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7/31/2019 Problem Book
1/24
V~jncgi
Njjh
-G`+
7/31/2019 Problem Book
2/24
K|b` N~bzmhk`
Bcg}b`d~ Nw~cbhb
B`butbukb {bnj|b
\cbdkucb| Umbvj|bcj|
Ib}ki Uvk|bhj|
Tzwemkg` Tmj
Dikt~{ \j~jn{g|
uwvjutbt.j~a
tg}tb`dvketw~gu
7/31/2019 Problem Book
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V~jncgi
Njjh
-G`+
7/31/2019 Problem Book
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7/31/2019 Problem Book
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X/Y K` Ib{ >62># cb~ag `wing~u jl ^wuukb`
ektkzg`u tjjh qbchu k` tmg ut~ggtu jl iboj~
ektkgu tj umjq tmgk~ dkuba~ggig`t qktm tmgv~gukdg`tkbc gcgetkj` ~guwctu. Tmg qbchu
qg~g dgckng~btgc{ jt b``jw`egd bu vjcktkebc
g|g`tu b`d qg~g dguka`gd tj tgut qmgtmg~
tmg bwtmj~ktkgu qjwcd dkuvg~ug b` w`ub`e)
tkj`gd v~jeguukj` tmbt k`|jc|gd `j ucjab`u#
bivckl{k`a grwkvig`t j~ uvgbhg~u. Ukikcb~
tbetkeu mbd tj ng bdjvtgd dwg tj tmg k`e~gbu)k`a v~betkeg jl n~wtbckt{ n{ tmg bwtmj~ktkgu
k` emb~ag jl uwvv~guuk`a j~ab`kzgd v~jtgutu.
Tmg bwtmj~ktkgu dkd jt k`tg~lg~g.
2. B~gb jl w`ugg` cw}w~{
Nwuk`guuib` dgekdgu tj umjq ujckdb~kt{ qktm tmg Tgut Qbch X/Y
n{ ut~jcck`a qktm mku qklg bcj`a tmg t~gg)ck`gd qbch b~jw`d mku
mjwug k` tmg _mwhj|hb Mkccu ejiiw`kt{.
J` tmg jtmg~ ukdg jl tmg Ijuejq k|g~# b` betk|kut grwkvvgd
qktm b ~ggc jl ej~d# igbuw~k`a tbvg b`d b v~jt~betj~ ib~hu jll b
ck`g ugaig`t ngtqgg` vjk`tu I b`d @# l~ji qmkem tqj dkbigt~k)
ebcc{ jvvjugd t~ggu -vjk`tu B b`d N+ eb` ng ugg` j` tmg qbchqb{
uw~~jw`dk`a tmg mjwug.
Ugaig`t I@ b`d tmg b`acgu kt lj~iu qktm tmg ck`gu ej``getk`a
ktu g`dvjk`tu tj vjk`tu B b`d N?
n9 I@ 9 5>.;4 i
9 BI@ 9 ==.55
9 NI@ 9 .7>
9 B@I 9 =7.47
9 N@I 9 222.;=
@
I
N
B
Lka. 2
5
7/31/2019 Problem Book
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V~jncgi?
Mjq cj`a qkcc tmg ujckdb~kt{ qbch tbhg# buuwik`a tmbt tmg eji)
iw`kt{ ku v~jtgetgd n{ b ugew~kt{ ug~|keg b`d tmbt tmg nwuk`guuib`
b`d mku qklg mb|g b` b|g~bag ut~jcck`a uvggd jl >.2;< hi*mjw~:
B`uqg~?
Tmgujckdb~kt{qbchqkcctbhg2>ik`wtgu.
>. Ijcgewcb~ ewkuk`g
Dgeging~. B |g`tkcbtkj` dwet cgbdk`a tj tmg uw~lbeg l~ji b uwumk
nb~ k` b` w`dg~a~jw`d umjvvk`a eg`tg~ giktu ubtw~btgd |bvj~ bt
b tgivg~btw~g jl (46 E. B mw`a~{ mjigcguu vg~uj` qb~iu mkiugcl
n{ tmg a~btk`a. Qmg` n~gbtmk`a j~ibcc{# mg k`mbcgu 6.57 cktg~u jl
|bvj~ k`tj mku cw`au k` b uk`acg n~gbtm -6.76 cktg~u+ b`d g}mbcgu 76
a~biu jl qbtg~ vg~ mjw~.
V~jncgi?
Mjq cj`a qkcc kt tbhg lj~ j`g vj~tkj` jl ikuj ujwv -576 a+ tj
ng bnuj~ngd k`tj mku cw`au kl ~gcbtk|g mwikdkt{ 9 266' b`d
tmg |bvj~u ijkutw~g ej`tg`t 9 72 a*i5: Mjq iwem ijku)
tw~g qkcc mg cjug tm~jwam n~gbtmk`a k` tmku ubig vg~kjd jl
tkig:
B`uqg~?
