954 Mathematics T [PPU] Semester 1 Topics
Transcript of 954 Mathematics T [PPU] Semester 1 Topics
7/31/2019 954 Mathematics T [PPU] Semester 1 Topics
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GAZT] ]EZN? CFLEJZC CIM LEBNE]ZQ
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Pezabm Fecziail Bu}dbne
3 Guid}abit :8 Dcimamc}et thbufm je cjfe }b?
3)3 Guid}abit 7 (c! t}c}e }he mbncai cim zcile bg c guid}abi& cim
gaim dbnpbta}e guid}abit;
(j! me}eznaie |he}hez c guid}abi at bie.}b.bie&
cim gaim }he aiwezte bg c bie.}b.bie guid}abi;
(d! tke}dh }he lzcpht bg tanpfe guid}abit&
aidfumail paede|ate.megaiem guid}abit;
3): Pbfqibnacf cim
zc}abicf guid}abit
8 (m ! ute }he gcd}bz }hebzen cim }he zencaimez
}hebzen;
(e! tbfwe pbfqibnacf cim zc}abicf esuc}abit cim
aiesucfa}aet;
( g ! tbfwe esuc}abit cim aiesucfa}aet aiwbfwail
nbmufut talit ai tanpfe dctet;
(l! medbnpbte c zc}abicf expzettabi ai}b pcz}acf
gzcd}abit ai dctet |heze }he meibnaic}bz hct
}|b mat}aid} faiecz gcd}bzt& bz c faiecz gcd}bz
cim c pzane sucmzc}ad gcd}bz;
3)4 Expbiei}acf cim
fblcza}hnad guid}abit
7 (h! zefc}e expbiei}acf cim fblcza}hnad guid}abit&
cflejzcadcffq cim lzcphadcffq;
(a! ute }he pzbpez}aet bg expbiei}t cim fblcza}hnt;
( o! tbfwe esuc}abit cim aiesucfa}aet aiwbfwail
expbiei}acf bz fblcza}hnad expzettabit;
3)= ]zalbibne}zad
guid}abit
8 (k ! zefc}e }he pezabmada}q cim tqnne}zaet bg }he
taie& dbtaie cim }cilei} guid}abit }b }heaz
lzcpht& cim amei}agq }he aiwezte taie& aiwezte
dbtaie cim aiwezte }cilei} guid}abit cim }heaz
lzcpht;
(f! ute jctad }zalbibne}zad amei}a}aet cim }hegbznufce gbz tai ( C ³ J!& dbt ( C ³ J! cim
}ci ( C ³ J!& aidfumail tai : C& dbt : C cim
}ci : C;
(n! expzett c tai + j dbt ai }he gbznt
z tai ( ³γ! cim z dbt ( ³γ!;
(i! gaim }he tbfu}abit& |a}hai tpedagaem ai}ezwcft&
bg }zalbibne}zad esuc}abit cim aiesucfa}aet)
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Pezabm Fecziail Bu}dbne
: Tesueidet cim Tezaet 38 Dcimamc}et thbufm je cjfe }b?
:)3 Tesueidet = (c! ute ci expfada} gbznufc cim c zeduztawe gbznufcgbz c tesueide;
(j! gaim }he fana} bg c dbiwezlei} tesueide;
:): Tezaet 8 (d! ute }he gbznufce gbz }he i}h }ezn cim gbz }he
tun bg }he gazt} i }eznt bg ci cza}hne}ad tezaet
cim bg c lebne}zad tezaet;
(m ! amei}agq }he dbima}abi gbz }he dbiwezleide bg c
lebne}zad tezaet& cim ute }he gbznufc gbz }he
tun bg c dbiwezlei} lebne}zad tezaet;
(e! ute }he ne}hbm bg maggezeidet }b gaim }he i}hpcz}acf tun bg c tezaet& cim memude }he tun bg
}he tezaet ai }he dcte |hei a} at dbiwezlei};
:)4 Jaibnacf expcitabit 7 ( g ! expcim (c + j!i
& |heze i ;
(l! expcim (3 + x!i
& |heze i & cim amei}agq }he
dbima}abi x 6 3 gbz }he wcfama}q bg }hat
expcitabi;
(h! ute jaibnacf expcitabit ai cppzbxanc}abit)
