Balances Metalurgicos

 

TLG_DR]GJ@J L@MGFL@K JD NT@LM@_DKGM@ NT@LM@_DKGM@ O`mukt`j jd Glidlgdrè` jd Hgl`s Mgvgk @hbgdlt`k Dsmudk` Srfodsgfl`k jd Glidlgdrè` jd Hgl`s

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]DJ@LF Z@WSD, H`ludk @.

 

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Jfmdltd

Jr. DLRGPTDQ JFL@GJRD], @h`jdf ]dhdstrd1

 

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Nu`lm`vdkgm` - Sdrñ 2307

 

H@LTDK @RM@LIDK ]DJ@LF Z

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H@LTDK @RM@LIDK ]DJ@LF Z

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B@K@LMD HDZ@KÑIGMF B@K@LMD JD H@ZDRG@K W HDZ@KÑRIGMF DL MGRMTGZF] JD OKFZ@MGÝL Dk tçrhglf ‛b`k`lmd‘ dl Srfmds`hgdltf jd Hgldr`kds dlikfb` tfjfs kfs màkmukfs hdt`kñ hdt `kñrig rigmfs mfs qud sd dodmtñ dodmtñ`l `l dl ul` Sk`lt` Sk`lt` Mfl Mflmdl mdltr` tr`jfr jfr`, `, p`r p`r` ` dv` dv`ku` ku`r  r  tçmlgm` y dmflýhgm`hdltd dk prfmdsf jd mflmdltr`mgýl pfr okft`mgýl dl dstd m`sf. Dl ul` Sk`lt` Mflmdltr`jfr` idldr`khdltd sd dodmtñ`l jfs tgpfs jd b`k`lmds, ` s`bdr10. B`k`lmd hdt`kñrigmf f mflt`bgkgj`j hdt`kñrigm`.2. B`k`lmd jd h`tdrg`kds (sýkgjfs, `iu`, dkdhdltf, dtm.).   B@K@LMD HDZ@KÑRIGMF. Dk b`k`lmd hdt`kñrigmf f mflt`bgkgj`j hdt`kñrigm` sd dodmtñ` dl ul` Sk`lt` Mflmdltr`jfr` p`r` jdtdrhgl`r k` prfjummgýl jg`rg`, k` dogm`mg` f rdmupdr`mgýl fbtdlgj`, k` m`kgj`j jd kfs mflmdltr`jfs, dtm. Idldr`khdltd sd dhpkd` jfs hçtfjfs prglmgp`kds jd mflt`bgkgj`j hdt`kñrigm`1 -

Dk ]gstd gstdh` h` rd rdtr trfs fspd pdmt mtgv gvd. d. Dk ssgst gstdh` dh` glspdm glspdmmgý mgýl l dltr dltr`j` `j`/gl /glspd spdmm mmgýl gýl s`kgj` s`kgj`..

Jd ul` u ftr` h`ldr`, dstfs jfs hfjfs jd b`k`lmd, dl okft`mgýl jd hgldr`kds, `k giu`k qud mu`kqugdr ftrf prfmdsf jd mflmdltr`mgýl, k` mu`ltgogm`mgýl sd pudjd dodmtu`r ` tr`vçs jd jfs dxprdsgflds h`tdhàtgm`s qud sd k`s jdlfhgl` R`zýl jd Mflmdltr`mgýl y Rdmupdr`mgýl.   R@QÝL JD MFLMDLZR@MGÝL (E). Dstd tç Dstd tçrh rhgl glf f gljg gljgrd rdmt mt`h `hdl dltd td sd rd rdogogdr drd d ` k` sdkd sdkdmt mtgv gvgj gj`j `j jd jdkk prfm prfmds dsf. f. Jgrdmt`hdltd dxprds` muàlt`s tfldk`j`s jd hgldr`k jd m`bdz` sd ldmdsgt`l prfm prfmds ds`r `r dl k` Sk`l Sk`lt` t` Mflm Mflmdl dltr tr`j `jfr fr` ` p` p`r` r` fb fbtd tdld ldrr ul ul` ` tfld tfldk` k`j` j` jd mflmdltr`jf. Dl mflsdmudlmg`, dst` r`zýl ds ul lñhdrf qud gljgm` muàlt`s vdmds sd mflmdltrý dk hgldr`k v`kgfsf mfltdlgjf dl k` hdl`. Dstd  Dstd  tçrhglf sd pudjd jdjumgr jdk sgiugdltd hfjf1 ]d` dk dsqudh` jd ul` Sk`lt` Mflmdltr`jfr`  @nfr` n`i`hfs ul b`k`lmd jd h`tdrg`kds h`tdrg`kds y jd hdt`k v`kgfsf mfltdlgjf dl m`j`

okuaf jd k` Sk`lt` Mflmdltr`jfr`. Dstf ds1 B`k`lmd jd h`tdrg`k1 O 8 M+Z …………… (9.0) B`k`lmd jd hdt`k1 Oo 8 Mm +Zt …………… (9.2)

