6) sko

∕ ∜

(;) sji

ସ଺ ቍ ଶର ରቁ

(15) sji

∕

∜

ସ଺

(∕5)

ସ଺

(∕5)

ସ଺

(5)

(1:) isi

ସ଺

(=)

(1>) sko

ସ଺

(1)

(51) iht

(57) iht (uogjfkojg uogjfkojg))

(10) ihs

(5=) sji

∕∜ 9

(11) ihs

ସ଺ ቍ ଶର ቁ

ସ଺ൢ

ସ଺

(5) iht

ସ଺ ଺ଶ

ସ଺ ቍ ଶର ቁ ∜

ସ଺ൢ ସ଺

∕∜ 9

൨

ቍቁ

159

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b. (1) isi

ସ଺

(∕5)

(7) isi

ସ଺

(1)

ସ଺ൢ

൨

∕∜ 9

(0) iht

(1=) ihs

(19) isi

ସ଺

ସ଺

ସ଺

(16) sko

(1;) isi

(1)

(∕5)

(=)

ସ଺ൢ

(55) sji

ସ଺

∜ 5

(1)

(:) sji

(∕5)

ସ଺

(>) tao

(=)

∜

ସ଺ൢ

(17) iht

∕∜ 9

൨

(59) iht

∜ 9

ସ଺

ସ଺

(5)

(;) isi

ସ଺ ቍ ଶର ରቁ

∕

∜

∜

(1:) ihs

ସ଺ ቍ ଶଶ ቁ ∕ ∜

(6) isi

(15) sko

∜

(5=) sko

(∕5)

ସ଺ ቍ ଶର ቁ

ସ଺ ቍ ଶର ରቁ ∕

ସ଺

(9) sji

ସ଺ ቍଶର ରቁ

(10) sji

∕

(11) isi

൨

ସ଺ ଺ ቍସ଺ ଶቁ

(5) ihs

(1>) isi

ସ଺ ቍ ଶଶ ቁ ∜

ସ଺ ቍ ଶର ରቁ ∕

(51) ihs

(57) sji

ସ଺

ସ଺

(=)

(5)

∜

ൢ൨

157

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺ ର ቍସ଺ ଶ ቁ ∜

(1) sko

(5) ihs

(uogjfkojg)

(7) isi

ସ଺

(0) tao

(1)

(>) ihs

ସ଺

ସ଺ൢ

∕∜ 9

൨

ସ଺ ቍ ଺ଶቁ ∕

(16) sko

(1;) ihs

ସ଺ ቍ଺ଶቁ

ସ଺

(55) iht

∜ 9

(6) iht (∕1)

(;) sji

∕ ∜

ସ଺ ቍ ଶଶ ቁ ∕ ∜

(11) sko

ସ଺

(17) tao

ସ଺

(10) sko

ସ଺ൢ

ସ଺ൢ

(1:) ihs

(1)

(1>) sji

ସ଺ ቍ ଶଶ ቁ ∕ ∜

∜

൨

∕∜ 5

(15) tao

(1)

ସ଺ ର

(59) tao

ସ଺

ସ଺ ቍ ଶଶ ቁ

(5=) ihs

ସ଺

(9) iht (1)

∕ ∜

(:) tao

(1=) iht (uogjfkojg)

(19) iht

ସ଺ ଺ ቍସ଺ ቍଶቁ ର ቁ ର

(51) isi

ସ଺

∕∜ 9

൨

(=)

൨

ସ଺ൢ

∜ 5

ସ଺ ቍ ଶର ରቁ

(57) sji

∕

ସ଺

∜

(uogjfkojg)

଺ൢ

൨

଺ ቍ ର ቁ

଺ 15:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺ ଺ ቍସ଺ ଶቁ ଶ ቍ ଶ ቁ

(1) sko

ସ଺

(5) iht (uogjfkojg)

∕ ∜

(7) ihs

ସ଺

(0) sko

(=)

ସ଺

ସ଺

(19) tao

(16) ihs

(∕1)

ସ଺ ቍ଺ଶቁ

ସ଺ൢ

(;) isi

∕∜ 9

ସ଺

(11) tao

(17) ihs

൨

(=)

ସ଺

(15) sji

ସ଺ ቍ ଶର ቁ ∕ ∜

ସ଺

∜

ସ଺

(∕1)

ସ଺

(1)

(5=) iht

ସ଺ ቍ ରର ቁ

(51) sji

(59) sko

(=)

(∕5)

ସ଺ ቍ ଶଶ ቁ

(1:) sko

(1>) tao

(uogjfkojg)

ସ଺

∜

(∕1)

(1)

ସ଺

(10) iht (∕1)

∜

(55) iht (=)

(6) sko

ସ଺

ସ଺ ቍ ଶର ቁ

(1;) sko

∕ ∜

(>) iht

(1=) iht (uogjfkojg)

(9) isi

ସ଺ ቍ ରର ቁ

(:) tao

(57) ihs

଺

଺ ቍ଺ଶቁ

଺

156

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺ ଶ ቍସ଺ ቍ଺ଶቁ ቁ ଶ ∜

(1) ihs

(7) sko

(5) sji

(:) sji

ସ଺ ቍ ରର ቁ

(0) tao

(>) isi

(∕1)

(11) ihs

(19) isi

ସ଺ ቍ ଶର ରቁ ∕

∜

ସ଺ ቍ ଶଶ ቁ ∜

(16) sko

(55) isi

ସ଺

ସ଺

ସ଺ൢ

∕∜ 5

(∕5)

൨

∕∜ 5

ൢସ଺ ൨

∕ ∜

(1=) isi

(1;) sji

ସ଺

(9) sji

ସ଺

(∕5)

ସ଺

(=)

(1)

(6) ihs

(5)

(;) sko

ସ଺

ସ଺

(1)

(17) sji

ସ଺

(uogjfkojg)

(10) sji

ସ଺

(1)

ସ଺ ቍ ଺ଶቁ

(59) sji

∕

∕

∜

(15) isi

ସ଺ൢ

(1:) isi

ସ଺

∜ 5

൨

(∕5)

ସ଺ସ଺

(1>) iht (∕1)

(5=) ihs

(=)

(51) ihs

(57) isi

ସ଺ ቍ ଶର ቁ ∜

∜

଺ ቍ ଶର ରቁ

଺

଺ ቍଶର ରቁ

150

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺

(1) iht (∕1)

ସ଺ ର ቍସ଺ ର ቁ

ସ଺ൢ

൨ ସ଺ ቍ ରର ቁ

∜

(5) tao

(7) iht

∕∜ 9

(:) tao

(0) tao

∕ ∜

(>) tao

(∕5)

(11) sji

ସ଺ ቍଶର ରቁ

(17) tao

(1=) sji

(19) isi

ସ଺

∜

ସ଺

(uogjfkojg)

(1;) tao

ସ଺

(=)

(55) tao

∜

(16) sji

(∕1)

ସ଺ൢ

൨

(;) isi

(5)

(15) sko

൨

∜

(5=) ihs

ସ଺ ቍ ଺ଶቁ

(59) isi

(∕5)

ସ଺

(5)

ସ଺ ቍ ଶଶ ቁ

∕∜ 9

ସ଺ ቍ ଶର ቁ

(10) sko

(1)

(6) isi

ସ଺ൢ

∜ 9

ൢସ଺ ൨

∜ 9

ସ଺

ସ଺

(9) iht

∕

ସ଺

(1:) iht (=)

