sDkf; / ?n/sf] k|of]u u/L lqeh' sf] /rgf ug{ !) lbOPsf cj:yfsf cfwf/df nufP/ . h:t}, lqe'hx¿sf] /rgf u/fpg] . tLgcf6] } e'hf AB = 5cm, BC = 6cm ;dfgfGt/ rt'e'h{ , ju{ / AC = 6cm ePsf] cfotsf lrqx¿af6 ltgLx¿sf lqeh' sf]0fx¿ tyf e'hfx¿ cnu cnu gfk]/ gfksf cfwf/df ;dfgfGt/ rt'e{h' , cfot tyf ju{sf u'0fx¿sf] vf]hL u/L lgisif{ kQf nufpg nufpg] . u'0fx¿ vf]hL ug]{ ;DaGwL ;d\"x ;xof]ufTds l;sfOsf sfos{ f] cjnf]sg /0fgLltx¿ k|ofu] u//] u//] ;dfgfGt/ rt'e'{h, ju{ / kfOyfuf]/; cfotsf u'0fx¿sf] vf]hL / ;fWocg;' f/ ;dsf]0f k/LIf0f u/fpg] lqeh' sf cfwf/, lhofa] f]8,{ u|fkmaf]8{ tyf l8hL6n nDa / s0fs{ f] PK;sf] k|of]uaf6 kfOyfuf]/; ;DaGw :yflkt ug{ ;fWosf] k'li6 ug{ nufpg] nufP/ ;a} ljBfyL{x¿nfO{ Ps Pscf]6f Hff8] f lqe'hx¿sf @ lqeh' jf cfot jf ju{ lbg] / ;DalGwt efux¿sf] cfkm\\gf] cfsf/;uF a/fa/ / gfkaf6 cg¿' k p:t} csf{] cfs[lt vfh] L u/L 56' o\\ fpg nufP/ ltgLx¿sf] ;DaGw vf]Hg nufpg] ul0ftLo cGt/ljm| ofTds PK;x¿sf] k|of]u u/L wf/0ffsf] cfwf/et\" lzIff -sIff ^–*_ kf7o\\ jm| d, @)&&
%=$ 7f]; j:t'x¿ /rgfTds ;f]r l;k 66] «fx]8«g, cS6fx8] «g, ;f]nL / an] gfsf ;xsfo{ l;k vfj] |mf gd'gf 6]6«fx]8«g, 3g, cS6fx8] «g, 8f8] ]sfx]8«g / cfOsf];fx8] g« sf] lsgf/f, ;tx / s'gfsf] ;DaGw %=%= lgb{z] fª\\sx¿ ;dfnfr] gfTds ;f]rfO tyf n]vflrqdf laGb'sf] lg0fo{ l;k lgbz{] fª\\s / cª\\sg k|of]u l;k -cIfx¿;Fu ;DffgfGt/ x'g] /]vfdf kg{] b'O{ laGbl' arsf] b'/L cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
ljsf; u/fpg] l;Gsf, cfn'sf 6'sf| x¿, uxF'sf 6]6«fx]8g« , cS6fx8] g« , ^ % 5\\jfnL, h;' kfOk, 86\\kg] sf ;fn] L / an] gfsf vfnL l/kmLnx¿, tf/ cflbk|of]u vf]jm| f gd'gf lgdf0{ f u//] 66] «fx]8«g, cS6fx8] «g, ;fn] L ug]{ kl/ofh] gf sfo{ / a]ngfsf vf]jm| f gdg' f lgdf{0f u/fP/ ug]{ ljm| ofsnfkx¿ ;d\"xdf u/fpg] . ;dx\" df 6]6«fx]8g« , 3g, cS6fx8] «g, 8f]8s] fx]8«g / cfOsf;] fx8] g« kb| fg u//] ltgLx¿sf lsgf/f, ;tx tyf s'gfx¿sf cfwf/df ltgLx¿sf] ;DaGw vf]Hg] lj|mofsnfkx¿ u/fpg] ul0ftLo cGt/ljm| ofTds PK;x¿sf] k|of]u u/L wf/0ffsf] ljsf; u/fpg] u|fkmaf8] s{ f] k|of]u u/L laGb'sf] laGb'sf] lgb{]zfª\\s lgbz{] fªs\\ kQf nufpg tyf lbO{ n]vflrqdf laGbn' fO{ n]vflrqdf cªs\\ g ug{ cª\\sg ug{ nufP/ nufpg] kZ| gf]Q/ ljlwaf6 k|bz{g ljlwaf6 n]vflrqdf bj' } nv] flrqdf laGb' 7f8f] jf bj' } laGb' t];f| ] cIfx¿;Fu /v] fdf klg x'g ;Sg] tyf ;DffgfGt/ x'g] cIfx¿;Fu ;dfgfGt/ xg' ] b'O{ /]vfdf kg]{ b'O{ 131
%=^= ;dldlt / l;hg{ fTds 6;] ]n];g ;fr] fO l;k /]vLo / laGb' ko| f]u l;k ;dldtLo lrqx¿ lqeh' sf] k|of]uaf6 6;] ]n];g %=&= :yfgfGt/0f ;dfnfr] gfTds ;f]rfO tyf :yfgfGt/0fsf] lg0f{o l;k kl/ro k|of]u l;k n]vflrqdf k/fjt{g -laGb' / /]vf_ X- cIf (+) jf Y- cIf (+) df laGb' / /v] fsf] lj:yfkg 132
laGbl' arsf] b'/L kQf nufpg] laGbl' arsf] b'/L lgsfNg nufP/ ljleGg ;dldlt lrqx¿af6 ;dldlt lrqaf6 $ /v] Lo / laGb' ;dldlt;DaGwL /]vLo / laGb' kf]i6/, lrq, kmf6] fx¿ k|bzg{ ;dldtLo lrq u/L 56' \\6f 5\\6\\6} ¿kdf /]vLo / 5'6o\\ fpg nufP/ laGb' ;dldlt rf6{ agfpg lqeh' sf] k|of]u u/L{ nufpg] 6;] ]n];g tof/ kfg{ ;dldtLo lrqx¿sf] cfwf nufO{ ;\"rgf kf6Ldf efux¿ lbP/ lrq k\"/f ug{ 6fF:g nufP/ nufpg] km/s km/s /ª\\usf sfuhnfO{ lqe'hfsf/ 6'j|mfx¿ agfpg nufO{ rf6{ k]k/df vfnL 7fpF gxg' ] u/L 6f:F g nufpg] tyf u|fkmdf lqe'hsf 9fFrfdf cfwfl/t 6];]n;] g tof/ kfg{ nufpg] Pg] f, 6r{nfO6, sfuh kmfl] N8ª, nv] flrqdf x-axis / % k/fjtg{ ePsf lrq jf y-axis xg' ] laGb' / kmf]6fx] ¿sf] k|of]uaf6 /v] fsf] k/fjt{g, 7f8f] / t];|f] /]vfdf k|ToIfLs/0f u/L :yfgfGt/0fsf] kl/ro lbg] . xg' ] laGb' / /]vfsf] l8lh6n jf efl} ts ;fdu|Lsf] lj:yfkg;DaGwL k|of]u u/]/ n]vflrqdf X-cIf / kl/ofh] gf sfo{ u/L ;\"rgf kf6Ldf 6fF:g Y- cIf x'g] laGb' / /v] fsf] cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
%=*= lbzf l:ylt / ;xsfo{ l;k :sn] 8O« ª k|of]u l;k lbzf l:ylt / :sn] 8O« ªsf] kl/ro lbzfl:yltsf] ko| f]u gS;f / lbzf ^ tYofª\\szf:q lbOPsf] jf ;ª\\sng /rgfTds ;f]r ul/Psf] l;k tYofªs\\ af6 /]vf l;sfO tyf nv] flrq agfpg ko| f]u l;k /]vflrq (line ;~rf/ l;k graph) af6 hfgsf/L lng lbg tYofª\\saf6 tLgcf]6f ;Dd tYosf] ax':tDelrq lgdf0{ f ug{ sIff * cfwf/e\"t lzIff -sIff ^–*_ kf7\\oj|md, @)&&
k/fjtg{ , 7f8f] / t;] |f] /]vfdf nufP/ x'g] laGb' / /]vfsf] lj:yfkg;DaGwL k|bz{g / 5nkmn ug]{ u/fpg] X- cIf / Y- cIfx¿sf] gS;fdf lbzf ko| f]u % k|ltR5b] gaf6 rf/cf]6} lbzfsf] ug]{ sfo{ lbP/ klxrfg u/fpg] . k|bzg{ ljlwaf6 gS;fsf] ko| fu] u/L lbzfsf] 5nkmn u/fpg] . lbzf / lbzfl:yltsf] k|of]u ;DaGwdf 5nkmn u/fO{ k|of]usf Ifq] kQf nufpg nufpg] . lbOPsf] jf ;ª\\sng ul/Psf] /v] flrq (line !) tYofªs\\ af6 /]vflrq (line graph) agfpg] / agfpg graph) lgdf0{ f ug{ nufpg] lj|mofsnfk ug{] sIff sfo{ / u[xsfo{ lbP/ lbOPsf] jf lgdf{0f ul/Psf] tLg cf]6f;Dd /]vflrq (line graph) af6 j:t' tYosf] ax:' tDelrq / dN\" o;DaGwL ;r\" gf lng] jf lgdf{0f ug{ sIffsfo{ lbg] lj|mofsnfk ug]{ / u[xsfo{ lbP/ lbOPsf] jf ;ªs\\ ng ul/Psf] tYofª\\saf6 tLgcf]6f ;Dd tYosf] ax':tDelrq lgdf0{ f u/L k|bz{g / 5nkmn ug]{ 133
jm| =; ljifoj:t'sf] ljifoj:ts' f] lj:tt[ Ls/0f Jojxf/s'zn ! Ifq] l;k !=!= ;d\"x ;d'x cnlUuPsf / vlK6Psf lg0f{o tyf ;d:of ;d\"xx¿ ;dfwfg l;k pkoS' t / cgk' o'St ;xsfo{ l;k pk;dx\" x¿ @= cª\\sul0ft @=!= jf:tljs ;ª\\Vof l;sfO l;k / k|of]u l;k -s_ ;ª\\Vof k4lt bzdnj ;ª\\Vof k4lt, låcfwf/ ;ªV\\ of k4lt / k~rcfwf/ ;ªVof k4ltsf] Ps cfk;df ¿kfGt/0f 134
;Defljt l;sfO sfos{ nfk ;Defljt d\"Nofªs\\ g sfo{306f k|ljm| of !) ljleGg lsl;dsf eg] lrqx¿ lbOPsf] jf % kb| zg{ u/L ;dx\" cnlUuPsf / ;ª\\slnt vlK6Psf ;d\"xx¿ 5'6\\ofpg j:tx' ¿sf] nufpg] ;dx\" af6 pko'St lbOPsf] jf ;ªs\\ lnt j:t'x¿af6 / cgk' oS' t pk;dx\" x¿ agfOPsf ;d\"xaf6 pko'St / lgdf0{ f ug{ nufO cg'koS' t pk;d\"xx¿ lgdf0{ f ug{ tL ;d\"xx¿nfO{ nufO tL ;d\"xx¿nfO{ e]g e]g lrqdf k|:tt' lrqdf k:| tt' ug{ nufpg] . ug{ nufP/ kl/of]hgf sfoa{ f6 cfkmg\\ f] ljBfno tyf 3/ j/k/ ;+slnt kl| tj]bg k|:t't ug{ nufP/ j:tx' ¿sf] ljleGg ;dx\" af6 pkoS' t / cg'koS' t pk;dx' x¿sf] lgdf0{ f u/L lt ;d\"xx¿sf] e]glrq agfO{ sIffdf k|:t't ug{ nufpg] . kfrF eGbf ;fgf k\"0f{ ;ªV\\ ofx¿sf] ljleGg ;ª\\Vofx¿ ;dx\" af6 låcfwf/ / k~rcfwf/ lbP/ o;af6 ;ª\\Vof k4ltsf] kl/ro lbg] k~rcfwf/, k~rcfwf/ / låcfwf/sf] låcfwf/ / :yfgdfg tflnsfsf ;fy} bzdnj ;ª\\Vof 5'6o\\ fpg nufP/ 3ftfªs\\ sf] lgodsf] rf6{ k|b{zg / 5nkmn u/L oL k4ltx¿nfO{ bzdnj bzdnj ;ª\\Vof k4ltdf ;ª\\Vofx¿nfO{ cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
