11
Uchymdmbhcr Jgmssos UDJ/Dmnbotcj Oeeojt `e Jurrobt :? K^X->/Ykyscjs HMXO < XCDO < 89 Dcbutos DMVAZ < Q P /=?T XOZX J@HO <DMN Q=T ZXMVX XCDO < OBH XCDO < XCDO XMAOB< YMVOBX–Z ZCNBMX_VO < Xkcs tost j`b tmcbs m t`tmg `e =? @flojtcvo Xy po ]uostc `bs. Omjk quos tc`b jmrrcos = dmra. Xkoro cs B@ BONMX CUO dmracbn . Jk``so tko j`rrojt mgtorbmtcvo. @bgy `bo jk`cjo cs j`rrojt. =. M g`bn cbsugmtoh j`ppor wcro cs jg`sogy w`ubh ms m spcrmg `e  B  turbs. Xko spcrmg kms cbbor rmhcus  m mbh `utor rmhcus  f. Xko spcrmg gcos cb tko  [ -S  pgmbo mbh m stomhy jurrobt  C  eg`ws tkr`unk tko wcro. Xko \ -j`dp`bobt `e tko dmnbotcj ecogh mt tko jobtro `e tko spcrmg cs < (M) 9 6  BC f gb f m m ¿     (F) 9 6  BC f m gb f m f m ¿   (J) 9 6  BC f gb f m ¿   (H) 9 6  BC f m gb f f m ¿   6. Jurrobt tkr`unk  MFJ  mbh  M F J   cs  C . ^kmt cs tko dmnbotcj ecogh mt  Y 0  FY FY r   (Koro  J F YFJ   mro j`ggcbomr) (M) = 6 8  C  F r ω  (F) 9 6 8  C  F r ¿ ω   (J) 9 8  C  F r ¿ ω   (H) zor` :. Xko dmnbotcj ecogh mt tko p`cbt `e cbtorsoj tc`b `e hcmn`bmgs `e m squmro w cro g``p `e scho G jmrrycbn m jurrobt C  cs < (M) 9  C  G ¿ ω (F) 9 6  C  G ¿ ω (J) 9 6  C  G ¿ ω (H) 9 6 6  C  G ¿ ω 8. M jurrobt c cs eg`wcbn tkr`unk tk o g``p. Xko hcrojtc`b `e tko jurrobt mbh tko skmpo `e tko g``p mro ms sk`wb cb tko ecnuro. Xko dmnbotcj ecogh mt tko jobtro `e tko g``p cs 9 c  V ¿  tcdo 6 39  DM V DF V HDM (M) =5 fut `ut `e tko pgmbo `e tko pmpor  (F) ? =5  , fut cbt` tko pgmbo `e tko pmpor (J) > =5 , fut `ut `e tko pgmbo `e tko p mpor  (H) > =5 , fut cbt` tko pgmbo `e tko pmpor ?.  Y] mbh  VZ mro g`bn pmrmggog j`bhujt`rs sopmrmtoh fy jortmcb hcstmbjo. D . cs tko dch-p`cbt fotwoob tkod (soo tko ecnuro). Xko bot dmnbotcj ecogh mt  D  c s F. B`w, tko jurrobt 6  M cs swctjkoh `ee. Xko ecogh mt D  b`w foj`dos. (M) 6  F  (F)  F (J) 6  F (H) :  F 5. Dmnbotcj ecogh mt tko jobtro `e m jcrjugmr j`cg `e r mhcus  V huo t` c eg`wcbn tkr`unk ct cs F. Xko dmnbotcj ecogh mt m p`cbt mg`bn tko mxcs mt hcstmbjo V er`d tko jobtro cs < (M) 6  F (F) 8  F (J) ;  F (H) ;  F

Jee 2014 Booklet7 Hwt Magnetic Effects of Current

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt :? K^X->/Ykyscjs

HMXO < XCDO < 89 Dcbutos DMVAZ < Q PPP /=?T XOZX J@HO < DMN Q=T

ZXMVX XCDO < OBH XCDO < XCDO XMAOB< YMVOBX–Z ZCNBMX_VO <

Xkcs tost j`btmcbs m t`tmg ̀ e =? @flojtcvo Xypo ]uostc̀ bs. Omjk quostc`b jmrrcos = dmra. Xkoro cs B@ BONMXCUO dmracbn.

Jk``so tko j`rrojt mgtorbmtcvo. @bgy `bo jk`cjo cs j`rrojt.

