garbhsanksar
TRANSCRIPT
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>& _gikr MzssgkfXmjf tgblg agjstr`, _gikr Mzssgkf xgs kf mks a`tmjr‛s x`ab, mks ngtmjr,
Zstgd Gllgm Rgimg zsjd t` bjgt lkhmtl{ xktm mks nkfhjrs `f mks a`tmjr‛sgbd`ajf&
8& Brktksm ~k`lkfkst [jmzdk AjfzmkfTmj nga`zs Brktksm ~k`lkfkst [jmzdk Ajfzmkf bjlkj~js tmgt mks `xf azskcgltgljft xgs ugrtl{ dzj t` tmj ngct tmgt mks ugrjfts xjrj glxg{s skfhkfh gfd
ulg{kfh azskc bjn`rj mj xgs b`rf&
Scmjdzlj n`r urjhfgft lgd{Sg{ . d` kf tmj a`rfkfh gntjr xgikfh zu& Uzt {`zr mgfds `f {`zr bjll{ . sujgi l`zdl{& Sujgi ~ksk`f sjftjfcjs&Gntjr 3 a`ftms`n urjhfgfc{, cmkld cgf mjgr `ztskdj ~`kcjs . s`zfds&
Xgij zu jgrl{ gt > . d` Ghfkm`trg gt tkakfh hk~jf kf cmgrt& Skt tmjrj . cmgft hg{gtrk agftrg 75= tkajs -h`ldjf jnnjct+, :: tkajs, `r 27 tkajs&Xm{ t` cmgft hg{gtrk agftrg 0
7& B`d{ u`kfts grj stkazlgtjd b{ tmks agftrg& U`sktk~j ~kbrgtk`fs grj crjgtjd .kt crjgtjs g ur`tjctk~j smkjld gr`zfd a`tmjr(s . bgb{(s b`d{&
2& Ulgfts gls` hr`x ngstjr . kf kaur`~jd ngsmk`f kf urjsjfcj `n hg{gtrk agftrgcmgftkfh&
3& Gfkagls hk~j a`rj akli, xmjf tmj{ lkstjf t` hg{gtrk agftrg&
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4=
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4;
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:5
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-stghj 3+M`ldkfh tmj r`d, bzt xktm {`zr szuu`rt&D` f`t gll`x mka t` d` tmks j}jrcksj kfdjujfdjftl{&Sxkfhkfh, bzt xktm szuu`rt&
:7
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-stghj 4+C`ftkfzj sxkfhkfh n`r a`rj dzrgtk`f&Kftr`dzcj uzll!zus, brjcmkgtk`f&
-stghj :+Cmkld cgf d` brjcmkgtk`f kfdjujfdjftl{&C`ftkfzj brjcmkgtk`f n`r a`rj dzrgtk`f&
F`x hk~j mka lgrhj `bojcts . tjll mka t` zsj tmja&j&h& tjll mka ` u`zr xgtjr nr`a ogr kft` hlgssjs, uzll tmj t`u `n tmj ujf .
uzt kt bgci, sjr~j hzjsts xktm sfgci, xgtjr, tjg, jtc&Bztt`fkfh . zfbztt`fkfh bztt`fs `n c`gt, xgsmkfh ulgtjs, kfsjrtkfh ij{s kfij{m`lj . `ujfkfh d``r, xgsmkfh cl`tms, t` uzt sm`js . s`cis `f mks `xf,
ulg{kfh kf sgfd, s`l~kfh tmj uz lj, clg{ t` ulg{&
-stghj >+
Gdd ~grkgtk`fs `n brjcmkgtk`f lkij 7& sikuukfh tmj r`d& 2& Rj~jrsj brjcmkgtk`f 3& Skdjxg{s brjcmkgtk`f 4& Txkstkfh . brjcmkgtk`fRjujgt brjcmkgtk`f& Hk~j mka sckjftknkc crjgtk~j t`{s&Ijju `fj xgll sujckgll{ n`r mka t` crjgtj drgxkfhs `r xrktkfh&Hk~j mka nrjjd`a t` xrktj, tmr`x bgll, o`~jlkgf tmr`x, b`x gf grr`x&