4 Nc}zadet 37 Dcimamc}et thbufm je cjfe }b?
4)3 Nc}zadet 30 (c! amei}agq iuff& amei}a}q& maclbicf& }zacilufcz cim
tqnne}zad nc}zadet;
(j! ute }he dbima}abit gbz }he esucfa}q bg }|b
nc}zadet;
(d! pezgbzn tdcfcz nuf}apfadc}abi& cmma}abi&
tuj}zcd}abi cim nuf}apfadc}abi bg nc}zadet |a}h
c} nbt} }hzee zb|t cim }hzee dbfunit;
(m ! ute }he pzbpez}aet bg nc}zax bpezc}abit;
(e! gaim }he aiwezte bg c ibi.tailufcz nc}zax utail
efenei}czq zb| bpezc}abit;
( g ! ewcfuc}e }he me}eznaici} bg c nc}zax;
(l! ute }he pzbpez}aet bg me}eznaici}t;
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Pezabm Fecziail Bu}dbne
4): Tqt}ent bg faiecz
esuc}abit
7 (h! zemude ci culnei}em nc}zax }b zb|.edhefbi
gbzn& cim me}eznaie |he}hez c tqt}en bg faiecz
esuc}abit hct c uiasue tbfu}abi& aigaia}efqnciq tbfu}abit bz ib tbfu}abi;
(a! cppfq }he Lcuttaci efanaic}abi }b tbfwe c
tqt}en bg faiecz esuc}abit;
( o! gaim }he uiasue tbfu}abi bg c tqt}en bg faiecz
esuc}abit utail }he aiwezte bg c nc}zax)
= Dbnpfex Iunjezt 3: Dcimamc}et thbufm je cjfe }b?
(c! amei}agq }he zecf cim anclaiczq pcz}t bg c
dbnpfex iunjez;
(j! ute }he dbima}abit gbz }he esucfa}q bg }|bdbnpfex iunjezt;
(d! gaim }he nbmufut cim czlunei} bg c dbnpfex
iunjez ai dcz}etaci gbzn cim expzett }he
dbnpfex iunjez ai pbfcz gbzn;
(m ! zepzetei} c dbnpfex iunjez lebne}zadcffq jq
necit bg ci Czlcim maclzcn;
(e! gaim }he dbnpfex zbb}t bg c pbfqibnacf
esuc}abi |a}h zecf dbeggadaei}t;
( g ! pezgbzn efenei}czq bpezc}abit bi }|b
dbnpfex iunjezt expzettem ai dcz}etaci gbzn;
(l! pezgbzn nuf}apfadc}abi cim mawatabi bg }|b
dbnpfex iunjezt expzettem ai pbfcz gbzn;
(h! ute me Nbawze‑t }hebzen }b gaim }he pb|ezt
cim zbb}t bg c dbnpfex iunjez)
5 Cicfq}ad Lebne}zq 3= Dcimamc}et thbufm je cjfe }b?
(c! }zcitgbzn c lawei esuc}abi bg c dbiad ai}b }he
t}cimczm gbzn;
(j! gaim }he wez}ex& gbdut cim mazed}zax bg c
pczcjbfc;
(d! gaim }he wez}adet& dei}ze cim gbda bg ci effapte;
(m ! gaim }he wez}adet& dei}ze& gbda cim ctqnp}b}et
bg c hqpezjbfc;
(e! gaim }he esuc}abit bg pczcjbfct& effaptet cim
hqpezjbfct tc}atgqail pzetdzajem dbima}abit
(exdfumail eddei}zada}q!;
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Pezabm Fecziail Bu}dbne
( g ! tke}dh dbiadt;
(l! gaim }he dcz}etaci esuc}abi bg c dbiad megaiem
jq pczcne}zad esuc}abit;
(h! ute }he pczcne}zad esuc}abit bg dbiadt)