(1>) isi

∜

ସ଺ ቍଶର ରቁ

(51) ihs

(57) ihs

∜

ସ଺

(=)

∕ ∜

଺ ቍ ର ቁ

15>

଺ ቍ ଶ ቁ

଺

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺

(1) tao

(7) sji

∕∜ 9

ൢସ଺ൢ ൨ ൨

(0) ihs

∜ 5

ସ଺

(1=) isi

∕∜ 5

ସ଺ൢ

∜ 9

(>) sji

൨

൨

ସ଺ ቍ ଶ ቁ

ସ଺ൢ

(1;) iht

∜

∕∜ 9

(55) iht (1)

ସ଺ ଶ ର ቍସ଺ ର ቁ

൨

∜

(5)

∕

(11) sji

(10) sji

(5=) sji

∜

∜ 5

ସ଺ൢ ସ଺

൨

(5)

(∕1)

(∕1)

ସ଺ ቍ ଶର ቁ ∕ ∜

ସ଺ ቍ ରର ቁ

൨

∜ 5

ସ଺

(6) ihs

(uogjfkojg)

ସ଺ൢ

(17) isi

(59) isi

ସ଺

(9) isi

ସ଺ ቍ ଶର ରቁ

∕

(:) sji

ସ଺ൢ

(16) ihs

(1)

(19) iht

(5) isi

∕ ∜

(;) iht

ସ଺ൢ

(15) iht

ସ଺

∕∜ 9

൨

(∕1)

(1:) tao

(1>) iht (uogjfkojg)

ସ଺

(51) isi

ସ଺ ቍ ଶର ରቁ

(57) sko

∕

∕

∜

଺

଺ ቍ ଺ଶቁ

଺

15;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺

ସ଺

(1)

(5) tao

(7) iht (1)

(:) tao

(>) sko

(1) isi

ସ଺

(0) ihs

ସ଺

(1)

ସ଺ ቍ ରର ቁ

(16) iht

(1;) sji

(55) sko

ସ଺

∕ ∜

ସ଺ ቍ଺ଶቁ

ସ଺

ସ଺

(9) isi

ସ଺ ቍ ରର ቁ

(1=) iht (∕1)

(19) iht (=)

(=)

∕ ∜

ସ଺ ଶ ର ቍସ଺ ର ቁ ∕

(∕1)

(6) tao

ସ଺

(;) sko

ସ଺

(17) ihs

ସ଺ ቍ ଺ଶቁ ∕

(1:) sji

ସ଺ ቍ ଶଶ ቁ

(1>) isi

(10) sko

ସ଺

(15) sko

∕ ∜

(∕5)

(5=) sko

(=)

∕

(59) isi

(∕1)

(=)

ସ଺ ቍ଺ଶቁ

(11) ihs

(=)

∜

ସ଺ൢ

ସ଺

∕∜ 5

൨

(1)

ସ଺

(51) iht (uogjfkojg)

(57) tao

(∕1)

19=

ସ଺ ቍ ଺ଶቁ

ସ଺

ସ଺

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b. (1) isi

ସ଺

(∕1)

ସ଺

(7) iht (uogjfkojg)

(0) isi

ସ଺

(∕1)

ସ଺

(=)

ସ଺

(∕5)

(1=) tao

(19) sji

ସ଺ ቍ ଶ ቁ

(16) sko

∜

ସ଺ ቍ ଶଶ ቁ

(1;) sko

(55) isi

∕ ∜

ସ଺ ର ቍସ଺ ଶ ቁ ∕ ∜

(5) ihs

(∕1)

ସ଺ ቍ଺ଶቁ

(;) tao

(11) isi

ସ଺

(17) ihs

(10) sji

ସ଺

(6) isi

(>) sko

(uogjfkojg uogjfkojg))

(uogjfkojg)

ସ଺

(1)

(:) sji

ସ଺

(9) iht (∕1)

(∕5)

ସ଺ ቍ଺ଶቁ

(15) sji

ସ଺

(1:) sko

ସ଺

(∕1)

(5=) tao

ସ଺

(uogjfkojg)

(59) sji

(1)

(1>) ihs

ସ଺

(5)

(∕1)

ସ଺ ቍ ଶ ቁ ∜

ସ଺

(51) iht (∕1)

(57) iht (uogjfkojg uogjfkojg))

ସ଺

ସ଺

ସ଺ 191

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺ ଶ ቍସ଺ ଶ ቁ ∕ ∜

(1) sko

(1)

(7) sko

(0) isi

ସ଺

(1=) isi

(∕1)

ସ଺

∕∜ 9

∜

ସ଺

(∕1)

ସ଺ ቍ଺ଶቁ

(;) iht

ସ଺

ସ଺ൢ

(∕5)

∕ ∜

ସ଺ൢ

∜ 5

ସ଺

൨

൨

∕∜ 9

(15) iht (1)

ସ଺ ቍ ଶଶ ቁ

(17) sko

(10) isi

(1)

(6) tao

(11) sji

ସ଺

(>) sko

൨

(9) isi

(=)

(:) sko

ସ଺ ቍ ରର ቁ

(16) tao

ସ଺

(∕5)

ସ଺ൢ

(19) iht

ସ଺

(5) iht (∕1)

ସ଺ ቍ ଶର ቁ ∕ ∜

(1:) sko

ସ଺ସ଺

(1>) iht (uogjfkojg)

(1;) tao

ସ଺ ቍ ରର ቁ ∕ ∜

(5=) iht (=)

(51) sko

(=)

(55) sko

∕ ∜

(59) sko

(57) isi

∕

ସ଺

ସ଺

∜

ସ଺ ቍ ଶ ቁ

195

ସ଺ ቍ଺ଶቁ

ସ଺ ቍ ଶର ରቁ

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺

(1) sji

(7) ihs

(uogjfkojg)

ସ଺ ቍ ଺ଶቁ ∕

ସ଺

(0) tao

(1=) isi

(1)

ସ଺

(∕5)

ସ଺

(=)

ସ଺

(∕5)

(19) tao

(16) sji

(1;) ihs

(>) sji

(5)

ସ଺

(∕5)

ସ଺

(17) ihs

(∕1)

ସ଺

(1)

ସ଺

(5=) sko

(59) tao

(=)

∕ ∜

ସ଺ ଶ ର ቍସ଺ ର ቁ ∜

(6) ihs

(1)

(;) ihs

ସ଺ ቍ ଶଶ ቁ ∜

(15) sji

ସ଺ ቍ ଶର ରቁ ∕

ସ଺

(1:) sko

ସ଺

(9) sji

(10) iht (∕1)

∜

(11) tao

∕

ସ଺ ର ቍସ଺ ର ቁ

(5) tao

(:) sji

ସ଺ ቍ ଺ଶቁ

(55) iht (=)

(=)

ସ଺

(1>) tao

∜

(1)

ସ଺ ቍ ଶର ቁ

(51) sko

(57) sji

∜

∕∜ 5

ସ଺ ቍ ର ቁ

ସ଺

ସ଺ൢ

൨

199

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj aos aoswjrs wjrs th jai jain n prhed prhedjc. jc. Chs Chstt hf tnj prhe prhedjc djcss nav navj j twh aoswjr aos wjrss (ko twh gkff gkffjrj jrjot ot Q Quag uagrao raots) ts).. Inj Injib ib yhur aos aoswjr wjrss ko ttnj nj ea eaib ib hf tnj ehh ehhb. b.