=. M g`bn cbsugmtoh j`ppor wcro cs jg`sogy w`ubh ms m spcrmg `e  B   turbs. Xko spcrmg kms cbborrmhcus  m  mbh `utor rmhcus  f. Xko spcrmg gcos cb tko  [ -S   pgmbo mbh m stomhy jurrobt   C   eg`wstkr`unk tko wcro. Xko \ -j`dp`bobt `e tko dmnbotcj ecogh mt tko jobtro `e tko spcrmg cs <

(M)

9

6

 BC fgb

f m m

¿    

(F)

96

 BC f mgb

f m f m

¿  

(J) 96

 BC fgb

f m

¿  

(H) 96 BC f m

gbf f m

¿  

6. Jurrobt tkr`unk  MFJ   mbh   M F J    cs   C . ^kmt cs tko dmnbotcj ecogh mt  Y 0   FY FY r   (Koro  J F YFJ   mro j`ggcbomr)

(M)= 6

8 C 

 Fr ω

  (F) 9 6

8

 C  F

¿

ω

 

(J) 98

 C  F

¿

ω

 

(H) zor`

:. Xko dmnbotcj ecogh mt tko p`cbt `e cbtorsojtc`b `e hcmn`bmgs `e m squmro wcro g``p `e scho G jmrrycbn m jurrobt C  cs <

(M) 9 C 

 G

¿

ω(F) 96   C 

 G

¿

ω(J) 96   C 

 G

¿

ω(H) 96 6   C 

 G

¿

ω

8. M jurrobt c cs eg`wcbn tkr`unk tko g``p. Xko hcrojtc`b `e tko jurrobt mbh tko skmpo `e tko g``p mro mssk`wb cb tko ecnuro. Xko dmnbotcj ecogh mt tko jobtro `e tko g``p cs 9c

 V

¿ tcdo

6 39 DM V DF V HDM

(M)=5

fut `ut `e tko pgmbo `e tko pmpor   (F)?

=5 , fut cbt` tko pgmbo `e tko pmpor

(J)>

=5, fut `ut `e tko pgmbo `e tko pmpor   (H)

>

=5, fut cbt` tko pgmbo `e tko pmpor

?.   Y]  mbh   VZ  mro g`bn pmrmggog j`bhujt`rs sopmrmtoh fy jortmcbhcstmbjo. D . cs tko dch-p`cbt fotwoob tkod (soo tko ecnuro). Xko botdmnbotcj ecogh mt D  cs F. B`w, tko jurrobt 6  M cs swctjkoh `ee. Xko

ecogh mt D  b`w foj`dos.(M) 6 F   (F)   F

(J)6

 F(H) : F

5. Dmnbotcj ecogh mt tko jobtro `e m jcrjugmr j`cg `e rmhcus V huo t` c eg`wcbn tkr`unk ct cs F. Xko dmnbotcj ecogh mt m p`cbt mg`bn tkomxcs mt hcstmbjo V er`d tko jobtro cs <

(M)6

 F(F)

8

 F(J)

;

 F(H) ; F

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt :> K^X->/Ykyscjs

HMXO < XCDO < 89 Dcbutos DMVAZ < Q PPP /=?T XOZX J@HO < DMN Q6T

ZXMVX XCDO < OBH XCDO < XCDO XMAOB< YMVOBX–Z ZCNBMX_VO <

Xkcs tost j`btmcbs m t`tmg ̀ e =? @flojtcvo Xypo ]uostc`bs. Omjk quostc`b jmrrcos = dmra. Xkoro cs B@ BONMXCUO dmracbn.

Jk``so tko j`rrojt mgtorbmtcvo. @bgy `bo jk`cjo cs j`rrojt.

=. M jcrjugmr j`cg `e 69 turbs mbh rmhcus =9jd cs pgmjoh cb ubce`rd dmnbotcj ecogh `e 9.=9  X  b`rdmg t` tko pgmbo `e tko j`cg. Ce tkojurrobt cb j`cg cs ? M, tkob tko t`rquo mjtcbn `b tko j`cg wcgg fo <(M) :=.8 Bd   (F) :.=8 Bd   (J) 9.:=8 Bd   (H) zor`

6. M jurrobt C  obtors m ubce`rd jcrjugmr j`cg `e rmhcus  V, frmbjkos cbt` tw` pmrts mbh tkobroj`dfcbos ms sk`wb cb tko jcrjuct hcmnrmd. Xko rosugtmbt dmnbotcj ecogh mt tko jobtro `e tko j̀ cg cs <

(M) zor`   (F) 96

 C 

 V

¿(J) 9:

8 6 C 

 V

¿

(H) 9=8 6

 C 

 V

¿

:. Xw` g`bn pmrmggog wcros jmrry jurrobts c= mbh c6 sujk tkmt = 6c c . ^kob tko jurrobts mro cb tko smdo hcrojtc`b, tko dmnbotcj ecogh mt

m p`cbt dchwmy fotwoob tko wcros cs 55 =9   X  . Ce tko hcrojtc`b `e  c6 cs rovorsoh, tko ecogh foj`dos ?: =9   X  . Xko rmtc` =

6

c

c cs <

(M) =/6   (F) 6   (J) 6/:   (H) :/6

8. M k`rcz`btmg `vorkomh p`worgcbo cs mt m kocnkt `e 8   d  er`d tko nr`ubh mbh jmrrcos m jurrobt `e =99  M  er`d omst t` wost.

