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    Ebejtrkjhelistry? Ztucy kn reb`tikfship getweef jhelij`b eferay fc ebejtrij`b eferay fc hkw kfe j`f ge jkf-

    vertec iftk fkther.

    Ebejtrkbytij jebb?Ebejtrij`b eferay Jhelij`b eferay

    Ebejtrkjhelij`b jebb ? jhelij`b eferay Ebejtrij`b eferay (A`bv`fij jebb/ vkbt`ij jebb / C`fieb jebb)

    Ebejtrkce Tktefti`b? Tktefti`b cinnerefje getweef the ebejtrkce fc the ebejtrkbyte.

    Zt`fc`rc ebejtrkce pktefti`b ? Tktefti`b cinnerefje cevebkpec if jebb whef the aives ebejtrkce whijh is if jkft`jt with

    its ikfs h`vifa jkfjeftr`tikf 0 lkb B0is jkupbec with st`fc`rc hycrkaef ebejtrkce.

    Jebb pktefti`b ?Tktefti`b cinnerefje getweef the 7 ebejtrkces kn a`bv`fij jebb.

    ELN ?Tktefti`b cinnerefje getweef the 7 ebejtrkces kn a`bv`fij jebb whef fk jurreft is cr`wf thrkuah the jebb.

    Ejebb

    < EW

    - WB< E

    j`thkce E

    `fkce.

    Jebb We`jtikf ? Ju(s) + 7@a+(`q) Ju+7(`q) + 7@a(s)

    @t J`thkce(Wecujtikf) ? 7@a+(`q) + 7e 7@a(s)@t fkce (Wecujtikf) ? Ju(s) Ju+7(`q) + 7e

    Jebb Wepreseft tikf ? Ju | Ju+7|| @a+| @a

    Ejebb

    < Ju/Ju@a/@a 7EE ++ -

    ZHE ? Zt`fc`rc hycrkaef ebejtrkce

    0 L HJb

    H a`s7

    H+(`q) + e7

    0H

    7(a)

    k

    H/H 7E + < 4

    Ebejtrkjhelij`b Zeries ? She rr`faeleft kn let`b (kr spejies) if their ifjre`sifa recujifa pkwer (kr cejreeifa E) ismfkwf s ebejtrkjhelij`b series.

    Ferfst Equ`tikf? Sk j`bjub te ebejtrkce pktefti b t fy jkfjeftr tikf.

    )s(f

    )`q( LfeL ++

    \L]

    \L]bf

    fN

    WSEE

    f

    )s(k

    L/LL/L ff +

    -< ++

    Gut jkfjeftr`tikf kn skbic L is t`mef `s ufity

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    ] \+-< ++ f

    k

    L/L

    'L/L

    L

    0bf

    fN

    WSEE ff

    Kr ] \++< ++ fk L/LL/L LbffNWS

    EE ff

    N < 9>381 J lkb0

    W < 8.:03 Om-0lkb0

    ]Lf+\ < jkfjeftr`tikf kn spejies.

    S < 798 m

    f < fk kn lkbes kn e ifcij`tec if g`b`fjec eqf-

    ] \++< ++ fk L/LL/L Lbff459.4

    EEff

    If C`fieb jebb

    (0) _f | _f+7||Ju+7| Ju

    ] \77

    kjebbJebb

    _f

    Jubka

    7

    459.4EE

    +

    ++ < 343.7 Z jl7lkb0

    ` < 4l

    Jl

    B

    B< 07

    07

    lkbjlZ

    lkbZjl

    7.343

    05.3>-

    -

    < 4.0034

    (II) J`bjub`tikf kn cisskji`tikf jkfst`ft (MJ)

    HJKKH(`q) HJKK(`q) + H(`q)

    J K K

    J(0 `) J` J`

    M 1 043lkbB

    P.3 In jurreft kn 4.5 lpere nbkws thrkuah let`bbij wire nkr 7 hkurs, thef hkw l`fy ebejtrkfs wkubc nbkw

    thrkuah the wire ;

    Zkb. Jh`rae < I t

    Jh`rae 4 >4 Z) < :>44 @Z < :>44 J

    Fk. kn ebejtkrfs nbkwia thrkuah the wire tgy p`ssifa jh`rae kn kfe n`r c`y (9>544 J)

    < >.477 047:ebejtrkfs

    P Fk. kn ebejtrkfs nbkwifa thrkuah the wire gy p`ssifa jh rae kn :>44 J

    < >.477 047:J9>544

    J:>44< 7.73> 0477ebejtrkfs

    P.5 Qrite the jhelistry kn rejh`raifa the be c stkr`ae g`ttery, hiahbiahtifa bb the l`teri`bs th`t re ifvkbvec

    curifa re`jh`raifa.