ସ଺ ଶ ቍସ଺ ଶ ቁ ∜

(1) sko

(7) tao

(0) sji

ସ଺

(1=) sji

(:) sko

(5)

(>) sji

(5)

ସ଺ ቍ ଶର ቁ ∜

(55) sko

∕ ∜

∜

ସ଺

(;) iht (uogjfkojg)

ସ଺ ቍ଺ଶቁ

(15) ihs

ସ଺

(1:) tao

(5)

∕ ∜

(59) ihs

(1>) sji

(51) ihs

(∕1)

(57) sko

∜ ∜ 5

(=)

(=)

ସ଺ ቍଶର ରቁ

൨

ସ଺ൢ

ସ଺

ସ଺

ସ଺ ቍ ଶର ቁ

(10) sko

(5=) sji

∕

(6) sko

(∕1)

(17) sji

ସ଺ସ଺

ସ଺ ቍ ଶଶ ቁ

ସ଺

ସ଺ ଺ ቍସ଺ ቍଶቁ଺ቁ ଶ

(9) sko

(11) sko

(16) iht (uogjfkojg)

(1;) ihs

∜ 9

ൢସ଺ ቍ଺ቁ ൨ ଶ

(=)

ସ଺

(19) ihs

ସ଺

(5) iht

∜

ସ଺ ቍ ଺ଶቁ ∕

197

ସ଺ ቍ ଶ ቁ

ସ଺ ቍ଺ଶቁ

ସ଺

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r > Ao Aosw swjr jrss ]a`j ]a `j 159

]a`j ]a `j 156

(1 (1) 15=½ =½, , 57 57=½ ((5) 5)7: 1: 1:=½ , 99 99=½ 9) =½, =½ 1>=½ =½ (7 (7))) 15 6= 6=½, ½, 9= 9==½ =½=½((:) :) 7:½, ½,=½, 91 91:½ :½ =½ ((6) 6)((9) 55 55:½ :½,,, 1> 91 91:½ :½ (0 (0)) 51 51=½ =½,, 99 99=½ =½ (> (>)) 55 55:½ :½,, 91 91:½ :½ (; (;)) 1: 1:=½ =½,, 51 51=½ =½ (1 (1=) =) 19 19:½ :½,, 91 91:½ :½ (11)) 15= (11 15=½, ½, 57= 57=½½ (1 (15) 5) 15 15=½ =½,, 57 57=½ =½ (1 (19) 9) 1: 1:=½ =½,, 51 51=½ =½ (17 (17)) 6= 6=½, ½, 9= 9==½ =½ (1 (1:) :) 51 51=½ =½,, 99 99=½ =½ (16 (16)) 7: 7:½, ½, 91 91:½ :½ (1 (10) 0) ;= ;=½, ½, 50 50=½ =½ (1 (1>) >) 6= 6=½, ½, 15 15=½ =½ ((1; 1;)) =½ (5=)) =½ (5 (5= (51) 1) 1:= 1:=½, ½, 99= 99=½½ (55 (55)) 19 19:½ :½,, 91 91:½ :½ (5 (59) 9) 9= 9=½, ½, 1: 1:=½ =½ ((57 57)) =½, =½, 1>= >=½½

(1) (1)) 19 9= 9=½, ½, 1: 1:=½ =½:½((5) 5) 1> 1>= ½99=½ (9 (9) ) 50 50=½ (7) (7 19:½ :½, , 55 55:½ (: (:))=½, 1: 1:=½ =½,=, 99 =½ ((6) 6)=½;= ;=½½ (0) (0) =½, =½, 1> 1>=½ =½ (>) (>) 1: 1:=½ =½,, 99 99=½ =½ (;) (;) =½, =½, 1> 1>=½ =½ (1=) (1=) =½, =½, 1> 1>=½ =½ (1 (11) 1) =½, =½, 1> 1>=½ =½ (1 (15) 5) 15 15=½ =½,, 57 57=½ =½ (19)) 19: (19 19:½, ½, 91: 91:½½ (1 (17) 7) 1: 1:=½ =½,, 51 51=½ =½ (1:) (1:) 7: 7:½, ½, 19 19:½ :½ (1 (16) 6) 6= 6=½, ½, 9= 9==½ =½ (10)) 19: (10 19:½, ½, 91: 91:½½ (1 (1>) >) 19 19:½ :½,, 91 91:½ :½ (1;) (1;) 6= 6=½, ½, 15 15=½ =½ (5 (5=) =) 6= 6=½, ½, 57 57=½ =½ ((51 51)) =½ (55) (55) ;= ;=½, ½, 50 50=½ =½ (5 (59) 9) =½, =½, 1>= >=½½ (5 (57) 7) 6= 6=½, ½, 9= 9==½ =½

]a`j 157 ]a`j (1 (1)) 51 51=½ =½,, 99 99=½ =½ (5 (5)) 15 15=½ =½,, 57 57=½ =½ (9 (9)) 15 15=½ =½,, 57 57=½ =½ (7 (7)) ;= ;=½½ (:) 15 15= =½, 57 57=½ =½ (6 (6)) 9= 9=½, ½, 1: 1:=½ =½ ((0) 0) 1: 1:=½ =½,, 99= 9=½½ (> (>)) =½, =½, 1> 1>=½ =½ (; (;)) 57 57=½ =½,, 9= 9==½ =½ (1 (1=) =) =½ ((11 11)) 6= 6=½, ½, 15 15=½ =½ (1 (15) 5) 6= 6=½, ½, 15 15=½ =½ (1 (19) 9) 51 51=½ =½,, 99 99=½ =½ (1 (17) 7) 1: 1:=½ =½,, 99 99=½ =½ (1: (1:)) 7: 7:½, ½, 91 91:½ :½ (1 (16) 6) =½, =½, 1> 1>=½ =½ (1 (10) 0) 1: 1:=½ =½,, 51 51=½ =½ (1 (1>) >) 57 57=½ =½,, 9= 9==½ =½ (1; (1;)) 7: 7:½, ½, 19 19:½ :½ (5 (5=) =) 55 55:½ :½,, 91 91:½ :½ (51 (51)) ;= ;=½, ½, 50 50=½ =½ (5 (55) 5) =½ ((59 59)) 9= 9=½, ½, 51 51=½ =½ ((57 57)) 6= 6=½, ½, 9= 9==½ =½

]a`j 150 ]a`j (1) (1) 7: 7:½, ½, 91 91:½ :½ (5 (5)) 19: 9:½, ½, 55: 5:½½ (9 (9)) 15 15=½ =½,, 57 57=½ =½ (7) (7) 9= 9=½, ½, 1: 1:=½ =½ (:) (:) =½ ((6) 6) ;= ;=½, ½, 50 50=½ =½ (0) (0) 1: 1:=½ =½,, 99 99=½ =½ ((>) >) 9= 9=½, ½, 1:= :=½½ (; (;)) =½, =½, 1> 1>=½ =½ (1=)) 50= (1= 50=½½ (1 (11) 1) =½ (15 (15)) 7: 7:½, ½, 19 19:½ :½ (19) (19) 57 57=½ =½,, 9= 9==½ =½ (17 (17)) ;= ;=½, ½, 50 50=½ =½ (1:) (1:) 51 51=½ =½,, 99 99=½ =½ (1 (16) 6) 7: 7:½, ½, 19 19:½ :½ (10 (10)) =½ (1>)) 19: (1> 19:½, ½, 91: 91:½½ (1 (1;) ;) 19 19:½ :½,, 55 55:½ :½ (5=) (5=) 15 15=½ =½,, 57 57=½ =½ (51 (51)) 9= 9=½, ½, 99 99=½ =½ (55)) 51= (55 51=½, ½, 99= 99=½½ (5 (59) 9) 1: 1:=½ =½,, 51 51=½ =½ (57) (57) 6= 6=½, ½, 15 15=½ =½ ]a`j ]a `j 15>