Xko dmnbotcj ecogh hcrojtgy fog`w ct `bo tko nr`ubh cs <    > =9 8 =9   XdM¿ ω

 

(M)>6 ? =9.

   s`utkwmrh   (F)5? 9 =9. X 

b`rtkwmrh

(J)5? 9 =9. X 

  , s`utkwmrh   (H)>6 ? =9. X 

, b`rtkwmrh

?. Xw` j`bjobtrcj j`cgs `e =9 turbs omjk mro pgmjoh cb tko smdo pgmbo. Xkocr rmhcc mro 69  jd mbh 89 jd mbh jmrry 9.6 M mbh 9.: Mjurrobt rospojtcvogy cb `pp`scto hcrojtc`bs. Xko dmnbotcj cbhujtc`b (cb tosmgm) mt tko jobtro cs <

(M) 9:

8¿   (F) 9

?

8¿   (J) 9

>

8¿   (H) 9

3

8¿

5. Jurrobt C cs eg`wcbn cb j`bhujt`r skmpoh ms sk`wb cb tko ecnuro. Xko rmhcus `e tko jurvoh pmrt cs  r  mbh tko gobntk `e strmcnkt p`rtc`bcs vory gmrno. Xko vmguo `e tko dmnbotcj ecogh mt tko jobtro @ wcgg fo <

(M) 9 :=

8 6

 C 

¿ ω

ω

(F) 9 :

=8 6

 C 

¿ ω

ω

(J) 9 =8 6

 C 

¿ ω

ω

(H) 9 =

8 6 C 

¿ ω

ω

>. M jcrjugmr jurrobt jmrrycbn j`cg kms m rmhcus  V. Xko hcstmbjo er`d tko jobtro `e tko j`cg `b tko mxcs `e tko j`cg, wkoro tko dmnbotcjcbhujtc`b cs =/;tk `e cts vmguo mt tko jobtro ̀ e tko j`cg cs <

(M) : V   (F) : V /    (J)6

:  V

(H)6 :

 V

;. Xko hcrojtc`b `e cbhujoh dmnbotcj ecogh   hF  huo t` jurrobt ogodobt   c hG , mt m p`cbt `e hcstmbjo r  er`d ct, wkob m jurrobt c  pmssos

tkr`unk m g`bn j`bhujt`r cs cb tko hcrojtc`b.

(M) `e p`sctc`b vojt`r   r  `e tko p`cbt   (F) `e jurrobt ogodobt  hG

(J) porpobhcjugmr t` f`tk mbhhG r    (H) porpobhcjugmr t`   hG  `bgy

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt :; K^X->/Ykyscjs

3. M jcrjugmr j`cg `e ? turbs mbh `e =9 jd domb hcmdotor cs j`bbojtoh t` m v`gtmno s`urjo. Ce tko roscstmbjo ̀ e j`cg cs =9Σ , tko v`gtmno

`e tko s`urjo s` cs t` buggcey tko k`rcz`btmg j`dp`bobt `e omrtk's dmnbotcj ecogh `e :9 M turb =d

 mt tko jobtro `e tko j`cg sk`ughfo<(M) 5U , pgmbo `e tko j`cg b`rdmg t` dmnbotcj dorchcmb(F) 6 U , pgmbo `e tko j`cg b`rdmg t` dmnbotcj dorchcmb

(J) 6 U , pgmbo `e tko j`cg mg`bn tko dmnbotcj dorchcmb(H) 8U , pgmbo `e tko j`cg b`rdmg t` dmnbotcj dorchcmb

=9. Cb tko ecnuro sk`wb, tko dmnbotcj ecogh cbhujtc`b mt tko p`cbt @ wcgg fo <

(M) 96

c

¿

ω(F)   9 6

8

c

¿ω

ω

(J)   9 =8

c

¿ω

ω

(H)   9 6

8c

¿ω

ω

==. ^kcjk `e tko e`gg`wcbn nrmpks roprosobt vmrcmtc`b `e dmnbotcj ecogh F wctk hcstmbjo r  e`r m strmcnkt g`bn wcro jmrrycbn jurrobt0

(M) (F) (J) (H)

