Module 2

 

Klbf`dl cf [hj @hirdfb Hrkhj`fb ln Khbllkhj, Djk. Uahsf 85 Uhkgh`f > Ibg 8 Blts 9-3, Ih`lj` [dbhj`, Khbllkhj Kdty

MLCVBF 9? MHSAFMHSDK[ dj taf Mlcfrj Plrbc Uhttfrjs hjc Jumifrs dj Jhturf hjc taf Plrbc (Pffg 9-;) D.

DJSYLCVKSDLJ Paht ds mhtafmh mhtafmhtdks< tdks< Sl slmf dt ds jumifrs, lpfrhtdl lpfrhtdlj j nrhktdlj nrhktdljs, s, pfrkfjt, pfrkfjt, hb`firh, hb`firh, khbkubus, klmputhtdljs hjc taf bdgf iut dj rfhbdty Mhta ds hs ifhutdnub hs hrt. Djstfhc ln phdjts hjc whtfr klblrs mhtafmhtdkdhjs usfs jumifr phttfrjs hjc fquhtdljs fquhtdljs tl fxprfss taf ifhuty ln  jhturf hjc wf clj—t ahvf tl if taht `llc tl sff taf wlrbc usdj` mhtafmhtdks. Pf lursfbvfs khj cfmystd cfmystdny ny taf ujdvf ujdvfrsf rsf dn wf kl klubc ubc oust sf sff f ph phttf ttfrjs rjs dj jh jhtu turf rf wfbb wfbb fv fvfj fj taf nhmlus nhmlus hstrljlmfrr ljkf shdc Mhtafmhtdks hstrljlmf Mhtafmhtdks ds taf bhj`uh`f wdta wadka @lc ahs wrdttfj taf ujdvfrsf iy @hbdbfl @hbdbfd (Mhtaugbhshj wdta [dr Yhm).

DD.

BFHYJDJ@ LIOFKSD^F/[ Dcfjtdny phttfrjs dj jhturf hjc rf`ubhrdtdfs dj taf wlrbc.  Hrtdkubhtf taf dmplrthjkf dmplrthjkf ln mhtafmhtd mhtafmhtdks ks dj ljf—s ljf—s bdnf.  Hr`uf hilut hilut taf jhturf jhturf ln ln mhtafmhtdks, mhtafmhtdks, waht dtdt ds, alw ds rfprfsfjt rfprfsfjtfc fc hjc usfc usfc Fxprfss hpprfkdhtdlj nlr mhtafmhtdks hs h aumhj fjcfhvlr. 







DDD.

BFHYJDJ@ HKSD^DSDF[

BF[[LJ D UHSSFYJ[ HJC JVMIFY[ DJ JHSVYF Uhttfrjs hrf klrf tlpdks dj mhtafmhtdks. Dj nhkt, mhtafmhtdks ds hbsl gjlwj hs taf skdfjkf ln phttfrjs. Adstlrdkhbby, mhtafmhtdkdhjs ahvf cfhbt wdta twl typfs ln phttfrjs-taf jumfrdk phttfrjs hjc taf `flmftrdk phttfrjs (lr mlrf hptby, phttfrjs ln sahpfs). H phttfrj ds nlrmfc wafj sfts ln sahpfs, jumifrs lr cfsd`js hrf rfpfhtfc lvfr hjc lvfr h`hdj7 tafrfnlrf dt ds rf`ubhr, rfpfhtfc hjc rfkurrdj` nlrms lr cfsd`j hjc ndjc bl`dkhb kljjfktdljs tl nlrm `fjfrhbdzhtdljs. Fxhmpbfs? 8. Padka ln taf nd`urfs nd`urfs khj if usfc usfc tl kljtdjuf kljtdjuf taf sfrdfs sfrdfs `dvfj ifblw5 l. 9. ALJ ALJFTKLMI ‛ MI ‛ H aljfyklmi aljfyklmi ds h mhss ln afxh`ljh afxh`ljhbb prdsmhtdk whx whx kfbbs iudbt iudbt iy aljfy aljfy iffs dj tafdr jfsts tl kljthdj tafdr bhrvhf hjc stlrfs ln aljfy hjc plbbfj. ( wdgdpfcdh). Pay iffs usfc afxh`lj dj mhgdj` aljfyklmi hjc jlt hjy ltafr plby`ljs<

 

Dt djvlbvfs ndjcdj` taf lptdmum mftalc ln ndbbdj` up h `dvfj sphkf suka hs h kuidk lr spafrdkhb kljthdjfr. [upplsf ylu ahvf kdrkbfs ln rhcdus 8km, fhka ln wadka wdbb tafj ahvf hj hrfh ln υkm 9. Pf hrf tafj `ldj` tl ndbb h pbhjf wdta tafsf kdrkbfs usdj` squhrf phkgdj` vs. afxh`ljhb phkgdj`.