]a`j 15: ]a`j (1 (1)) 6= 6=½, ½, 15 15=½ =½ ((5) 5) 6= 6=½, ½, 9= 9==½ =½ ((9) 9) 7: 7:½, ½, 55 55:½ :½ (7 (7)) =½, =½, 1> 1>=½ =½ ((:) :) 1: 1:=½ =½,, 99 99=½ =½ ((6) 6) 19 19:½ :½,, 91 91:½ :½ (0 (0)) 7: 7:½, ½, 55 55:½ :½ ((>) >) 19 19:½ :½,, 55: 5:½½ (;) 19 19:½ :½,, 55 55:½ :½ (1 (1=) =) =½, =½, 1> 1>=½ =½ (1 (11) 1) 55 55:½ :½,, 91 91:½ :½ (15)) 15= (15 15=½, ½, 9== 9==½½ (1 (19) 9) 1: 1:=½ =½,, 99 99=½ =½ (1 (17) 7) 7: 7:½, ½, 55 55:½ :½ (1 (1:) :) ;= ;=½, ½, 50 50=½ =½ (16)) 51= (16 51=½, ½, 99= 99=½½ (1 (10) 0) ;= ;=½½ (1 (1>) >) 7:½ 7:½,, 91 91:½ :½ (1 (1;) ;) 6= 6=½, ½, 9= 9==½ =½ (5 (5=) =) 19 19:½ :½,, 55 55:½ :½ (5 (51) 1) 57 57=½ =½,, 9= 9==½ =½ (55 (55)) 9= 9=½, ½, 51 51=½ =½ (5 (59) 9) 9= 9=½, ½, 51 51=½ =½ (5 (57) 7) ;= ;=½, ½, 50 50=½ =½

(1) (1) 19 19:½ :½,, 91 91:½ :½ ((5) 5) 9= 9=½, ½, 51= 1=½½ (9 (9)) 9= 9=½, ½, 51 51=½ =½ (7) (7) 1: 1:=½ =½,, 99 99=½ =½ (: (:)) 19 19:½ :½,, 91 91:½ :½ ((6) 6) ;= ;=½½ (0) (0) 1: 1:=½ =½,, 99 99=½ =½ ((>) >) 6= 6=½, ½, 57= 7=½½ (; (;)) 9= 9=½, ½, 1: 1:=½ =½ (1=) (1=) 15 15=½ =½,, 57 57=½ =½ (11 (11)) 6= 6=½, ½, 9= 9==½ =½ (15) (15) 7: 7:½, ½, 19 19:½ :½ (1 (19) 9) 6= 6=½, ½, 15 15=½ =½ (17) (17) 15 15=½ =½,, 9= 9==½ =½ (1: (1:)) ;= ;=½, ½, 50 50=½ =½ (16) (16) ;= ;=½, ½, 50 50=½ =½ (1 (10) 0) 6= 6=½, ½, 15 15=½ =½ (1>) (1>) 6= 6=½, ½, 15 15=½ =½ ((1; 1;)) =½, =½, 1>= >=½½ (5=) (5=) 15 15=½ =½,, 57 57=½ =½ (51 (51)) ;= ;=½, ½, 50 50=½ =½ (55) (55) 9= 9=½, ½, 51 51=½ =½ (59) (59) 51 51=½ =½,, 99 99=½ =½ (57) (57) 19 19:½ :½,, 55 55:½ :½

Ohtj) >) 1: 1:=½ =½,, 51 51=½ =½ ((;) ;) 15 15=½ =½,, 9= 9==½ =½ (1 (1=) =) 55 55:½ :½,, 91 91:½ :½ (11 (11)) ;= ;=½, ½, 50 50=½ =½ (1 (15) 5) 1: 1:=½ =½,, 99 99=½ =½ (19 (19)) 9= 9=½, ½, 51 51=½ =½ (1 (17) 7) 7: 7:½, ½, 19 19:½ :½ (1 (1:) :) 19 19:½ :½,, 91 91:½ :½ (1 (16) 6) 7: 7:½, ½, 91 91:½ :½ (1 (10) 0) 7: 7:½, ½, 91 91:½ :½ ((1> 1>)) =½, =½, 1> 1>=½ =½ (1 (1;) ;) 1: 1:=½ =½,, 99 99=½ =½ (5= (5=)) 6= 6=½, ½, 9= 9==½ =½ (5 (51) 1) 57 57=½ =½,, 9= 9==½ =½ (55 (55)) 7: 7:½, ½, 55 55:½ :½ (59)) 50= (59 50=½½ (5 (57) 7) 51 51=½ =½,, 99 99=½ =½

]a`j 195 ]a`j (1) (1) 55 55:½ :½,, 91 91:½ :½ (5 (5)) 19 19:½ :½,, 91 91:½ :½ ((9) 9) ;= ;=½½ (7) (7) ;= ;=½½ (: (:)) =½, =½, 1> 1>= =½ (6 (6)) 19 19:½ :½,, 91 91:½ :½ (0) (0) 50 50=½ =½ ((>) >) 9= 9=½, ½, 1:= :=½½ (;) 1: 1:=½ =½,, 99 99=½ =½ (1=)) 51= (1= 51=½, ½, 99= 99=½½ (1 (11) 1) 15 15=½ =½,, 57 57=½ =½ (15) (15) 7: 7:½, ½, 55 55:½ :½ (19) (19) 1: 1:=½ =½,, 99 99=½ =½ (17)) 55: (17 55:½, ½, 91: 91:½½ (1 (1:) :) 57 57=½ =½,, 9= 9==½ =½ (16) (16) 9= 9=½, ½, 51 51=½ =½ (1 (10) 0) 7: 7:½, ½, 19 19:½ :½ ((1> 1>)) =½, =½, 1> 1>=½ =½ (1;) (1;) 1: 1:=½ =½,, 99 99=½ =½ (5= (5=)) ;= ;=½, ½, 50 50=½ =½ (51) (51) =½, =½, 1> 1>=½ =½ (5 (55) 5) 55 55:½ :½,, 91 91:½ :½ (59) (59) 9= 9=½, ½, 1: 1:=½ =½ (57) (57) 57 57=½ =½,, 9= 9==½ =½

]a`j 19= ]a`j (1 (1)) ;= ;=½½ (5 (5)) =½, =½, 1> 1>=½ =½ ((9) 9) 57 57=½ =½,, 9= 9==½ =½ (7 (7)) 7: 7:½, ½, 55 55:½ :½ ((:) :) 1: 1:=½ =½,, 99= 9=½½ (6) 19 19:½ :½,, 91 91:½ :½

]a`j 199 ]a`j (1) (1) ;= ;=½, ½, 50 50=½ =½ ((5) 5) 9=½, =½, 51 51=½ =½ ((9) 9) 9= 9=½, ½, 99 99=½ =½ (7) (7) 15 15=½ =½,, 57 57=½ =½ ((:) :) 6= 6=½, ½, 9== ==½½ (6 (6)) =½