H@LTDK @RM@LIDK ]DJ@LF Z

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Huktgpkgm`ljf k` dmu`mgýl (9.0) pfr t y rdst`ljf jd k` dmu`mgýl (9.2) sd fbtgdld kf sgiugdltd1 Ot 8 Mt+Zt O (o -t) 8 M (m-t) Jd jfljd sd fbtgdld k` r`zýl jd mflmdltr`mgýl, ds jdmgr1 E 8 O/M 8 (m-t) / (o-t) RDMTSDR@MGÝL Dstd tçrhglf sd rdogdrd ` k` dogmgdlmg` y rdljghgdltf jdk prfmdsf jd okft`mgýl. Ds jdmgr, ds k` p`rtd jd hgldr`k v`kgfsf qud sd fbtgdld dl dk mflmdltr`jf, mfl rdspdmtf jdk hgldr`k v`kgfsf mfltdlgjf dl dk hgldr`k jd m`bdz`. ]d dxprds` dl pfrmdlt`ad y su dxprdsgýl h`tdhàtgm` ds1 R8 Mm/Oo x 033 ]g sd sustgtuyd dl k` oýrhuk` (9.:) dk v`kfr jd M/O dl oulmgýl jd k`s kdyds, sd fbtgdld1 R 8 (o-t) / (m-t) x m/o x 033 ……………. (9.4) K` dxprdsgýl (9.4) sgrvd p`r` kfs màkmukfs mu`ljf n`y ul sfkf dkdhdltf v`kgfsf, mfhf sd vdrà ul` jdjummgýl hàs mfhpkdt` dl `jdk`ltd. Mu`ljf n`y hàs jd ul dkdhdltf v`kgfsf, dk sgstdh` jd màkmukf sd mfhpkgm`, pdrf sd h`ltgdld k` hgsh` ogkfsfoè` jd màkmukf jd k`s dxprdsgflds `ltds jdtdrhgl`j`s. Dstd sgstdh` jd màkmukf sd hudstr` hàs `jdk`ltd.

]G]ZDH@ RDZRF]SDMZG_F Dl ds dstd td sg sgst stdh dh` ` sd `s `suh uhd d qud qud k` rd rdmu mupd pdr` r`mg mgýl ýl tdýr tdýrgm gm` ` ds mf mfrr rrdm dmt` t` y k` prfjummgýl jd mflmdltr`jfs sd m`kmuk` ` p`rtgr jdk hgldr`k qud dltr` ` k` Sk`lt` Mflmdltr`jfr` y jd kfs dls`yfs quèhgmfs jd k` `kghdlt`mgýl, mflmdltr`jf(s) y rdk`vd. Dl dstd sgstdh` lf n`y glspdmmgýl sfbrd k` rdmupdr`mgýl rd`k qud sd fbtgdld. Jd `mudrjf ` k` sghpkgmgj`j f mfhpkdagj`j jd k`s hgsh`s, ds jdmgr, jd `mudrjf `k lñhdrf jd dkdhdltfs v`kgfsfs qud mfltgdld sdrà1

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Jd jfs prfjumtfs ul dkdhdltf v`kgfsf.

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Jd trds prfjumtfs jfs dkdhdltfs v`kgfsfs.

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Jd mu`trf prfjumtfs trds dkdhdltfs v`kgfsfs.

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Jd ‛l‘ prfjumtfs hàs jd trds dkdhdltfs v`kgfsfs.

  H@LTDK @RM@LIDK ]DJ@LF Z

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@) B@K@LMD HDZ@KÑRIGMF JD JF] SRFJTMZF]1 ]d dhpkd` mu`ljf k` hdl` qud tr`t` ul` pk`lt` mflmdltr`jfr` mfltgdld ul sfkf sf kf dkdh dkdhdl dltf tf v`kg v`kgfs fsf f pr prgl glmg mgp` p`k,k, pf pfrr mfl mfl sg sgiu iugd gdlt ltd d sf sfkf kf sd prfj prfjum umgr grà à ul mflmdltr`jf y ul rdk`vd. Kfs dls`yfs quèhgmfs ldmds`rgfs sdràl jdk `kghdltf, jdk mflmdltr`jf ogl`k y jdk rdk`vd ogl`k. S`r` dk dst`bkdmghgdltf jd k` oýrhuk` sd p`rtgrà jdk sgiugdltd dsqudh`1

 @què pfjdhfs fbsdrv`r fbsdrv`r qud kfs pultfs jd jd hudstrdf sfl1 0. M`bdz` qud mfrrdspfljd `k hgldr`k jd o`a` qud `kghdlt` jd k` tfkv` jd oglfs `k hfkglf, f jdk rdbfsd r dbfsd jdk mk`sgogm`jfr. 2. Mflmdltr`jf. =. Rdk`vd. ]d dst`bkdmdl k`s sgiugdltds rdk`mgflds1 B`k`lmd jd h`tdrg`kds Dltr`j` 8 ]`kgj`O 8 M + Z …………. (9.?) B`k`lmd jdk hdt`k v`kgfsf O.o 8 M.m + Z.t ………………………… (9.9) ( 9.9) Huktgpkgm`ljf k` dmu`mgýl (0) pfr t sd fbtgdld1 O.t 8 M.t + Z.t ………………………… (9.>) Rdst`ljf 9.> jd 9.9 sd tdljrà1 O (o - t) 8 M(m - t) M/O 8 (o - t) / (m ” t)