;. [SYDUF[ - H strdpf ds h bdjf lr ihjc taht cdnnfrs dj klblr lr tljf nrlm hj hcohkfjt hrfh. Uhttfrjs fxadid fxa didtfc tfc dj taf fxtf fxtfrjh rjhbb hppf hppfhrh hrhjkf jkfs s ln hjdmh hjdmhbs. bs. Saf Saf td` td`fr fr bllgs bllgs hj hjc c ayfjh ayfjh—s —s sp splt lt,, tafsf tafsf sffmdj`by rhjclm cfsd`js hrf ifbdfvfc tl if `lvfrjdj` iy mhtafmhtdkhb fquhtdlj. Hkklrcdj` tl taflry ln Hbbhj Sudrdj` taf kafmdkhb nhktlrs dj taf kfbb cftfrmdjf `rlwta, phttfrjs, hjc djnbufjkf nhktlrs bdgf ahdr klblr. Safrf hrf twl kafmdkhb prlkfssfs? rfhktdlj hjc cdnnusdlj.

3. [UDYHB[ - H spdrhb ds h kurvfc phttfrj taht nlkusfs lj h kfjtrf pldjt hjc h sfrdfs ln kdrkubhr  sahpfs taht rfvlbvf hrlujc dt. Fxhmpbfs ln spdrhbs hrf pdjf kljfs, pdjfhppbfs7 aurrdkhjfs.Safrf ds h cfndjdtf phttfrj ln kblkgwdsf hjc klujtfrkblkgwdsf hrk ln spdrhbs fxtfjcdj` lutwhrc nrlm taf kfjtfr ln taf nblwfr. Hs taf sjhdbs `rlw, tafdr safbbs hbsl fxphjc prlplrtdljhbby. prlplrtdljhbby. Sads prlkfss rfsubts dj h rfndjfc spdrhb strukturf, dt ds khbbfc hs fqudhj`ubhr fqudhj`ubhr spdrhb.

6. NBLP NBLPFY FY UFSH UFSHB[ B[ - Nblwfrs wdta ndvf pfthbs hrf shdc tl if taf mlst klmmlj. Jumifrs ln pfthbs hrf hbb Ndiljhkkd jumifrs.

>. ULUV ULUVBH BHSD SDLJ LJ @YLP @YLPSA SA Mhtafmhtdks usfc tl mlcfb plpubhtdlj `rlwta wdta taf nlrmubh?  = 〞【 Pafrf H ds taf sdzf ln taf plpubhtdlj hntfr dt `rlws, U ds taf djdtdhb jumifr ln pflpbf, r ds taf rhtf ln `rlwta, t ds tdmf hjc f ds taf Fubfr—s kljsthjt wdta hj hpprlxdmhtfby vhbuf 9.081. Fxhmpbf?

 

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Saf Saf fxp fxplj ljfj fjtd tdhb hb `rlw `rlwta ta mlcf mlcfbb H = ;5 f 5.59t  cfskrdifs taf plpubhtdlj ln h kdty dj taf Uadbdppdjfs dj talushjcs, t yfhrs hntfr 8446. h) Paht whs taf plpubhtdlj ln taf kdty dj 8446< i) Paht wdbb if taf plpubhtdlj dj 9580< [lbutdlj?  H =;5 f5.59 t  ( )

5.59 5

 H = ;5 f

5    H =;5 f  H =¼ ;5 (8)     H = ;5 tafr tafrfn fnl lrf, rf, taf taf plpu plpubh bhtd tdlj lj dj 84 8446 46 whs whs ;5 ;5,5 ,555 55.. Pf jf jffc fc tl ndjc ndjc H nl nlrr ta taf f yfhr 9580. Sl ndjc t, wf suitrhkt 9580 hjc 8446 tl `ft t=99, wadka wf tafj pbu` dj tl lur fxpljfjtdhb `rlwta mlcfb. 5.59 t 

 H =;5 f

5.59 99

       

 H =;5 f

( )

5.33

 H =;5 f

 H =¼ ;5

(8.66908) H = 3>.618; tafrfnlrf, taf kdty plpubhtdlj wlubc if hilut 3>,618 dj 9580.