-v_ cgfg'kflts ;ªV\\ ofx¿ l;sfO l;k / ko| f]u l;k cgfgk' flts ;ªV\\ ofx¿ cgfgk' flts ;ªV\\ ofnfO{ ;ª\\Vof /v] fdf k|:t't -√2_ cfgk' flts / cgfgk' flts ;ªV\\ ofsf] ;DaGw ;ªV\\ ofsf] j}1flgs ;ª\\s]t @=#= cgk' ft / ;dfg'kft lg0f{o tyf ;d:of cg'kft / ;dfg'kftsf cfwf/e\"t lzIff -sIff ^–*_ kf7\\ojm| d, @)&&
¿kfGt/0f ug{ nufpg] . bzdnj k~rcfwf/ / ;ªV\\ ofnfO{ j|mdzM @ / % n] efu låcfwf/ ;ª\\Vof k4ltdf ¿kfGt/ u//] zi] fnfO{ tnaf6 dflylt/ ug{ nufP/ /fVg nufO{ låcfwf/ ;ª\\Vof k~rcfwf/ / k4lt / k~rcfwf/ ;ª\\Vof låcfwf/ k4ltdf ¿kfGt/0f ug{ nufpg] ;ª\\VofnfO{ bzdnj ;ªV\\ ofdf ¿kfGt/ ug{ nufP/ k'g/fj[lQ xg' ] / gxg' ] bzdnj ljleGg jf:tljs !@ ;ªV\\ ofaf6 cgfg'kflts ;ªV\\ ofx¿af6 ;ª\\Vofsf] wf/0ff ljsf; u/fpg] . cfg'kflts / cgfg'kflts √2 nfO{ ;ª\\Vofdf k|:t't ug{ ;ª\\Vofx¿ nufpg] 56' \\ofpg nufP/ . cfg'kflts / cgfgk' flts ;ªV\\ ofx¿ aLr tn' gf ug{ nufO ;ªV\\ ofx¿nfO{ ;DaGw vf]hL ug{ nufpg] . j}1flgs ;ª\\s]tdf n]Vg nufP/ 3ftfªs\\ sf] lgod rf6{ / j1} flgs bzdnj leGgsf] ko| f]uaf6 ;ª\\s]tnfO{ ;ªV\\ ofx¿nfO{ j}1flgs ;ª\\s]tdf bzdnj / j1} flgs ;ª\\st] x¿nfO{ ;ªV\\ ofdf n]Vg bzdnj ;ª|\\Vofdf n]Vg cEof; u/fpg] nufP/ ;d\"xdf 5nkmn u/fO{ cg'kft;DaGwL ^ cg'kft;DaGwL ;d:ofx¿ ;d:ofx¿ 135
;d:ofx¿ ;dfwfg l;k @=$= gfkmf / gf]S;fg lg0f{o tyf 5'6 k|ltzt ;dfjz] ;d:of ;dfwfg l;k ePsf gfkmf / gfS] ;fg;DaGwL ;xsfo{ l;k ;d:ofx¿ lg0f{o tyf @=%= Pl] ss lgod ;d:of kT| oIf ljr/0f / ;dfwfg l;k ckT| oIf ljr/0f -tLgcf]6f;Dd r/ ;dfjz] ePsf_ 136
;dfwfg ug{ nufpg] . ;dfwfg ug{ nufP/ lbOPsf cg'kftx¿sf] tn' gf u/L ;dfg'kftdf ePsf] jf gePsf] ;dfgk' ft;DaGwL hfFRg nufpg] ;d:ofx¿sf] xn ug{ nufP/ lgbl{] zt vfh] ljlwaf6 ;dfg'kftdf ePsf rf/ ;ª\\VofdWo] tLg cf]6faf6 rf}yf]sf] dfg lgsfNg nufpg] ;dx\" df 5nkmn u/fO{ ;dfg'kft;DaGwL ;d:ofx¿ ;dfwfg ug{ nufpg] . ahf/sf] ed| 0f u/fO{ 5'6sf] 56' kl| tzt ^ af/]df 5nkmn u/fpg] . -cyjf ;dfj]z ePsf ahf/sf] cg'ej 5nkmn u/fpg]_ gfkmf / gfkmf, gf]S;fg / 5'6 tyf ltgsf gf]S;fg;DaGwL ;d:ofx¿sf] sIff kl| tzt;d]t ;dfj]z ePsf sfo{ / u[xsfo{ ;d:ofnfO{ ;dx\" df 5nkmn ug{ nufP/ u/fO{ ;dfwfg u/fpg] . k|ToIf ljr/0f / ckT| oIf kT| oIf ljr/0f / * ljr/0fsf bl} gs hLjgdf k|of]u ckT| oIf ljr/0fsf] x'g] lj|mofsnfkx¿sf] k|of]u ug]{ ;d:of pbfx/0faf6 tLgcf]6f r/ -h:t} ;dfwfg ug{ sfd, lbg / ;ªV\\ of_ sf nufP/ ;d:of;Fu kl/lrt u/fO{ ljr/0fsf] lgodaf6 ;d:of ;dfwfg ug{ nufpg] cfwf/e\"t lzIff -sIff ^–*_ kf7\\ojm| d, @)&&
@=^= ;fwf/0f Aofh lg0f{o tyf ;fwf/0f Aofh ;d:of ;dfwfg l;k k|of]u l;k # Ifq] ldlt #=!, If]qkmn / cfotg ;xsfo{ l;k lqe'hsf] Ifq] kmn ko| f]u l;k -;dsf0] fL, ;dl4afx' / lg0fo{ tyf ;dafx' lqeh' ;dt] sf] ;d:of Ifq] kmn_ ;dfwfg l;k ;dfgfGt/, ;dnDa / ;dafx' rt{'e'hsf] Ifq] kmn -;q' :yflkt / ko| f]u_ j[Qsf] If]qkmn -;q' :yflkt / k|of]u_ cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
:yfgLo?kdf ul/g] C0f sf/f]af/ P]lss lgod tyf * !% tyf ljQLo ;+:yfsf] e|d0faf6 ;'qsf] k|of]u u/L 5nkmn u/L ;fjF f, Aofh, ;do ;fwf/0f Aofhb/ / ld>wg;DaGwL Aofh;DaGwL wf/0ffsf] ljsf; u/fpg] . Pl] ss ;d:of ;dfwfg lgodsf] k|of]u u/L ltgLx¿sf] ug{ nufP/ ;DaGw :yflkt ug{] . aª} s\\ + tyf JolStaf6 lnOg] C0fsf pbfx/0f k|:t't u/L ;fwf/0f Aofh;DaGwL Jofjxfl/s ;d:ofsf] ;dfwfg ug{ nufpg] ljleGg lqe'h / rt'e{'hsf] k|Zgf]Q/ tyf Ifq] kmn kQf nufpg] ;q\" sf JolStut / ;d\"x ;DaGwdf 5nkmn u/L ;\"q sfo{sf cfwf/df :yflkt ug{ nufpg] / j/k/sf d\"Nofª\\sg ug{] j:t'x¿sf] lqe'hfsf/ / rt'eh'{ fsf/ ;txsf] If]qkmn lqeh' / lgsfNg nufpg] rte' h{' sf] If]qkmn;DaGwL j[Qsf] If]qkmn kQf nufpg] ;d:of ;dfwfg ljleGg km/s km/s ug{ nufP/ ls|ofsnfkx¿ u/fO{ ul0ftLo ;d:ofx¿ ;fdfwfgsf j[Qsf] lso| fsnfkx¿ u/fpg] Ifq] kmn;DaGwL Jofjxfl/s ;d:ofx¿ ;dfwfg ug{ nufP/ 137
$ aLhul0ft $=!= 3ftfªs lg0fo{ tyf 3ftfª\\ssf lgod (am an ;d:of am+n, am an = am-n, a0 = ;dfwfg l;k 1, (ab)m = ambm, ( )m = l;sfO tyf ko| f]u l;k , am = ) k|of]u u/L ;/nLs/0f $=@= cleJo~hs l;sfO tyf v08Ls/0f k|of]u l;k ;femf u'0fgv08 lnP/ kb Pslqt u//] ;d:of a2 ‒ b2 :j¿ksf] ;dfwfg l;k k\"0f{ ju{ x'g] ax2 + bx + c :j¿ksf] v08Ls/0f lalwaf6 b'Oc{ f]6f cleJo~hs;Ddsf] dxQd ;dfkjt{s (Highest Common Factor) / n3'Qd ;dfkjTo{ (Lowest Common Multiple) aLhLo leGgsf] kl/ro b'Oc{ f]6f ;Dd aLhLo 138
cfudg ljlwaf6 3ftfª\\ssf 3ftfªs\\ sf % lgod (am an am+n, am an lgodx¿sf] ;\"rL = am-n, a0 = 1, (ab)m = ambm, agfpg nufP/ ( )m = , am = ) kQf 3ftfª\\ssf lgod k|of]u ePsf nufpg] / tT;DaGwL ;/n ;/nLs/0fsf] u/fpg] sIffsfo{ / u[xsfo{ ug{ nufP/ aLhLo klQx¿ sf] k|of]u u/L sIffsfo{ / !% ;femf u'0fgv08 lnP/ kb ;dx\" sfo{sf] Pslqt u/]/, a2 _ b2 :j¿ksf,] k\"0f{ ju{ xg' ] / ax2 + bx + c cjnf]sg u//] :j¿ksf] v08Ls/0f;DaGwL cleJo~hsx¿sf] v08Ls/0f, dxQd 5nkmn u/fpg] ;dfkjt{s km/s ;dx\" nfO{ km/s (Highest cleJo~hsx¿ lbP/ ltgLx¿sf] Common ;femf u'0fg v08 kQf nufpg] Factor) / n3'Qd ;dfkjTo{ ls|ofsnfk u/fpg] (Lowest Common e]g lrqsf] dfWodaf6 dxQd ;dfkjts{ (Highest Common Multiple) kQf Factor) / n3Q' d ;dfkjTo{ nufpg / aLhLo leGgsf] ;/n ug{ (Lowest Common Multiple) nufP/ lgsfNg] cEof; u/fpg] cªs\\ ul0ftLo leGgsf] wf/0ff k|of]u u/L bO' {cf6] f ;Ddsf cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ jm| d, @)&&
leGgsf] ;/nLs/0f $=#= ;dLs/0f / u|fkm lg0fo{ tyf ;d:of nv] flrq ljlwaf6 b'O{ ;dfwfg l;k rno'St ou' kt/v] Lo ;dLs/0fsf] xn l;sfO tyf k|of]u l;k v08Ls/0f ljlwaf6 ju{ ;dLs/0fsf] xn % Hofldlt %=!= /v] f / sf0] fx¿ ;dfnf]rgfTd s ;f]r tyf b'Oc{ f]6f ;/n /v] fx¿nfO{ lg0fo{ l;k Pp6f 5]bsn] sf6\\bf aGg] sf]0fx¿ -PsfGt/ l;sfO tyf sf0] fx¿, ;+ut sf0] fx¿ / k|of]u l;k qmdfut leqLsf0] fx¿_ b'O{cf]6f ;dfgfGt/ /]vfx¿nfO{ Pp6f 5]bsn] sf6\\bf aGg] sf]0fx¿ ;DaGwsf] vfh] L cfwf/et\" lzIff -sIff ^–*_ kf7\\oj|md, @)&&
aLhLo leGgsf] kl/ro lbg] / o;sf] ;/nLs/0f u/fpg] k|bz{ g ljlw / n]vflrq ljlwsf] u|fkmdf b'O{ !) ko| f]u u/L bO' { rno'St ou' kt rnoS' t ou' kt /]vLo ;dLs/0f xn ug{ /]vLo ;dLs/0fsf] nufpg] . xn ug]{ kl/of]hgf ljBfyL{sf ;dx\" df lbOPsf sfo{ ug{ nufP/ . ;dLs/0fx¿sf] kbsf l8u|L kQf ju{ ;dLs/0f xn nufpg] / o;sf] 5nkmnsf ug]{ sIffsfo{ / cfwf/df ju{ ;dLs/0fsf] kl/ro ux[ sfo{ ug{ nufP/ lbg] v08Ls/0f ljlwaf6 ju{ ;dLs/0f xn ug{ nufpg] . l8lh6n PK;sf] ko| f]uaf6 ;dLs/0fx¿sf] xn u/fpg] k|fsl[ ts tyf efl} ts lgdf0{ fdf b'O{cf]6f l;wf tyf ^ /xs] f b'O{ ;/n /]vf / 5]bs ;dfgfGt/ ePsf cj:yfx¿sf] vf]hL ug{ /v] fx¿nfO{ Pp6f nufpg] . 5b] sn] sf6\\bf ;dx\" df 5nkmn u/fO{ b'Oc{ f]6f aGg] ljleGg hf]8f sf0] fx¿;DaGwL l;wf /]vfx¿nfO{ Pp6f 5b] sn] sf6b\\ f aGg] sf]0fx¿sf] ;\"rL ;d:ofx¿ tof/ kfg{ nufpg] ;dfwfg ug{ bO' {cf]6f l;wf /v] fx¿nfO{ Pp6f nufP/ 5b] sn] sf6\\bf aGg] sf0] fx¿df tnsf u0' fx¿ ePsf sf]0fx¿ 139