J`gvj~tkj`jlikujujwvqkccngbnuj~ngdk`tjtmgmjigcguuvg~uj`u
cw`auk`>5.54mjw~u.Dw~k`atmkutkig#mgqkcccjug2.2
7/31/2019 Problem Book
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5. B` betk|kutu d~gbi
Tmg wing~ jl v~jtgutg~u ku ej`utb`tc{ ~kuk`a. J` @j|ging~ 1#
46#666 vgjvcg umjq wv j` gd Urwb~g tj dgij`ut~btg babk`ut
aj|g~`ig`t bnwugu. K` Ib{# b e~jqd jl =6#666 flccu gd Urwb~g.
J` Owc{ 24# tmg~g b~g 2>6#666 dgij`ut~btj~u# g}eggdk`a tmg
urwb~gu ebvbekt{ n{ ug|g~bc tmjwub`d. Tmg qbccu jl tmg nwkcdk`au
uw~~jw`dk`a gd Urwb~g b~g a~bdwbcc{ vwumgd nbeh n{ tmg umgg~
vjcktkebc vjqg~ jl tmgug mwib` ibuugu ...
^gd Urwb~g# nj~dg~gd n{ tmg Mkutj~kebc Iwugwi# AWI#
Ut. Nbukcu Ebtmgd~bc b`d tmg Cg`k` Ibwujcgwi# ku b ~getb`awcb~
b~gb qktm ukdgu igbuw~k`a? 9 =7 i# n 9 4b 9 546 i. E~jqd dg`ukt{bt dgij`ut~btkj`u b|g~bagu tm~gg dgij`ut~btj~u vg~ urwb~g igtg~.
V~jncgi?
Mjq ib`{ igtg~u dj tmg nwkcdk`au nj~dg~k`a gd Urwb~g mb|g tj
ng ij|gd k` j~dg~ tj beejiijdbtg 2>6#666 dgij`ut~btj~u:
B`uqg~?
TmgH~gick`qbccu#Ibwujcgwib`dAWImb|gtjngij|gdnbeh1.7i.
TmgMkutj~kebcIwugwib`dUt.Nbukcumb|gtjngij|gdnbeh56i.
4. Wuglwc b~gb jl b utbdkwi
@k`tm)a~bdg~ Vgtg ~w`u tm~gg cbvu b~jw`d tmg uemjjc utbdkwi k`
5.4 ik`wtgu bt b` b|g~bag uvggd jl 21.>)utj~g{ jlfleg nwkcdk`au qktm jj~ uvbeg jl >
gbem qkcc flt k`ukdg tmg utbdkwi:
7
7/31/2019 Problem Book
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B`uqg~?Tmguemjjcutbdkwiqkccmjcd
<
7/31/2019 Problem Book
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V~jncgi?
Mjq ib`{ Utjv ebvktbckui" ucjab`u eb` ng ibdg wuk`a j`g
466)ic eb`: Mjq iwem djgu gbem b`tk)ebvktbckui ucjab` ejut:
B`uqg~?
2.2.Gbemb`tk)ebvktbckuiucjab`ejutu26.;6~wncgu.
7/31/2019 Problem Book
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V~jncgi?
Mjq ib`{ dgij`ut~btkj`u iwut Ektkzg` @ qj~h k` j~dg~ tj
ub|g g`jwam ij`g{ tj vb{ tmgug mk~gd dgij`ut~btj~u# tbhk`a
k`tj beejw`t tmg lbet tmbt n~kabdg cgbdg~u -j`g n~kabdg cgbdg~
vg~ tqg`t{ ba)qb|g~u+ b~g vbkd tg` tkigu ij~g tmb` ~b`h)
b`d)flcg dgij`ut~btj~u -b>+ b`d tmbt vb~t{ lw`etkj`b~kgu -j~ab)
`kzg~u b`d uvk` djetj~u+ b~g vbkd tg` tkigu ij~g tmb` n~kabdg
cgbdg~u -b5+.
B`uqg~?
Ektkzg`@iwutqj~h>#766dgij`ut~btkj`uk`j~dg~tjvb{btmjw)
ub`dejccgbawgutjbttg`dmkudgij`ut~btkj`k`uwvvj~tjlqj~h)
g~u~kamtulj~mk~gddgij`ut~btj~u.
1. Ibtt~guugu ncjeh ~k|g~u# nwt jvg` gq qb{u"
Tmg jt)tjj)dkutb`t lwtw~g. Ijuejq mbu ngg` tbhg` j|g~ n{ vjckeg
lj~egu. @gb~ tmg H~gick`# tmg Ijuejq b`d [bwzb ~k|g~u b~g tggi)
k`a qktm v~jtgutg~u. Vgjvcg b~g wuk`a k`btbncg ibtt~guugu tj lj~i
jbtk`a ebivu. @b|kabtkj` ku ejivcgtgc{ ncjehgd# b`d nb~agu b`d
tjw~kut njbtu b~g w`bncg tj vbuu. Tmg ekt{ mbu tmwu ljw`d gq emb`)
`gcu jl v~jtgut.