(0 (0)) =½ (> (>)) 9= 9=½, ½, 1: 1:=½ =½ (; (;)) =½, =½, 1> 1>=½ =½ (1 (1=) =) 19 19:½ :½,, 91 91:½ :½ (11 (11)) ;= ;=½, ½, 50 50=½ =½ (1 (15) 5) 9= 9=½, ½, 1: 1:=½ =½ (1 (19) 9) ;= ;=½, ½, 50 50=½ =½ (17)) 15= (17 15=½, ½, 57= 57=½½ (1 (1:) :) 19 19:½ :½,, 55 55:½ :½ (16)) 15= (16 15=½, ½, 9== 9==½½ (1 (10) 0) 55 55:½ :½,, 91 91:½ :½ (1 (1>) >) ;=½ (1 (1;) ;) 15 15=½ =½,, 57 57=½ =½ ((5= 5=)) =½, =½, 1> 1>=½ =½ ((51 51)) =½, =½, 1> 1>=½ =½ (55)) 51= (55 51=½, ½, 99= 99=½½ ((59) 59) 50 50=½ =½ (5 (57) 7) 19 19:½, :½, 91 91:½ :½

(0) (0) 7: 7:½, ½, 55 55:½ :½ ((>) >) 15= 5=½, ½, 57= 7=½½ (; (;)) 7: 7:½, ½, 91 91:½ :½ (1=)) 51= (1= 51=½, ½, 99= 99=½½ (1 (11) 1) 19 19:½ :½,, 91 91:½ :½ (15) (15) 1: 1:=½ =½,, 51 51=½ =½ ((19 19)) =½, =½, 1> 1>=½ =½ ((17 17)) =½ (1:) (1:) =½, =½, 1> 1>=½ =½ (1 (16) 6) 15 15=½ =½,, 57 57=½ =½ (10) (10) 19 19:½ :½,, 91 91:½ :½ (1> (1>)) 7: 7:½, ½, 55 55:½ :½ (1;) (1;) 15 15=½ =½,, 57 57=½ =½ (5 (5=) =) =½, =½, 1> 1>=½ =½ (51) (51) 6= 6=½, ½, 15 15=½ =½ (5 (55) 5) ;= ;=½, ½, 50 50=½ =½ (59)) 1:= (59 1:=½, ½, 99= 99=½½ (5 (57) 7) 19 19:½ :½,, 55 55:½ :½

]a`j 191 ]a`j (1 (1)) 50 50=½ =½ (5 (5)) 1: 1:=½ =½,, 51 51=½ =½ (9 (9)) 19 19:½ :½,, 91 91:½ :½ (7 (7)) =½, =½, 1> 1>=½ =½ (:) (:) =½ (6) (6) =½, =½, 1> 1>=½ =½ (0 (0)) 50 50=½ =½ ((>) >) 9= 9=½, ½, 1: 1:=½ =½ ((;) ;) 19 19: :½, 91 91:½ :½ (1 (1=) =) =½, =½, 1> 1>=½ =½ (1 (11) 1) 51 51=½ =½,, 99 99=½ =½ (1 (15) 5) 6= 6=½, ½, 9= 9==½ =½ (1 (19) 9) 15 15=½ =½,, 57 57=½ =½ (17)) 6=½ (17 6=½,, 9= 9==½ =½ (1 (1:) :) 50 50=½ =½ (1 (16) 6) 7:½ 7:½,, 19 19:½ :½ (10)) 1>= (10 1>=½½ (1 (1>) >) 7: 7:½, ½, 91 91:½ :½ (1 (1;) ;) 55: 55:½, ½, 91: 91:½½ (5 (5=) =) ;= ;=½, ½, 50 50=½ =½ (5 (51) 1) 19 19:½ :½,, 91 91:½ :½ (5 (55) 5) =½, =½, 1> 1>=½ =½ ((59 59)) =½ ((57 57)) =½, =½, 1> 1>=½ =½

]a`j 197 ]a`j (1) (1) 7: 7:½, ½, 19 19:½ :½ ((5) 5) 9=½, =½, 51 51=½ =½ ((9) 9) 9= 9=½, ½, 1: 1:=½ =½ (7) (7) =½, =½, 1> 1>=½ =½ (:) (:) 9= 9=½, ½, 1: 1:= =½ ((6) 6) 51 51=½ =½,, 99 99=½ =½ (0) (0) 6= 6=½, ½, 9= 9==½ =½ ((>) >) 1>= >=½½ (; (;)) =½, =½, 1> 1>=½ =½ (1=) (1=) 6= 6=½, ½, 9= 9==½ =½ (1 (11) 1) 9= 9=½, ½, 1: 1:=½ =½ (15) (15) ;= ;=½, ½, 50 50=½ =½ (1 (19) 9) 9= 9=½, ½, 99 99=½ =½ (17) (17) 6= 6=½, ½, 9= 9==½ =½ ((1: 1:)) =½, =½, 1>= >=½½ (1 (16) 6) =½, =½, 1> 1>=½ =½ (10) (10) 57 57=½ =½,, 9= 9==½ =½ (1> (1>)) 9= 9=½, ½, 99 99=½ =½ (1;) (1;) 7: 7:½, ½, 91 91:½ :½ (5 (5=) =) 7: 7:½, ½, 91 91:½ :½ (51)) 15= (51 15=½, ½, 57= 57=½½ (5 (55) 5) 55 55:½ :½,, 91 91:½ :½ (59)) 1>= (59 1>=½½ (5 (57) 7) 9= 9=½, ½, 1: 1:=½ =½

196

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inaptjr ;< Wnj Daw hf Ykojs aog tnj Daw hf Ihskojs Wnj daw hf sko skojs js ao aog g daw hf ihs ihskoj kojss arj js jspji pjikad kaddy dy usj usjfud fud fh fhrr shdv shdvko` ko` fh fhrr uobo uobohwo hwo ao ao`dj `djss aog skgjs ko aiutj (addgh ao`dj ao`djs djss tnao aog hetus hetusj (hoj ao`dj `rjatjr tjr tnao trkao`djs ’ k.j. trkao`djs trkao `djs tnat ohts navj rk`nt;=½) (;=½) ao` ao`djs. djs. j Fkrst Fkrst, , wj wkdd`rja gjrkvj tnj tnjsj sj;=½) daws daws,trkao , aog`djs tnjo wj wkdd gks gksius iusss nhw tth h ap appd pdy y tnj tnjc. c.

‫ܪ‬

‫ܪ‬

‫ܬ‬

Ihoskgjr tnj trkao`dj kddustratjg aehvj ho tnj djft (wnkin ks aiutj, eut tnj rjsudtko` dawss tna daw tnatt wj gjrk gjrkvj vj wkdd ap appdy pdy ko `jo `jojra jrad). d). Ko hur oht ohtatk atkho, ho, tnj up uppjr pjrias iasj j djt djttjr tjrss , , aog ‫ܪ‬ rjprjsjot tnj djo`tns hf tnj skgjs, wnkdj tnj ihrrjsphogko` dhwjriasj djttjrs , , aog rjprjs rjp rjsjo jott tnj ao` ao`djs djs hpp hpphsk hsktj tj th tnj rjs rjspji pjitkv tkvj j skg skgjs js.. Wnj sacj trkao`dj ks adsh kddustratjg aehvj th tnj rk`nt, wktn tnj aggktkho hf a gasnjg njk`ntt gkvkgj gkvkgjss tnj hrk`ko hrk`koad ad trka trkao`dj o`dj vjrtkiad dkoj th rjprjsjot tnj trkao`dj‛s njk`nt, ‫ܬ‬. Wnj njk`n koth kot h twh rk rk`nt `nt ttrka rkao` o`djs djs.. Djt u uss wrkt wrktj j ghwo a ao o jq jquat uatkho kho ffhr hr tnj skojs skojs hf ao` ao`djs djs aog <

sko

3

‫ܬ‬

,

‫ܪ‬

sko

3

‫ܬ‬

Pj iao iao jd jdkc kcko koat atj j tnj tnj nj njk` k`nt, nt, ‫ܬ‬, ey shdvk shdvko` o` fh fhrr kt a ad`je d`jerakia rakiaddy ddy ko ja jain in jq jquatkho uatkho= + 5: 3 67 ∕ 7= + 5: 3 7; 7; 5 ‫ݗ‬30

ଶ

Jxac Jx acpd pdj j 9=½ aog

3 15=½.)