PsfGt/ sf]0fx¿ j|mdfut leqL sf]0fx¿ ;ªu\\ t sf]0fx¿ %=@ ;dtnLo cfs[ltx¿ ;dfnfr] gfTd lqeh' sf u'0fx¿sf] s ;fr] fO tyf lg0f{o vf]hL u/L k/LIf0f l;k lqe'hsf sf]0fx¿sf] l;sfO tyf of]ukmn 180º x'G5 . ko| f]u l;k ;dafx' lqeh' sf ;a} /rgfTds sf]0fx¿ a/fa/ x'G5g\\ . ;f]r l;k ;dlåafx' lqe'hsf cfwf/sf sf0] fx¿ 140
klxrfg ug{ nufpg] o 5]bssf] Ps}lt/ k/]sf leqL cgf;Gg sf]0fx¿ o 5b] ssf] b'j}lt/ k/]sf leqL cgf;Gg sf]0fx¿ o 5b] ssf] Ps}lt/ k/s] f Pp6f aflx/L / csf]{ leqL cgf;Gg sf]0fx¿ bO' c{ f]6f ;dfgfGt/ /v] fx¿nfO{ Pp6f 5b] sn] sf6\\bf aGg] sf0] fx¿ ;DaGwsf] vfh] L ug{ nufpg] ;Dej eP;Dd ul0ftLo cGt/ljm| ofTds PK;x¿sf] ko| f]u u/L sf]0fx¿sf] ;DaGwsf] k|bzg{ u/L ltgLx¿ ;DaGwsf] wf/0ff ljsf; u/fpg] ljBfyL{x¿sf ;dx\" x¿ lgdf0{ f lqe'hsf !$ u/L kT| o]s ;d\"xn] km/s km/s u0' fx¿sf] ko| f]u lqe'hx¿ lgdf0{ f u/]/ ltgLx¿sf u/L ;DalGwt u'0fx¿sf] k|of]ufTds k/LIf0f ug{ ;d:ofx¿ nufpg] ;dfwfg ug{ ;dafx' rt'e{'h, ;dnDa rte' {h' nufP/ / rª\\ufsf u0' fx¿sf] vfh] L ;dafx' rt'e{'h, ;dnDa rte' {'h / ugs{ f nflu km/s km/s ;d\"xx¿nfO{ km/s km/s rª\\ufsf cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
a/fa/ x'G5g\\ ;dsf0] fL ;dlåafx' lqe'hsf kT| o]s cfwf/ sf0] fx¿ 45º x'G5g\\ ;dafx' rt'e'{h, ;dnDa rt'e{'h / rª\\ufsf u0' fx¿sf] vfh] L / k/LIf0f lbOPsf] cj:yfdf ju,{ cfot / ;dfgfGt/ rte' {'hsf] /rgf ug{ - sDkf;sf] k|of]uaf6_ cfot -cf;Gg eh' f lbOPdf_ ju{ -Pp6f e'hf lbOPdf_ ;dfgfGt/ rt{'e'h - cf;Gg e'hfx¿ / ltgLx¿ larsf] sf0] fsf] gfk lbOPdf, cf;Gg eh' fx¿ / Pp6f ljs0f{sf] gfk lbOPdf, Pp6f e'hf / Pp6f ljs0f{sf] gfk / ltgLx¿ larsf] sf]0fsf] gfk lbOPdf_ cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
rte' h'{ x¿ pknAw u/fP/ u'0fx¿sf] k|of]u u/L eh' fx¿ tyf sf0] fx¿ gfKg nufO u0' fx¿ vfh] L ug]{ rte' {h' ;DaGwL ;d:ofx¿ lso| fsnfkx¿ u/fpg] kb| zg{ ljlwaf6 cfot, ju{ / ;dfwfg ug{ ;dfgfGt/ rt'e'h{ sf] /rgf nufP/ u/fpg] cfot, ju{ / ax'eh' x¿sf lrqx¿sf] ;dfgfGt/ cjnfs] g u/fP/ ;dx\" df 5nkmn rt'e{h' sf] /rgf u/fO{ eh' fx¿sf] ;ªV\\ ofsf] ug{ nufP/ cfwf/df lgtLx¿sf] gfd cgd' fg axe' 'hx¿sf] leqL ug{] lj|mofsnfkx¿ u/fpg] tyf aflx/L sf0] fx¿ kQf ljBfyL{x¿sf ;dx\" x¿nfO{ Ps nufpg] Pscf]6f km/s km/s ax'e'hx¿ ;d:ofx¿ ;dfwfg ug{ k|bfg u/]/ leqL sf]0fx¿sf] nufP/ ofu] kmn kQf nufO{ ;dx\" sfon{ fO{ sIffdf k|:t't ug]{ lj|mofsnfkx¿ u/fpg] cfudg lalwaf6 lgoldt axe' h' sf] leqL tyf aflx/L sf0] fx¿sf] gfk kQf nufpg nufpg . ljleGg lgoldt ax'e'hx¿ - lqe'h, ju{, k~re'h, if8\\e'h_ sf] lrq lbO aflx/L sf0] f / leqL sf]0fsf] gfk kQf nufpg nufP/ e'hfsf] ;ª\\Vofsf] cfwf/df tL 141
ax'eh' sf] kl/ro / ;dfnfr] gfTd lgoldt axe' 'hsf] leqL s ;fr] fO tyf aflx/L sf]0fx¿sf] l;k gfk / ltgLx¿sf] ;DaGw :yflkt ;d:of ;dfwfg l;k %=# cg¿' ktf / ;d¿ktf ;xsfo{ l;k lqeh' x¿ cg¿' k xg' ] cj:yfx¿sf] k/LIf0f cg¿' k lqe'h;DaGwL ;d:ofx¿ ;d¿k cfsl[ tx¿sf] lrgf/L %=$ 7f]; j:t'x¿ /rgfTds ;fr] l;k lqeh' fsf/ lk|Hd / lk/fld8larsf] ;DaGw ;xsfo{ l;k -cfwf/, lzifl{ aGb', ;tx cflbsf] cfwf/df_ ;lxt lrgf/L 142
sf]0fx¿sf] ;DaGw :yflkt u/fpg] . ;dx\" df hf8] f cg'¿k lqeh' x¿ cg¿' k % lbO{ ltgLx¿sf efux¿sf] gfk / lqe'hx¿sf] cjnf]sgaf6 cg'¿k x'g] u0' fx¿sf] cj:yfx¿ k/LIf0f u/fpg] . cfwf/df cg'¿k lqe'hx¿sf] u'0fx¿sf] ltgLx¿sf cfwf/df ltlgx¿sf ljleGg ljleGg efux¿sf] dfg kQf nufpg] efux¿sf] dfg kQf nufpg] ;d:ofx¿ ljm| ofsnfkx¿ u/fpg] ;dfwfg ug{ ;a} ljBfyL{x¿nfO{ Ps Pscf]6f nufP/ . lqeh' jf cfot jf ju{ lbg] / Hff8] f lqeh' x¿sf cfkm\\gf] cfsf/;Fu p:t} csf]{ ;DalGwt cfs[lt ePsf] ;fyL vf]hL u/L efux¿sf] hf8] Ldf ltgLx¿sf] ;DaGw vf]Hg gfkaf6 ;d¿k nufpg] 5'6\\ofpg nufP/ l;Gsfx¿ tyf h'; kfOkx¿ 7f]; j:tx¿, % ko| f]uaf6 tof/ ul/Psf l;Gsfx¿, tyf gdg' fx¿ k|of]u u/L lqeh' fsf/ h'; kfOkx¿ lk|Hd / lk/fld8sf] kl/ro ko| f]uaf6 tof/ u/fpg] ul/Psf gdg' fx¿ sfuhsf] ko| f]u u/L ljleGg 3g, ko| f]u u/L if8\\dv' f, 6]6f« x]8«g, ;f]nL / lqeh' fsf/ lk|Hd cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ jm| d, @)&&
3g, if8\\dv' f, 6]6«fx]8g« , ;f]nL / a]ngfsf hfnLx¿ %=%= lgbz{] fª\\sx¿ lg0f{o tyf ;d:of kfOyfuf]/; ;fWosf] ;dfwfg l;k k|of]u u/L b'O{ laGb' larsf] b'/L l;sfO tyf ko| f]u l;k %=^= ;dldlt / 6];]n];g lg0fo{ tyf ;d:of axe' h' sf k|of]uaf6 ;dfwfg l;k lgoldt / cwl{ goldt 6;] ]n];g /rgfTds ;f]r l;k %=&= :yfgfGt/0f lg0f{o tyf ;d:of nv] flrqdf X- cIf / ;dfwfg l;k Y- cIfdf k/fjtg{ ko| f]u l;k -lqeh' _ /rgfTds ;f]r l;k X-axis (+) jf Y- axis (+) df bfFof / dfly] lj:yfkg -laGb' / /v] f_ cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
a]ngfsf/ 7f]; cfsl[ tx¿af6 / lk/fld8sf ltgLx¿sf hfnLx¿ agfpg vf]jm| f gd'gfx¿ nufpg] tyf hfnLx¿ agfpg nufP/ kfOyfuf]/; ;fWosf] k|of]u u/L kfOyfuf]/; % b'O{ laGb' larsf] b/' L lgsfNg] ;q\" ;fWosf] k|of]u / lx;fa ;d:of ;dfwfg u/L b'O{ laGb' ljlwaf6 ug{] larsf] b'/L lgsfNg sIffsfo{ / u[xsfo{ ug{ nufP/ ;dafx' lqeh' , ju{ / lgoldt ;dafx' lqeh' , % if8eh' sf 9fFrfdf cfwfl/t ju{ / lgoldt lgoldt / cw{lgoldt 6;] n] ];g if8e'hsf 9fFrfdf tof/ kf/]/ b]vfpg] / ljBfyLn{ fO{ cfwfl/t 6];]n];g klg 6];n] ;] g agfpg nufpg] tof/ kfg{ kl/ofh] gf sfo{ ug{ nufP/ l8lh6n jf ef}lts ;fdu|L lgb]z{ fªs\\ lbP/ ^ (Digital or Physical tool) sf] laGb' / /v] fsf] k|of]u u/]/ n]vflrqdf lqe'hsf] bfoF f / dfly k/fjt{g, lgb{]zfª\\ssf] cfwf/df lj:yfkg ug{ nufP/ laGb' / /v] fsf] bfoF f / dfly lj:yfkg Pjd\\ pbud laGb'df n]vflrqdf wgfTds / C0ffTds 90 df lqeh' sf] k/fjtg{ , x'g] laGb,' /v] f / lqeh' sf] pbud laGbd' f 143
pbud laGbs' f] cfwf/df wgfTds / C0ffTds 90 df kl/qmd0f -laGb,' /]vf / lqe'h_ %=*=lbzf l:ylt / :sn] lg0fo{ tyf 8O« ª ;d:of ;dfwfg l;k lbzf l:ylt / :sn] 8«Oªsf] ko| fu] ko| f]u l;k ^ tYofªs\\ zf:q ^=!= tYofª\\szf:q /rgfTds j[Qlrqsf] cWoog / ;f]r l;k tYofª\\saf6 j[Qlrq l;sfO tyf ko| f]u l;k lgdf0{ f dWos, dlWosf / l/t -j}olSts >0] fL_ ;~rf/ l;k 144