:2
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7&
:3
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4&@ztd``r hgajs grj ~jr{ kau`rtgft&
Agtmjagtkcs -D`t cgrd tjcmfkwzj+M`x agf{ `n {`z l`~j agtmjagtkcs 0
Agf{ lgdkjs d`f‛t lkij agtms, bjgczgsj kt xgs f`t tgzhmt ur`ujrl{&Mjfcj,xm`lj jdzcgtk`f s{stja ks s`ajxmjrj xr`fh&Bjcgzsj kf tmks tmjrj ks g sjssk`f `n 35 akfztjs `n sckjfcj, agtms, Jfhlksm,
jtc&Gntjr s`ajtkaj, xj hjt b`rjd . rjstljss&Tmjrj grj tx` t{ujs `n aja`rkjs
7& Sm`rt tjra aja`r{2& L`fh tjra aja`r{
7& Sm`rt tjra aja`r{ ? @zr czrrjft jdzcgtk`f s{stja ks bgsjd `f sm`rt tjra aja`r{&Ajgfs xmgtj~jr ks tgzhmt, {`z rjajabjr kt gt tmgt a`ajft . gntjr s`ajtkaj {`z n`rhjt&
j&h& c`auztjr t{ukfh – lkhmt h`fj! aja`r{ h`fj! d`czajft ~gfksmjd&
2& L`fh tjra aja`r{ ? Rj~ksj tmj agtjrkgl `fcj rjgd& Tmjf kt hjt st`rjd kf tmj szbc`fsck`zsakfd gzt`agtkcgll{& Tmr`zhmt`zt lknj, xj c`zld f`t n`rhjt kt& J&h& fzrsjr{ rm{ajs, `r u`jas&T` kaur`~j tmks a`a`r{, d` ajdktgtk`f . cmgftkfh&j&h& c`auztjr t{ukfh – lkhmt h`fj!bzt sg~jd ! aja`r{ bgcizu! d`czajft ur`tjctjd&
^kf`bg bmg~j a`ftjssgr{ trgkfkfh tjcmfkwzjs&Agtms ks kf~`l~jd kf j~jr{ stju `n lknj&j&h& xmjf z c``i rkcj . c`zft m`x agf{ ujrs`f x`zld kt 0, xmjf z c`zft cl`tms
bjn`rj hk~kfh t` dm`bk0J~jr{ akfztj `n lknj rjwzkrjs agtms& Xmjf {`z agij rjlgtk`f xktm rjglkt{, cmkldljgrfs ngst& Tmks ks cglljd nzfxg{ ljgrfkfh ajtm`d&Ljts ulg{ nlgsm cgrd `r jfc{cl`ujdkg bjgts,jtcCmkld xkll glxg{s bj kftjrjstjd . xkll rjlgtj j~jr{tmkfh xktm tmj ngct `r rjglkt{&Xmklj tjgcmkfh cmkld, stgrt nr`a glrjgd{ if`xf tmkfh . jfd zu t` zfif`xf tmkfh&J&h& Gb`zt Gzt`bgfs mkhmxg{ kf Hjragf &1 r`gd fj}t t` `zr c`l`f{, agkf r`gd,mkhmxg{, fgtk`fgl mkhmxg{, kftjrfgtk`fgl mkhmxg{,jtc&J&h& Gb`zt sjg, 1 tgu xgtjr, u`fd xgtjr, rk~jr xgtjr, sjg xgtjr Ljgrfkfh ks c`abkfgtk`f `n lkstjfkfh, sujgikfh , rjgdkfh . xrktkfh& Tmzs, tmjrjujgtgtk`f mg~j t` mguujf& T`fkfh ks ~jr{ kau`rtgft& -mkhm!l`x uktcm kf ~`kcj+Xm{ sm`zld xj tjgcm agtms0Kt ks mkhmjst nzfctk`f `n tmj brgkf . kt stkazlgtjs tmj brgkf ag}kaza&M`x t` tjgcm agtms ks b{ d`t cgrd tjgcmfkwzj&Sxgak ~k~jigfgfd mgd um`t` aja`r{& Tmj{ ozst rjwzkrj g a`ajft t` rjgd g ughj `n