JVMIFY UHSSFYJ 8. Paht Paht wdbb wdbb taf taf jfx jfxtt jumi jumifr fr if< if< 5, ;, >, 4, 89, 86, \\\\\\\\\\  9. Paht Paht s ta taf f jfx jfxtt jumi jumifr fr< < 6, ;, 8, -8, -;, -6, -0 \\\\\\\\  Uhttfrjs rfnfr tl usuhb typfs ln prlkfcurfs lr rubfs taht khj if nlbblwfc klmf hntfr h sft h jumifrs taht hrf hrrhj`f hrrhj`fc c dj h phrtdkub phrtdkubhr hr lrcfr. lrcfr. Sads hrrhj`fmfj hrrhj`fmfjtt ln jumifrs jumifrs ds khbbfc khbbfc h sfqufjk sfqufjkf. f. Saf jumifrs taht hrf dj taf sfqufjkf hrf khbbfc tfrms.

Pafj taf sfqufjkf `lfs lj nlrfvfr dt ds khbbfc hj djndjdtf sfqufjkf sfqufjkf,, ltafrwdsf dt ds h ndjdtf sfqufjkf. Fxhmpbf? 8. Ndjc taf ndrst ndvf tfrms ln taf sfqufjkf h j= 9j-;. [lbutdlj? h8= 9(8 (8)) ‛ ; h9= 9(9) ‛ ;   h8 = - 8

h;= 9(;) ‛ ;

h9 = 8

h3= 9(3) ‛ ;

h6= 9(6) ‛ ;

h; = ;

h3 = 6

h6 = 0

Safrfnlrf taf ndrst ndvf tfrms hrf -8, 8, ;, 6, hjc 0. Fxhmpbf? 9. Ndjc taf 63ta tfrm ln taf sfqufjkf h j= j ‛ ;j. [lbutdlj? h6; = 6; ‛ ;(6;) h6; = -85> FQFYKD[F #8 Dn ylu tadjg taf sthtfmfjt ds klrrfkt, wrdtf H@YFF, ltafrwdsf wrdtf CD[H@YFF.  \\\\\8.. Mhtafmhtdks  \\\\\8 Mhtafmhtdks ds fxadidtfc fxadidtfc ljby tarlu`a tarlu`a jumifrs. jumifrs.  \\\\\9.. Mhtafmhtdks  \\\\\9 Mhtafmhtdks khj prl`rfss prl`rfss fvfj fvfj wdtalut wdtalut jumifrs.  \\\\\;.. Fvfry pafjlmfjl  \\\\\; pafjlmfjlj, j, waftafr waftafr skdfjtdndk lr lr slkdhb, khj khj if fxpbhdjfc fxpbhdjfc iy mhtafmhtdks. mhtafmhtdks.  \\\\\3. Uhttfrjs taht lkkur  \\\\\3. lkkur dj jhturf jhturf hrf ljby nlr hrts hpprfkdhtdl hpprfkdhtdlj j hjc jlt jlt nlr mhtafmhtdkhb mhtafmhtdkhb fxpblrhtdljs.  \\\\6. Mhtafmhtdks Mhtafmhtdks ds jlt mfhjt mfhjt tl if bfhrjfc iy iy fvfryljf. fvfryljf.

BF[[LJ DD HYDSAMFSDK [FXVFJKF 9.8 -

 H sfqufjkf sfqufjkf ln jumifr jumifr wal—s wal—s taf cdnnfrfjkf cdnnfrfjkf iftwffj iftwffj kljsfkutdvf kljsfkutdvf tfrms tfrms ds taf shmf. shmf.

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Nlrmubh? hj = h8 + (j-8) c wafrf? h 8= ndrst tfrm7 j= jumifr ln tfrm7 c= klmmlj cdnnfrfjkf

^frdny waftafr taf nlbblwdj` sfqufjkf ds hrdtamftdk.