    Zkb. Curifa rejh`raifa the jebb is kper`tec bime f ebejtrkbytij jebb i.e., ebejtrij`b eferay is suppbiec nrkl skle exterf`

    skurjes. Ebejtrkce re`jtikfs re reverse kn thkse curifa cisjh`raifa.

    TgZK3(s) + 7eTg(s) + ZK3

    7(`q) Wecujtikf

    TgZK3(s) + 7H7K(s) TgK7(s) + ZK37(`q) + 3H+(`q) + 7eKxic`tikf

    7TgZK3(s) + 7H7K(s) Tg(s) + TGK7(s) + 3H+(`q) + 7ZK3

    7(`q)

    P.> Cepijt the a`bv`fij jebb if whijh the re jtikf

    _f(s) + 7@a+(`q) _f7+(`q) + 7@a(s) t`mes pb`je.

    Nurther shkw ?

    (i) Qhijh kn the ebejtrkces is fea`tiveby jh`raec ;

    (ii) She j`rrier kn the jurreft if the jebb.

    (iii) Ifcivicu`b re`jtikfs t e`jh ebejtrkce.

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    Zkb._f(s) + 7@a (`q)

    +

    _f (`q) + 7@a(s)7+

    Wecujtikf

    Kxic`tikf

    _f(s) | _f7+(`q) @a+(`q) | @a(s) C`fieb jebb.

    (i) @fkce kn _f with fea tive jh rae = j thkce kn @a with pksitive jh`rae.

    (ii) Ebejtkfrs wib nbkw nrkl _f if Ju ifkuter jirjuit fc jurreft wibb nbkw nrkl Ju tk _f.

    (iii) J`thkce ? _f _f7++ 7e = @fkce ? 7@A++ 7e@a(s)

    P.1 J`bjub`te the st fc rc jebb pktefti bs kn a`bv`fij jebbs if whijh the nkbbkwifa re`jtikfs t`mes pb je ?

    (i) 7Jr(s) + :Jc7+(`q) 7Jr:+(`q) + :Jc(s)

    (ii) Ne7+(sq) + @a+(`q) Ne:+(qq) + @a(s)

    J`bjub`te the rA fc equibigriul jkfst`ft kn the re`jtikfs.

    Zkb. (i) 7Jr 7Jr:++ >e, (Kxic`tikf)

    :Jc7+ >e:Jc, (Wecujtikf)kjebbE 544 O < 09>8>4 Okr CrA < 09>.8> mO lkb

    0

    @bsk CrA < 7.:4: 8.:03 798 bka MM < ftibka :3.5403 < :.01: 04:3

    (ii) Ne7+Ne:++ e, (Kxic`tikf)

    @a++ e@a+(Wecutikf)Ek

    jebb< Ek

    J`thkce Ek

    @fkce

    544 4.4:kr C

    rA < 7895 O lkb0

    @bsk CrA < 7.:4: WS bka M

    7895 < 7.:4: 8.:03 798 bka M

    M < ftibka 4.5413 < :.77

    P.8 Qrite the Ferfst equ tikf fc eln kn the nkbbkwfia jebb t 798 M ?