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8 O x {(o - t) / (m-t)} ……... (9.7)

Dltflm Dltf lmds ds dk p` p`sf sf jd mflm mflmdl dltr tr`j `jf f fb fbtd tdlg lgjf jf dst` dst`rà rà j` j`jf jf pfr pfr k` sg sgiu iugd gdlt ltd d oýrhuk`1 M 8 O x {(o - t) / (m-t)} t/jè` f tfl/jè` ……………… (9.03)

H@LTDK @RM@LIDK ]DJ@LF Z

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K` rdmupdr`mgýl fbtdlgj` jd hdt`k v`kgfsf dst`rà j`j pfr1 Rd 8 (Mm / Ot) x 033 …………………………… (9.00) Rd 8 {(o - t) / (m ” t)} x m/o x033 ………………... (9.02) K` r`zýl jd mflmdltr`mgýl dstà j`j` pfr1 E 8 O / M 8 (m-t) / (o-t) …………………………. (9.0=)

B) B@K@LMD HDZ@KÑRIGMF S@R@ ZRD] SRFJTMZF] Dstd b` Dstd b`k` k`lm lmd d sd dhpk dhpkd` d` mu mu`l `ljf jf k` hdl` hdl` qu qud d sd tr`t tr`t` ` dl ul ul` ` pk pk`l `lt` t` mflmd mf lmdltr ltr`jf `jfr` r` mfltgd mfltgdld ld jfs dkd dkdhdl hdltfs tfs hdt hdtàkg àkgmf mfss v`k v`kgfs gfsfs fs y sd dhpkd` dhpkd` k` okft`mgýl sdkdmtgv` f jgodrdlmg`k, ds jdmgr, sd fbtgdld jfs prfjumtfs v`kgfsfs qud mfrrdspfljdl ` jfs mflmdltr`jfs qud mfltgdldl ` m`j` hdt`k v`kgfsf y ul prfjumtf lf v`kgfsf qud mfrrdspfljd `k rdk`vd.  @pkgm`ljf dk prglmgpgf jd mflmdltr`mgýl jd k` h`tdrg`, sd dodmtñ` dk b`k`lmd jd h`tdrg`kds, jd `mudrjf `k sitd. Jg`ir`h`.

Zfldk`ad jd dltr`j` 8 Zfldk`ad jd s`kgj` O 8 @ + B + Z ……………. (9.0:) B`k`lmd jdk hdt`k v`kgfsf @. O` 8 @`0 + B`2 + Z`= …. (9.04) B`k`lmd jdk hdt`k v`kgfsf B Ob 8 @b0 + Bb2 + Zb= …. (9.0?) Dl mflsdmudlmg`, tdldhfs ul sgstdh` jd trds dmu`mgflds mfl trds glmýilgt`s. Jgvgjgdljf k`s trds dmu`mgflds dltrd O sd fbtgdld1 0 8 @/O + B/O + Z/O …. (9.09) ` 8 `0 (@/O) + `2 (B/O) + `= (Z/O) ….. (9.0>) H@LTDK @RM@LIDK ]DJ@LF Z

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b 8 b0(@/O) + b2(B/O) + b=(Z/O) ……. (9.07) Dl dstd sgstdh` kfs v`kfrds mflfmgjfs sfl O, `, `0, `2, `=, b, b0, b2 y b= qud dstà ds tàl l j`jf j`jfss pf pfrr dk `kgh `kghdl dltf tf y pr prfj fjum umtf tfss jd k` Sk Sk`l `lt` t` mf mflm lmdl dltr tr`j `jfr fr` ` y mflsgil`jfs dl dk rdpfrtd jd dls`yf quèhgmf. Dstf ds1 Srfjumtfs   M`bdz`

Sdsfs, t O

Kdyds %@ %B %@ ` b

Mflm. @ Mflm. B Rdk`vd

@ B Z

`0 `2 `=

b0 b2 b=

]g n`mdhfs ul m`hbgf jd v`rg`bkd dl k`s dmu`mgflds (9.09), (9.0>) y (9.07) tdljrdhfs1 o0 8 @/O 5 o2 8 B/O 5 o= 8 Z/O Kudif1 0 + o2 o=……………… (9.23) `8 8 o0 `0o0 ++ `2o2 + `=o= ……. (9.20) b 8 b0o0 + b2o2 + b=o= ……. (9.22) dstd sgstdh` sd pudjd rdsfkvdr pfr dk hçtfjf jd jdtdrhgl`ltds y pfr dk hçtfjf h`trgmg`k f t`hbgçl `kidbr`gm`hdltd.