=6. Cb m kyhr`nob mt`d, tko ogojtr`b cb dmacbn =?5 5 =9.     rps  cb m jcrjugmr pmtk `e rmhcus9 ?:Ï. . ^kmt cs tko dmnbotcj cbhujtc`b

pr`hujoh mt tko jobtro ̀ e `rfct0(M) 5.: X    (F) =6.5 X    (J) =;.3 X    (H) 6?.6 X 

=:. M jogg cs j`bbojtoh fotwoob tko p`cbts. M mbh J `e m jcrjugmr j`bhujt`r MFJH wctk @ ms

jobtro mbh mbngo M@J 4 59 . Ce  = 6mbh F F  mro tko dmnbctuhos `e tko dmnbotcj ecoghs mt

@ huo t` tko jurrobts cb MFJ  mbh MHJ  rospojtcvogy, tkob rmtc` =

6 F

Ζ .

(M) =(F) 6(J) ?(H) 5

=8. Cb tko mhlmjobt ecnuro cs sk`wb m jg`soh pmtk   Y.   M  g`bn strmcnktj`bhujt`r jmrrycbn m jurrobt C pmssos tkr`unk @ mbh porpobhcjugmr t`tko pgmbo `e tko pmpor. Xkob wkcjk `e tko e`gg`wcbn k`ghs n``hs0

(M) 9

 p

 F . hg    (F) 9

Y

 F . hg C ¿

(J) 9

Y

 F .hg C ¿   (H) B`bo `e tkoso

=?. M wcro `rcobtoh cb tko omst-wost hcrojtc`b jmrrcos m jurrobt omstwmrh. Hcrojtc`b `e tko dmnbotcj ecogh mt m p`cbt t` tko s`utk `e tkowcro cs<(M) vortcjmggy h`wb   (F) vortcjmggy up   (J) b`rtk-omst   (H) s`utk-omst

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt :3 K^X->/Ykyscjs

HMXO < XCDO < 89 Dcbutos DMVAZ < Q PPP /=?T XOZX J@HO < DMN Q:T

ZXMVX XCDO < OBH XCDO < XCDO XMAOB< YMVOBX–Z ZCNBMX_VO <

Xkcs tost j`btmcbs m t`tmg ̀ e =? @flojtcvo Xypo ]uostc̀ bs. Omjk quostc`b jmrrcos = dmra. Xkoro cs B@ BONMXCUO dmracbn.

Jk``so tko j`rrojt mgtorbmtcvo. @bgy `bo jk`cjo cs j`rrojt.

=. Xko ecnuro sk`ws tko jr`ss-sojtc`b `e m g`bn jygcbhrcjmg j`bhujt`r `e rmhcus m jmrrycbn m ubce`rdgy hcstrcfutoh jurrobt  c. Xko dmnbotcjecogh huo t` jurrobt mt Y cs <

(M)   69 6cr / m¿ ω   (F)   6

9 6cr / m¿ ω

(J)   69 6cm / r  ¿ ω   (H)   6 6

9cm / r  ¿ ω

6. E`r tko dmnbotcj ecogh t` fo dmxcdud huo t` m sdmgg ogodobt `e jurrobt jmrrycbn j`bhujt`r mt m p`cbt, tko mbngo fotwoob tkoogodobt mbh tko gcbo l`cbcbn tko ogodobt t` tko ncvob p`cbt dust fo <

(M) 9   (F) 39   (J) =;9   (H) 8?

:. Dmnbotcj cbhujtc`b mt tko jobtro `e m jcrjugmr g``p `e mrom 6dω  cs 9.= X . Xko dmnbotcj d`dobt `e tko g``p cs < ( 9¿  4 pordomfcgcty

`e mcr)

(M)9 =

9.   ω

¿(F)

9

9 6.   ω

¿(J)

9

9 :.   ω

¿(H)

9

9 8.   ω

¿

8. M g`bn strmcnkt wcro jmrrycbn m jurrobt `e :9   M  cs pgmjoh cb mb oxtorbmg ubce`rd dmnbotcj ecogh `e cbhujtc`b 88 =9   X  .

Xko dmnbotcj ecogh cs mjtcbn pmrmggog t` tko hcrojtc`b `e jurrobt. Xko dmnbctuho `e tko rosugtmbt dmnbotcj cbhujtc`b cb tosgm mt m

p`cbt 6.9 jd mwmy er`d tko wcro    >9 8 =9   K / d¿ ω

 

(M)8=9

(F)8: =9   (J)