Tmg uw~lbeg b~gb jl tmg [bwzb b`d Ijuejq ~k|g~u k`ukdg tmg Ab~)dg` k`a ku 1. jbtk`a ibtt~guu# 2=; 1< ei# a~b{ qktm mgbd~gut#
cb~ag g`jwam lj~ tqj bdwctu b`d tqj emkcd~g`
=
7/31/2019 Problem Book
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5. jbtk`a ibtt~guu# 2=5 1 b`d
ebut k` n~j`zg k` 2;41. Tmg vcbutg~ ebut ku
utj~gd k` tmg T~gt{bhj| Abccg~{. K` 2;#666 betk|kutu qg~g dgtbk`gd bu b ~guwct
jl ecbumgu qktm vjckeg. Qmg` tmku tg}t qbu
ngk`a v~gvb~gd# 2< vgjvcg mbd ngg` emb~agd
qktm ~kjtk`a.
;
7/31/2019 Problem Book
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k` Ib{# v~jtgutg~u wugd vkgegu jl buvmbct vb|k`a bu qgbvj`u# uk`eg
Njcjt`b{b Urwb~g b`d tmg uw~~jw`dk`a b~gb# qmg~g tmg g|g`tu jl
Ib{ < w`ljcdgd# mbd w`lj~tw`btgc{ jt ngg` vb|gd qktm tmg gbukg~)
tj)mb`dcg utj`gu.
V~jncgi?
Mjq iwem qjwcd kt mb|g ejut ekt{ bwtmj~ktkgu tj b~i
16#666 ib~emg~u -bu gutkibtgd n{ tmg g|g`tu j~ab`kzg~u+ qktm j`g
utb`db~d)ukzg vb|k`a utj`g gbem lj~ j`g qgcc)bkigd tm~jq:
B`uqg~?
Ktqjwcdmb|gejutekt{bwtmj~ktkgu4#4>=#;66~wncgutjb~i
16#666dgij`ut~btj~u.
;. gdwetkj` lbetj~
Beej~dk`a tj vjckeg utbtkutkeu# 566 vgjvcg umjqgd wv bt tmg Ib~em
>7 dgij`ut~btkj` lj~ mj`gut gcgetkj`u k` l~j`t jl Ib~kk`uh{
Vbcbeg k` Ut. Vgtg~unw~a. Beej~dk`a tj mwib` ~kamtu betk|kutu#
576 dgij`ut~btj~u qg~g b~~gutgd. Bltg~ tmg b~~gutu mbd ngg`
ibdg# bt cgbut 766 dgij`ut~btj~u ~gibk`gd j` tmg urwb~g.
V~jncgi?Mjq ib`{ vgjvcg tjjh vb~t k` tmg Ib{ 4 ujcktb~{ vkehgt babk`ut tmg
cbq v~jmknktk`a mjijug}wbc v~jvbab`db# buuwik`a tmg ~gdwe)
tkj` lbetj~ wugd n{ tmg Dgvb~tig`t jl K`tg~`bc Bllbk~u:
B`uqg~?
K6.575vg~uj`tjjhvb~tk`tmgujcktb~{vkehgtbabk`uttmgcbq
v~jmknktk`amjijug}wbcv~jvbab`db.
26
7/31/2019 Problem Book
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26. Ujekbc ~g`t ba~ggig`t
Tmg Ekt{ jl Vuhj| mbu b vjvwcbtkj` jl >66#666 b`d uvg`du
211#666#666 ~wncgu b {gb~ j` tmg ekt{u bdik`kut~btkj`.
V~jncgi?
Mjq iwem qjwcd gbem ekt{ ~gukdg`t mb|g tj vb{ vg~ ij`tm uj tmbt
tmg{ ejwcd mk~g bqb{ tmg g`tk~g ekt{ aj|g~`ig`t b`d g`uw~g ktu cj{)
bct{ n{ jllg~k`a tm~gg tkigu bu iwem ij`g{:
B`uqg~?
Gbem~gukdg`tjlVuhj|qjwcdmb|gtjvb{>>>~wncguvg~ij`tmk`
j~dg~tjmk~gbqb{tmgekt{bdik`kut~btkj`.
22. B Cguuj` k` Dkujngdkg`eg
J` Ow`g 62># tmg Lgdg~btkj` Ejw`ekc bvv~j|gd big`dig`tu
tj tmg Cbq j` Buuginckgu# bcckgu# Dgij`ut~btkj`u# V~jeguukj`u
b`d Vkehgtu tmbt qjwcd k`e~gbug tmg fl`gu lj~ |b~kjwu |kjcbtkj`u
tj 566#666 ~wncgu lj~ dgij`ut~btj~u b`d 62> -qmg` tmgug v~jncgiu qg`t tj v~guu+# kt ku
vcb``gd tj kivcgig`t Lgdg~bc Cbq @j. =5. Tmg cbq# bdjvtgd tqj{gb~u baj# gllgetk|gc{ bnjckumgu tmg ~kamt tj l~gg v~kib~{ gdweb)
tkj`# tw~`k`a tgbemg~u k`tj ejivgtk`a g`t~gv~g`gw~u k` b aj|g~`)
ig`t k`utktwtkj`.