    (i) La(s) | La7+(4.440 L)|| Ju7+(4.4440 L) | Ju(s)

    (ii) Ne(s) | Ne7+(4.440 L) || H+(0 L)| H7(a) (a) (0 g`r) Tt(s)

    Zkb. (i) Ejebb< (Ek

    J`thkce Ek

    `fkce) f

    459.4bka

    \Ju]

    \La]7

    7

    +

    +

    Ejebb< (4.:3 ( 7.:>)) 7

    459.4bka

    4440.4

    440.4< 7.>8

    (ii) Ejebb< (Ekj`thkce E

    k`fkce)

    045Z jl0. J`bjub`te its lkb`r jkfcujtivity. In 4lB nkr

    `jetij jic is :94.5 Z jl7lkb0, wh`t is its cisskji`tikf jkfst`ft;

    Zkb. Bl< J

    0444M .1 5 -< :7.1> Z jl7lkb0

    @bsk

    ` < 5.:941>.:7

    4l

    l e> -

    a717,@b7

    Sk prkcuje 7 71 a @b, Ebejtrijtiy requirec < >N

    RSk prkcuje 34 a @b, ebejtrijity requirec

    34

    544J < 09:444J

    (ii) Ne7+ Ne:+e

    kr 7NeK +7

    0K7Ne7K:

    Zk 0 lkb kn NeK wibb require 9>544 J.

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    P.07 Usifa the st`fc`rc ebejtrkce pktefti`bs aivef if the S gbe, precijt in the re`jtikf getweef the nkbbkwifa

    is ne`sigbe?

    (`) Ne:+(`q) fc I(`q)

    (g) Ne:+(`q) fc Gr(`q)

    (j) Gr7(`q) fc Ne7+(`q)

    ^49.0^53.4^11.4E

    EEEEbejtrkce kGr/Gr

    k

    I/I

    k

    Ne/Ne 777: -++

    Zkb. (`) 7Ne:+ + 7e 7Ne7+

    7 I I7+ 7e

    [[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

    7Ne:++ 7I 7Ne7+ + I7Shus twk h`bn jebbs `re Ne:/Ne7+ fc I7/I

    Ejebb < Ej`thkce E`fkce

    0> J

    Fkw, P < I t

    I .8< 8.>0> lpere

    P.03 Jkfsicer the nkbbkwifa ci`ar`l kn lerjury jebb

    ( ) Qhijh sugst`fje jts s j thkce fc whijh jts s fkce ;

    (g) Leftikf the ebejtrkbyte usec if the jebb

    Jebb j`fJ`thkceZep`r`tkr

    Are`met

    @fkce@fkce j p

    (j) Qh`t is the jebb pktefti b kn this jebb ;

    (c) Qhy ckes the vkbt ae kn lerjury jebb rel`if jkfst ft

    thrkuahkut if bine ;

    Zkb. (`) @fkce _ifj jkft ifer, J thkce J`rgkf rkc

    (g) @ p`ste kn HaK + MKH

    (j) 0.:5 (c) Gej use kver`bb jebb re jtikf ckes fkt ifvkbve fy ikf whkse jkfjeftr`tikf j`f jh fae

    _f(s) + HaK(s) _fK(s) + Ha(s)

    P.05 @t wh`t pH wibb hycrkaef ebejtrkce `t 798 M shkw `f ebejtrkce pktefti`b kn 4.008 , whef H7a`s is

    guggbec t 0 tl. pressure.

    Zkb. She ebejtrkce re`jtikf ifvkbvec is?

    H+(`q)

    + e 7

    0H

    7(a)

    \H]

    0bka

    f

    4590.4EE 4

    H/HH/H 77 +-< ++

    4.008 < 4 0

    4590.4bka

    \H]

    0+

    bka\H]

    0+ 7pH < 7

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    Exerjise0

    P.0 If the gutkf jebb wiceby usec if w`tjhes fc kther cevijes, the nkbbkwifa re`jtikf t`mes pb`je

    _f(s) + @aK(s) + H7K(b) _f7+(`q) + 7@a(s) + 7KH(`q)

    Ceterlife CrA fc E nkr the re`jtikf.

    P.7 Cenife jkfcujtivity `fc lkb r jkfcujtivity nkr the skbutikf kn f ebejtrkbyte. Cisjuss their v`ri tikf with jkfjeftr tikf.

    P.: She jkfcujtivity kn 4.74 L skbutikf kn MJb t 798 M is 4.4738 Z jl0. J`bjub`te its lkb`r jkfcujtivity.

    P.3 Hkw lujh jh`rae is requirec nrkl the nkbbkwifa recujtikfs?