7 Wed}bzt :0 Dcimamc}et thbufm je cjfe }b?
7)3 Wed}bzt ai }|b cim
}hzee maneitabit
8 (c! ute uia} wed}bzt cim pbta}abi wed}bzt;
(j! pezgbzn tdcfcz nuf}apfadc}abi& cmma}abi cim
tuj}zcd}abi bg wed}bzt;
(d! gaim }he tdcfcz pzbmud} bg }|b wed}bzt& cim
me}eznaie }he cilfe je}|eei }|b wed}bzt;
(m ! gaim }he wed}bz pzbmud} bg }|b wed}bzt& cim
me}eznaie }he czec c pczcffefblzcn cim bg c
}zacilfe;
7): Wed}bz lebne}zq 3: (e! gaim cim ute }he wed}bz cim dcz}etaci esuc}abit
bg faiet;
( g ! gaim cim ute }he wed}bz cim dcz}etaci esuc}abit
bg pfciet;
(l! dcfdufc}e }he cilfe je}|eei }|b faiet& je}|eei
c faie cim c pfcie& cim je}|eei }|b pfciet;
(h! gaim }he pbai} bg ai}ezted}abi bg }|b faiet& cimbg c faie cim c pfcie;
(a! gaim }he faie bg ai}ezted}abi bg }|b pfciet)
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TEDBIM ]EZN? DCFDUFUT
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Pezabm Fecziail Bu}dbne
< Fana}t cim Dbi}aiua}q 3: Dcimamc}et thbufm je cjfe }b?
<)3 Fana}t 7 (c! me}eznaie }he exat}eide cim wcfuet bg }he feg}.
hcim fana}& zalh}.hcim fana} cim fana} bg c
guid}abi;
(j! ute }he pzbpez}aet bg fana}t;
<): Dbi}aiua}q 7 (d! me}eznaie }he dbi}aiua}q bg c guid}abi c} c
pbai} cim bi ci ai}ezwcf;
(m ! ute }he ai}eznemac}e wcfue }hebzen)
8 Maggezei}ac}abi :8 Dcimamc}et thbufm je cjfe }b?
8)3 Mezawc}awet 3: (c! amei}agq }he mezawc}awe bg c guid}abi ct c fana};
(j! gaim }he mezawc}awet bg xi
(i !& e x& fi x&
tai x& dbt x& }ci x& tai3 x& dbt
3 x& }ci
3 x& |a}h
dbit}ci} nuf}apfet& tunt& maggezeidet&
pzbmud}t& sub}aei}t cim dbnpbta}et;
(d! pezgbzn anpfada} maggezei}ac}abi;
(m ! gaim }he gazt} mezawc}awet bg guid}abit megaiem
pczcne}zadcffq;
8): Cppfadc}abit bg
maggezei}ac}abi
37 (e! me}eznaie |heze c guid}abi at aidzectail&
medzectail& dbidcwe up|czm cim dbidcwe
mb|i|czm;
( g ! me}eznaie }he t}c}abiczq pbai}t& ex}zenun
pbai}t cim pbai}t bg aigfexabi;
(l! tke}dh }he lzcpht bg guid}abit& aidfumail
ctqnp}b}et pczcffef }b }he dbbzmaic}e cxet;
(h! gaim }he esuc}abit bg }cilei}t cim ibzncft }b
duzwet& aidfumail pczcne}zad duzwet;
(a! tbfwe pzbjfent dbideziail zc}et bg dhcile&aidfumail zefc}em zc}et;
( o! tbfwe bp}anatc}abi pzbjfent)
1 Ai}elzc}abi :8 Dcimamc}et thbufm je cjfe }b?
1)3 Aimegaia}e ai}elzcft 3= (c! amei}agq ai}elzc}abi ct }he zewezte bg
maggezei}ac}abi;
(j! ai}elzc}e xi
(i !& e x& tai x& dbt x& ted
: x& |a}h
dbit}ci} nuf}apfet& tunt cim maggezeidet;
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Pezabm Fecziail Bu}dbne
(d! ai}elzc}e zc}abicf guid}abit jq necit bg
medbnpbta}abi ai}b pcz}acf gzcd}abit;
(m ! ute }zalbibne}zad amei}a}aet }b gcdafa}c}e }he
ai}elzc}abi bg }zalbibne}zad guid}abit;
(e! ute cflejzcad cim }zalbibne}zad tujt}a}u}abit
}b gaim ai}elzcft;
( g ! pezgbzn ai}elzc}abi jq pcz}t;
1): Megaia}e ai}elzcft 3= (l! amei}agq c megaia}e ai}elzcf ct }he czec uimez c
duzwe;
(h! ute }he pzbpez}aet bg megaia}e ai}elzcft;
(a! ewcfuc}e megaia}e ai}elzcft;( o! dcfdufc}e }he czec bg c zelabi jbuimem jq c
duzwe (aidfumail c pczcne}zad duzwe! cim faiet
pczcffef }b }he dbbzmaic}e cxet& bz je}|eei }|b
duzwet;
(k ! dcfdufc}e wbfunet bg tbfamt bg zewbfu}abi cjbu}
bie bg }he dbbzmaic}e cxet)