M) B@K@LMD HDZ@KÑRIGMF S@R@ MT@ZRF SRFJTMZF] Dstd b`k` Dstd k`l lmd sd ut utgkgkgz gz` ` mu mu` `ljf k` hdl` dl` qud sd tr`t tr`t` ` dl ul` pk pk`l `lt` t` mflmd mf lmdltr ltr`jf `jfr` r` mfltgd mfltgdld ld trd trdss dkdhdl dkdhdltfs tfs hdt hdtàkg àkgmfs mfs v`kgfs v`kgfsfs fs y sd dhpkd` dhpkd` k` okft`mgýl sdkdmtgv` f jgodrdlmg`k, ds jdmgr, sd fbtgdld trds prfjumtfs v`kgfsfs qud mfrrdspflj` ` kfs mflmdltr`jfs qud mfltgdldl ` m`j` hdt`k v`kgfsf y ul prfjumtf lf v`kgfsf qud mfrrdspfljd `k rdk`vd. Mfhf dl dk m`sf `ltdrgfr, `pkgm`ljf dk prglmgpgf jd k` mflsdrv`mgýl jd k` h`tdrg`, sd dodmtñ` dk b`k`lmd jd h`tdrg`kds, jd `mudrjf `k sgiugdltd jg`ir`h`1  

ZFLDK@AD JD DLZR@J@ 8 ZFLDK@AD JD ]@KGJ@ H@LTDK @RM@LIDK ]DJ@LF Z

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HGLDR@K M@BDQ@ 8 Mflm. @ + Mflm. B + Mflm. M + Rdk`vd O 8 ^ + W + Q + Z ……. (9.2=) B`k`lmd jdk hdt`k v`kgfsf @. O` 8 ^`0 + W`2 + Q`= + Z`: …… (9.2:) B`k`lmd jdk hdt`k v`kgfsf B. Ob 8 ^b0 ^b0 + Wb2 + Qb= + Zb: …. (9.24) B`k`lmd jdk hdt`k v`kgfsf M. Om 8 ^m0 + Wm2 + Qm= + Zm: …… (9.2?) Jgvgjgdljf m`j` dmu`mgýl dltrd O tdldhfs 0 8 ^/O + W/O + Q/O + Z/O ` 8 `0(^/O) + `2(W/O) + `=(Q/O) + `:(Z/O) b b0(^/O) ++ m2(W/O) b2(W/O) ++ m=(Q/O) b=(Q/O) ++ m:(Z/O) b:(Z/O) m 88 m0(^/O) N`mgdljf ul m`hbgf jd v`rg`bkd tdldhfs o0 8 ^/O 5 o2 8 W/O 5 o= 8 Q/O 5 o: 8 Z/O Dk sgstdh` `ltdrgfr sd mflvgdrtd dl1 o0 + o2 + o= + o: 8 0 ……………… (9.29) `0o0 + `2o2 + `=o= + `:o: 8 ` ….. (9.2>) b0o0 + b2o2 + b=o= +b:o: 8 b …… (9.27) m0o0 + m2o2 + m=o= + m:o: 8 m ……(9.=3) Dl dstd sgstdh`, kfs j`tfs mflfmgjfs sfl dk tfldk`ad jd `kghdltf `k mgrmugtf jd okft`mgýl y k`s kdyds jd kfs dkdhdltfs hdtàkgmfs qud dstàl dl kfs mflmdltr`jfs y qud sd fbtgdldl jdk rdpfrtd jd dls`yf quèhgmf.

Srfjumtfs   M`bdz` Mflm. @ Mflm. B Mflm. M Rdk`vd

Kdyds %@ %@ ` `0 `2 `= `:

%B b b0 b2 b= b:

%M m m0 m2 m= m:

]G]ZDH@ JD GL]SDMMGÝL JD DLZR@J@/GL]SDMMGÝL DLZR@J@/GL]SDMMGÝL ]@KGJ@ H@LTDK @RM@LIDK ]DJ@LF Z

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Dstd ds sgl juj` dk hçtfjf hàs s`tgso`mtfrgf p`r` mflt`bgkgz`r k` prfjummgýl dl ul` pk`lt` mflmdltr`jfr`, y sg dstd sgstdh` sd `pkgm`, k` dltr`j` jd hgldr`k ` k` pk`lt` sd pds` mfl ul `ktf ir`jf jd dx`mtgtuj y sd dls`y` jg`rg`hdltd k` dltr`j` y kfs prfjumtfs jd s`kgj`, jd hfjf qud, hdlsu`khdltd sd mflfmdl dx`mt`hdltd kfs pdsfs y dls`yfs jd m`bdz` y mflmdltr`jf.  @sè ds pfsgbkd fbtdldr k`s rdmupdr`mgflds tdýrgm`s y rd`kds jd pk`lt` mflmdltr`jfr`, qud mflmudrj`l n`st` n`st` 3.4 ` 0% dl ul pdrgfjf jd = hdsds Dl k` t`buk`mgýl jdk b`k`lmd jd h`s` sd h`lgogdst` k` rdmupdr`mgýl rd`k y mu`kqugdr jgsmrdp`lmg` dl dk pdsf jdk hdt`k sd mflsgjdr` mfhf ul` pçrjgj` lf mflt`bgkgz`j`, ds jdmgr, sd `suhd qud kfs pdsfs jdk h`tdrg`k sfl tft`khdltd dx`mtfs y mu`kqugdr pçrjgj` sd gltrfjumd sfk`hdltd pfr hudstrdf f dls`yf. Kýigm`hdltd k`s pçrjgj`s oèsgm`s jd h`tdrg`k v`kgfsf sd prdsdlt`l sfk`hdltd dl k` pk`lt`, jdbgjf ` oui`s jd pukp` dl k`s bfhb`s, jdrr`hd dl k`s m`l`kdt`s jd k`s mdkj`s, `tfrf jd k`s tubdrè`s jdrr`hd dl kfs t`lquds jd `kh`mdl`hgdltf tdhpfr`k, dtm., qud jdsjd kudif jdbd tr`t`r sgdhprd jd h`ltdldrk`s t`l b`a`s mfhf mf hf sd sd` ` pfsg pfsgbk bkd. d. S`r` S`r` sf sfku kumg mgfl fl`r `r ds dstd td prfb prfbkd kdh` h`,, sd jd jdbd bd jg jgrg rgig igrr ds dstf tfss jdrr`hds n`mg` ul mfkdmtfr, jdk mu`k pfr bfhbdf sd rdtfrl` r dtfrl` `k prfmdsf. Tl b`k`lmd rdprdsdlt`tgvf p`r` ul` pk`lt` mflmdltr`jfr` qud prfjumd ul mflmdltr`jf jd pkfhf, sd hudstr` dl dk sgiugdltd mu`jrf1  

Dl dstd mu`jrf kfs pdsfs y kfs dls`yfs sd hgjgdrfl mfl dx`mtgtuj. Dl mflsdmudlmg`, k` rdmupdr`mgýl rd`k p`r` dstd sgstdh` ds jdk 73.7:% y k` rdmupdr`mgýl tdýrgm` sdrà dltflmds1 Rt 8 Rr + Sr 8 73.9: + 0.39 8 70.>0% B@K@LMD JD H@ZDRG@KD] Mfhf ndhfs jgmnf `ltdrgfrhdltd, ul `spdmtf ghpfrt`ltd jd tfjf dstujgf jd prfmds`hgdltf jd hgldr`kds ds ul `làkgsgs jd k` ofrh` dl qud dstà jgstrgbugjf dk h`tdrg`k dl kfs pultfs dl qud sd jgvgjdl f sd mfhbgl` kfs okuafs jdltrf jdk mgrmug mgr mugtf. tf. Ds pf pfrr mflsgi mflsgiugd ugdltd ltd ldm ldmds` ds`rgf rgf mfl mflfm fmdr dr dst dstd d `s `spdm pdmtf tf p`r p`r` ` jgs jgsdð` dð`r  r  `jdmu`j`hdltd ul jg`ir`h` jd prfmdsf y ds t`hbgçl dsdlmg`k p`r` n`mdr  dstujgfs jd dv`ku`mgýl y fptghgz`mgýl jd pk`lt`s dl fpdr`mgýl. Dst` sdrgd jd H@LTDK @RM@LIDK ]DJ@LF Z

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màkmukfs qud sd rd`kgz`l sd mflfmdl mfhf ‛B`k`lmd jd h`tdrg`kds‘, dk mu`k sd b`s` dl dk prglmgpgf jd k` mflsdrv`mgýl jd k` h`tdrg`. Dl idldr`k1 DLZR@J@ ” ]@KGJ@ 8 @MTHTK@MGÝL

Sdrf dl dk m`sf jd pk`lt`s mflmdltr`jfr`s dk sgstdh` ds mfltgluf y dl kf pfsgbkd sd h`ltgdld dl dst`jf dst`mgfl`rgf f dst`bkd, pfr kf t`ltf lf n`y `muhuk`mgýl. Kudif k` rdk`mgýl sd mflvgdrtd dl1  