8? =9   (H)85 =9

?. Mb ogojtr`b mbh m pr`t`b mro d`vcbn `b strmcnkt pmrmggog pmtk wctk smdo vog`jcty. Xkoy obtor m sodc-cbecbcto ronc`b `e ubce`rddmnbotcj ecogh porpobhcjugmr t` tko vog`jcty. ^kcjk `e tko e`gg`wcbn stmtodobt(s) cs/mro truo0(M) Xkoy wcgg bovor j`do `ut tko dmnbotcj ecogh ronc`b(F) Xkoy wcgg j`do `ut trmvoggcbn mg`bn pmrmggog pmtks(J) Xkoy wcgg j`do `ut mt tko smdo tcdo(H) Xkocr pmtk wcgg b`t fo pmrmggog

5. ^kcjk `e tko ecogh pmttorb ncvob cb tko ecnuro cs vmgch e`r ogojtrcj ecogh ms wogg ms e`r dmnbotcj ecogh0

(M) (F) (J) (H)

>. M tkcb jcrjugmr hcsa `e rmhcus  V  cs ubce`rdgy jkmrnoh wctk hobscty 9ϊ     por ubct mrom. Xko hcsa r`tmtos mf`ut cts mxcs wctk m

ubce`rd mbnugmr spooh   σ . Xko dmnbotcj d`dobt `e tko hcsa cs <

(M)66   Vω ϊσ   (F)

86   Vω ϊσ   (J)

8

6

 Vωϊσ   (H)

8

8

 Vωϊσ

;. M pr`t`b, m houtr`b mbh mb pmrtcjgoν    kmvcbn tko smdo acbotcj oborny mro d`vcbn cb jcrjugmr trmlojt`rcos cb m j`bstmbt dmnbotcj

ecogh. mbh p h r r r ν  hob`to rospojtcvogy tko rmhcc `e tko trmlojt`rcos `e tkoso pmrtcjgo, tkob

(M) h pr r r ν     (F) m h pr r r    (J) h pr r r ν     (H) h pr r r ν  

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt 89 K^X->/Ykyscjs

3. M boutr`b, m pr`t`b, mb ogojtr`b mbh mb pmrtcjgoν   obtor m ronc`b `e ubce`rd dmnbotcj ecogh wctk

tko smdo vog`jctcos. Xko dmnbotcj ecogh cs porpobhcjugmr mbh hcrojtoh cbt` tko pgmbo `e tko pmpor.tko trmjas `e tko pmrtcjgos mro gmfoggoh cb tko ecnuro. Xko ogojtr`b e`gg`ws tko trmja(M)   H   (F)   J 

(J)   F   (H)   M

=9. Xko ecnuro sk`ws tkroo sctumtc`bs wkob mb ogojtr`b wctk vog`jcty   v  trmvogs tkr`unk m ubce`rd dmnbotcj ecogh   F . Cb omjk jmso,

wkcjk cs tko hcrojtc`b `e dmnbotcj e`rjo `b tko ogojtr`b 0

(M) mxcs mxcs mxcsvo z vo x vo y   (F) mxcs mxcs mbh zor`vo z vo x (J) mxcs mxcs mbh zor`vo z vo y   (H) mxcs mxcs mbh zor`vo z vo y

==. Xko rmhcus `e tko pmtk `e mb ogojtr`b d`vcbn mt m spooh `e  >: =9   d / s  porpobhcjugmr t` m dmnbotcj ecogh cs bomrgy

(M) =? jd   (F) 8? jd   (J) 6> jd   (H) :8 jd

=6. Xko dmxcdud vog`jcty t` wkcjk m pr`t`b jmb fo mjjogormtoh cb m jyjg`tr`b `e =9 DK z eroquobjy mbh rmhcus ?9 jd cs

(M);5 6; =9. d / s   (F)

;: =8 =9. d / s   (J)>5 6; =9. d / s   (H)

>: =8 =9. d / s

=:. Xw` pmrtcjgos `e dmssos mbhm fd d  mbh smdo jkmrno mro pr`lojtoh cb m porpobhcjugmr dmnbotcj ecogh. Xkoy trmvog mg`bn jcrjugmr

pmtks `e rmhcus mbhm fr r   sujk tkmt   m fr r  . Xkob wkcjk cs truo0

(M) m m f fd v d v   (F) mbhm f m fd d v v

(J) mbhm f m fd d v v   (H) f f m md v d v

=8. Mb ogojtr`b d`vos cb m jcrjugmr `rfct wctk m ubce`rd spooh v. Ct pr`hujos m dmnbotcj ecogh F mt tko jobtro `e tko jcrjgo. Xko rmhcus`e tko jcrjgo cs pr`p`rtc`bmg t` <

(M)  F

v(F)

  v

 F(J)

  v

 F(H)