b``i& Smjumjrds mg~j um`t` aja`r{ t``& Smjumjrds c`zft tmjkr smjjus t`` ngst&Tmj{ ozst rjwzkrj `fj a`ajft t` c`zft tmja&
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Tmjrj grj > stjus ?_jr` stju ?Dzrgtk`f ? 5 t` 3 a`ftmsCgrd sk j – G4 sk jD`t sk j ± kfcm kf dkgajtjr C`l`zr – rjd
T`tgl !2= cgrds
Ajtm`d `n sm`xkfh ks sgaj gs tmgt `n jr` stju `n nlgsm cgrd tjcmfkwzj&
xjjis Fzabjrs t`tgl f`&7
2 -rj~ksj+ 7 t` 8 83-rj~ksj+
4:-rj~ksj+ = t` 74 8>-rj~ksj+
8=-rj~ksj+ 7: t` 27 8;-rj~ksj+
7577-rj~ksj+ 22 t` 2= 872-rj~ksj+
T`tgl 72 xjjis 1 3 a`ftms T`tgl 2= x`rds
Sm`x tmj cgrd 75 tkajs g dg{, jgcm tkaj 75!72 sjc`fds&
Stju 7 1 Wzgftkt{ rjc`hfktk`f
Dzrgtk`f – 4 t` : ± a`ftms - 2± a`ftms+
Cgrd sk j – G4 sk jD`t sk j ¶ kfcm kf dkgajtjr C`l`zr – rjdT`tgl !757 cgrds -5 t` 755+Agij : hr`zus `n 25! 25 cgrds
7& 5 t̀ 25 1 27cgrds2& 27 t` 451 25 cgrds3& 47 t` >5 1 25 cgrds4& >7 t `=5 1 25 cgrds
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:& =7 t` 755 1 25 cgrdsSm`x j~jr{ hr`zu tmrkcj n`r 2 xjjis&
Sm`x : hr`zus lkijxksj n`r : ± a`ftms&
25 cgrds sm`zld rjwzkrj 25!2: sjc&
Stju 2 1 jwzgtk`f
Dzrgtk`f – : ± t` = a`ftms - 2± a`ftms+Sm`x ; jwzgtk`fs ujr dg{, A`rfkfh -3+, gntjrf``f -3+ . j~jfkfh -3+
A`rfkfh Gntjrf``f J~jfkfh7 ) 2 1 3 4 ) 4 1 = 8 ) 2 1 ;2 ) 2 1 4 : ) 3 1 = 3 ) 2 1 :3 ) 4 1 8 7 ) 4 1 : = ) 4 1 72
Sm`x ; jwzgtk`fs ujr dg{, n`r 2 xjjis&J~jr{tkaj jwzgtk`f sm`zld bj fjx& -72> t`tgll{ fjxjwzgtk`fs+& 74 dg{s ] ; jwzgtk`fs 172> jwzgtk`fs&
D`f(t kftr`dzcj s{ab`ls& Xmklj sm`xkfh jwzgtk`f, xmklj ur`f`zfckfh s{ab`l,tmjrj sm`zld f`t bj gf{ d`t cgrd kf nr`ft `n cmkld& Blgfi Sgaj xg{, tjgcm szbstrgctk`f -2 xjjis+, azltkulkcgtk`f -2xjjis+, dk~ksk`f -2xjjis+, gll ak}-2 xjjis+J&h& `n ak} 1 `rdjr `n ak} jwzgtk`f sm`zld bj Dk~ksk`f, azltkulkcgtk`f,szbstrgctk`f . gddktk`f&
A`rfkfh Gntjrf``f J~jfkfh75 / 2 ] = ! 35 ) 4 174 74 / 2 ] 4 ! 72 ) : 1 27 7> / 4 ] = ! 24 ) 78 1 2:= / 4 ] 2 ! 3 ) > 1 8 72 / > ] : !7: ) = 1 23 7= / 2 ] 4 ! 7: ) 77 1 32> / 3 ] = ! 75 ) 75 1 7> 7: / : ] ; ! = ) > 1 25 25 / : ] 3 ! = ) ; 1 73
Sm`x ; jwzgtk`fs ujr dg{, n`r 2 xjjis&J~jr{tkaj jwzgtk`f sm`zld bj fjx& -72> t`tgll{ fjxjwzgtk`fs+& 74 dg{s ] ; jwzgtk`fs 172> jwzgtk`fs&
Stju 3 1 Ur`blja s`l~kfh
Dzrgtk`f – = t` = ± a`ftms -7: dg{s+
:>
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