DLZR@J@ 8 ]@KGJ@

K` rdk`mgýl `ltdrgfr ds huy sghpkd, pdrf mu`ljf sd tr`t` jd dv`ku`r tfj`s k`s fpdr`mgflds pfr k`s qud p`s` dk hgldr`k n`st` sdp`r`rsd dl ulf f v`rgfs prfjumtfs v`kgfsfs y lf v`kgfsfs, dstd prglmgpgf sd `pkgm` dl k` hgsh` ofrh` dl m`j` pultf dl mudstgýl qud sd dv`kñd jdltrf jd k` pk`lt`, ds jdmgr, sd dltr` dl jdt`kkd jdk prfmdsf dl sg. Dstd Ds td tr`b tr`b` `af sd do dodm dmtñ tñ` ` pfr kf hdl hdlfs ul` vdz vdz `k hd hdss, p`r` `r` dv dv` `ku ku`r  `r  mflvdlgdltdhdltd kfs mgrmugtfs jd tfj` k` pk`lt`, pfr dkdhdltfs dl ofrh` jdt` jd t`kkkk`j `j`, `, ds jd jdmg mgr, r, trgtu trgtur` r`mg mgýl ýl ” mr mrgb gb`j `jf, f, hf hfkgkgdl dlj` j` prgh prgh`r `rg` g`,, hf hfkgd kgdlj lj` ` sdmu sd mulj lj`r `rg` g` ” mk`s mk`sgogogm gm`m `mgý gýl, l, okft okft`m `mgý gýl l jd jdsb jdsb`s `std td (rfu (rfuin indr dr), ), okft okft`m `mgý gýl l jd rdmupdr`mgýl (sm`vdlidr) y okft`mgýl jd kghpgdz` (mkd`ldr), dspds`hgdltf jd mflmdltr`jfs jd rdk`vds, ogktr`jfs jd mflmdltr`jfs, sdm`jf jd mflmdltr`jfs y jdpfsgmgýl jd rdk`vds. Dk fbadtgvf ds mflst`t`r sg dl dstd gltdrv`kf sd n`l prfjumgjf `lfh`kè`s dl k`s m`ri`s mgrmuk`ltds y dogmgdlmg`s p`rmg`kds jd dxtr`mmgýl jd kfs hdt`kds v`kgfsfs u ftr`s pdrturb`mgflds jdk prfmdsf qud pujgdrfl `odmt`r k` dogmgdlmg` ikfb`k jd k` pk`lt` mflmdltr`jfr` y qud sd`l `trgbugbkds, pfr dadhpkf, ` jdsi`stds jd dqugpf, okumtu`mgflds dl k` kdy jdk hgldr`k, v`rg`mgflds dl k`s prfpgdj`jds oèsg oèsgm` m`ss jd jdkk hg hgld ldr` r`k,k, tgpf tgpf jd hgld hgldr` r`kgz kgz`m `mgý gýl l (t`h (t`h`ð `ðf f jd ir`l ir`lf f jd jdkk hg hgld ldr` r`kk prdmgfsf) ir`jf jd jdir`j`mgýl f `kiul` ftr` m`us` mfltrfk`bkd.  @kiul`s vdmds ds ldmds`rgf dst`bkdmdr ul` rdodrdlmg` mflfmgj` mfhf b`sd, kf mu`k mflsgjdr` `rbgtr`rg`hdltd mfhf oga` y tfjfs kfs jdhàs j`tfs sfl rdk`tgvfs ` dst` b`sd. Dst` b`sd pudjd sdr ul vfkuhdl, ul` h`s`, ul pdrgfjf jd tgdhpf f ul rçighdl jd okuaf f m`uj`k. Sfr t`ltf, k` dkdmmgýl jd ul` b`sd `jdmu`j` sd vd mf`jyuv`j` pfr k` dxpdrgdlmg` jdk glidlgdrf hdt`kurigst`, pdrf p`r` j`r  h`yfrds kumds ` kfs prfodsgfl`kds lf dxpdrghdlt`jfs, `k n`mdrsd k` sdkdmmgýl jdbd mflsgjdr`rsd kfs sgiugdltd1 -

¶J ¶Jd dq quç uç glo glofr frh` h`mg mgýl ýl sd jg jgsp spfl fld6 d6

-

¶P ¶Puç uç glofrh glofrh`mg `mgýl ýl sd dst dstà à tr`t`l tr`t`ljf jf jd fbt fbtdld dldr6 r6 H@LTDK @RM@LIDK ]DJ@LF Z

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- ¶Mu ¶Muàk àk ds k` b`s b`sd dj jd d màkm màkmukf ukf hàs mflvd mflvdlgd lgdltd ltd6 6 Kudif p`r` dodmtu`r k` dv`ku`mgýl jd k` pk`lt` mflmdltr`jfr`, sd prfmdjdrà ` tfh`r hudstr`s jd kfs pultfs jdk mgrmugtf dl mudstgýl prdodrgbkdhdltd jur`ltd ul tgdhpf jd 2: nfr`s mfl glmrdhdltfs jd m`j` nfr` f jd m`j` hdjg` nfr`.   Dk tgdhpf rdqudrgjf p`r` dodmtu`r tfjfs kfs màkmukfs pdrtgldltds ds b`st`ltd, pfr kf qud ds mflvdlgdltd dk`bfr`r ul prfir`h` `jdmu`jf hdjg`ltd hfjdkfs h`tdhàtgmfs sdlmgkkfs, p`r` fbtdldr k` glofrh`mgýl dl ul tgdhpf hèlghf, jd hfjf qud pudj` sdrvgr p`r` dodmtu`r kfs mfrrdmtgvfs pdrtgldltds.  @kiulfs hdt`kurigst`s gljgm`l qud ds hàs mflvdlgdltd ul hudstrdf jd fmnf jè`s, ndmnf qud lf ds rdout`bkd, pdrf p`r` qugdlds, dl `mtgvgj`j dl ul` pk`lt` mflmdltr`jfr`, qud dstf lf ds t`l mflog`bkd, pudstf qud tfjfs kfs jè`s lf sd pudj pu djd d h` h`lt ltdl dldr dr gi giu` u`kd kdss k` k`ss mflj mfljgm gmgf gfld ldss jd fp fpdr dr`m `mgý gýl, l, pf pfrr ul ul` ` sd sdrgd rgd jd prfbkdh`s fpdr`mgfl`kds qud grrdhdjg`bkdhdltd sd sudkdl prfjumgr.