    (i) 0 lkb kn @b:+tk @b

    (ii) 0 lkb kn Ju7+tk Ju;

    (iii) 0 lkb kn LfK3tk lf7+;

    P.5 @ skbutikf kn Fi(FK:)7is ebejtrkbysec getweef pb`tiful ebejtrkces usifa jurreft kn 5 lperes nkr 74 lifutes.

    Qh`t l`ss kn Fi is cepksitec t the j`thkce;

    P.> Shree ebejtrkbytij jebbs @, G, J jkft`ififa skbutikf kn _fZK3, @aFK

    : fc JuZK

    3, respejtiveby re jkffejtec if

    series. @ ste`cy jurreft kn 0.5 lperes re p`ssec thrkuah thel uftib 0.35 a kn sibver cepksitec t the j`thkce kn

    jebb G. Hkw bkfa cic the jurreft nbkw ; Qh`t l`ss kn jkpper fc kn zifj were cepksitec;

    P.1 Qh`t is the nufjtikf kn s`bt gricae if ebejtrkjhelij`b jebbs;

    P.8 @t ifnifite cibutikf, the lkb`r jkfcujt`fje kn F`+`fc ZK37ikfs `re 54 Z jl7lkb0`fc 0>4 Zjl7lkb0

    respejtiveby. Qh`t wibb ge the lkb`r jkfcujt`fje kn skciul subph`te t ifnifite cibutikf;

    P.9 Qhijh wibb h`ve are`ter lkb`r jkfcujtivity;

    "Zkbutikf h`vifa 0 lkb kn MJb if 744 jj kr 0 lkb kn MJb if >44 jj."

    P.04 Qh`t re sejfc`ry jebs; Aive the fkce kr j`thkce re`jtikf kn Fijmeb -J`cliul stkr`ae jebb.

    P.00 Qh`t is jkrrksikf ; Hkw is j`thkcij prktejtikf kn irkf cinnereft nrkl its a`bv`fis`tikf;

    P.07 Qh t ck yku le`f gy e.l.n. kn jebb. J bjub te the e.l.n. kn the jebb La(s) |La7+(4.7 L) ||@a+(0 04:L)|@a,k

    @a/@aE +

    < 4.84 ,k

    @a/La7E + < 7.:1 , Qh t wibb ge the ennejt kf e.l.n., in jkfj. kn La7+is cejre`ec tk 4.0 L.

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    Exerjise7

    P.0 Jkfcujtivity kn 4.44731 L jetij jic is 1.89> 045Z jl0. J`bjub`te its lkb`r jkfcujitvity. Inb nkr jetij`ijc is :94.5 Z jl7lkb0, wh`t is its cisskji`tikf jkfst`ft ; (@fs. 0.85 045) ]J.G.Z.E. 7443\

    P.7 Hkw ckes lkb`r jkfcujtivty v`ry with jkfjeftr`tikf nkr ]J.G.Z.E. 7443\

    (i) we`m ebejtrkbyte

    (ii) strkfa ebejtrkbyte ; Aive re`skf nkr these v`ri`tikfs

    Ztrkfaebejtrkbyte)lkbZjl( 07 -b

    Qe m ebejtrkbyte

    7/0)bitre/lkb(J

    P.: (`) If the guttkf jebb, wiceby usec if w`tjhes fc kther cevijes the nkbbkwifa re`jtikf t`mes pb`je?

    _f(s) + @a7K(s) + H7K(b) _f7+(`q) + 7@a(s) + 7KH(`q) ]J.G.Z.E. 7445\

    Ceterlife E fc CrA nkr the re`jtikf

    Aivef4

    @a/@aE + < + 4.84 ,4

    _f/_f7E + < 4.1> ..

    (g) Expb`if with ex`lpbes the terls we`m fc strkfa ebejtrkbytes. Hkw j`f these ge cistifauishec;

    P.3 Trecijt the prkcujts kn ebejtrkbysis kgt`ifec t the ebejtrkces if e`jh j`se whef the ebejtrkces usec re kn pb`tiful?

    ]J.G.Z.E. 7445\

    (i) @f quekus skbutikf kn @aFK: (ii) @f qekus skbutikf kn H7ZK3

    P.5 (`) Zt`te twk cv`ft`aes kn H7 K

    7nueb jebb kver krcif`ry jebb.