  F

v

=?. Xw` jkmrnoh pmrtcjgos mro pr`lojtoh cbt` m ronc`b cb wkcjk m dmnbotcj ecogh cs porpobhcjugmr t` tkocr vog`jctcos. Metor tkoy obtor tkodmnbotcj ecogh, y`u jmb j`bjguho tkmt(M) tko jkmrnos mro hoegojtoh cb `pp`scto hcrojtc`bs   (F) tko jkmrnos j`btcbuo d`vo cb m strmcnkt gcbo(J) tko jkmrnos d`vo cb jcrjugmr pmtks   (H) tko jkmrnos d`vo cb jcrjugmr pmtk fut cb `pp`scto hcrojtc`bs

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt 8= K^X->/Ykyscjs

HMXO < XCDO < 89 Dcbutos DMVAZ < Q PPP /=?T XOZX J@HO < DMN Q8T

ZXMVX XCDO < OBH XCDO < XCDO XMAOB< YMVOBX–Z ZCNBMX_VO <

Xkcs tost j`btmcbs m t`tmg ̀ e =? @flojtcvo Xypo ]uostc̀ bs. Omjk quostc`b jmrrcos = dmra. Xkoro cs B@ BONMXCUO dmracbn.

Jk``so tko j`rrojt mgtorbmtcvo. @bgy `bo jk`cjo cs j`rrojt.

=. ^kcjk `e tko e`gg`wcbn pmrtcjgos wcgg hosjrcfo tko sdmggost jcrjgo wkob pr`lojtoh wctk tko smdo vog`jcty porpobhcjugmr t` tkodmnbotcj ecogh0

(M) Ogojtr`b   (F) Yr`t`b   (J) pmrtcjgoν     (H) Houtor`b

6. E`ur jkmrnoh pmrtcjgos mro pr`lojtoh porpobhcjugmrgy cbt` tko dmnbotcj ecogh wctk oqumg. ^kcjk wcgg kmvo dcbcdud eroquobjy `e r`rmtc`b0(M) Yr`t`b   (F) Ogojtr`b   (J)   Gc+

(H)   Ko+

:. Mb ogojtr`b mbh m pr`t`b `e oqumg gcbomr d`dobtud obtor cb tko hcrojtc`b porpobhcjugmr t` ubce`rd dmnbotcj ecogh. Ce tko rmhcc `e 

tkocr jcrjugmr pmtk fo   or  mbh   pr   rospojtcvogy, tkob   o

 p

r , cs oqumg t`   od    dmss `e ogojtr`b,   pd    dmss `e pr`t`b.

(M)

= 6 /  p

o

d

d

(F)  p

o

d

d(J)

= 6 / 

o

 p

d

d

(H) =

8. ^kcjk `e tko e`gg`wcbn wkcgo cb d`tc`b jmbb`t fo hoegojtoh fy dmnbotcj ecogh0(M) Yr`t`bs   (F) Jmtk`ho rmys   (J) Mgpkm pmrtcjgos   (H) Boutr`bs

?. Xw` pmrtcjgos `e oqumg jkmrnos metor focbn mjjogormtoh tkr`unk tko smdo p`tobtcmg hceeorobjo obtor m ubce`rd trmbsvorso dmnbotcjecogh mbh hosjrcfo jcrjugmr pmtk `e rmhcc V= mbh V6 rospojtcvogy. Xkob tko rmtc` `e tkocr dmss ( D = /  D 6) cs

(M) =

6

 V

 V(F)

6=

6

 V

 V

(J) 6

=

 V

 V(H)

66

=

 V

 V

5. Xko dmnbotcj e`rjo `b m jkmrnoh pmrtcjgo d`vcbn cb tko ecogh h`os b`t w`ra, fojmuso.

(M) acbotcj oborny `e tko jkmrnoh pmrtcjgo h`os b`t jkmbno(F) tko jkmrno ̀ e tko pmrtcjgo rodmcbs smdo(J) tko dmnbotcj e`rjo cs pmrmggog t` vog`jcty `e tko pmrtcjgo(H) tko dmnbotcj e`rjo cs pmrmggog t` dmnbotcj ecogh

>. Chobtcey tko j`rrojt stmtodobt er`d tko e`gg`wcbn(M) Jyjg`tr`b eroquobjy cs hopobhobt `b spooh `e tko jkmrnoh pmrtcjgo(F) Acbotcj oborny `e jkmrnoh pmrtcjgo cb jyjg`tr`b h`os b`t hopobhobt `b cts dmss(J) Jyjg`tr`b eroquobjy h`os b`t hopobh `b spooh `e jkmrnoh pmrtcjgo(H) Acbotcj oborny `e jkmrnoh pmrtcjgo cb jyjg`tr`b cs cbhopobhobt `e cts jkmrno

;. M pr`t`b wctk oborny `e 6 DoU  obtors m ubce`rd dmnbotcj ecogh `e 6.? X  b`rdmggy. Xkob dmnbotcj e`rjo `b tko pr`t`b cs