SRFBKDH@ Dl ul` pk`lt` mflmdltr`jfr` qud tr`t` ` ul` hdl` jd mfbrd, sd n` hudstrd`jf dk mgrmugtf jd okft`mgýl qud sd hudstr` dl k` ogiur`, n`bgçljfsd fbtdlgjf kfs sgiugdltds rdsukt`jfs, O 8 :>33 t/jè` STLZF 0 2 = : 4 ? 9 >

% MFBRD 2.33 2.04 =.>4 0:.33 0.30 =.33 24.33 3.>:

jd

H@LTDK @RM@LIDK ]DJ@LF Z

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]d pgjd kf sgiugdltd1 @) Dk b`k`l b`k`lmd md jd jd h`tdrg h`tdrg`kds. `kds. B) Dk b b`k`l `k`lmd md hdt`kñ hdt`kñrigmf rigmf tft`k. tft`k. M) Dk b`k`lmd hdt`kñrigmf jd jd m`j` dt`p` jdk mgrmugtf jd okft`mgýl. ]FKTMGÝL1 @) Tl Tl`` ofrh ofrh`` jd rdsf rdsfkv kvdr dr sd sdrè rè`` ut utgk gkgz gz`l `ljf jf dk mf mflm lmdp dptf tf jd o`mt o`mtfr fr jd jgstrgbumgýl.

H@LTDK @RM@LIDK ]DJ@LF Z

0 =

 

Màkmukf jd kfs o`mtfrds jd jgstrgbumgýl dl oulmgýl jdk jg`ir`h` `ltdrgfr1 ]O0 8 (2.04 - 0.30) / (0: ” 0.30) 8 3.3>99?3 ]O2 8 (0: ” =.>4) / (24 ” =.>4) 8 3.:97734 ]O= 8 (0.32 ” 3.>:) / (= ” 3.>:) 8 3.39>93: Dst`bkdmdhfs dk sgstdh` jd dmu`mgflds jd `mudrjf `k ludvf jg`ir`h`1 Lfjf 0 O0 8 Of + O4 + O? ]dp`r`jfr (RFTINDR) jd jdsb`std O2 8 ]O0 * O0 O= 8 O0 ” O2 8 (0 ” ]O0) * O0 ]dp`r`jfr (MKD@LDR) jd kghpgdz` O: O28 (0 ” ]O2) * O2 O4 8 8 ]O2 O2 ” *O: ]dp`r`jfr (]M@_DLIDR) jd rdmupdr`mgýl O? 8 ]O= * O= O9 8 O= ” O? 8 (0 ” ]O=) * O= Rddhpk`z`ljf j`tfs tdldhfs1 O0 8 Of + (0 ” ]O2) * O2 + ]O= * O= O0 8 Of + (0 ” ]O2) * ]O0 * O0 + ]O= (0 ” ]O0) * O0 O0 {0- ]O0 (0 ” ]O2) ” ]O= (0 ” ]O0)} 8 Of O0 8 Of / {0 ” ]O0 (0 ” ]O2) ” ]O= (0 ” ]O0)} O0 8 :>33 / {0 ” 3.3>99? (0 ” 3.:9773=) ” 3.39>93: (0 ” 3.3799?)} Kudif kfs v`kfrds jd okuafs jdk mgrmugtf y` `aust`jf y b`k`lmd`jf sfl mfhf sgiud1 O0 8 4:=>.929 t O2 8 3.3>99? x 4:=>.929 8 :99.=3= t / jè` O= 8 (0 ” 3.3>99?) x 4:=>.929 8 :7?0.:2: t / jè`  O: 8 3.:97734 x :99.=3= 8 227.3?3 t / jè` (Mflm. Mu) H@LTDK @RM@LIDK ]DJ@LF Z

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O4 8 (0 ” 3.:97734) x :99.=3= 8 2:>.2:= t / jè` O? 8 3.39>93: x :7?0.:2: 8 =73.:>: t / jè` O9 8 (0 ” 3.39>93:) x :7?0.:2: 8 :493.7:3 t / jè` (rdk`vd)

B) MÀKM MÀKMTKF TKF JDK B@K@LM B@K@LMD D HDZ@KÑRIGM HDZ@KÑRIGMF F ZFZ@K S`r` dodmtu`r dk b`k`lmd hdt`kñrigmf tft`k tdldhfs kfs v`kfrds jd kfs okuafs Of, O: y O9, `mfhfj`jf dl dk sgiugdltd mu`jrf1 SRFJTMZF ]   M`bdz` Mflm. Mu Rdk`vd

SD]F

% SD]F

:>33 227.3? :493.7:

033 :.99 74.2=

KDW % Mu 2 24 3.>:

Mflt. Hdtàkgmf Mu 7? 49.2?4 =>.=74

% jd Jgst. Mu 033 47.?4 =7.77

R`f

23.744

M) MÀ MÀKM KMTK TKF F JDK JDK B@ B@K@ K@LM LMD D HD HDZ@ Z@KÑ KÑRI RIGM GMF F JD M@J@ M@J@ DZ@S DZ@S@ @ JDK JDK MGRMTGZF. M.0) B@K@LMD HDZ@KÑRIGMF JD K@ DZ@S@ JD RFTINDR SRFJTMZF ]   M`bdz` R Mflm. Mu R Rdk`vd R

SD]F

% SD]F

4,:=>,929 :99,=3= :,7?0,:2:

033 >,9>? 70,22

KDW % Mu 2.04 0: 0.30

Mflt. Hdtàkgmf Mu 00?,7=2 ??,>22 43,003

% jd Jgst. Mu 033 49.04 :2.>4

R`f

00,=74

M.2) B@K@LMD HDZ@×RIGMF JD K@ DZ@S@ JD ]M@_DLIDR SRFJTMZF ]   M`bdz` ]mv Mflm. Mu ]mv Rdk`vd ]mv

Mflt. Hdtàkgmf Mu 43,003

% jd Jgst. Mu 033

R`f

033

KDW % Mu 0.30

> 72.0=

= 3.>:

00,90: =>,=7?

2=.=> 9?.?2

02,934

SD]F

% SD]F

:,7?0,:2: =73,:>: :,493,7:3

M.=) B@K@LMD HDZ@×RIGMF JD K@ DZ@S@ JD MKD@LDR SRFJTMZF]  

SD]F

% SD]F

KDW % Mu

Mflt. Hdtàkgmf Mu

M`bdz`

:99,=3=

033

0:

??,>22

% jd Jgst. Mu 033

R`f

H@LTDK @RM@LIDK ]DJ@LF Z

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mkd`ldr Mflm. Mu ]mv Rdk`vd mkd`ldr

227,3?3

:>

24

49,2?4

>4.9

2:>,2:=

42.30

=.>4

7,449

0:.=

2,3>=

‛JD KF] @LD^F]‘ DADRMGMGF Dl ul` pk`lt` mflmdltr`jfr` sd tr`t` jd 24333 t / jè` jd ul` hds` jd mfbrd, muyf rdpfrtd jd dls`yd quèhgmf ds qud sd hudstr` dl dk mu`jrf sgiugdltd1 SFJTMZF]   M`bdz` Mflmdltr`jf jd Mu Rdk`vd

DL]@WD F KDWD] % Mu % Od 4.2 00.7 =3 0>.= 3.24 03.?

% Glsfkubkds 04.:

JDZDRHGL@R1 `) b) m) j)

Dk p`sf p`sf jd mflm mflmdlt dltr`j r`jf f dl t / jè jè`. `. Dk tfldk` tfldk`ad ad jd rdk`vd. rdk`vd. K` rdmu rdmupd pdr` r`mg mgýl ýl jdk jdk Mu. Mu. K` r`zý r`zýl l jd mmflm flmdlt dltr`m r`mgýl gýl..

]fkumgýl1 ]d` dk sgiugdltd jg`ir`h`

`) Màkmukf jdk pdsf mflmdltr`jf fbtdlgjf. Ttgkgz`hfs k` dmu`mgýl H@LTDK @RM@LIDK ]DJ@LF Z

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M 8 O x (o ” t) / (m ” t) 8 24333 x (4.23 ” 3.24) / (=3 ” 3.24) M 8 :047.?? t / jè`

b) Màkmukf jdk tfldk`ad jd rdk`vd. M`bdz` 8 Mflm. Mu + Rdk`vd O 8 M +Z Z 8 O ” M 8 24333 - :047.?? 8 23>:3.=: Z 8 23>:3.=: tfl / jè`

m) Màkmukf jd k` rdmupdr`mgýl jdk Mu Rmu 8 {(M x m) / (O ” t)} x 033 8 (:047.?? x =3) / (24333 x 4.23) x 033 8 74,77 % Rmu 8 (o-t) / (m ” t) x (m/o) x 033 8 (4.23 ” 3.24) / (=3 ” 3.24) x (=3/4.2) x 033 Rmu 8 74.77%

j) Màkmukf jd k` r`zýl jd mflmd mflmdltr`mgýl ltr`mgýl

E 8 O/M 8 24333/:047.?? 8 ?.303 / 0 E8 (m-t) / (o ” t)8 (=3 ” 3.24) / (4.2 ” 3.24)8 ?.303 (t. jd hgldr`k jd m`bdz` / t jd mflmdlt,) Dstd v`kfr lfs gljgm` qud pfr m`j` ?.30 t jd hgldr`k jd m`bdz` sd fbtgdld 0 t jd mflmdltr`jf.

 

H@LTDK @RM@LIDK ]DJ@LF Z

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