30 Maggezei}acf Esuc}abit 3= Dcimamc}et thbufm je cjfe }b?
(c! gaim }he leiezcf tbfu}abi bg c gazt} bzmez
maggezei}acf esuc}abi |a}h tepczcjfe wczacjfet;(j! gaim }he leiezcf tbfu}abi bg c gazt} bzmez faiecz
maggezei}acf esuc}abi jq necit bg ci ai}elzc}ail
gcd}bz;
(d! }zcitgbzn& jq c lawei tujt}a}u}abi& c gazt} bzmez
maggezei}acf esuc}abi ai}b bie |a}h tepczcjfe
wczacjfet bz bie |hadh at faiecz;
(m ! ute c jbuimczq dbima}abi }b gaim c pcz}adufcz
tbfu}abi;
(e! tbfwe pzbjfent& zefc}em }b tdaeide cim
}edhibfblq& }hc} dci je nbmeffem jq maggezei}acfesuc}abit)
33 Ncdfcuzai Tezaet 3: Dcimamc}et thbufm je cjfe }b?
(c! gaim }he Ncdfcuzai tezaet gbz c guid}abi cim }he
ai}ezwcf bg dbiwezleide;
(j! ute t}cimczm tezaet }b gaim }he tezaet expcitabit
bg }he tunt& maggezeidet& pzbmud}t& sub}aei}t
cim dbnpbta}et bg guid}abit;
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Pezabm Fecziail Bu}dbne
(d! pezgbzn maggezei}ac}abi cim ai}elzc}abi bg c
pb|ez tezaet;
(m ! ute tezaet expcitabit }b gaim }he fana} bg c
guid}abi)
3: Iunezadcf Ne}hbmt 3= Dcimamc}et thbufm je cjfe }b?
3:)3 Iunezadcf tbfu}abi bg
esuc}abit
30 (c! fbdc}e c zbb} bg ci esuc}abi cppzbxanc}efq jq
necit bg lzcphadcf dbitamezc}abit cim jq
teczdhail gbz c tali dhcile;
(j! ute ci a}ezc}awe gbznufc bg }he gbzn
3 g ( !i i
x x }b gaim c zbb} bg ci esuc}abi }b c
pzetdzajem melzee bg cdduzcdq;
(d! amei}agq ci a}ezc}abi |hadh dbiwezlet bz
mawezlet;
(m ! ute }he Ie|}bi.Zcphtbi ne}hbm;
3:): Iunezadcf ai}elzc}abi = (e! ute }he }zcpeaun zufe;
( g ! ute tke}dh lzcpht }b me}eznaie |he}hez }he
}zcpeaun zufe lawet ci bwez.et}anc}e bz ci
uimez.et}anc}e ai tanpfe dctet)
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]HAZM ]EZN? T]C]AT]ADT
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Pezabm Fecziail Bu}dbne
34 Mc}c Metdzap}abi 3= Dcimamc}et thbufm je cjfe }b?
(c! amei}agq matdze}e& dbi}aiubut& uilzbupem cim
lzbupem mc}c;
(j! dbit}zud} cim ai}ezpze} t}en.cim.fecg maclzcnt&
jbx.cim.|hatkez pfb}t& hat}blzcnt cim
dunufc}awe gzesueidq duzwet;
(d! t}c}e }he nbme cim zcile bg uilzbupem mc}c;
(m ! me}eznaie }he nemaci cim ai}ezsucz}afe zcile
bg uilzbupem cim lzbupem mc}c;
(e! dcfdufc}e }he neci cim t}cimczm mewac}abi bg uilzbupem cim lzbupem mc}c& gzbn zc| mc}c
cim gzbn lawei }b}cft tudh ct3
( !i
a
a
x c
cim
3
:( !
i
a
a
x c
;
( g ! tefed} cim ute }he cppzbpzac}e nectuzet bg
dei}zcf }eimeidq cim nectuzet bg matpeztabi;
(l! dcfdufc}e }he Pecztbi dbeggadaei} bg tke|iett;
(h! metdzaje }he thcpe bg c mc}c mat}zaju}abi)
3= Pzbjcjafa}q 3= Dcimamc}et thbufm je cjfe }b?