kl/j|md0f ;d:of ;dfwfg ljlw wgfTds / / 5nkmn ljlwaf6 ug{] C0ffTds 90 df x'g] laGb', /]vf / k|bz{g tyf vf]h ljlwaf6 lqe'hsf] lbzfl:ylt / :sn] 8«Oªsf] kl/j|md0f;DaGwL ko| f]usf] 5nkmn u/fpg] kl/ofh] gf sfo{ ug{ nufP/ lbzfl:ylt / :sn] $ 8O« ªsf] kl/of]hgf sfo{ ug{ nufP/ lbOPsf] jf ;ªs\\ ng ul/Psf] ;dx\" df jQ[ lrq !) tYofª\\saf6 j[Qlrq lgdf0{ f ug{ lgdf{0f ug{ nufpg] / ;d:of ;dfwfg ug]{ nufP/ . jQ[ lrqaf6 rf/cf6] f ;Dd j}olSts >]0fLsf] j:ts' f] hfgsf/L lng]lbg] dWos, dlWosf ;DaGwdf 5nkmn / ;d:of / l/t lgsfNg] ;dfwfg ug]{ sIffsfo{ / Pp6f a]Grdf a:g] ;d\"xdf ux[ sfo{ ug{ ;as} f] pd]/ hf]8]/ hDdf ljBfyL{ nufP/ ;ª\\Vofn] efu ug{ nufpg] / k|fKt glthfsf] af/d] f 5nkmn u/fpg] lahf/] ;ª\\Vofdf ljBfyL{x¿nfO{ sIffdf cufl8 prfOcg';f/ pleg nufP/ l7s lardf kg{] cfwf/et\" lzIff -sIff ^–*_ kf7\\oj|md, @)&&
cfwf/et\" lzIff -sIff ^–*_ kf7o\\ jm| d, @)&&
ljBfyLs{ f] prfOsf] af/]df 5nkmn u/fpg] hf]/ ;ª\\Vofdf ljBfyLx{ ¿nfO{ sIffdf cufl8 prfOcg';f/ pleg nufP/ l7s lardf kg]{ ljBfyLs{ f] prfOsf] af/d] f 5nkmn u/fpg] sIffsf ljBfyLx{ ¿sf] pd/] l6kf]6 ug{ nufpg] / ldnfg lrxg\\ sf] k|of]uaf6 ;a}eGbf a9L bfx] fl] /Psf] pd/] lgsfNg nufpg] j}olSts >]0fLsf] dWos, dlWosf / /L`t;DaGwL ;d:of ;dfwfg ug{ nufpg] . 145
%= k|ofu] fTds÷kl/ofh] gf sfos{ f nflu ;Defljt ljm| ofsnfkx¿ sIff ^ ;Defljt ko| f]ufTds÷kl/of]hgf sfo{ jm| =;= ljifo If]q != ;dx\" != tkfOsF f] 3/df ePsf ;fdfgx¿sf] ;\"rL agfpg'xf];\\ . ;dfg u'0fsf] @= cªs\\ ul0ft cfwf/df ltgLx¿sf] ;dx\" x¿ lgdf{0f u/L sIffsf7] fdf k|:t't ugx{' f];\\ . #= If]qldlt != ! bl] Vf @% ;Ddsf u'0fgv08 tflnsf agfO{ Pp6fdfq u0' fgv08 xg' ,] b'O6{ fdfq u'0fgv08 xg' ] / bO' {eGbf a9L u0' fgv08 x'g] ;ª\\Vofx¿ 56' 6\\ ofO{ ¿9 ;ª\\Vofx¿ / ;o+ 'Qm ;ª\\Vofx¿ kQf nufpg'xf];\\ / ¿9 ;ª\\Vofx¿nfO{ /ª nufpgx' f];\\ . clg sIffsf]7fdf k:| t't ug'{xf];\\ . @= Ps ju{ PsfO ePsf sx] L jufs{ f/ 6'j|mfx¿ agfpgx' f;] \\ / To;af6 slt tl/sfaf6 cfot agfpg ;lsbF f] /x]5 xg] x{' f];\\ . o;sf] cfwf/df ^, *, (, !), !@ cflbsf] u0' fgv08;Fu ;DalGwt cfot agfO{ 7'nf] sf8a{ f]8{ k]k/df 6f;F L k|:t't ug{x' f];\\ . #= u'0fg tflnsf agfpgx' f;] \\ / To;sf] ko| f]u u/L u'0fgv08 / ckjTox{ ¿ kQf nufpg] tl/sf tyf ltgLx¿sf] ;DaGw af/]df l6kf]6 u/L k:| tt' ug{'xf;] \\ . $= leGgsf hf]8, 36fp, u'0fg / efusf Ps Pscf]6f ;d:ofx¿ lbP/ kf/bzL{ kfgf (transparency sheet) sf] ko| fu] u/L df]8n] x¿ agfpgx' f];\\ / k|:t't ug{'xf];\\ . %= glhs}sf] Pp6f k;ndf hfg'xf;] \\ / k;n];F+u s]lx ;fdfgsf] gfd, To;sf] j|mo d\"No, ljj|mo d\"No l6kf]6 ugx{' f];\\ . To; ;fdfg a]Rbf xg' ] gfkmf /sd, gfS] ;fg /sd kQf nufO{ sIffsf7] fdf k|:t't ugx'{ f];\\ . ^= glhss} f] Ps k;ndf hfg'xf];\\ / k;n];uF ;fw] /] km/s km/s kfrF j6f j:tx' ¿sf] PsfO dN' osf] l6kf]6 ug{'xf;] \\ / tL d'Nosf] cfwf/df */* j6f j:t'sf] d'No slt knf{ kQf nufO k|:t't ug{'xf];\\ . &= tkfO{sF f] ;d'bfodf ePsf bz kl/jf/sf ;b:ox¿sf] gfd, pd]/ / lnªu\\ l6kf]6 u/L tnsf k|Zgx¿sf] pQ/ vfh] L ug{x' f];\\ / sIffdf k:| t't ug{'xf];\\ . s_ k'?if slt k|ltzt /x]5g\\ < v_ dlxnf slt kl| tzt /x]5g\\ < u_ h]i7 gful/s slt kl| tzt /x5] g\\ < != 7'nf] sf7] fx¿ ePsf] Pp6f uf| km k]k/df lgoldt tyf clgoldt HofldtLo lrqx¿ agfpgx' f;] \\ / sf]7f ug]/ If]qkmn kQf nufpg'xf];\\ / sIffdf k:| t't ug{'xf];\\ . @= tkfO+{sf] sIffsf7] fsf] nDafO, rf8} fO / prfO d]hl/ª 6]kn] gfKg'xf];\\ / 146 cfwf/e\"t lzIff -sIff ^–*_ kf7\\ojm| d, @)&&
sfkLdf l6kf]6 ugx'{ f;] \\ . To;kl5 ;f] sf7] fsf] kl/ldlt, If]qkmn / cfotg lgsfnL sIffsf]7fdf k|:t't ug'x{ f];\\ . nDafO rf}8fO prfO kl/ldlt If]qkmn cfotg $= aLhul0ft != tkfOsF f ;fyLx¿sf] tf}n ;fw] L ;\"rL agfpg'xf;] \\ / To;nfO{ l6s« f]6f]dL lgodsf] ko| f]u u/L ;fyLx¿sf] tf}nsf] t'ngf ug'x{ f];\\ . tfn} sf] t'ngf ul/Psf] rf6{ tof/ ugx{' f];\\ / sIffsf7] fdf k:| t't ugx'{ f];\\ . %= Hofldlt != Pp6f cfotfsf/ sfuhsf] kfgf d]6fsf8{ lng'xf];\\ . To;nfO{ laraf6 7f8f] / t;] f]{ l7s bO' { a/fa/ efu x'g] u/L k6\\ofpgx' f];\\ . km]l/ cfd'Gg] ;fdG' g]sf zLifl{ aGbx' ¿nfO{ lnP/ k6o\\ fpg'xf;] \\ . /ª\\uLg ;fOgk]gn] o;/L ags] f /]vfv08x¿nfO{ tyf lsgf/fx¿nfO{ 56' \\6f5'66\\ } /ªsf x'g]u/L hf]8\\g'xf];\\ . zLifl{ aGb'x¿nfO{ tyf sfl6Psf] laGbn' fO{ A, B, C, D, … gfd lbgx' f;] \\ . ca k6\\ofPsf] sfuh vf]Ngx' f];\\ / To;nfO{ 7'nf] sf8a{ f8] { k]k/df 6fF:g'xf];\\ / nDa/v] fx¿, k|ltR5l] bt /v] fx¿ / ;dfgfGt/ /]vfx¿ klxrfg u/L tflnsfdf n]Vgx' f];\\ / sIffsf]7fdf k:| t't ugx{' f];\\ M nDa/]vfx¿ k|ltR5l] bt /v] fx¿ ;dfgfGt/ /]vfx¿ @= h'; kfOk tyf l;Gsfx¿ k|ofu] u/]/ 3g / if8\\d'vfsf vf]jm| f gd'gfx¿ lgdf0{ f ugx{' f];\\ / ltgLx¿sf] ;tx, lsgf/f / sg' fsf] ;ª\\Vof l6kf]6 u/L ;DaGw kQf nufpg'xf];\\ . #= cfotsf/ / jufs{ f/ sfuhsf 6'j|mfx¿nfO{ rf6{ k]k/ jf jufª{ \\lst sfuhdf vfnL gx'g] u/L 6fF;/] 6l] ;n];g 9frF f tof/ kfgx{' f;] \\ . $= 6]gu|fd, lhof]af]8{ nufotsf :yfgLo ?kdf ;fdu|Lx¿ jf ljleGg l8lh6n cGt/lqmofTds dfWod -APP_ x¿sf] ko| f]u u/L km/s km/s cfsf/sf rt'e{'h / lqe'hx¿ lgdf{0f ug'{xf];\\ / ltgLx¿sf] ;DaGw klxrfg u//] k:| tt' ugx'{ f];\\ . ^= tYofªs\\ zf:q != tkfOFsf ljBfnosf #) hgf ljBfyL{x¿sf] pd]/ ;f]wL ldnfg lrx\\gsf] ko| f]uaf6 l6kf6] ugx'{ f;] \\ / o;nfO{ af/Daf/tf tflnsfdf k|:t't ug'x{ f];\\ / :tDelrq agfO{ sIffdf k:| t't ugx{' f];\\ . sIff & ;Defljt k|of]ufTds÷kl/ofh] gf sfo{ jm| =;= ljifo If]q != ;d\"x != tkfOFsf] sIffsf]7fdf ePsf j:tx' ¿sf] ;\"rL tof/ ugx'{ f];\\ . u0' fsf cfwf/df ;dx\" x¿ agfpgx' f];\\ . tL k|To]s ;d\"xaf6 aGg] pk;d\"xx¿ lgdf0{ f u/L k:| t't ug'x{ f];\\ . cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ jm| d, @)&& 147