171

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Jxac Jx acpd pdj j 7∜ 5ihs 5 ihs 3 5 + 16 ∕ 1= 3 > > 1 ∜ 5 ∜ 5 ihs

3

3

3

>∜ 5 ∜ 5 ∜ 5 5 Ohw tab tabj j ao kkovj ovjrsj rsj iihsk hskoj oj ho e ehtn htn sskgj kgjss hf tnj jq jquat uatkho kho=½.)

Fkrst, t, dae daejd jd , , ‫ ܪ‬, , , aog , as wj gkg gkg h ho o ttnj nj rk rk`n `ntt gk gka` a`ra rac. c. Jxac Jx acpd pdj j :=½< ܿ 3 1>=½ 1>=½ ∕ ∕ 3 1>=½ 1> =½ ∕ 0:½ 0:½ ∕ 7:½ 7:½ 3 6=½ 6=½. Ohw Ohw wj usj usj tn tnj j daw daw hf skojs kojs 6=½ :

>

1= ∜ 1= 7:½

‫ݗ‬

1:9

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Fhr jain rk`nt trkao` Kostruitkhos< trkao`dj, dj, gjtjrck gjtjrckoj oj tnj kogkiatjg uobo uobohwo hwo gkstaoi gkstaoij j hr ao`dj ao`dj.. Injib Inj ib yh yhur ur ao aosw swjr jrss ko tn tnj j ea eaib ib hf tnj eh ehhb hb.. Oh ia iadi diuda udathr thr kkss oj ojjg jgjg jg.. Ohtj< Wnj trkao Ohtj< trkao`djs `djs arj oht gra grawo wo th siadj. siadj. Jxijp Jxijptt fhr hetusj ttrkao`d rkao`djs js wnjrj tnj da dar`js r`jst t ao`dj ao` dj ao aog g dho dho`js `jstt skgj skgj arj arj,, ko fai fait, t, dar dar`js `jst, t, a skgj skgj tna tnatt dhh dhhbs bs dho dho`jr `jr tnao ao aohtn htnjr jr cay aituad ait uaddy dy ej snh snhrtj rtjrr aog ao a ao`d o`dj j tna tnatt dhhbs dar dar`j `jrr tnao a aoht ohtnjr njr ca cay y ait aituad uaddy dy ej sc scadd addjr. jr. (1) ‫ ݗ‬3 8

‫ݗ‬

(5) ‫ ݗ‬3 8

:∜ 5 7:½

7:½ 0∜ 5

(9)

∜ 9

38

17

6

1=:½

‫ݗ‬

(7)

38

9 1=

∜ 9

9=½

1:7

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Fhr jain rk`nt trkao` Kostruitkhos< trkao`dj, dj, gjtjrck gjtjrckoj oj tnj kogkiatjg uobo uobohwo hwo gkstaoi gkstaoij j hr ao`dj ao`dj.. Injib Inj ib yh yhur ur ao aosw swjr jrss ko tn tnj j ea eaib ib hf tnj eh ehhb hb.. Oh ia iadi diuda udathr thr kkss oj ojjg jgjg jg.. Ohtj< Wnj trkao Ohtj< trkao`djs `djs arj oht gra grawo wo th siadj. siadj. Jxijp Jxijptt fhr hetusj ttrkao`d rkao`djs js wnjrj tnj da dar`js r`jst t ao`dj ao` dj ao aog g dho dho`js `jstt skgj skgj arj arj,, ko fai fait, t, dar dar`js `jst, t, a skgj skgj tna tnatt dhh dhhbs bs dho dho`jr `jr tnao ao aohtn htnjr jr cay aituad ait uaddy dy ej snh snhrtj rtjrr aog ao a ao`d o`dj j tna tnatt dhhbs dar dar`j `jrr tnao a aoht ohtnjr njr ca cay y ait aituad uaddy dy ej sc scadd addjr. jr. (1) ‫ ݗ‬3 8

(5)

38

∜ 5 1:=½

; 7:½

5∜ 9

∜ 9

(9) ‫ ݗ‬3 8

7:½ 1 :

(7)

38

∜ : ∜ 5

1

1::

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Inap In aptj tjr r ; Ao Aosw swjr jrss ]a`j ]a `j 177

Ohtj ((9) 9) 7: 7:½½ (7) (7) : ]a`j ]a `j 176 (1) 7:½ (5 (5)) 7: 7:½½ ((9) 9) ∜ : ( (7 7) 9 ]a`j ]a `j 170 (1 (1)) 5 ((5) 5) ∜ 9 (9) 15= 15=½½ (7 (7)) ∜ 5 ]a`j ]a `j 17> (1) ∜ 5 (5) 1=: 1=:½½ ((9) 9) 6=½ ((7) 7) ∜ 9 ]a`j ]a `j 17; (1 (1)) > ((5) 5) ∜ 6 (9) 9=½ (7 (7)) 5∜ 6 ]a`j ]a `j 1:= (1) 7:½ (5 (5)) 9∜ 9 (9) 19: 19:½½ (7 (7)) 15 15=½ =½ ]a`j ]a `j 1:1 (1 (1)) 7 ((5) 5) ∜ 5 (9 (9)) 7: 7:½½ ((7) 7) 17 ]a`j ]a `j 1:5 (1) ∜ : (5 (5)) 6 (9 (9)) 9= 9=½½ ((7) 7) 7∜ 5 ]a`j ]a `j 1:9 (1) ∜ 1: 1: (5) (5) 0 ((9) 9) 0 ((7) 7) ∜ : ]a`j ]a `j 1:7 (1 (1)) > ((5) 5) ∜ 6 (9) (9) 15= 15=½½ ((7) 7) 15 15=½ =½ ]a`j ]a `j 1:: (1) 0∜ 9 (5 (5)) 0:½ (9) 7∜ 5 (7 (7)) 19 19:½ :½

rjfjr th tn rjfjr tnj j Bko Bkogdj gdj jgkt jgktkho kho (oht tnj prkot j jgktkho gktkho). ).

1:6

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Ina napt ptjr jr 1=< Dja jaro ro aog Ap Appd pdy y Wr Wrk` k` Kg Kgjo jottkt ktkj kjss Wnjrj arj sjvjrad ihccho aog usjfud trk`hohcjtrki kgjotktkjs, wnkin iao ej njdpfud fhr shdvko` a varkjty hf prhe shdvko` prhedjcs djcs aog fhr gjrkv gjrkvko` ko` usj usjfud fud fhrcuda fhrcudass ko catn aog sikjoi sikjoij. j. Pj wkdd fkrst gjrkvj sjvjrad trk`hohcjtrki kgjotktkjs, aog tnjo fhius ho nhw th appdy tnjc th shdvj prhedjc prhe djcss hr gjrk gjrkvj vj htnj htnjrr fhrc fhrcuda udas. s.