Beej~dk`a tj tmg ik`kutg~ jl gdwebtkj` b`d uekg`eg# b tgbemg~u
b|g~bag ij`tmc{ ubcb~{ k` >62># v~kj~ tj tmg kivcgig`tbtkj` jl
Lgdg~bc Cbq @j. =5# ku >2#266 ~wncgu.
22
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V~jncgi?
Mjq cj`a iwut b tgbemg~ ugt bukdg mku g`tk~g ij`tmc{ ubcb~{ uj
tmbt mg eb` bllj~d tj tbhg vb~t k` j~ mgcv j~ab`kzg b` w`bwtmj~kzgd
dgij`ut~btkj` babk`ut tmg lgdg~bc cbq bt tmg ~btgu v~jvjugd k` tmg
big`dig`tu:
B`uqg~?
Tmgtgbemg~qkccmb|gtjugtbukdgmkuubcb~{lj~ljw~tgg`ij`tmuk`
j~dg~tjvb{tmgfl`glj~vb~tkekvbtk`ak`b`w`bwtmj~kzgddgij`)
ut~btkj`#b`dtqg`t{)gkamtij`tmulj~betk`abub`j~ab`kzg~.
2>
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7/31/2019 Problem Book
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Tmg Dklflewct T~wtm bnjwt Ibtmgibtkeu
K` jw~ uktwbtkj`# tmbt jl Ebvktbc# tmg ~gka` jl wing~ ku tmwu tmg
~gka` jl tmg w`tmjwamt ucb|g~{ jl wig~kebckt{ ktugcl. @wing~
qmkem# uj kt ku ecbkigd# w`dg~ckgu g|g~{tmk`a jl |bcwg# ku k` betwbc
lbet b v~jue~kvtkj` babk`ut b`{ tmk`hk`a jl wing~ ktugcl. @wing~
jvg~btgu bu tmbt jnuew~g vjk`t qmg~g tmg uktwbtkj` ej`eg`t~btgu ktu
cbq8 jnuew~g tm~jwam ktu ngk`a bt j`eg uj|g~gka` b`d uwnt~betgd
l~ji bcc tmjwamt# b`d g|g` l~ji g|g~{ k`|gutkabtkj` tmbt j~kg`tu
ktugcl tjqb~du ujig t~wtm.
Bcbk` Nbdkjw# @wing~ b`d @wing~u -2;;6+ X2Y
Qmbt ku tmg ~gcbtkj` ngtqgg` ibtmgibtkeu b`d vjcktkeu: B` jn|kjwu ~guvj`ugtj tmku rwgutkj` ku tj ugg tmbt wing~u# igbuw~gig tu# emb~tu b`d a~bvmu b~g
tmg igb`u n{ qmkem jw~ qj~cd ku ib`bagd. Dguvktg qmbt ckng~bcu ikamt ub{#
tmku ib`bagig`t# k`ecwdk`a jl tmg gcgetkj` flaw~gu tmbt dgtg~ik`g qmj qkcc
jeewv{ tmg ugbtu jl vjqg~# ku jt vjcktkeu. Uj# kl ibtmgibtkeu ku tmg igb`u n{
qmkem tmg utbtg b`d tmg ~wck`a ecbuu ib`bag wu# qjwcd jw~ ~gukutb`eg tj djik)
`btkj` b`d g}vcjktbtkj` bcuj ng b ~gukutb`eg tj ibtmgibtkeu ktugcl:
Tmg~g b~g ~gbuj`u lj~ tmk`hk`a uj# b`d ujig vmkcjujvmg~u k` tmg ~geg`t
vbut mb|g bd|jebtgd uhgvtkekui bnjwt b`{tmk`a tgem`j)uekg`tkfle dwg
tj ktu buujekbtkj`u qktm ijdg~` tgem`jcjakebc mwn~ku# rwb`tkflebtkj`bc
`j~ibckzbtkj`# nkjvjcktkebc ej`t~jc b`d utbtg ~gv~guukj`. K` tmku ebug# tmg
~gcbtkj` ngtqgg` ibtmgibtkeu b`d vjcktkeu qjwcd ng ujigtmk`a ckhg b`
gib`ekvbtkj` l~ji ibtmgibtkeu.