@= cª\\sul0ft != glhs}sf] k;ndf uO{ cfkmn\" ] bl} gs pkefu] ug]{ ljleGg k|sf/sf t/sf/Lx¿sf] gfd, To;sf] j|mo dN\" o, ljj|mo dN\" o l6kf6] ug{x' f];\\ . To; ;fdfg aR] bf xg' ] gfkmf /sd, gfkmf k|ltzt, gfS] ;fg /sd, gf]S;fg k|ltzt kQf nufO{ sIffsf7] fdf k|:tt' ugx{' f;] \\ . @= xfd|f] bl} gs hLjgdf k\"0f{ ;ª\\Vof / k\"0ff{ªs\\ sf] k|of]u sxfF / s;/L ePsf] 5 . OG6/g]6af6, k':tsfnoaf6 cWoog u/L cyjf cfk\"meGbf cu'jf (senior) x¿;Fu ;fw] ]/ kTtf nufO{ k|fKt glthfsf] lgisifnfO{ sIffsf]7fdf k|:tt' ug{'xf;] \\ . #= cfk\"m cWoog ug]{ ljBfnosf] clGtd % jifs{ f] ljBfyLx{ ¿sf] ;ªV\\ ofsf] ljj/0f vf]hL ugx'{ f];\\ . k|To]s jifs{ f] ljBfyLx{ ¿ / clxn]sf] ljBfyLx{ sf] ;ªV\\ ofsf] cg'kft, k|Tos] jif{ ePsf 5fq / 5fqflarsf] cg'kft kQf nufpg'xf];\\ . k|fKt cg'kftn] s] bv] fpF5 < JofVof ugx'{ f];\\ / lgZsifn{ fO{ sIffsf]7fdf k|:tt' ugx'{ f];\\ . #= If]qldlt != Pp6f j[Qfsf/ 7f;] j:t' -h:tM} l;Ssf, s6' k]k/ jf 6'«G8nlx\\jn _ lng'xf];\\ / wfuf]n] l7s Ps kmGsf] nufpgx' f];\\ / ?n/sf] ;xfotfn] ;f] wfufs] f] gfk -kl/lw_ lngx' f];\\ clg sfkLdf l6kf]6 ug'{xf'];\\ . ca ?n/ / ;]6 :Sjfo/sf] ko| f]u u/L kl/lwsf 5]p5]psf b'O{ laGb;' Ddsf] ;aeGbf nfdf] b/' L -Jof;_ sf] gfk lngx' f];\\ . To;kl5 kl/lwnfO{ Jof;n] efu ugx{' f];\\ . efukmn slt cfp5F l6kf]6 ug'{xf];\\ / lgisif{ nfO{ sIffsf7] fdf k|:t't ug'{xf;] \\ . $= aLhul0ft != (������ + ������)2 sf] lj:t[t ?ksf] gdg' f (model) agfO{ k:| t't ug'{xf];\\ . %= Hofldlt != Pp6f cfotsf/ sfuhsf kfgf lngx' f];\\ . To;nfO{ k6o\\ fO{ vlK6g] eh' fx¿ / sf]0fx¿ cjnf]sg ug]{ , lj|mofsnfk u/L cfotsf u'0fx¿ vf]hL ug'x{ f];\\ . cfkmn\" ] u/]sf] kT| o]s ljm| ofsnfksf] l6kf]6 u/L ;fyLx¿;uF 5nkmn u/]/ k|:t't ugx'{ f];\\ . @= tkfOs{F f] ljBfno kl/;/df ePsf km/s km/s kfFrcf]6f cg¿' k cfs[ltx¿sf] l6kf]6 ugx{' f];\\ / cg'¿k x'g'sf sf/0fx¿ cWoog u/L ;fyLx¿;uF 5nkmn u/]/ sIffsf7] fdf k:| t't ugx{' f];\\ . #= sfuh, l;Gsf tyf cfn'sf 6'j|mfx¿, h'; kfOk, tf/, vfnL l/lkmn, l;of] wfuf] jf :yfgLo :t/df kfOg] cGo ;fduL| x¿ ko| f]u u//] 7f]; j:t' -6]6f« x8] «g, cS6fx8] «g, ;fnL / a]ngf_ sf vf]sf| gdg' fx¿ lgdf{0f ug{'xf];\\ . ltgLx¿sf] zLifl{ aGb,' lsgf/f / sg' fsf ;ª\\Vofx¿ l6kf]6 u/L ;DaGw tflnsf agfO{ sIffsf]7fdf k:| t't ugx{' f];\\ . $= km/s km/s /ªu\\ sf sfuhnfO{ lqe'hfsf/ 6j' |mfx¿ agfO{ rf6{ k]k/df vfnL 7fpF gx'g] u/L 6f;F ug'{xf];\\ / cfkmn\" ] agfPsf] 6l] ;n;] gnfO{ sIffdf k:| t't ugx{' f];\\ . % tYofª\\szf:q != tkfOs{F f] ljBfnodf ePsf hDdf ljBfyL{ ;ªV\\ of, hDdf 5fq ;ª\\Vof Pjd\\ hDdf 5fqf ;ª\\Vof l6kf6] u/L ax':tDe lrq agfpgx' f;] \\ . 148 cfwf/et\" lzIff -sIff ^–*_ kf7\\ojm| d, @)&&
sIff * @= /]l8of,] 6]lnlehg jf kqklqsf nufotsf cGo ljleGg dfWodx¿af6 jm| =;= ljifo If]q Ps xKtf;Ddsf tfkjm| dsf] l6kf6] ug'{xf];\\ / To;nfO{ /v] f nv] flrqdf != ;d\"x bv] fO{ sIffsf]7fdf k:| t't ug'x{ f;] \\ . @= cªs\\ ul0ft ;Defljt ko| f]ufTds÷kl/ofh] gf sfo{ != cfkm\"nfO{ / ;fyLnfO{ dgkg{] kmnkm\"nsf] gfd l6kf6] ug{'xf;] \\ . To;sf] cfwf/df b'O{ km/s ;d\"x agfpgx' f];\\ / To;nfO{ sf8{af]8{ k]k/df e]glrq agfO{ cnlUuPsf jf vlK6Psf s:tf] ;d\"x aGof] sIffsf]7fdf k:| t't ug'x{ f];\\ . != Pp6f jo:s xflQsf] cf};t tfn} vfh] L u/L SjLG6ndf nV] g'xf;] \\ . To;nfO{ j|mdzM lsnfu] |fd, uf| d / ldnLu|fddf ?kfGt/0f ug{'xf;] \\ / To;nfO{ a1} flgs ;ª\\s]tdf nV] g'xf];\\ . @= xf6 ahf/ jf k':ts k|bzg{ L jf tkfOsF f] glhs}sf] k;ndf uO{ ljleGg 5'6, 5'6sf cj:yfx¿ ;s+ ng u/L gfkmf / gfS] ;fg ;DalGw ;d:ofx¿ / To;sf] ;dfwfg u/]/ sIffsf7] fdf k:| t't ugx{' f];\\ . #= cfkmg\\ f] glhs}sf] ljQLo ;:+ yf jf as+} df hfg'xf];\\ jf OG6/g6] af6 vf]hL u/L km/s km/s vftfsf] Jofhb/sf] hfgsf/L lng'xf];\\ / s'g vftfdf /sd hDdf ubf{ jflif{s ?kdf a9L Jofh kfObf] /x5] < kQf nufpgx' f];\\ / k:| tt' ug{'xf];\\ . #= Ifq] ldlt != tkfOF{sf] ljBfno j/k/ ePsf lqe'hfsf/ / rt'e{'hfsf/ cfwf/ ePsf j:t' -kw| fgfWofkssf] gfd nl] vPsf] lqe'hfsf/ cfwf/ ePsf j:t,' lstfa, z}Ifl0fs kf6L cflb_ sf] ;txx¿sf] cfwf/, prfO gfkL To;sf] If]qkmn lgsfNg'xf;] \\ . $= aLhul0ft !=a2 ‒ 36, x2 + 5x + 6 h:tf aLhLo cleJo~hssf] v08Ls/0fsf] gd'gf (model) agfO{ k:| t't ugx'{ f];\\ . @= s'g} b'Oc{ f6] f aLlho cleAo~hs lngx' f];\\ / pQm cleAo~hx¿sf] v08Ls/0f ug{'xf;\\ . ;femf / afsF L u'0fgv08x¿ kQf nufO{ e]g lrqdf b]vfpgx' f];\\ . To;sf] cfwf/df dxQd ;dfkjts{ -d=;=_ / n3'Qd ;dfkjTo{ -n=;=_ lgsfNg'xf];\\ . %= Hofldlt != rf6{kk] /df 3g, if8d\\ 'vf, 66] «fx8] «g, ;f]nL / a]ngfsf hfnLx¿ tof/ kf/L k6\\ofP/ 7f]; j:t' agfpg'xf];\\ / sIffsf]7fdf k|:t't ug{'xf;] \\ . @= Pp6f sfuhsf] kfgfnfO{ b'O{ a/fa/ efudf ljefhg xg' ] u/L kmfN] 8 ugx'{ f];\\ / Psfkl6\\6 s'g} lqeh' sf] lrq agfpg'xf];\\ / csf]{ kl6\\6 klxn] agfPsf] lrqsf cfwf/df 6«;] ug'{xf];\\ . ca sfuh vfN] g'xf];\\ . s:tf] lrq aGof] sf8{af8] { k]k/df 6fF:g'xf;] \\ . b'O{ lqe'hsf] t'ngf u/L lgZsif{ lgsfNg'xf];\\ / k|ltj]bg tof/ u/L sIffsf]7fdf k:| t't ug'{xf];\\ . cfwf/e\"t lzIff -sIff ^–*_ kf7\\oj|md, @)&& 149
^= tYofª\\szf:q != tkfO{Fsf] 3/df dfl;s ¿kdf vfgf, nQfsk8f, lzIff, :jf:Yo / ljljw zLifs{ df slt slt vr{ x'G5, cleefjs;Fu ;fw] L jQ[ lrqdf k|:tt' ug'x{ f];\\ . kl/of]hgf÷k|of]ufTds sfo{ ljifoj:ts' f] k|s[lt, ;f| ]t ;fwgsf] pknAwtf / pkoQ' mtfsf] cfwf/df JolStut jf ;fdl\" xs ¿kdf ug{ ;lsg5] . oL sfo{x¿ ;DkfbgkZrft\\ sIffsf]7fdf k:| t'tLs/0f ug'{kg{] 5 . k|:tt' Ls/0fdf df}lvs, lnlvt jf sDKo'6/ k|ljlwsf] k|of]u ug{ ;lsg] 5 . oxfF lbOPsf kl/of]hgf sfo{x¿ gdg' f dfq x'g\\ . lzIfsn] ljifoj:t'sf] k|sl[ tcg';f/ ljBfyLx{ ¿nfO{ cGo kl/ofh] gf sfo{x¿ u/fpg' kg{]5 . ^= l;sfO ;xhLs/0f ljlw tyf kl| j|mof o; kf7o\\ j|mdn] ljBfyLx{ ¿df ul0ftLo ljifoj:tx' ¿sf] wf/0ff ljsf; u/L ul0ftLo l;ksf ;fy} Jojxf/s'zn l;k ljsf;sf nflu ;xof]ufTds, /rgfTds, cGj]if0ffTds nufotsf ljlwx¿sf] dfWodåf/f ;/naf6 hl6n tyf d\"t{af6 cdt\" s{ f] j|mddf k:| t't ub}{ lj|mofsnfkd'vL l;sfO ;~rfngdf hf8] lbG5 . . sIff ^–* df ljm| ofsnfkd'vL l;sfO lj|mofsnfk ;~rfngsf nflu ko| f]u ug{ ;lsg] sx] L ljlw / k|lj|mof pbfx/0fsf ¿kdf k|:tt' ul/Psf] 5 . lzIfsn] oL / cGo lj|mofsnfkd'vL / ljBfyLs{ l] Gb|t l;sfO ljlw tyf k|lj|mof 5gf6] u/L lzIf0f l;sfO ljm| ofsnfk ;~rfng ug'{kb{5 . o;sf ;fy;fy} cfwf/e\"t tx sIff ^–* df ul0ft lzIf0f ubf{ ul0ftnfO{ Jofjxfl/s b}lgs hLjgsf ;d:ofx¿ / ul0ftsf] k|ToIf k|of]u ePsf÷ul/Psf cj:yfx¿af6 ;'? u/]/ ul0ft lzIf0f ug{' pko'St x'G5 . ul0ft lzIf0fdf k|ofu] ug{ ;lsg] sx] L ljlwx¿ M jm| = ljlw ljlw kl| jm| of ul0ftdf k|of]u x'g] ;Defljt ljifoj:t' ;=+ != cfudg ljlw ;\"rgfx¿sf] ;ª\\sng, aLhul0ft cGtu{tsf kf7x¿ lzIf0f ug{ cjnfs] g / lgisif{ Ifq] kmn, kl/ldlt / cfotg;DaGwL ;\"qx¿ cg'dfg, ljZn]if0f, kl' i6 kQf nufpg / lgisif{ dWos, dlWosfsf ;\"qx¿ kQf nufpg @= lgudg ljlw ;d:ofsf] k:| t'lt aLhul0ft cGtu{tsf kf7x¿ lzIf0f ug{ cfjZos ;q\" sf] klxrfg If]qldlt cGt{ut Ifq] kmn, kl/ldlt / / k|of]u cfotg;DaGwL ;d:ofx¿ ;dfwfg ug{ JofVof, ljZni] f0f / cÍul0ft cGt{utsf ;d:ofx¿ ;dfwfg lgisif{ ug{ #= ;d:of ;d:ofnfO{ a'‰g], b}lgs hLjgsf ;fdfGo ;d:ofx¿ klxrfg ;dfwfg u//] ul0ftLo 1fg / l;ksf] k|of]u u/L ljlw of]hgf lgdf0{ f, ;dfwfg ug]{ . of]hgf sfof{Gjog, cª\\sul0ftLo ;d:ofx¿ ;dfwfg, tYofªs\\ zf:q lzIf0f ug{ cl3Nnf sfo{sf] kg' /fjnf]sg ug]{ / 150 cfwf/e\"t lzIff -sIff ^–*_ kf7\\ojm| d, @)&&