(Xmao dmss `e pr`t`b fo6>

= 5 =9. an

)(M)

=6: =9   B    (F)=9; =9   B    (J)

=6; =9   B    (H)=96 =9   B 

3. Xko jyjg`tr`b eroquobjy `e mb ogojtr`b nrmtcbn cb m dmnbotcj ecogh `e = X  cs mppr`xcdmtogy(M) 6; DKz   (F) 6;9 DKz   (J) 6.; NKz   (H) 6; NKz

=9. M j`bhujtc`b r`h `e = d gobntk mbh = an dmss cs suspobhoh fy t`w vortcjmg wcros tkr`unk cts obhs. Mb oxtorbmg dmnbotcj ecogh `e 6X  cs mppgcoh b`rdmg t` tko r`h. B`w tko jurrobt t` fo pmssoh tkr`unk tko r`h s` ms t` dmao tko tobsc`b cb tko wcros zor` cs <

QXmao n 4 =9 6ds

T

(M) 9.? M   (F) =? M   (J) ? M   (H) =.? M

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt 86 K^X->/Ykyscjs

==. M wcro Y]V cs fobt ms sk`wb cb ecnuro mbh cs pgmjoh cb m ronc`b `e ubce`rd dmnbotcj ecogh F. Xko gobntk `e  Y] 4 ]V 4 g. M jurrobt C mdporo eg`ws tkr`unk tko wcro ms sk`wb. Xko dmnbctuho `e tko e`rjo`b Y] mbh ]V wcgg fo <(M)   FCg, 9   (F) 6 FCg, 9

(J) 9, FCg   (H) 9, 9

=6. ^kob m p`sctcvogy jkmrnoh pmrtcjgo obtors m ubce`rd dmnbotcj ecogh wctk ubce`rd vog`jcty, cts trmlojt`ry jmb fo <=. m strmcnkt gcbo   6. m jcrjgo   :. m kogcx(M) = `bgy   (F) = `r 6   (J) = `r :   (H) Mby `bo `e =, 6 mbh :

=:. M jkmrno pmrtcjgo `e dmss d  mbh jkmrno q obtors m ronc`b `e ubce`rd dmnbotcj ecogh F porpobhcjugmr `e cts vog`jcty v. Xko pmrtcjgocbctcmggy mt rost wms mjjogormtoh fy m p`tobtcmg hceeorobjo  U   (v`gts) foe`ro ct obtoroh tko ronc`b `e dmnbotcj ecogh. ^kmt cs tkohcmdotor `e tko jcrjugmr pmtk e`gg`woh fy tko jkmrnoh pmrtcjgo cb tko ronc`b `e dmnbotcj ecogh0

(M)6:

dU 

q(F)

6 6dU 

 F q(J)

6dU  F

q(H)

6 F dU 

q F

=8. M tkcb egoxcfgo wcro `e gobntk  G  cs j`bbojtoh t` tw` mhlmjobt ecxohp`cbts mbh jmrrcos m jurrobt C  cb tko jg`jawcso hcrojtc`b, ms sk`wb cbtko ecnuro. ^kob tko systod cs put cb m ubce`rd dmnbotcj ecogh `e strobntk F n`cbn cbt` tko pgmbo `e tko pmpor, tko wcro tmaos tko skmpo`e m jcrjgo. Xko tobsc`b cb tko wcro cs <

(M)   CFG   (F)  CFG

ω(J)

6 CFG

ω(H)

8 CFG

ω

=?. Xw` g`bn pmrmggog wcros mro mt m hcstmbjo 6h  mpmrt. Xkoy jmrry stomhy oqumg jurrobt eg`wcbn `ut `e tko pgmbo `e tko pmpor ms sk`wb.

Xko vmrcmtc`b `e tko dmnbotcj ecogh mg`bn tko gcbo   [[   cs ncvob fy

(M) (F)

(J) (H)

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt 8: K^X->/Ykyscjs

HMXO < XCDO < 89 Dcbutos DMVAZ < Q PPP /=?T XOZX J@HO < DMN Q?T

ZXMVX XCDO < OBH XCDO < XCDO XMAOB< YMVOBX–Z ZCNBMX_VO <

Xkcs tost j`btmcbs m t`tmg ̀ e =? @flojtcvo Xypo ]uostc̀ bs. Omjk quostc`b jmrrcos = dmra. Xkoro cs B@ BONMXCUO dmracbn.

Jk``so tko j`rrojt mgtorbmtcvo. @bgy `bo jk`cjo cs j`rrojt.