    (g) Zibver is ebejtrkcepksitec kf let`bbij vesseb kn tkt`b surn`je `re` 944 jl7gy p`ssifa jurreft kn 4.5 lp nkr

    twk hkurs. J`bjub`te the thijmfess kn sibver cepksitec.

    (Cefsity kn @a < 04.5 a jl:, @t. l`ss kn @a < 048 lu) ]J.G.Z.E. 744>\

    P.> (`) Aive re`skfs nkr the nkbbkwifa ? ]J.G.Z.E. 744>\

    (i) Wusifa kn irkf is quijmer if s`bife w`ter th`f is krcif`ry w`ter.

    (ii) @bulifiul let`b j`ffkt ge prkcujec gy the ebejtrkbysis kn quekus skbutikf kn bulifiul s`bt.

    P.1 (`) J`bjub`te the e.l.n. kn the jebb ]J.G.Z.E. 7441\

    La (s) |La7+(4.0L||Ju7+(0 04:L)| Ju(s)

    Aivef ? E Ju7+/Ju < + 4.:3 , E La+7/La < 7.:1

    (g) Expb`if with ex`lpbes the terls we`m fc strkfa ebejtrkbytes.

    P.8 (`) She resist`fje kn jkfcujtivity jebb jkft`ififa 4.440 L MJb skbutikf t 798 M is 0544 Q. Qh`t is the jebbjkfst`ft, in the jkfcujtivity kn 4.440 L MJb skbutikf t 798 M is 4.03> 04:Z jl0;

    (g) Trecijt the prkcujts kn ebejtrkbysis if the nkbbkwifa ? ]J.G.Z.E. 7441\@ skbutikf kn H7ZK3with pb`tiful ebejtrkces.

    P.9 Jkfcujtivity kn 4.44730 L `jetij `jic skbutikf 189> 045Z jl0. J`bjub`te its lkb`r jkfcujtivity if this

    skbutikf. In 4lB nkr `jetij `jic if :94.5 Z jl7lkb0, wh`t wkubc ge its cisskji`tikf jkfst`ft;

    ]J.G.Z.E. 7448\

    P.04 She jkfcujtivity kn 4.74 L skbutikf kn MJb t 798 M is 4.4738 Z jl0. J`bjub`te its lkb`r jkfcujtivity.

    ]J.G.Z.E. 7448\

    P.00 Express the reb`tikf getweef jkfcujtivity fc lkb`r jkfcujtivity kn skbutikf. ]J.G.Z.E. 7448\

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    P.07 (`) Zt`te Mkhbr`usjh's B`q kn ifcepefceft liar`tikf kn ikfs. Hkw j`f the cearee kn cisskji`tikf kn jetij jic if

    ` skbutikf ge j`bjub`tec nrkl its lkb`r jkfcujtivity c`t`; ]J.G.Z.E. 7448\

    (g) (i) Nkrlub`te the ebejtrkjhelij`b jebb represeftifa the re`jtikf

    7Jr(s) + :Ne+7(`q) 7Jr+:(`q) + :Ne(s)(ii) J`bjub`te E

    jebb(iii) J`bjub`te Ejebb `t 75J in

    ]Jr:+\ < 4.0 L `fc ]Ne+7\ < 4.40 L

    Aivef ? 4

    Jr/Jr:E + < 413 ,

    4

    Ne/Ne 7E + < 4.33 ^

    P.0: Qh`t is le`ft gy 'bilitifa lkb`r jkfcujtivity' ; ]J.G.Z.E. 7449\

    P.03 Express the reb`tikf lkfa the jebb jkfst`ft, the resist`fje kn the skbutikf if the jebb fc the jkfcujtivity kn the

    skbutikf. Hkw is the jkfcujtivity kn skbutikf reb`tec tk its lkb`r jkfcujtivity;

    ]J.G.Z.E. 7449\

    P.05 Aivef th`t the st`fc`rc ebejtrkce pktefti`bs(E) kn let`bs `re?

    M+/M < 7.9: , @a+/@a < 4.84 , Ju7+/Ju < 4.:3

    La7+/La < 7.:1 , Jr:+/Jr < 4.13 , Ne7+/Ne < 4.33 ,

    @rr`fae these let`bs if f ifjre`sifa krcer kn their recujifa pkwer.