kl/0ffdnfO{ hfFRg] $= cGj]if0f ;d:of jf kZ| gsf] s'g} klg ul0ftLo ljifoj:t'nfO{ vfh] L tyf vf]h k|:t'lt ug'{kg{] vfnsf k|Zgx¿ lbP/ ljBfyLx{ ¿nfO{ vfh] L ug{ nufO{ cfjZos vf]h sfo{sf] nflu 1fg lgdf{0f . h:t} M 7f]; j:ts' f cfjZos ;fwg tyf ;dtnLo ;txx¿, lqe'hsf tyf tl/sfsf af/]df 5nkmn rt'eh' s{ f u0' fx¿sf] vfh] L ug{ ljBfyL{x¿åf/f vfh] sfo{ ;~rfng lgisif{ / k|:t'lt k[i7kfi] f0f %= kl/of]hgf ;d:ofsf] k:| t'lt ul0ftsf ;a} l;sfO If]qx¿df o;sf] ljlw ofh] gf lgdf0{ f k|of]u ug{ ;lsg] ofh] gfsf] sfofG{ jog /s] 8{ /fVg] sfo{ ljZni] f0f / lgisif{ k|:t'tL ^= ko| f]ufTds ;d:ofsf] k|:t'lt sg' } klg ul0ftLo wf/0ffx¿ ljsf; u/fpg . h:t} M HofldtLo tYox¿sf] k/LIf0f ug{ ljlw ;dfwfgsf] tof/L ;fdu|L ;ª\\sng / ko| f]u JofVof, ljZni] f0f, kl' i6 &= gdg' f lrq0f ;d:ofnfO{ a'em\\g] cªs\\ ul0ft tyf aLhul0ftsf zflAbs ;d:ofx¿ ;dfwfg ug{ ljlw ;d:ofnfO{ lrqfTds (Model drawing ?kdf k|:t't method) lrqsf] dfWodaf6 ;d:of ;dfwfg *= k|of]uzfnf ;d:ofsf] klxrfg Ifq] ldlt cGtu{tsf If]qkmn / cfotg ljlw k|of]uzfnfdf lzIfssf] ;DaGwL ;q' x¿ :yflkt u/L ;d:of ;xof]udf jf ljBfyL{ ;dfwfg ug{ cfFkm}n] ;fduL| sf] k|of]u HofldtLo tYox¿ k|of]ufTds tl/sfn] u/L ;d:ofsf] ;dfwfg k'li6 ug{ cflb . (= ;/+ lrt ;d:ofsf] k|:t'tL ;a} kf7x¿ lzIf0f ug{ ;d:of JolStut, hf]8L / cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&& 151
;dfwfg ;dx\" df ;dfwfg ljlw k|:t'tLs/0f / 5nkmn ;f/f+z / lgisif{ (Structured problem solving method) !)= v]n ljlw ljifoj:t'nfO{ v]nsf ljleGg vn] x¿sf] dfWodaf6 ul0ftLo dfWodaf6 k|:tt' u/L wf/0ffx¿;Fu kl/lrt u/fpg . h:t} M cEof; aLhul0ftdf dfg kQf nufpg] laª\\uf] cflb . !!= el\" dsf ;d:ofsf] k:| t'lt ;d\"x, cªs\\ ul0ft cGtu{tsf kf7x¿ lgjfx{ ljlw ;d:ofcg;' f/ lzIf0f ug{ . ljBfyLx{ ¿nfO{ ljleGg el\" dsf k|bfg ljBfyLx{ ¿nfO{ clego ug{ nufpg] lgisif{ !@= /rgfTds dlit:s dGyg -Brain lqeh' tyf rt{e' h' sf u0' fx¿sf] vfh] L tyf l;sfO ljlw storming_ k|dfl0ft ug{ (constructive learning kf7;DaGwL k\"j{1fgsf] 7f;] j:tx' ¿sf ljz]iftfx¿ tyf ;DaGwsf] klxrfg lzIf0f ug{ method) cGt/lj|mofTds sfo{ - aLhLo wf/0ff ljsf; ug{ . j}olSts lrGtg, ;dx\" k|To]s kf7sf] k'g/jnfs] g ug{ sfo,{ kZ| gf]Q/_ If]qkmn tyf cfotg ;DaGwL wf/0ff cfjZostfcg';f/ lgdf0{ f ug{ ;xof]u k|bfg cª\\sul0ftsf ljifoj:t' lzIf0f ug{ cflb ljrf/ cfbfg kb| fg lgisif{ !#= ;xof]ufTds ;dx\" lgdf0{ f ul0ftsf ;a} l;sfO If]qx¿df o;sf] l;sfOsf ;d:ofsf] k:| t'lt ko| f]u ug{ ;lsg] ljlw ;dx\" df 5nkmn, ljZn]if0f / lgisif{ !$= If]q e|d0f ;DalGwt :yndf uO{ ;fwf/0f Aofh, gfkmf / gfS] ;fg cflbsf] tYox¿sf] ;ª\\sng, wf/0ff lzIf0f ug{ . ljZni] f0f / lgisif{ 152 cfwf/e\"t lzIff -sIff ^–*_ kf7\\ojm| d, @)&&
!%= kb| zg{ ljlw ;fdu|L ;ªs\\ ng jf HofldtLo tYox¿ kd| fl0ft ug{ lgdf{0f /rgf lzIf0f ug{ r/0fa4 ?kdf ;fdu|Lx¿ k|bzg{ cª\\sul0ft, aLh ul0ftsf cjwf/0ff lzIf0f ug{ cflb cg'dfg, 5nkmn, ljZn]if0f / lgisif{ !^= kZ| gf]Q/ lzIfs—ljBfyL{, ljBfyLx{ ¿df sg' } klg ul0ftLo wf/0ffsf] ljlw ljBfyL{—lzIfs, ljsf; ugs{ f nflu k\"j{1fg klxrfg tyf ljBfyL{—ljBfyL lardf l;sfOsf] d\"Nofªs\\ g ug{ . k|Zg / pQ/ ug{ ;lsG5 . h:t}M æolb o:tf] eP ===æ h:tf cj:yfhGo k|Zgx¿ ug{ ;lsG5 . -APPLE Technique ckgfpg ;lsG5 M A: Ask question in whole class P: Pause for a while P: Pick a student L: Listen answer carefully E: Evaluate_ ul0ft Ps Jofjxfl/s / ko| f]ufTds ljifo xf] . o; ljifonfO{ k|ofu] fTds ¿kdf l;sfO lj|mofsnfk ;~rfng u/L ljBfyL{x¿df ul0ftLo 1fg, l;k l;sfpg ;fdu|Lsf] ko| fu] ckl/xfo{ 5 . cfwf/e\"t tx -sIff ^−*_ df ul0ft l;sfOsf nflu pkof]uL sx] L ;fdu|Lx¿nfO{ If]qut ¿kdf lgDgfg';f/ k|:t't ul/Psf] 5 M ljifo Ifq] sf cfwf/df s]xL zI} fl0fs ;fduL| x¿sf] ;r\" L jm| =;= Ifq] PsfO zI} fl0fs ;fdu|Lx¿ ljleGg :yfgLo ;fdfu|Lx¿, Hofldlt aS; != ;dx\" ;dx\" l;Gsfx¿, tf/x¿, 9ª' \\ufx¿ @= cª\\s ul0ft k0\" f{ ;ª\\Vof k\"0ff{ª\\s Base ten blocks, låcfwf/, k~rcfwf/ ;ª\\Vof rf6{ ljleGg rf6x{ ¿, cg'kflts ;ª\\Vofx¿ jf:tljs cªs\\ rf6{x¿, cfwf/et\" lzIff -sIff ^–*_ kf7\\oj|md, @)&& 153
;ª\\Vofx¿ leGg / bzdnj kf/bzL{ kfgf (Transparency sheet), uf| kmk]k/x¿, sf6]/ 6j' |mf kfg{ ;lsg] j:t'x¿, jQ[ af]8{ lhof] af8] {, Base ten blocks cgk' ft, kf/bzL{ kfgf (Transparency sheet), uf| kmk]k/x¿, Base ten ;dfg'kft / blocks k|ltzt gfkmf / gfS] ;fg ljleGg lanx¿, dN\" o ;\"rL P]lss lgod ljBt' sf lanx¿, rf6{ ;fwf/0f Aofh a}ªs\\ x¿df Aofh lt/]sf /l;bx¿, :yfgLo td;'sx¿, e/kfO{x¿, aª} \\ssf a|f];/ #= If]qldlt kl/ldlt, If]qkmn Tff/, wfuf], l;Gsfx¿, lhof]af8] ,{ ljleGg :yfgLo 7f;] / cfotg j:t'x¿ -gdg' fx¿_ $= aLh ul0ft aLh ul0ftLo kk] / sl6ªx¿, ljleGg bO' { jf ltg cfoflds df8] ]nx¿, cleJo~hs aLh ul0ftLo gdg' fx¿, 6fon, bzcfwf/ Ansx¿ %= Hofldlt /]vf / sf0] f wfuf], h;' kfOk, l;Gsfx¿, uxs'F f] 5\\jfnL, afF;sf l;Ssf, h;' kfOk, j[Q af8] {, ds] fgf] l:6«k, tf/af6 agfpg ;lsg] ljleGg sf0] fx¿sf] gd'gf ;dtnLo Tff/x¿, wfuf,] l;Gsfx¿, lhofa] f]8,{ uxs'F f] 5\\jfnL, afF;sf] cfs[ltx¿ l;Ssf, h;' kfOk, j[Q af8] {, ds] fgf] l:6«k ;d¿ktf / Tff/x¿, wfuf,] l;Gsfx¿, lhof]af]8{, sIffsf7] fdf kfOg] cg¿' ktf :yfgLo ;fduL| x¿, kmf]6f] / lrqx¿, uxsF' f] 5j\\ fnL, af;F sf] l;Ssf, h;' kfOk, d]sfgf] l:6«k cflb j[Q wfuf,] r/' f, kfOkx¿, srf}/f lunf;sf lkFw jf cfwf/ / 3/] f, j[Qaf]8{, 3/, kl/jf/ jf jftfj/0fdf kfOg] j[Qfsf/ gdg' fx¿ 7f;] cfsf/x¿ efF8fjt{g, an, sf7sf 6'j|mfx¿, ;fag' , aLhLo kQL gdg' fx¿ -6S] 6fOn_ lgbz]{ fª\\s lhofa] f]8{, u|fkmaf]8{, sIffsf7] fdf ljBfyL{sf] a;fO Joj:yfkg kl/ldlt, Ifq] kmn Tff/, wfuf], l;Gsfx¿, lhof]af8] ,{ ljleGg :yfgLo 7f;] / cfotg j:tx' ¿ -gdg' fx¿_ 154 cfwf/et\" lzIff -sIff ^–*_ kf7o\\ jm| d, @)&&