(c! cppfq }he cmma}abi pzaidapfe cim }he
nuf}apfadc}abi pzaidapfe;
(j! ute }he gbznufce gbz dbnjaic}abit cim
peznu}c}abit ai tanpfe dctet;
(d! amei}agq c tcnpfe tpcde& cim dcfdufc}e }he
pzbjcjafa}q bg ci ewei};
(m ! amei}agq dbnpfenei}czq& exhcut}awe cim
nu}ucffq exdfutawe ewei}t;
(e! ute }he gbznufc
P( C J! > P( C! + P( J! P( C J!;
( g ! dcfdufc}e dbima}abicf pzbjcjafa}aet& cim amei}agq
aimepeimei} ewei}t;
(l! ute }he gbznufce
P( C J! > P( C! P( J v C! > P( J! P( C v J!;
(h! ute }he zufe bg }b}cf pzbjcjafa}q)
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Pezabm Fecziail Bu}dbne
35 Pzbjcjafa}q Mat}zaju}abit :7 Dcimamc}et thbufm je cjfe }b?
35)3 Matdze}e zcimbnwczacjfet
7 (c! amei}agq matdze}e zcimbn wczacjfet;
(j! dbit}zud} c pzbjcjafa}q mat}zaju}abi }cjfe gbz c
matdze}e zcimbn wczacjfe;
(d! ute }he pzbjcjafa}q guid}abi cim dunufc}awe
mat}zaju}abi guid}abi bg c matdze}e zcimbn
wczacjfe;
(m ! dcfdufc}e }he neci cim wczacide bg c matdze}e
zcimbn wczacjfe;
35): Dbi}aiubut zcimbn
wczacjfet
7 (e! amei}agq dbi}aiubut zcimbn wczacjfet;
( g ! zefc}e }he pzbjcjafa}q meita}q guid}abi cimdunufc}awe mat}zaju}abi guid}abi bg c
dbi}aiubut zcimbn wczacjfe;
(l! ute }he pzbjcjafa}q meita}q guid}abi cim
dunufc}awe mat}zaju}abi guid}abi bg c
dbi}aiubut zcimbn wczacjfe;
(h! dcfdufc}e }he neci cim wczacide bg c
dbi}aiubut zcimbn wczacjfe;
35)4 Jaibnacf mat}zaju}abi = (a! ute }he pzbjcjafa}q guid}abi bg c jaibnacf
mat}zaju}abi& cim gaim a}t neci cim wczacide;
( o! ute }he jaibnacf mat}zaju}abi ct c nbmef gbz
tbfwail pzbjfent zefc}em }b tdaeide cim
}edhibfblq;
35)= Pbattbi mat}zaju}abi = (k ! ute }he pzbjcjafa}q guid}abi bg c Pbattbi
mat}zaju}abi& cim amei}agq a}t neci cim
wczacide;
(f! ute }he Pbattbi mat}zaju}abi ct c nbmef gbz
tbfwail pzbjfent zefc}em }b tdaeide cim
}edhibfblq;
35)5 Ibzncf mat}zaju}abi 7 (n! amei}agq }he leiezcf gec}uzet bg c ibzncf
mat}zaju}abi& ai zefc}abi }b a}t neci cim
t}cimczm mewac}abi;
(i! t}cimczmate c ibzncf zcimbn wczacjfe cim ute
}he ibzncf mat}zaju}abi }cjfet;
(b! ute }he ibzncf mat}zaju}abi ct c nbmef gbz
tbfwail pzbjfent zefc}em }b tdaeide cim
}edhibfblq;
( p! ute }he ibzncf mat}zaju}abi& |a}h dbi}aiua}q
dbzzed}abi& ct ci cppzbxanc}abi }b }he
jaibnacf mat}zaju}abi& |heze cppzbpzac}e)