 

8. 0, 88, 86, 84, … , 3j+;

c=3

9. 8, 3, 0, 85, …, ;j-9

c=;

Fxhmpbf? 8. Ndjc taf nlrmubh nlr taf jta tfrm ln hj hrdtamftdk sfqufjkf wdta klmmlj cdnnfrfjkf ln ; hjc walsf ndrst tfrm ds 89. Nlrmubh? hj = h8 + (j-8) c

[lbutdlj?

@dv dvf fj? h8 = 89

hj = 89 + (j-8) ;

c=;

hj = 89 + (;j-;)

hj = ;j + 4

9. @dvfj taf taf ndrst 3 tfrms ln taf hrdtamftdk hrdtamftdk sfqufjkf? sfqufjkf? {85, 1, >, 3} ndjc taf 9;rc tfrm ln taf sfqufjkf. [lbu [l butd tdlj lj??

{8 {85, 5, 1, >, 3}

@dv dvf fj? h8 = 85

Nl Nlrm rmub ubh? h? hj = h8 + (j-8) c h9; =<

c = -9

h9; = 85 + (9;-8) (-9)  h9; = 85 + (99) (-9) h9; = 85 ‛ 33  h9; = -;3

tafrfnlrf taf 9;rc tfrm lr h9; ds -;3.

;. @d @dvf vfj j ttaf af nd ndrs rstt tfr tfrm m h8= 57 c= -37 Ndjc h>=< [lbutdlj?

h>= 5 + (>-8) -3 h>= 5 + (6) -3 tafrfnlrf taf >ta tfrm lr h> ds -95.

h>= -95

3. Ndjc hj hrdta hrdtamftd mftdk k mfh mfhj j iftwff iftwffj j 6 hjc hjc 84< 84< [lbutdlj?

6, \\, 84

@dvfj? h8=6 h9=   =

h9=<

h;=84

h8 + h;

84 = 6 + (;-8) c

9

+

6 84 9

hj = h8 + (j-8) c

h9= 89

84-6=9c 83 9

=

9c 9

c=0

Yfmfmifr tads hrdtamf Yfmfmifr hrdtamftdk tdk sfqufj sfqufjkf kf lr hrdt hrdtamf amftdk tdk prl`rfs prl`rfssdlj sdlj ds h sfqufjk sfqufjkf f dj wadka wadka taf cdnnfrfjkf iftwffj hjy twl sukkfssdvf tfrms ds h kljsthjt. Sads kljsthjt ds khbbfc taf klmmlj cdnnfrfjkf. Saf nlrmubh nlr taf jta tfrm ln hj hrdtamftdk sfqufjkf ds h j  =h8  + (j-8) c. Saf tfrms iftwffj twl tfrms ln hj hrdtamftdk sfqufjkf hrf khbbfc hrdtamftd hrdt amftdk k mfhjs mf hjs.R .R  FQFYKD[F #9 D.

DD.

Ndjc hj hr hrdtamftdk mfhj iftwffj? 8. 9. ;. 3. 6.

6 hjc 84 3 hjc 89 86 hjc 36 8 hjc ; 85 hj hjc 85 8555

NDILJHKKD [FXVFJKF 9.9 Bfljhrcl Udshjl ‛ Ndiljhkkd •

Ndiljhkkd ds taf `rfhtfst Furlpfhj mhtafmhtdkdhj ln taf mdccbf h`fs.

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Ilrj dj 8805 Dthby hjc cdfc dj 8935.

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Ndiljhkk Ndilj hkkdd cfrdv cfrdvfc fc nrlm nrlm Ndbdu Ndbdus s Iljh Iljhkkd kkd mfhjs mfhjs slj ln Iljh Iljhkkd kkd.. Ads nhtafr—s jhmf ds @u`bfdbml Iljhkkd. Af djtrlcukfc taf Hrhidk jumifr systfm dj Furlpf.

 

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Ndiljhkkd sfqufjkf whs cdsklvfrfc hntfr hj djvfstd`htdlj lj taf rfprlcuktdlj ln rhiidts.

Ndiljhkkd sfqufjkf? •

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Ds hj djtf`fr dj taf djndjdtf sfqufjkf 8, 8, 9, ;, 6, 1, 8;, … ln wadka taf ndrst twl tfrms hrf 8 hjc 87 fhka sukkffcdj` tfrm ds taf sum ln taf twl dmmfcdhtfby prfkfcdj`.  Hcc taf bhst twl tfrm tfrm tl `ft taf jfxt jfxt tfrm.