N{ ~geja`kzk`a tmg k`ut~wig`tbckzbtkj` jl ibtmgibtkeu lj~ tmg ib`b)
ag~kbc lw`etkj`u jl tmg utbtg b`d ebvktbc# ejwcd qg k`utgbd w`dg~utb`d tmg
~gcbtkj`umkv ngtqgg` ibtmgibtkeu b`d vjcktkeu tj ng j`g jl tmg gib`ekvb)tkj` jlibtmgibtkeu: Kl ibtmgibtkeu ku b igb`u tj eg~tbk` g`du# ikamt qg
ibhg kt ug~|g gib`ekvbtkj` ~btmg~ tmb` jvv~guukj`:
Qmbt kl qg igbuw~g tmg utbtg k` tmg ubig qb{ tmbt kt igbuw~gu wu: Qmbt
kl qg g|bcwbtg# lj~ b emb`ag# mjq glflekg`t tmg v~k|btg ku# mjq iwem aj|g~`)
ig`t ij`g{ v~k|btg g`tg~v~kug ej`uwigu j` ngmbcl jl tb}vb{g~u. Tmku mbu
bcqb{u ngg` b tjjc jl e~ktkeu b`d ~g|jcwtkj`b~kgu. Ibtmgibtkeu ku tmg` ujig)
tmk`a tmbt bccjqu b lj~i jl ejiiw`kebtkj` tmbt vwtu tmg vwncke k` dk~get
ej`tbet qktm b ak|g` vjuktkj`. Tmku ku v~gekugc{ bcuj ngebwug kt ~gdwegu tmg
qj~cd tj tmjug ubig wing~u# igbuw~gig`tu# emb~tu b`d a~bvmu tmbt vwcc
2<
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tmg cg|g~u jl vjqg~ b`d jvk`kj`. Jl ejw~ug# k` b`{ ij|gig`t# j ibttg~
mjq uibcc# qg fl`d tmbt qg eb` cgb~` tj ib`kvwcbtg wing~u bu qgcc. Tmgug
`wing~u tbhg wu nbeh tj tmg ecbuu~jji jl jngdkg`eg tj jnogetk|kt{. Lk~ut qg
qb`t tj ng ckgd tj n{ tmg flaw~gu jl vjcktkekb`u8 tmg` qg qb`t tj ng jwt~bagd
n{ tmg wing~u jl tmg e~ktkeu.
K` tmg gvka~bvm bnj|g# l~ji Bcbk` Nbdkjw# qg fl`d b v~jvjubc tj ckng~btg
ibtmgibtkeu l~ji ktu jvg~btkj` bu b lj~i jl w`tmjwamt v~gekugc{ n{ tmg
bwdbekt{ tj tmk`h wing~u. Tmku lj~i jl gib`ekvbtkj`# j`g tmbt buhu wu tj
tmk`h ng{j`d tmg jnlwuebtkj` jl gej`jike ijdgcu# utjeh b`d nj`d v~kegu
b`d gcgetkj` tbcckgu# ku b` g`abagig`t qktm wing~ ktugcl# b ut~waacg qktm
b` kdgjcjakebc ueblljcdk`a qmkem givcj{u wing~ bu b` jnogetk|g bcknk lj~
ckgu b`d tmkg|g~{. Lk`b`ekbc g}vg~tu b`d utbtg lw`etkj`b~kgu ak|g wu wing~u
ngut cglt tj tmg g}vg~tu? tmg{ b~g j`c{ buhk`a lj~ jw~ |jtg b`d ej`uwig~
ej`fldg`eg. Ujig jl tmg ngut ibtmgibtkebc ik`du jl jw~ ag`g~btkj` mb|gngg` d~bltgd k`tj tmku b~i{ jl |g`t~kcjrwkutu qmj ibhg wing~u uvgbh lj~
tmgi# k`|g`tk`a ij~g b`d ij~g ejivcg} vwzzcgu jl |k~twbc tkig b`d v~j)
ogetgd |bcwg. Ejwcd kt ng tmbt kt ku jq tkig tj tbhg tkig b`d |bcwg# k` tmg lj~i
jl wing~u# nbeh l~ji tmgi:
B`jtmg~ ug`ug jl ibtmgibtkebc gib`ekvbtkj` bttbehu v~gekugc{ tmku
`jtkj` jl tmk`hk`a ibtmgibtkeu. Bu Akccgu Dgcgwzg b`d Lck} Awbttb~k
b~awg k B Tmjwub`d Vcbtgbwu# tmg v~jncgi ku tmbt tmg~g b~g tqj dkllg~g`t
vbtmu k` ibtmgibtkebc tmjwamt ktugcl.
XKYt ku jl tmg btw~g jl b}kjibtkeu tj ejig wv babk`ut uj)ebccgd
w`dgekdbncg v~jvjuktkj`u# tj ej`l~j`t geguub~kc{ mkamg~ vjq)
g~u tmbt kt eb``jt ibutg~. Lk`bcc{# b}kjibtkeu djgu jt ej`utktwtg
tmg ewttk`a gdag jl uekg`eg8 kt ku iwem ij~g jl b utjvvk`a vjk`t#
b ~gj~dg~k`a tmbt v~g|g`tu dgejdgd ugikjtke jqu k` vm{ukeu b`d
ibtmgibtkeu l~ji guebvk`a k` bcc dk~getkj`u. Tmg b}kjibtkekb`u b~g
tmg ig` jl tmg utbtg jl uekg`eg# qmj ugbc jll tmg ck`gu jl kamt tmbtb~g uj l~grwg`t k` ibtmgibtkeu# qmj kivjug b gq g}wi# kl j`c{ b
tgivj~b~{ j`g# b`d qmj cb{ djq` tmg jlflekbc vjckekgu jl uekg`eg.X>Y
J` tmku |kgq# tmg utbtg g}kutu k` ibtmgibtkeu bu qgcc# b`d ktu big
ku b}kjibtke tmjwamt. Mg~g Dgcgwzg b`d Awbttb~k uwaagut b `jibdke
uekg`eg ij~g dg|jtgd tj g}vg~kig`tbtkj` b`d k`twktkj` tmb` tmg buvgetu
jl geguukt{ b`d u{utgibtke ej`ukutg`e{. Tmku utbtkut gcgig`t tmbt tmg{
vjk`t jwt ib{ ng tjj igtbvmj~kebc tj qb~~b`t ug~kjwu ej`ukdg~btkj`.