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]bpad]ecdhail
Pezabm Fecziail Bu}dbne
37 Tcnpfail cim Et}anc}abi :7 Dcimamc}et thbufm je cjfe }b?
37)3 Tcnpfail 3= (c! mat}ailuath je}|eei c pbpufc}abi cim c tcnpfe&cim je}|eei c pczcne}ez cim c t}c}at}ad;
(j! amei}agq c zcimbn tcnpfe;
(d! amei}agq }he tcnpfail mat}zaju}abi bg c t}c}at}ad;
(m ! me}eznaie }he neci cim t}cimczm mewac}abi bg
}he tcnpfe neci;
(e! ute }he zetuf} }hc} X hct c ibzncf mat}zaju}abi ag
X hct c ibzncf mat}zaju}abi;
( g ! ute }he dei}zcf fana} }hebzen;
(l! me}eznaie }he neci cim t}cimczm mewac}abi bg }he tcnpfe pzbpbz}abi;
(h! ute }he cppzbxanc}e ibzncfa}q bg }he tcnpfe
pzbpbz}abi gbz c tuggadaei}fq fczle tcnpfe tae;
37): Et}anc}abi 3: (a! dcfdufc}e uijactem et}anc}et gbz }he pbpufc}abi
neci cim pbpufc}abi wczacide;
( o! dcfdufc}e ci uijactem et}anc}e gbz }he
pbpufc}abi pzbpbz}abi;
(k ! me}eznaie cim ai}ezpze} c dbigameide ai}ezwcf
gbz }he pbpufc}abi neci jctem bi c tcnpfegzbn c ibzncffq mat}zaju}em pbpufc}abi |a}h
kib|i wczacide;
(f! me}eznaie cim ai}ezpze} c dbigameide ai}ezwcf
gbz }he pbpufc}abi neci jctem bi c fczle
tcnpfe;
(n! gaim }he tcnpfe tae gbz }he et}anc}abi bg
pbpufc}abi neci;
(i! me}eznaie cim ai}ezpze} c dbigameide ai}ezwcf
gbz }he pbpufc}abi pzbpbz}abi jctem bi c fczle
tcnpfe;(b! gaim }he tcnpfe tae gbz }he et}anc}abi bg
pbpufc}abi pzbpbz}abi)
7/31/2019 954 Mathematics T [PPU] Semester 1 Topics
http://slidepdf.com/reader/full/954-mathematics-t-ppu-semester-1-topics 11/11
]bpad]ecdhail
Pezabm Fecziail Bu}dbne
3< Hqpb}hetat ]et}ail 3= Dcimamc}et thbufm je cjfe }b?
(c! expfcai }he neciail bg c iuff hqpb}hetat cimci cf}ezic}awe hqpb}hetat;
(j! expfcai }he neciail bg }he taliagadcide fewef
bg c }et};
(d! dczzq bu} c hqpb}hetat }et} dbideziail }he
pbpufc}abi neci gbz c ibzncffq mat}zaju}em
pbpufc}abi |a}h kib|i wczacide;
(m ! dczzq bu} c hqpb}hetat }et} dbideziail }he
pbpufc}abi neci ai }he dcte |heze c fczle
tcnpfe at utem;
(e! dczzq bu} c hqpb}hetat }et} dbideziail }hepbpufc}abi pzbpbz}abi jq mazed} ewcfuc}abi bg
jaibnacf pzbjcjafa}aet;
( g ! dczzq bu} c hqpb}hetat }et} dbideziail }he
pbpufc}abi pzbpbz}abi utail c ibzncf
cppzbxanc}abi)
38 Dha.tsuczem ]et}t 3= Dcimamc}et thbufm je cjfe }b?
(c! amei}agq }he thcpe& ct |eff ct }he neci cim
wczacide& bg c dha.tsuczem mat}zaju}abi |a}h c
lawei iunjez bg melzeet bg gzeembn;
(j! ute }he dha.tsuczem mat}zaju}abi }cjfet;
(d! amei}agq }he dha.tsuczem t}c}at}ad;
(m ! ute }he zetuf} }hc} dfcttet |a}h tncff exped}em
gzesueidaet thbufm je dbnjaiem ai c dha.
tsuczem }et};
(e! dczzq bu} lbbmiett.bg.ga} }et}t }b ga} pzetdzajem
pzbjcjafa}aet cim pzbjcjafa}q mat}zaju}abit |a}h
kib|i pczcne}ezt;
( g ! dczzq bu} }et}t bg aimepeimeide ai dbi}aileidq
}cjfet (exdfumail Qc}et dbzzed}abi!)