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Yfkursdvf nlrmubh Nj=Nj-9 + Nj-8

•

Pafrf N8 hjc N9 = 8

Fxhmpbf #8

Fxhmpbf #9 Cftfrmdjf taf 88ta tfrm ln taf Ndiljhkkd jumifr. @dvfj taht taf 89 ta tfrm ds 833 hjc taf 85ta tfrm ds 66.

@lbcfj Yhtdl Saf rhtdlj ln taf twl quhjtdtdfs ds taf shmf hs taf rhtdl ln tafdr sum tl taf bhr`fr vhbuf ln taf twl quhjtdtdfs. •

h •

i

 =

h +i h

•

Saf `lbcfj rhtdl ds lntfj cfjltfc iy taf @rffg smhbb bfttfr Uad (ώ).

•

Sads ds hpprlxdmhtfby fquhb tl 8.>81.

FQFYKD[F #; D. Hjswfr taf nlbblwdj` qufstdljs? 8. Saf ndrst nlur Ndiljhkkd jumifrs hrf 5, 8, 8 hjc 9, waht ds taf twfbnta jumifr< 9. Dn taf ndrst tarff Ndiljhkkd jumifrs hrf `dvfj hs x 8 = 8, x9 = 8 hjc x; = 9, tafj waht ds taf bfhst vhbuf ln j nlr wadka x j : 655< ;. Saf @lbcfj Yhtdl = 8.>815;;41103414313195... = 8.>81 klrrfkt tl ; cfkdmhb pbhkfs. Dn xj hrf tfrms ln taf Ndiljhkkd sfqufjkf, tafj waht ds taf bfhst vhbuf ln j nlr wadka

DD. @dvfj taf rfkursdvf nlrmubh nlr taf Ndiljhkkd sfqufjkf N j = Nj-9 + Nj-8, Ndjc taf nlbblwdj`?

8. DDD.

N;

9. N3 ;. N6 3. N3 6. N> ta Ndjc taf 85  tfrm ln taf sfqufjkf 8, ;, 3, 0, 88, 81, 94, 30 …

BF[[LJ DDD SAF NVJKSDLJHBDST LN MHSAFMHSDK[ Saf @frmhj padblslpafr Dmmhjufb Ghjt ljkf shd, ‒Mhtafmhtdks ds taf djcdspfjshibf djstrumfjt ln hbb paysdkhb rfsfhrkafs”. Sads sfktdlj prfsfjts taf bdjg iftwffj mhtafmhtdks hjc ltafr ndfbcs nlkussdj` phrtdkubhrby lj dts cdvfrsf hppbdkhtdljs hs nhr hs phttfrjs lj jhturf hjc dj taf wlrbc hrf kljkfrjfc kljkfrjfc.. Dj paysdks paysdks,, paysdkh paysdkhbb mlcfbs mlcfbs hrf nlrmubhtfc nlrmubhtfc dj taf bhj`uh`f bhj`uh`f ln 

 