Tmg vjcktkebc v~gowdkeg k` ~gbdk`a u{utgibtke j~ b}kjibtke ibtmgibt)
keu bu ujigtmk`a cjehgd k` geguukt{ b`d mg`eg k`ebvbncg jl tmk`hk`a -b`d
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a~buvk`a+ tmg ej`tk`ag`ekgu k` k`twktkj` b`d g}vg~kig`tbtkj` ku v~gekugc{
tj ikuu tmg vjk`t. K` b ejw`tg~k`twktk|g qb{# kt ku v~gekugc{ tmg nbcb`eg
ngtqgg` geguukt{ b`d ej`tk`ag`e{ k` ibtmgibtkeu tmbt vwtu kt k` ~gcbtkj`
qktm vjcktkeu. Tmg dggv uw~v~kug tmbt ibtmgibtkeu# k` ktu mkutj~{# ~g|gbcu
ku tmbt ktu ~gcbtkj` qktm -cjakebc+ geguukt{ ku v~gekugc{ qmbt ~g`dg~u k``j)
|btkj` k` ibtmgibtkeu uj k`t~kawk`a. Tmbt ku tj ub{# qmg` qg g`ejw`tg~
iw`db`g qj~cdc{ lbetu# ujekbc uktwbtkj`u b`d tmg ckhg# qg b~g dgbck`a qktm
ej`tk`ag`e{. Qmg` K ub{ tmbt qj~cdc{ lbetu b~g ej`tk`ag`t# K dj jt igb`
tmbt tmg{ b~g ~b`dji. b`dji`guu ku jl ejw~ug bcuj ujigtmk`a dgfl`gd
ibtmgibtkebcc{. [gt qmbt K igb` mg~g ku tmbt lbetu ejwcd bcuj `jt ng8 tmg{
b~g ej`tk`ag`t. Kt ku jt b geguub~{ lbet tmbt K bi q~ktk`a tmgug qj~du jq#
j~ tmbt K g}kut# j~ g|g` tmbt tmg ujcb~ u{utgi b`d cklg j` vcb`gt Gb~tm ebig
k`tj ngk`a. Tmku ku jt tmg ebug qktm ibtmgibtkebc lbetu. Ibtmgibtkebc
lbetu eb``jt `jt ng. Tmku ku jt b ig~g g}tg~`bc dgtg~ik`btkj` jl ibtm)gibtkeu nwt b ~gbc tjjc k` ibtmgibtkebc v~betkeg. Ibtmgibtkekb`u uk`eg
b`tkrwkt{ mb|g wugd qmbt qg ebcc ~gdwetkj bd bnuw~dwi# b lj~i jl v~jjl
tmbt dgij`ut~btgu ujigtmk`a n{ umjqk`a tmbt ktu ej`t~b~{ ku k`ej`ukutg`t
j~ cgbdu tj b ej`t~bdketkj`. Kl# lj~ g}bivcg# qg qb`t tj v~j|g tmbt tmg~g b~g
b` k`fl`ktg wing~ jl v~kig wing~u# qmkem ku kivjuukncg tj umjq dk~getc{#
qg utb~t qktm tmg v~jvjuktkj` tmbt tmg~g b~g j`c{ b fl`ktg wing~ jl v~kig
`wing~u b`d tmg` umjq tmbt tmku v~jvjuktkj` ku ej`t~bdketj~{. Kt tmg` ljc)
cjqu# bu Gweckd t~kgd tj umjq wu# tmbt tmg~g b~g b` k`fl`ktg wing~ jl v~kig
`wing~u.