:yfgfGt/0f lhof]af]8,{ wfuf,] Pg] f, sf8{af]8,{ 6r{nfO6 ;dldlt / wfuf], sfk{]6sf gdg' f lrqx¿, lhof]af]8{ 6;] ]n];g lbzfl:ylt / lhofa] f8] {, gS;fdf ko| fu] ePsf] :sn] :s]n 8O« ª ^= tYofªs\\ tYofªs\\ zf:q l;Gsfx¿, u|fkm jf]8{, /ªu\\ Lg kk] /x¿ lhof]af]8{, zf:q plNnlvt ljlw tyf ;fdu|Lx¿ pbfx/0fsf ¿kdf jf ;fdfGo kyk|bzg{ sf ¿kdf dfq k|:t't ul/Psf] xf] . kl/l:yltcg';f/ pkoS' t pkfox¿ ckgfO{ lzIf0f l;sfO ljm| ofsnfknfO{ cem k|efjsf/L agfpg' cfjZos x'G5 . &= ljBfyL{ d\"Nofª\\sg kf7o\\ jm| dn] ckI] ff u/s] f ;Ifdtf / l;sfO pknlAw xfl;n ePgePsf] ;'lgZrt ug{ lgdf0{ ffTds / lg0fo{ fTds d\"Nofª\\sg cjnDag ul/g] 5 . cfGtl/s dN\" ofª\\sgsf] d'Vo p2]Zo lg/Gt/ d\"Nofª\\sg / ki[ 7kf]if0fsf dfWodaf6 ljBfyLs{ f] l;sfOdf ;'wf/ ug'{ xf] . l;sfOsf nflu ul/g] o:tf] cfGtl/s d\"Nofª\\sg lzIf0f l;sfO kl| jm| ofsf] cleGg cªu\\ sf ¿kdf /xg' kb{5 . cfGtl/s dN\" ofª\\sgdf ljBfyL{sf] d\"Nofªs\\ gsf nflu ljleGg cf}krfl/s tyf cgf}krfl/s tl/sf k|of]u ug{k' 5{ . cfGtl/s d\"Nofªs\\ gdf sIff ljm| ofsnfk, ljBfyL{sf sfo{ tyf sfo;{ Dkfbgsf] cjnf]sg, u[xsfo,{ kl/ofh] gf sfo{, df}lvs tyf lnlvt sfo{, PsfO tyf qd} fl;s k/LIffx¿, :j tyf ;xkf7L dN\" ofªs\\ gnufotsf ;fwg ko| f]u ug{ ;lsG5 . ljBfyL{ dN\" ofªs\\ g ubf{ d'Vo l;sfO pknlAw ljBfyL{n] xfl;n u/s] f] l;sfO :t/sf] dN\" ofªs\\ gsf nflu ljBfyL{sf sfo{ tyf ;d:of ;dfwfgsf] cjnf]sg, dfl} vs tyf lnlvt kZ| gf]Q/, sIff tyf PsfO k/LIff, Jojxf/ cjnf]sgnufotsf tl/sf ko| fu] ug{ ;lsG5 . o;sf nflu ?h\";\"rL tyf >]0fL dfkg nufotsf Jojxf/ cjnf]sg kmf/d, ljleGg txsf l;sfO Ifdtf dfkg ug]{ kZ| gx¿, Jofjxfl/s ;d:ofnufot sIff ;xeflutf, sIff sfo{, u[xsfo{, kl/of]hgf sfo,{ ko| f]ufTds sfo{ cflbdf ljBfyLs{ f] ;xeflutf / pknlAwsf ljifodf lzIfssf] clen]v jf gf]6 cflb d'Vo l;sfO pknlAwdf ljBfyL{sf] l;sfO :t/ dN\" ofªs\\ g ug{ k|of]u x'g;Sg] ;fwgx¿ xg' \\ . o:tf] dN\" ofªs\\ g ljifoj:ts' f] kT| os] Ifq] jf PsfOsf] l;sfOkZrft\\ u/L ;f] If]q jf PsfOcGtut{ sf d'Vo l;sfO pknlAwdf ljBfyL{sf] l;sfO :t/ k/LIf0f ljleGg ;fwgx¿sf] ko| f]uaf6 ugk'{ 5{ . o;/L l;sfO pknlAw k/LIf0f ubf{ ljBfyL{n] Gog\" td l;sfO :t/ xfl;n u/s] f] gkfOPdf ;w' f/fTds l;sfOsf] cj;/ k|bfg u/L kg' M k/LIf0f u/L Gog\" td l;sfO:t/ ;'lglZrt u/L yk jf dflyNnf] :t/sf] l;sfOsf] cj;/ kb| fg ug{' kb5{ . k6sk6ssf] ;w' f/fTds l;sfO kZrft klg Go\"gtd :t/sf] l;sfO :t/ xfl;n ug{ g;Sg] ljBfyL{sf nflu pkrf/fTds l;sfOsf] ofh] gf lgdf0{ f u/L To:tf ljBfyL{nfO{ ;xof]u ug'{kb{5 . -s_ cfGtl/s dN\" ofª\\sg cfGtl/s d\"Nofª\\sgsf] cªs\\ sf] lglZrt ef/ cfGtl/s d\"Nofªs\\ gsf ¿kdf clen]lvt ug'{k5{ . o;sf nflu cfGtl/s d\"Nofªs\\ gnfO{ clenl] vt u/L k|Tos] ljBfyL{sf] sfo{;~rlosf (Portfolio) Jojl:yt u/L /fVgk' 5{ . o:tf] clen]vsf cfwf/df lgDglnlvt kIfdf tf]lsPcg;' f/sf] ef/sf] cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ j|md, @)&& 155
cª\\s cfGtl/s dN\" ofª\\sgsf ¿kdf ;dfj]z ul/g] 5 M l;=g+= d\"Nofª\\sgsf kIf ef/ ! ;xeflutf M sIffdf pkl:ylt / sIff sfod{ f ;xeflutf $ @ dV' o l;sfO pknlAwdf ljBfyLs{ f] l;sfO:t/ @) # k|of]ufTds÷kl/of]hgf !^ $ qd} fl;s k/LIffx¿ !) cfGtl/s d\"Nofªs\\ gsf ;fwgx¿ / k|of]u jm| =;= ;fwg ko| fu] ! ?laS| ;/ >0] fL ljBfyL{n] u/]sf ko| f]ufTds sfo÷{ kl/ofh] gf sfo{sf] d\"Nofª\\sg dfkg ugs{ f nflu ?laS| ;/>0] fL dfkgsf] ljsf; u/L ko| f]u ug{'k5{ . @ Jojxf/ ul0ftsf kl| j|mofut l;kx¿sf] d\"Nofª\\sg, kf7ut ¿kdf ljBfyL{n] cjnfs] g kmf/d l;Sg'kg]{ l;k tyf ltgsf] k|ofu] / Jojxf/sz' n l;ksf] dfkg ug{ ?h\";\"rL, >]0fL dfkgnufotsf Jojxf/ cjnf]sg kmf/d ko| f]u ug{ ;lsG5 . # lzIfssf] kT| o]s kf7df sIff ;xeflutf, u[xsfo{, kl/of]hgf sfo{, ko| fu] fTds clenv] sfos{ f j|mddf ljBfyL{x¿n] b]vfPsf] ;ljm| otf, l;hg{ fTdstf, l;sfO Jojxf/, sfdsf] :t/sf, kb| lz{t Jojxf/s'zn l;kx¿ kf7\\oj|mddf lgwfl{ /t l;sfO pknlAwsf cfwf/df s'g :t/sf] /x]sf] lzIfsn] JolQmut ¿kdf clen]v /fVg' kg]{5 . $ sIff k/LIff kf7 jf PsfO lzIf0fsf j|mddf ul/g] lnlvt sfo{ tyf lnOg] 5f]6f] k/LIff, q}dfl;s k/LIff % dfl} vs k|Zgf]Q/ lzIf0f l;sfOs} j|mddf ;fl] wg] kZ| gx¿ o;cGtu{t kb{5g\\ . o;sf] glthf clen]lvLt ug{' kg{] ePdf lzIfssf] clen]vdf pNnv] ugk{' g]{ 5 . ljBfyLs{ f] lg0f{ofTds d\"Nofª\\sgsf nflu cfGtl/s d\"Nofª\\sgaf6 kf| Kt lglZrt cª\\snfO{ cfGtl/s d\"Nofª\\sgsf ¿kdf %) kl| tzt ef/ lgwf{l/t u/L afFsL %) kl| tzt ef/sf] clGtd k/LIff ;~rfng ul/g] 5 . -v_ cfjlws d\"Nofª\\sg lg0fo{ fTds dN\" ofª\\sgdf clGtd k/LIffsf] ef/ %) k|ltzt x'g5] . k|To]s k/LIffdf k|Zg ;fW] bf z}lIfs ;qsf] ;?' bl] v k9fO ePsf ;a} kf7x¿af6 ;dl] 6Psf] xg' 'kg]{ 5 . o; ljifosf] k/LIffdf ljz]if u//] 1fg / af]w, ko| f]u / pRr bIftfdf cfwfl/t x'g] 5g\\ . kf7\\oj|mdn] lgwf{/0f u/s] f p2Z] ocg¿' k ljBfyL{x¿n] 1fg, l;k, clejl[ Q k|fKt u/] gu/]sf] dN\" ofªs\\ g u/L To;sf] cfwf/df k|df0fLs/0f ul/G5 . clGtd k/LIffsf] k|Zgkq kf7\\oj|md ljsf; sG] b|n] tof/ u/s] f] ljlzi6Ls/0f tflnsfnfO{ cfwf/ dfgL lgdf0{ f ul/g'k5{ . 156 cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
cfwf/e\"t lzIff -sIff ^—*_ kf7o\\ jm| d, @)&& lj1fg tyf kl| jlw != kl/ro lj1fgn] k|s[lt / a|Xdf08sf af/]df Jojl:yt cWoog / vf]hL ugs'{ f ;fy} kl| jlwo'St ljsf;nfO{ cl3 a9fpg dbt ub{5 . xfd|f] hLjgsf x/s] ljm| ofsnfknfO{ lj1fgn] lgb]{lzt u/s] f] x'G5 . lj1fg / cfljisf/sf dfWodaf6 dfgj hLjgnfO{ ;xh agfpg] gjLgtd j:t' tyf ;]jfsf] pTkfbgdf ko| fu] ul/g] ljlw / k|ljm| ofsf] ;ª\\sng kl| jlw xf] . ;+;f/df eO/xs] f] csNkgLo ljsf; lj1fg / kl| jlwsf] sf/0faf6 ;Dej ePsf] xf] . kl/jlt{t ;;+ f/df cfkm\"nfO{ cg'sn\" agfpg, kf| Kt ;|f]t / ;fwgx¿sf] ;xL ¿kdf pkof]u ug,{ lj1fg / kl| jlwsf] ljsf;n] l;h{gf u/]sf cj;/x¿nfO{ cfTd;ft ug{ / jftfj/0f kl/jt{gk|lt ;r]t x'g j}1flgs ;e' mae' msf] h?/t kb{5 . j1} flgs ;'ema'em;lxtsf] c;n / bIf gful/s tof/ ug{ afnaflnsfx¿df ;fg} pd/] b]lv pgLx¿df j1} flgs ;f]r, lrGtg / clejl[ Qkl| t ;sf/fTds efjgfsf] ljsf; ug{' cfjZos 5 . g]kfnsf] ljBdfg z}lIfs gLlt, ljleGg ;dodf ul7t cfofu] x¿sf ;e' mfjx¿sf ;fy} b]zsf] kl/jlt{t ;ª\\3Lo ;+/rgf tyf cGt/fl{ i6«o kl/jz] n] lj1fg / ;r\" gf kl| jlwnfO{ ljBfno lzIffsf] ljifo / dfWodsf ¿kdf Jojl:yt ug{ ;e' mfPsf 5g\\ . lzIffnfO{ :yfgLo cfjZostf tyf dN\" o / dfGotfdf cfwfl/t agfpg klg plQs} vfFrf] 5 . ;fy} kT| o]s gful/snfO{ cTofjZos hLjgfk] of]uL / Jojxf/s'zn l;kx¿ ljsf; ug]{ u/L kf7o\\ j|mdnfO{ ;Ifdtfdf cfwfl/t agfpg]nufotsf kl/jt{gsf] 68\\sf/f] cfjZostf bl] vPsf] 5 . ljZjdf cfPsf] kl/jt{g;Fu} ;fdflhs ¿kfGt/0fcg;' f/sf] rfxgf / cfjZostf;d]tsf cfwf/df o; kf7\\oj|mdn] ljifoIfq] x¿ lgwf/{ 0f u/s] f] 5 . lj1fg tyf k|ljlwdf ePsf] cfd\"n kl/jt{g tyf ljsf;cg's\"n ;dfofh] g ub{} ;do;fk]If tyf Jofjxfl/s agfpg cfjZos bl] vPsfn] /fli6«o kf7o\\ jm| d kf| ¿k, @)&^ n] sIff ^ bl] v * ;Dd lj1fg tyf kl| jlw ljifo ;dfj]z ug{] Joj:yf u/c] g';f/ of] kf7\\oj|md ljsf; ul/Psf] xf] . cfwf/e\"t txbl] v g} afnaflnsfdf lj1fgsf cfwf/e\"t 1fg, lj1fg k|ljm| ofut l;k, j1} flgs sf/0f, ;d:of ;dfwfg, j}1flgs cg';Gwfg l;k tyf j}1flgs clej[lQ;lxt j}1flgs ;e' mae' m ePsf gful/s pTkfbg ug{ o; kf7\\oj|mdn] hf8] lbPsf] 5 . o;sf nflu ;r\" gf / kl| jlw;DaGwL ;fIf/tf ljsf;, k|fs[lts jftfj/0fsf] ;+/If0f / ;b'kof]u ug]{ pkfox¿ vf]hL ug{] afgLsf] ljsf; tyf hLjg / jftfj/0flarsf] cGt/;DaGw af]w u/fpg] p2Z] on] o; ljifodf j}1flgs l;sfO, ;\"rgf tyf ;~rf/ kl| jlw, hLjx¿ / ltgLx¿sf] agf6] , hl} js ljljwtf / jftfj/0f, hLjx¿sf] hLjg k|ljm| of, an / rfn, bl} gs hLjgdf zlSt, ljBt' \\ / rD' as, kbfy{, bl} gs ko| fu] sf kbfyx{ ¿ / k[YjL tyf cGtl/If u/L !! cf6] f ljifoIfq] ;dfj]z ul/Psf 5g\\ . o; kf7o\\ j|mdn] k|of]ufTds tyf kl/ofh] gfdf cfwfl/t l;sfOsf dfWodaf6 afnaflnsfx¿df kT| oIf l;sfO cge' j u/fpg] ljm| ofsnfkx¿df hf8] lbPsf] 5 . ljBfyLs{ l] Gb|t l;sfO lj|mofsnfkx¿sf dfWodaf6 ck]lIft l;sfO pknlAw xfl;n u/fpg] / tL pknlAwx¿ xfl;n eP gePsf] ;'lglZrt ug{ lgdf0{ ffTds / lg0f{ofTds dN\" ofªs\\ gsf ;fwgx¿sf] k|efjsf/L k|of]u ug{] kIfdf ;dt] o; kf7o\\ j|mdn] hf8] lbPsf] 5 . o;sf ;fy} lj1fg / kl| jlwlar cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ j|md, @)&& 157
Pscfk;df cGof]Gofl>t ;DaGw ePsfn] ;\"rgf tyf ;~rf/ kl| jlwnfO{ dfWod / ljifoj:t'sf ¿kdf k:| t't ul/Psf] 5 . @= txut ;Ifdtf cfwf/e\"t tx -sIff ^–*_ sf] cGTodf ljBfyL{x¿df lgDglnlvt ;Ifdtf xfl;n xg' ] 5g\\ M != j1} flgs l;sfO kl| jm| ofsf] af]w tyf lj1fgsf k|lj|mofut l;ksf] k|of]u @= ;\"rgf / ljrf/x¿sf] cfbfgkb| fg, ljZni] f0f tyf ;\"rgf kl| jlwsf] ;dl' rt k|of]u #= h}ljs ljljwtf / jftfj/0flarsf] cGt/;DaGwsf] a'emfO kb| z{g tyf ;+/If0fsf] ko| f; $= hLjx¿ / hLjg k|lj|mofsf] hfgsf/L tyf dxŒj af]w %= bl} gs hLjgdf an / pks/0fsf] ko| f]u:fDaGwL cfwf/e\"t kIfx¿sf] klxrfg / k|of]u ^= b}lgs hLjgdf ko| fu] xg' ] zlStsf ljleGg ¿ksf ljzi] ftfsf] cfwf/e\"t 1fg, ltgLx¿sf] plrt ko| f]u / ;+/If0fkl| t tTk/tf &= kbfy{sf u'0fx¿sf ;DaGwdf hfgsf/ eO{ bl} gs hLjgdf pkof]u *= bl} gs hLjgdf k|of]u ul/g] kbfyx{ ¿sf] klxrfg / ;d'lrt ko| f]u (= k[YjL / cGtl/If;DaGwL cfwf/e\"t hfgsf/L / a'emfOsf] k|bz{g 158 cfwf/e\"t lzIff -sIff ^–*_ kf7\\ojm| d, @)&&
#= sIffut l;sfO pknlAw jm| =;= ljifo If]q l;sfO pknlAw sIff & sIff ^ != j1} flgs !=! j}1flgs l;sfO k|ljm| ofsf] !=! lj1 l;sfO kl/ro lbg tyf cjnDag kl| t ug{ !=@ lj1 !=@ gfkdf PsfOsf] k|of]u / df]8 dxŒj atfpg j0f !=# gfKgsf k|rlnt :yfgLo PsfOx¿ klxrfg ug{ / P; cfO{ (SI) PsfOsf] dxŒj atfpg !=$ efl} ts kl/df0fx¿sf gfksf 7n' f tyf ;fgf PsfOx¿ -units and sub-units_ atfpg tyf ko| f]u ug{ @= ;\"rgf tyf @=! ;fdfGo kl| jlw / cfw'lgs @=! ;\"r ;~rf/ kl| jlwsf] kl/ro / pbfx/0f ;fw k|ljlw lbg lbg @=@ b}lgs hLjgdf df]afOn / @=@ OG6 sDKo6' /sf] k|of]u atfpg kl/ @=# Nofk6k, 8]:s6k, 6\\ofan6] , @=# :k8]| cfOKof8, :df6k{ mf]g ;an} fO{ lx; cfwf/e\"t lzIff -sIff ^–*_ kf7o\\ jm| d, @)&&
sIff * 1fgsf k|of]ufTds sfo{sf] !=! lglZrt ljlw ko| f]u u/L tj]bg tof/ kfg{ !=@ k|of]uzfnf leq jf aflx/ ;/n 1fg;Fu ;DalGwt j:t'sf] cg;' Gwfg;j]{If0f ug{ / ;f]sf] 8n] lgdf{0f ug{ / kl| j|mof k|ltj]bg tof/ ug{ f{g ug{ lj1fgsf k|of]ufTds sfo{ ubf{ ckgfpg' kg]{ ;fjwfgLx¿ cjnDag ug{ rgf tyf ;~rf/ kl| jlwsf @=! cfOl;6Lsf ;fwgx¿sf] wgx¿sf] kl/ro / pbfx/0f @=@ ;fwf/0f k|of]u ug{ g @=# ;r{ OlGhg, j]a;fO6, 6/g6] , Odn] / a|fph/sf] cfOP;kLsf] kl/ro lbg /ro lbg / ;fdfGo k|of]u ug{ ;f];n g]6jls{ª ;fO6sf] 8l;6 ;km\\6j/] df ;fwf/0f ;fdfGo kl/ro lbg / k|of]u ;fa ug{ tyf u|fkm / rf6{sf] ug{ 159
@=$ sDKo6' /sf] ¿kdf kl/eflift @=$ lgd @=% ug{ @=% kmf]6 sDKo'6/sf efux¿ klxrfg lkh| ug{ @=^ @=& sD j8{ k|f;] ];/, :k|8] l;6 / lgb lkh| G] 6];g ;km\\6j]/sf] ;fdfGo k|of]u ug{ ;k sD cfr ug #= hLjx¿ / #=! hgfj/ / la?jfsf ljzi] f #=! kmn\" ltgLx¿sf] agf]6 cgs' \"ntfsf nIf0f tyf efu cgs' \"ngsf cª\\ux¿ klxrfg / j0fg{ ug{ #=@ la? -h/ #=@ vfgfsf cfwf/df ug hgfj/x¿sf] juLs{ /0f ug{ / sfo pbfx/0f lbg #=# 9f8 #=# 9f8 ePsf hgfj/x¿sf] juL{s/0f u/L x/s] ju ;fd ;d\"xx¿sf] ;fdfGo nIf0fx¿ atfpg #=$ hg cj #=$ kmn\" kmN' g] / km\" n gkmN' g] la?jfx¿lar ;dfgtf / leGgtf 5'6\\ofpg 160
df{0f ug{ @=$ ;fOa/ ck/fw, sDKo'6/ cfrf/;l+ xtf, ;fOj/ sfg\"g / 6f] tyf 6S] :6;lxtsf] OG6/g]6 ;/' Iffsf] ;fdfGo h]G6];g tof/ u/L k|:t't ug{ kl/ro lbg DKo'6/df nfUg] efO/;, o;sf] @=% /f]af]l6S; / er'c{ n bfg / ;'/Iffsf pkfo atfpg jf:tljstfsf] kl/ro lbg km6\\ j]/sf k|sf/sf] kl/ro lbg @=^ cfl6{lkml;on OG6l] nh]G; / DKo6' / ko| f]u;DaGwL Snfp8 sDKo'l6ªsf] kl/ro rf/;+lxtf atfpg tyf kfngf lbg / ;fdfGo k|of]u ug{ g{ n km'Ng] la?jfsf ljleGg #=! hgfj/ sfi] f / la?jf sfi] fsf] usf sfox{ ¿ j0fg{ ug{ cjojx¿sf sfox{ ¿ j0f{g ug{ ?jfsf ¿kfGtl/t cª\\ux¿ | #=@ la?jf sf]if / hgfj/ sf]if lar /f, sf08 / kft_ sf] klxrfg ;dfgtf / leGgtf 5'6\\ofpg g{, ltgLx¿sf] agf]6 / o{x¿sf] JofVof ug{ #=# dfgj z/L/df sfi] f, tGt' / cª\\usf] cGt/;DaGw JofVof 8 gePsf hgfj/x¿sf] ug{ uL{s/0f u/L x/s] ;dx\" sf] #=$ ;I\" d hLjx¿ -cldaf, kmGhfO, dfGo nIf0fx¿ atfpg AofS6l] /of, efO/;_ sf ;fdfGo kl/ro lbg tyf logLx¿sf gfj/ / jg:klt sf]ifsf kmfObf, xfgL atfpg / jojx¿sf] klxrfg ug{ xfgLaf6 aRg] pkfo cjnDag ug{ #=% vfgf s'lxg glbg] pkfox¿ klxrfg ug{ / cjnDag ug{ cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
$ h}ljs $=! Jfftfj/0fsf] kl/ro lbg / $=! kf| s[l ljljwtf / jftfj/0fd}qL Jojxf/ dx jftfj/0f cjnDag ug{ $=@ hn; $=@ Kffl/l:ylts k|0ffnLsf] kl/ro kl/ lbg / jg Kffl/l:ylts at k0| ffnLsf cjojx¿sf] j0f{g $=# k|fs[l ug{ /c $=$ 7f;] -3R %= hLjg %=! hLjx¿sf] kf]if0f kl| j|mof %=! la? kl| jm| of -mode of nutrition_ sf] j0f{g ug{ kl/ %=@ hg cfwf/et\" lzIff -sIff ^–*_ kf7o\\ j|md, @)&&
#=^ hLjx¿sf] juLs{ /0f;DaGwL b'O{ hut\\ k0| ffnL / kfFr hut\\ k|0ffnLsf ;fdfGo hfgsf/L lbg lts ;f| t] sf] kl/ro lbg, $=! h}ljs ljljwtfsf] kl/ro lbg / xTj atfpg / juL{s/0f ug{ jtd{ fg l:ylt tyf dxTj atfpg ;f| ]t, hnfwf/ / l;d;f/sf] /ro lbg / ltgLx¿sf] dxTj $=@ hl} js ljljwtf x|f; x'gsf tfpg sf/0fx¿ / pbfx/0fx¿ atfpg lts ;|f]tsf] ljgf;sf] sf/0f c;/x¿ atfpg $=# k|rlnt :yfgLo cfi} flwhGo la?jfx¿ / ltgLx¿sf] ; kmf]xf/] dn} fsf] Joj:yfkg pkofu] sf] klxrfg ug{ Rs_ ug{ $=$ hl} js ljljwtf ;+/If0fsf pkfox¿ klxrfg ug{ $=% lbuf] ljsf;sf] cjwf/0ff / dxTj atfpg $=^ h}ljs ljljwtf ;+/If0f ;DaGwL lbuf] ljsf; nIox¿ xfl;n ug{ g]kfndf ePsf ko| f;x¿ JofVof ug{ ?jfx¿ / hgfj/x¿df x'g] %=! la?jf / hgfj/df x'g] cd}y'lgs /jxg k|ljm| ofsf] JofVof ug{ k|hggsf] ;fdfGo kl/ro lbg gfj/ / la?jfdf x'g] lgisf;g %=@ la?jfdf xg' ] el] h6]l6e 161