mhtafmhtdks, spfkdndkhbby tarlu`a cdnnfrfjtdhb fquhtdljs. Fxhmpbfs hrf dj Gfpbfr—s cdsklvfry mhtafmhtdks, cdsklvfry ln  pbhjfthry lridthb pfrdlcs, Jfwtlj—s Bhw ln `rhvdty, Fdjstdfj—s Saflry ln Yfbhtdvdty, Kahrbf—s Bhw ln taf fxphjsdlj ln `hsfs hjc [karlcdj`fr—s fquhtdlj ln quhjtum mfkahjdks, hmlj` ltafrs. Kafmds mdstry ds hjltaf tafr hrfh rfh taht aht ahs ahs fst fsthibd hibds safc fjcur curdj` hjc hjc fxph xphjcdj` dj` djtfrcfpfjcfjkf djtfrcfp fjcfjkf wdta mhtafmhtdks. Hb`firh hjc khbkubus hrf typdkhb tllbs dj rfhktdlj gdjftdks. Bdjfhr hb`firh hjc mhtrdx taflry hrf usfc tl kahrhktfrdzf mlbfkubfs wafj tafy kahj`f nrlm ljf fjfr`y sthtf tl hjltafr. Saf rlbf ln mhtafmhtdks dj idlbl`y ds typdkhbby cfmljstrhtfc dj hrfhs bdgf ( iut jlt bdmdtfc bdmd tfc tl) idlsthtd idlsthtdstdk stdks, s, idlskdfj idlskdfjkf, kf, hjc mfcdkhb mfcdkhb rfsfhrka rfsfhrka.. Dt nlkusfs nlkusfs lj cfvfblpd cfvfblpdj` j` jfw mlcfbs hjc khrrdfs lut sdmubhtdljs ln kfrthdj idlbl`dkhb qufstdljs phrtdkubhrby talsf taht ahvf slmftadj` tl cl wdta phttfrjs dj rfhktdlj-cdnnusdlj fquhtdljs hs wfbb hs klmidjhtlrdhb prlibfms kljkf kljkfrj rjdj dj` ` CJH-Y CJH-YJH JH kljn kljnd`u d`urht rhtdl dljs. js. Dj twl twl djcfp djcfpfj fjcfj cfjtt stucdf stucdfs s hilu hilutt paysd paysdlbl lbl`dk `dkhb hb `fjlmdks, mhtafmhtdkhb mlcfbs (usdj` systfms ln phrtdhb cdnnfrfjtdhb fquhtdljs) lj taf afhbdj` prlkfss ln dskafmdk wlujcs wfrf nlrmubhtfc. [dmdbhrby, Nrdfcmhj mlcfbbfc taf `rlwta ln  khjkfr tumlr taht usuhbby lkkurs dj nbudc-bdgf tdssufs bdgf taf mhmmhry `bhjc hjc taf irhdj. FQFYKD[F #3 D.

Fxpbh Fxpbhdj dj alw alw mhtaf mhtafmht mhtdks dks ds usfc usfc dj dj taf taf nlbbl nlbblwdj wdj` `h hrfh rfhs. s. Hjswf Hjswfrr dj dj j jlt lt mlrf mlrf tah tahj j ndvf ndvf sfjtfjkfs. 8. Uaysdks 9. Kafmdstry ;. Idlbl`y 3. Fj`dj djf ffrd rdj j` 6. Musd Musdk k hjc hjc hrts hrts

DD.

Dn ylu tad tadjg jg taf sthtf sthtfmfj mfjtt ds kl klrrf rrfkt kt,, wrdt wrdtf f H@Y H@YFF FF.. Lta Ltafrw frwdsf dsf,, wrdt wrdtf f CD[H CD[H@Y @YFF FF..

 \\\\\8.. Mhtafmhtdkhb  \\\\\8 Mhtafmhtdkhb mlcfbs hrf jfvfr hkkurhtf. hkkurhtf.  \\\\\9.. Saflrfms dj  \\\\\9 dj mhtafmhtdks mhtafmhtdks hrf hislbutf hislbutf trutas trutas wadka khj sthjc ushidbdty lvfr lvfr tdmf.  \\\\\;. Safrf ds jl  \\\\\;. jl hspfkt ln ln aumhj hjc slkdhb slkdhb hnnhdr taht taht clfs jlt jlt djvlbvf mhtafmhtdkhb mhtafmhtdkhb rfhsljdj`.  \\\\\3.. Mhtafmhtdks  \\\\\3 Mhtafmhtdks ds dmplrthjt dmplrthjt dj taf hrts hjc slkdhb slkdhb skdfjkfs skdfjkfs hs dt ds dj taf paysdkhb paysdkhb skdfjkfs. skdfjkfs.  \\\\\6.. Saf vhbuf ln h mhtafmhtdkhb  \\\\\6 mhtafmhtdkhb kljkfpt kljkfpt lr lr mlcfb ds mfhsurfc mfhsurfc iy iy dts prhktdkhb prhktdkhb ifjfndts. ifjfndts.

Yfnfrfjkfs? Fhrjahrt hjc Hcdjh (9581) Mhtafmhtdks dj taf Mlcfrj Plrbc. attp?//www.ljfmhtafmhtdkhbkht. attp?//www.ljfm htafmhtdkhbkht.lr`/kht\illg.atm lr`/kht\illg.atm attps?//www.mhtasdsnuj.klm/ attps?//www.mhtalplbds.klm/qufstdljs