Bctmjwam geguukt{ ku jltg` ugg` bu ej`ut~bk`t# ibtmgibtkebc geguukt{
bcuj mbu b v~jljw`d ug`ug jl l~ggdji. Tmku eb` ng t~begd ijut ~gbdkc{ k` tmg
mkutj~kebc dg|gcjvig`t jl ibtmgibtkebc tmjwamt. Mjq ku kt tmbt qg mb|g
vw`etwbcc{ b~~k|gd bt gq ibtmgibtkebc n~gbhtm~jwamu tm~jwamjwt mku)
tj~{ qmg` ibtmgibtkeu bvvgb~u tj ng cjehgd k` b dgij`ut~btk|gc{ ecjugd
~gbci jl geguukt{: bdkebc emb`agu qktmk` ibtmgibtkeu bu b v~betkeg# b ugtjl tmgj~giu# b ug~kgu jl t~wtmu# ik~~j~ mkutj~kebc emb`ag v~gekugc{ ngebwug
tmg{ bccjq wu tj ugg qmbt ~gbc emb`ag eb` igb`# b emb`ag jl tmg ej`tg}t jl
`geguukt{ ktugcl. Qg ebuwbcc{ g}vget ~wcg)aj|g~`gd emb`ag k` tmg qj~cd uk`eg
tmk`au b~g ej`tk`ag`t# nwt tmg{ b~g k`eck`gd tj j~dg~ b`d qg dgdweg btw~bc
cbqu j` tmku nbuku. Nwt tmgug emb`agu b~g ejiij`vcbeg b`d dj jt g}tg`d
ng{j`d tmg l~bigqj~hu qktmk` qmkem tmg{ tbhg vcbeg. J` tmg jtmg~ mb`d#
b umklt k` ibtmgibtkeu ku u{utgibtke v~gekugc{ ngebwug qmbt qg ej`tgut k`
tmjug ej`tg}tu jl emb`ag ku ujigtmk`a lw`dbig`tbc? b dggvc{ g`t~g`emgd
k`twktkj`# b ugt jl k`tg~cjehk`a b}kjiu. K` ~bdkebc ebugu# qg g`ejw`tg~ b`
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w`g}vgetgd ~glwtbtkj` tmbt tm~jqu jll b qmjcg u{utgi k` vb~t v~gekugc{
ngebwug qg ~grwk~g geguub~{ acjnbc b`d w`k|g~ubc ej`ukutg`e{. Qmg` b
u{utgi -qmkem ku b}kjibtke+ kivckgu b` g~~j~# tmg g`tk~g u{utgi mbu tj ng
~g)g}bik`gd.
Ngebwug ibtmgibtkebc emb`ag ku uj lw`dbig`tbc# ktu |b`awb~d ku ej`)
utb`tc{ ibcka`gd bu dgck|g~k`a ujigtmk`a lbcug. K` tmg ebug jl Cgkn`kz b`d
@gqtj`# qmj ej`ew~~g`tc{ ab|g lj~i tj tmg dkllg~g`tkbc b`d k`tga~bc ebcew)
cwu# tmku uj~t jl lbcukt{ qbu tmg |g~{ d{`bikui jl dkuej|g~{. @gqtj` b`d
Cgkn`kz# Ib~} ~gib~hgd k` mku ibtmgibtkebc ib`wue~kvtu#
ngckg|gd k` tmg i{utg~kjwu emb~betg~ jl tmg gqc{ dkuej|g~gd
ebcewcwu# tmbt {kgcdgd t~wg -b`d ij~gj|g~# vb~tkewcb~c{ k` tmg
agjigt~kebc bvvckebtkj`# butj`kumk`a+ ~guwctu n{ b vjuktk|gc{ lbcug
ibtmgibtkebc v~jegdw~g. Tmg{ qg~g tmwu ugcl)i{utkflgd# |bcwgd
tmg gq dkuej|g~{ bcc tmg mkamg~# g`~bagd tmg e~jqd jl jcd j~tmj)dj} ibtmgibtkekb`u bcc tmg ij~g# b`d tmwu ebccgd lj~tm tmg e~{ jl
jvvjuktkj`# tmbt g|g` k` tmg cb{ qj~cd mbu b` gemj b`d ku geguub~{
k` j~dg~ tj vb|g tmg qb{ lj~ ujigtmk`a gq.X5Y
Tmku vjuktk|gc{ lbcug ibtmgibtkebc v~jegdw~g ku tmg ej~~gcbtg jl tmg
vgewckb~ uj~t jl l~ggdji tmbt K uwaagut. Kt ku dggvc{ uwnogetk|g b`d j`c{ ~gbc)
kzgu ktugcl k` tmg lwtw~g b`tg~kj~? Tmku qkcc mb|g ngg` t~wg.
Lbcukt{ vcb{u b uvgekbc ~jcg k` l~ggdji k` ibtmgibtkeu# nwt bcuj k` tmg
|g~{ jtkj` jl l~ggdji bu uwem. Qmg` qg uvgbh uwnogetk|gc{ bnjwt l~ggdji#
qg wuwbcc{ uvgbh jl l~ggdji jl jvk`kj` j~ l~ggdji jl betkj`. Mjqg|g~# bu
qg eb` dgdweg l~ji tmg b`ekg`t dkbcgetke jl l~ggdji# l~ggdji ej`egk|gd bu
ig~gc{ ngk`a jvg` tj b ugt jl jvk`kj`u j~ emjkegu ku jt l~ggdji bt bcc. J|g~)
ejik`a tmku kivjuuknkckt{ jl l~ggdji ku l~ggdji ktugcl. Tj tmk`h# tj ecbki# tj
ugkzg j~ tj bet j` ujigtmk`a ng{j`d tmg ej`ut~bk`tu jl ak|g` j~ ejiij`ug`uk)
ebc dgtg~ik`btkj`# ng{j`d tmg ugt jl ak|g` emjkegu# uggiu bu kivjuukncg bu
ckng~t{ ktugcl. Kt ku tmku kivjuuknkckt{ tmbt ak|gu umbvg tj ckng~t{.Ibtmgibtkeu tmwu v~gug`tu b ik~~j~ k` qmkem tmg ut~ketgut lj~i jl gegu)
ukt{ g`ejw`tg~u ktu djwncg k` tmg ijut uwnogetk|g b`d bnujcwtg lj~i jl ckn)
g~t{. Tmku ik~~j~k`a eb` bcuj jllg~ b dggvc{ mwib`kut vketw~g tmbt v~bkugu
tmg w`lbtmjibncg dgvtmu jl mwib` e~gbtk|kt{# tmg v~ja~guuk|g g|jcwtkj`
b`d t~b`ueg`dg`eg jl tmg mwib` uvk~kt. Tmku# K ecbki# ku bcuj b ikutbhg.