Wnj ]ytna`hrjao kgjotktkjs arj trk`hohcjtrki vjrskhos hf tnj ]ytna`hrjao tnjhrjc. Fhr tnj tnj rk`nt trka trkao`dj o`dj kddus kddustratj tratjg g ae aehvj, hvj, tnj ]ytn ]ytna`hrja a`hrjao o tnj tnjhrjc hrjc ks

ଶ ଶ ଶ

+ 3 ‫ܪ‬

Ykckdar dardy, dy, skoij skoij ihs 3 /‫ ܪ‬, wj iao wrktj Ykoij sko 3 /‫ܪ‬, wj iao wrktj 3 ‫ ܪ‬sko . Ykck 3 ‫ ܪ‬ihs . Pj sue suest stktut ktutj j tnj tnjsj sj jxp jxprjs rjsskh skhos os kot koth h tnj ]y ]ytna tna`hrj `hrjao ao tnj tnjhrj hrjc< c<

ଶ ଶ ଶ ଶ ଶ ଶ ଶ ଶ

(‫ ܪ‬ihs ) + (‫ ܪ‬sko ) 3 ‫ܪ‬ ‫ ܪ‬ ihs + ‫ ܪ‬sko 3 ‫ܪ‬

ଶ ଶ

Ohtj, fhr jxacpdj, tnat  ihs cjaos th fkrst fkog tnj ihskoj hf tnj ao`dj , aog tnjo squarj ihs wnkin n ks ihc ihcch cho o tth h ja jain in ttjrc jrc,, wj fko fkog g tn tnat at tnj rjsu rjsudt. dt. Iaoi Iaoijddko` jddko` hut tnj ‫ ܪ‬, wnki

ihs

ଶ

ଶ

+ sko

31

Pj iao hetak hetako o a sj sjihog ihog ] ]ytna` ytna`hrjao hrjao kgjot kgjotkty kty ey gkvkgko gkvkgko` ` tnks jqua jquatkho tkho e ey y ihs

ihs

ଶଶ ଶଶ ଶ ଶ ଶ +

sko

3

1

ihs ihs ihs 1 + tao 3 sji

ଶ

<

A tnkr tnkrg g ]y ]ytna tna`hr `hrjao jao kgjo kgjotkt tkty y rjs rjsudts udts ey gkv gkvkgko kgko` ` tnj hrk` hrk`ko koad ad ]ytn ]ytna`h a`hrja rjao o kgj kgjotk otkty ty ey sko

ଶ

<

1:0

Kcprhvj [hur Catn Fdujoiy Yjrkjs

ଶଶ ଶଶ ଶ ଶ ଶ

ihs

+

sko iht

ߒ

‫ܦ‬

sko

1

3

sko sko + 1 3 isi

‫ܮ‬

‫ܦ‬

ߜ

‫ܫ‬

‫ܮ‬

‫ܫ‬ ‫ܠ‬

ߛ

‫ܠ‬

‫ܪ‬

‫ܪ‬

Pj wkd wkddd usj tnj gka gka`ra `rac c ae aehv hvj j th pr prhv hvj j tn tnj j ao ao`dj `dj suc suc kgj kgjot otkt ktkj kjs. s. Oht Ohtj j tnat tnat tn tnj j sa sacj cj gka`rac appjars ho tnj djft aog rk`nt2 tnj gkffjrjoij ks tnat àcca ( ߒ ) ks daejdjg as tnjta ( ), aog adp dpna na (ߛ) aog ejta (ߜ ) na nav vj ejj jjo o rjch rjchv vjg. Oh Ohtj tj tn tna at  ߛ 3 ;= ;=½ ∕ skoij ߛ + + ;=½ 3 1>=½. Adsh, ߜ 3 ߛ ej ejia iaus usj j tn tnjy jy ar arj j vj vjrt rtki kiad ad ao ao`d `djs js.. Fu Furt rtnj njrc rch hrj rj,, ߒ 3 ;= ;=½ ∕ ߜ skoij ߜ + ߒ + ;=½ 3 1>=½. Wnks cj cja ao ttn nat  ߒ 3 ;=½ ;=½ ∕ ߛ (skoij ߜ 3 ߛ). Ihcparj tnks wktn 3 ;=½ ∕ ߛ (wnkin ihcjs frhc tnj hrk`koad jquatkho, ߛ 3 ;= ;=½ ∕ ). Wnus, wj navj prhvjo tnat   3 ߒ. Wnks ks wny wny tnj gka gka`ra `rac c th tnj rk`nt na nass ko pdaij hf  ߒ. Njoi Nj oijf jfhrt hrtn, n, wj wk wkdd dd usj tn tnj j gka gka`r `rac ac ho tnj rk rk`n `ntt th prhv prhvj j tn tnj j ao ao`d `dj j suc suc kgjo kgjotk tktkj tkjs. s. Fkrst, Fkrs t, wj jxprj jxprjss ss sko skoj j aog ihs ihskoj koj fhr ja jain in dae daejdj jdjg g ao`dj ko tnj fhu fhurr rk`n rk`ntt trkao trkao`d `djs js

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Pj na navj vj lust lust gj gjrkv rkvjg jg tn tnj j ao ao`d `dj j su suc c kgj kgjot otkt kty y fh fhrr skoj skoj (1)

∜ ∜

(5) ∕∜ 6 ∕ ∜ 5 (9) ∕∜ 6 ∕ ∜ 5

(7) 5 + ∜ 9 (:) ∕5 ∕ ∜ 9 ]a`j ]a `j 16; (1) ∜ 9 (5) ∕1 (9) (9) 5 ((7) 7) = ((:) :) ]a`j 10= ]a`j (1 (1)) = ((5) 5) ∕5 (9) uog uogjfk jfkojg ojg (7) uo uogj gjfk fkoj ojg g (:) = ]a`j ]a `j 101 (1)

ଶରର

ඪ ଶିଶି ଶ ଼ସ଼ସ ଶ ଶ ାඪ ଺ଶ ච ାସାସ ଼ସ଼ଶସ ଶ ଺ଶ ච ାିାି ଼ସ଼ଶସ ଶ ඪ ା ଻ ଻ ଶ ଶ ଺ର ର ∜

(5)

∜

∜ ∜

(9) 1 + ∜ 5

(7) 5 ∕ ∜ 9 (:) ∕ 7 + 5 ∜ 5 ]a`j ]a `j 105 (1)

∜ ∜

(5)

∜ ∜

(7) 7 + 5 ∜ 5 (:) 5 ∕ ∜ 9 ]a`j ]a `j 109 (1) ± (5) ±∜ : (9) ± (7) ±5∜ 5 (:) ± ]a`j ]a `j 107

∜

(9) 1 + ∜ 5

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th ttnj nj Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

∜

∜

(1) ±∜ 9 (5) ± (9) ± (7) ±

ର଻ ାଲ ଶ଻

∜

(:) ±∜ 9

1>=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Inap In aptj tjr r 11 119

Kcprhvj [hur Catn Fdujoiy Yjrkjs

ଶ

Jxacpdj Jxa cpdj 1= 1=

(5) 5 3 ∜ 5 sji

(7) :ihs

ଶ

(6) 7iht

∕ 5∜ 9 3 ∜ 9 ∕ ihs

∕5 35

1>:

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj ao`dj ao`djss tna tnatt shd shdvj vj jain prhedj prhedjc c ey appdy appdyko` ko` ad`j ad`jera era aog, wnjrj wnj rj ap appdk pdkiae iaedj, dj, trk trk`ho `hohcj hcjtrki trki kgj kgjotk otktk tkjs js.. Inji Injib b yhur ao aoswj swjrs rs ko tnj ea eaib ib hf tnj ehhb ehhb.. (1) tao(5

(9) ∜ 9 3

) ∕ ∜ 9 3 5 ta tao( o(5 5 )

∕9iht(9 )

(:) ∜ 6 ih ihss( + /7) 3 ∜ 9

(5) ∜ 9 isi( isi(

/5) 3 ∕5

ଶ

(7) >sko (5 ) 3 5

(6) 9 sji(9 sji(9 ) 3 sji(9

)∕7

1>6

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj ao`dj ao`djss tna tnatt shd shdvj vj jain prhedj prhedjc c ey appdy appdyko` ko` ad`j ad`jera era aog, wnjrj wnj rj ap appdk pdkiae iaedj, dj, trk trk`ho `hohcj hcjtrki trki kgj kgjotk otktk tkjs js.. Inji Injib b yhur ao aoswj swjrs rs ko tnj ea eaib ib hf tnj ehhb ehhb..