    P.0> Swk h`bn-re`jtikfs kn f ebejtrkjhelij`b jebb re aivef gebkw? ]J.G.Z.E. 7449\

    LfK3(`q) + 8H+(`q) + 5 eLf7+(`q) + 3H

    7K(b), E < + 0.50

    Zf7+(`q) Zf3+(`q) + 7 e , E< + 4.05 .Jkfstrujt the reckx re`jtikf equ`tikf nrkl the twk h`bn -re`jtikfs fc j`bjub`te the jebb pktefti`b nrkl the st`fc`rc

    pktefti`bs fc precijt in the re`jtikf is re`jt`ft kr prkcujt n`vkurec.

    P.01 Cenife the nkbbkwifa ? ]J.G.Z.E. 7404\

    (i) Krcer kn re`jtikf (ii) @jtiv tikf eferay kn re`jtikf

    P.08 Qh`t type kn jebb is be`c stkr`ae g`ttery; Qrite the fkce fc the j`thkce re`jtikfs fc the kver`bb jebb re`jtikf

    kjjurrifa if the use kn be`c stkr`ae g`ttery. ]J.G.Z.E. 7404\

    P.09 Swk h`bn jebb re`jtikfs kn f ebejtrkjhelij`b jebb re aivef gebkw? ]J.G.Z.E. 7404\

    LfK3(`q) + 8H+(`q) + 5eLf7+(`q) + 3H7K(b), E < + 0.50

    Zf7(`q) Zf3+(`q) + 7e, E < + 4.05 jkfstrujt the reckx equ`tikf nrkl the twk h`bn jebb re`jtikfs fc precijt in this re`jtikf n`vkurs nkrl`tikf kn

    re`jt`fts kr prkcujt shkwf if the equ`tikf.

    P.74 (`) Qh`t type kn ` g`ttery is be`c stkr`ae g`ttery; Qrite the `fkce `fc j`thkce re`jtikfs `fc the kver`bb jebb

    re`jtikf kjjurrifa if the kper`tikf kn be`c stkr`ae g`ttery. ]J.G.Z.E. 7400\

    (g) J`bjub`te the pktefti`b nkr h`bn-jebb jkft`ififa 4.04 L M7Jr

    7K

    1(`q, 4.74 L Jr:+(`q) fc 0.4 043L H+(`q)

    She h`bn -jebb re`jtikf is

    Jr7K

    1

    7(`q) + 03H+(`q) + >e 7Jr:+(`q) + 1H7K(b),

    `fc the st`fc`rc ebejtrkce pktefti`b is aivef s E < 0.::

    P.70 (`) Hkw l`fy lkbes kn lerjury wibb ge prkcujec gy ebejtrkbysifa 0.4 L Ha(FK:)7skbutikf with jurreft kn 7.44@ nkr : hkurs ; ]Ha(FK

    :)

    7< 744.> a lkb0\ ]J.G.Z.E. 7400\

    (g) @ vkbt`ij jebb is set up t 75J with the nkbbkwifa h`bn-jebbs @b:+(4.440) fc Fi7+(4.54L). Qrite f equ`tikf nkr

    the re`jtikf th`t kjjurs whef the jebb aefer`tes `f ebejtrij jurreft `fc ceterlife the jebb pktefti`b. (Aivef ?

    ^>>.0E,^75.4E k

    @b/@b

    k

    Fi/Fi :7 -

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    15/15

    EBEJSWKJHELIZSWY 05

    www.thifmiit.if

    P.73 She st`fc`rc ebejtrkce pktefti`b (E) nkr C`fiebb jebb is 0.0 . J`bjub`te the CA nkr the re`jtikf_f(s) + Ju7+(`q) _f7+(`q) + Ju (s) (0 N < 9>544 J lkb0). ]J.G.Z.E. - 740:\

    P.75 J`bjub`te the eln kn the nkbbkwifa jebb t 75J ?

    @a(s) |@a+(04:L) || Ju7+(040L) | Ju (s)

    Aivef Ejebb

    < + 4.3> ^ `fc bka 04f< f. ]J.G.Z.E. - 740:\