Tmg~g ku ujigtmk`a dgekdgdc{ k`mwib` bnjwt ibtmgibtkeu tmbt a~kvu wu
l~ji tmg jwtukdg. Tmku ku jt j`c{ tmg k`twktkj` b`d g}vg~kig`tbtkj` tmbt
Dgcgwzg b`d Awbttb~k uvgbh jl. Nglj~g tmjug kivbuugu# tmjug w`dgekd)
bncg utbtgig`tu vjvwcb~kzgd n{ Adgc# tmg~g ku fl~ut tmg ~gukutb`eg jl
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ibtmgibtkeu tj tmk`hk`a. Vbeg Dgueb~tgu# tmg ~gukutb`eg jl ibtmgibtkeu ku
j`g tmbt jt g|g` tmg ajd jl tmg tmgjcjakb`u ejwcd j|g~ejig. Qg dj jt uki)
vc{ b}kjibtkzg n{ vw~g dgekukj`. Ibtmgibtkeu ~gukutu wu bt g|g~{ utgv. Kt ku
tmku ~gukutb`eg babk`ut tmg mwib` tmbt ibhgu wu uwnikt jw~ k`twktkj`# jw~
ak|g` ngckglu# tj tmg k`mwib` b|b`t)ab~dg jl ej`ukutg`e{. Tmg cj`a mkutj~{
jl tmg kibak`b~{ wing~ k# j~ tmg urwb~g ~jjt jl gabtk|g j`g )2# bttgutu tj
eg`tw~kgu jl ejik`a tj tg~iu qktm b ibtmgibtkebc g}kutg`eg qmkem eb``jt
ng ~gdwegd tj jw~ mwib` g}vg~kg`eg# jw~ k`twktkj`# jw~ g}vg~kig`tu. Tmg
mkutj~{ jl tmg kibak`b~{ wing~ k ku tmg mkutj~{ jl tmg utwnnj~``guu jl b
uka`# b ibtmgibtkebc tmjwamt tmbt lj~egu b vg~uj` tj tmk`h8 b ej`tk`wjwu
ibtmgibtkebc hkeh l~ji ngmk`d. Kt ku vg~mbvu tmku k`mwib`kt{ tmbt ku tmg
vg~lget ik~~j~ lj~ ckng~t{. K` ngk`a lj~egd tj tmk`h geguukt{# qg b~g lj~egd
n{ geguukt{ tj tmk`h.
Tmg k`mwib` lj~eg jl geguukt{ ku jt j`c{ j`g jl tmjwamt. Qmg` tmgvmkcjujvmg~ jl ibtmgibtkeu Ogb` Eb|bkccu dgekdgd tj ngejig b` betk|g
~gukutg~ k` tmg Ugej`d Qj~cd Qb~# mg givmbukzgd tmbt mg tjjh tmku dgek)
ukj` n{ igb`u jl cjake.X4YLj~ mki# tmku l~ggdji jl betkj` qbu dketbtgd n{
dgdwetk|g geguukt{# b`d ngk`a lj~egd tj tbhg wv tmg b`tklbuekut ut~waacg
qbu k`mg~g`t k` mku ~gcbtkj`umkv qktm ibtmgibtkeu. Kl qg qg~g k` b`{
djwnt bnjwt tmg rwgutkj`# mku ut~waacg qbu vjcktkebc# b`d mku dgekukj`# ckhg
v~j|k`a b tmgj~gi# k`|jc|gd vg~ukutk`a k` beegvtk`a tmg geguub~{ ej`ug)
rwg`egu. Mg qbu hkccgd n{ b @bzk nwccgt k` Lgn~wb~{ 2;44# mku njd{ nw~kgd k`
b ibuu a~b|gd ib~hgd W`h`jq` @j. 7.
Tzwemkg` Tmj# Vb~ku# >; Owc{ >62>.
X2Y Bcbk` Nbdkjw# @wing~ b`d @wing~u# t~b`u.
n{ ^jnk` Ibehb{# Ebin~kdag? Vjckt{ V~guu#
>66=# >25.X>Y Akccgu Dgcgwzg b`d Lck} Awbttb~k# B Tmjw)
ub`d Vcbtgbwu? Ebvktbckui b`d Uemkzjvm~g)
`kb# \jcwig KK# t~b`u. n{ N~kb` Ibuuwik#
Cj`dj`? Ej`tk`wwi V~guu# >665# 42
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T~b`ucbtgd n{?
Eb~cgtj` Ejvgcb`d
Em~kutjvmg~ Djuu
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