∕sko

(1) ∜ 5ihs 5 ihs

ଶ

3 ihs

ଶ

(9) 1 ∕ sj sjii (5 ) 3 tao (5 )

ଶ

(:) ∜ 5 3

∕7sko ihs

ଶ

ଶ

(5) sko

(7) 5ihs

ଶ

(6) sko

+ 9 ih ihss

ଶ

ଶ

∕ 5sk 5 skoo

39

3 ∕∜ ∕ ∜ 9

ଶ

ଶ

∕ 1 3 iihs hs

1>0

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj ao`dj ao`djss tna tnatt shd shdvj vj jain prhedj prhedjc c ey appdy appdyko` ko` ad`j ad`jera era aog, wnjrj wnj rj ap appdk pdkiae iaedj, dj, trk trk`ho `hohcj hcjtrki trki kgj kgjotk otktk tkjs js.. Inji Injib b yhur ao aoswj swjrs rs ko tnj ea eaib ib hf tnj ehhb ehhb.. (1) 7ihs

3 9sji

(5) tao(5 ) 3 9 ih iht( t(5 5 )

3 ∕5sko

(7) 9isi

3 ∕6iht

(:) sko(5 ) 3 ihs

(6) 5tao

3 ∕ ∜ 5sji 5 sji

(9) tao

1>>

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj ao`dj ao`djss tna tnatt shd shdvj vj jain prhedj prhedjc c ey appdy appdyko` ko` ad`j ad`jera era aog, wnjrj wnj rj ap appdk pdkiae iaedj, dj, trk trk`ho `hohcj hcjtrki trki kgj kgjotk otktk tkjs js.. Inji Injib b yhur ao aoswj swjrs rs ko tnj ea eaib ib hf tnj ehhb ehhb..

ଶ

(1) 5sko

(9) 5 ∕ isi isi

3 1 + sko

ଶ

3 isi

(5) 9 + 7 ih ihss

ଶ

3 7∜ 9ihs 9 ihs

ଶ

(7) 5∜ 9tao(5 9 tao(5 ) + tao (5

) 3 ∕9

1>;

Kcprhvj [hur Catn Fdujoiy Yjrkjs

Kostruitkhos< Gj Kostruitkhos< Gjtjr tjrcko ckoj j tnj ao`dj ao`djss tna tnatt shd shdvj vj jain prhedj prhedjc c ey appdy appdyko` ko` ad`j ad`jera era aog, wnjrj wnj rj ap appdk pdkiae iaedj, dj, trk trk`ho `hohcj hcjtrki trki kgj kgjotk otktk tkjs js.. Inji Injib b yhur ao aoswj swjrs rs ko tnj ea eaib ib hf tnj ehhb ehhb..

ଶ

(1) 5∜ 5sji 5 sji

∕ 5 3 sji

(9) ∜ 9ihs 9 ihs

∕ ∜ 9 3 sko

ଶ

(5) 5sko (9 ) 3 9 sko( sko(9 9

(7) 5ihs

3 9 tao

)∕1

1;=

Wrk`hohcjt Wrk`ho hcjtry ry Jss Jssjotka jotkads ds ]rai ]raitkij tkij Phrbe Phrbehhb hhb wktn Aosw Aoswjrs jrs

Aoswjr Bjy Inapt Ina ptjr jr 11 Ao Aosw swjr jrss< ]a`j 1>: ]a`j (1 (1)) 57 57=½ =½,, 9= 9==½ =½ (5 (5)) 7: 7:½, ½, 91: 1:½½ (9) 19 19:½ :½,, 91 91:½ :½ (7 (7)) 9= 9=½, ½, 99 99=½ =½ ((:) :) 1= 1=:½ :½,, 16: 6:½½ (6 (6)) 7: 7:½, ½, 19 19:½ :½,, 55 55:½ :½,, 91 91:½ :½ ]a`j ]a `j 1>6 (1 (1)) 6= 6=½, ½, 1: 1:=½ =½ ((5) 5) 7> 7>=½ =½,, 6== ==½½ (9 (9)) 7= 7=½, ½, 1= 1==½ =½ (7 (7)) 1: 1:½, ½, 0: 0:½, ½, 1= 1=:½ :½,, 16 16:½ :½ (:) =½, =½, 50 50=½ =½ (6) (6) 7= 7=½, ½, >= >=½½ ]a`j ]a `j 1>0 (1 (1)) 7: 7:½, ½, 91 91:½ :½ (5 (5)) =½, =½, 1> 1>= =½ (9 (9)) =½, =½, ;= ;=½½ (7) 0:½ 0:½,, 1= 1=:½ :½ (: (:)) 11 115. 5.:½ :½,, 1: 1:0.: 0.:½½ (6 (6)) ;= ;=½, ½, 50 50=½ =½ ]a`j ]a `j 1>> (1 (1)) 9= 9=½, ½, 1: 1:=½ =½,, 51 51=½ =½,, 99 99=½ =½ (5 (5)) 9= 9=½, ½, 6= 6=½, ½, 15 15=½ =½,, 1: 1:=½ =½ (9 (9)) =½, =½, 15 15=½ =½,, 1> 1>=½ =½,, 57 57=½ =½ (7) 15 15=½ =½,, 57 57=½ =½ (: (:)) 9= 9=½, ½, ;= ;=½, ½, 1: 1:=½ =½,, 50 50=½ =½ (6) 55 55:½ :½,, 91 91:½ :½ ]a`j ]a `j 1>; (1 (1)) ;= ;=½, ½, 51 51=½ =½,, 99 99=½ =½ (5 (5)) 9=½, =½, 99 99=½ =½ (9 (9)) ;= ;=½, ½, 51 51=½ =½,, 99 99=½ =½ (7 (7)) 6=½, =½, 1: 1:=½ =½ ]a`j ]a `j 1;= (1 (1)) 7: 7:½, ½, 91 91:½ :½ (5 (5)) 1= 1=½, ½, 9= 9=½, ½, := :=½½ (9 (9)) =½, =½, 9= 9==½ =½ (7) (7) 9= 9=½, ½, 1: 1:= =½

Ohtj< Wnj Ohtj< Wnjsj sj pa pa`j `j ou ouce cejr jrss rjfjr rjf jr th ttnj nj Bko Bkogdj gdj jgk jgktkho tkho (oht tnj prkot j jgktkho gktkho). ).

Trigonometry Essentials Practice Workbook With Answers Master Basic Trig Skills by Chris McMullen

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