=. Xw` jcrjugmr j`bjobtrcj g``ps `e rmhcc = 669 mbh :9r jd r jd   mro

pgmjo cb tko  [ -S  pgmbo ms sk`wb cb tko ecnuro. M jurrobt  C  4 > M  cseg`wcbn tkr`unk tkod. Xko dmnbotcj d`dobt `e tkcs g``p systod cs <

(M)     69 8. a Md   (F)     6= ?. a Md

(J)     6= =. a Md   (H)     6= :. l M d

6. :M `e jurrobt cs eg`wcbn cb m gcbomr j`bhujt`r kmvcbn m gobntk `e 89  jd. Xko j`bhujt`r cs pgmjoh cb m dmnbotcj ecogh `e strobntk

?99 nmuss mbh dmaos mb mbngo `e :9  wctk hcrojtc`b `e tko ecogh, Ct oxporcobjo m e`rjo `e dmnbctuho

(M)8: =9   B    (F)

6:?=9   B    (J)6: =9   B    (H)

8: =9   B 

:. M jcrjugmr g``p mbh m squmro g``p mro e`rdoh er`d tko smdo wcro mbh tko smdo jurrobt cs pmssoh tkr`unk tkod. Ecbh tko rmtc` `e tkocr hcp`go d`dobts.

(M) 8ω   (F)8ω

(J)6ω

(H) 6ω

8. M tmbnobt nmgvmb`dotor cs j`bbojtoh hcrojtgy t` mb chomg fmttory. Ce tko budfor `e turbs cb tko j`cg cs h`ufgoh, tko hoegojtc`b wcgg.(M) cbjromso   (F) hojromso   (J) rodmcb ubjkmbnoh   (H) octkor cbjromso ̀ r hojromso

?. Ztmtodobt = < ^kob rmhcus `e jcrjugmr g``p jmrrycbn jurrobt cs h`ufgoh, cts dmnbotcj d`dobt foj`dos e`ur tcdos.

Ztmtodobt 6 < Dmnbotcj d`dobt hopobhs `b mrom `e tko g``p.(M) Ztmtodobt-= cs Xruo, Ztmtodobt-6 cs Xruo mbh Ztmtodobt-6 cs m j`rrojt oxpgmbmtc`b e`r Ztmtodobt-=.(F) Ztmtodobt-= cs Xruo, Ztmtodobt-6 cs Xruo mbh Ztmtodobt-6 cs B@X m j`rrojt oxpgmbmtc`b e`r Ztmtodobt-=.(J) Ztmtodobt-= cs Xruo, Ztmtodobt-6 cs Emgso.(H) Ztmtodobt-= cs Emgso, Ztmtodobt-6 cs Xruo.

5. Ce m jurrobt cs pmssoh cb m sprcbn, ct <(M) nots j`dprossoh   (F) not oxpmbhoh   (J) `sjcggmtos   (H) rodmcbs ubjkmbnoh

>. M jurrobt jmrrycbn strmcnkt wcro cs aopt mg`bn tko mxcs `e m jcrjugmr g``p jmrrycbn m jurrobt. Xko strmcnkt wcro.(M) wcgg oxort mb cbwmrh e`rjo `b tko jcrjugmr g``p(F) wcgg oxort mb `utwmrh e`rjo `b tko jcrjugmr g``p

(J) wcgg oxort m e`rjo `b tko jcrjugmr g``p pmrmggog t` ctsoge (H) wcgg b`t oxort mby e`rjo `b tko jcrjugmr g``p

;. Xko dmnbotcj hcp`go d`dobt `e m jurrobt g``p cs cbhopobhobt `e (M) dmnbotcj ecogh cb wkcjk ct cs gmycbn   (F) budfor `e turbs(J) mrom `e tko g``p   (H) jurrobt cb tko g``p

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Uchymdmbhcr Jgmssos

UDJ/Dmnbotcj Oeeojt ̀e Jurrobt 88 K^X->/Ykyscjs

3. Mb ogojtr`b cs d`vcbn cb mb ̀ rfct `e rmhcus V wctk m tcdo porc`h X  ms sk`wb cb tko ecnuro. Xko dmnbotcj d`dobt pr`hujoh dmy foncvob fy <

(M)6   | o | M

 D X 

ω   (F)

6   | o | M D 

ω

(J)

  | o | M

 D  X    (H)

  | o | M

 D  X | o | roprosobts tko dmnbctuho `e tko ogojtr`b jkmrno

=9. Xko rosugtmbt e`rjo `b tko jurrobt g``p Y]VZ  huo t` m g`bn jurrobt jmrrycbn j`bhujt`r wcgg fo

(M)8=9   B 

(F)8: 5 =9. B    (J)

8= ; =9. B    (H)8? =9   B 

==. X`r`ch cs <(M) rcbn skmpoh jg`soh s`gob`ch   (F) rojtmbnugmr skmpoh s`gob`ch(J) rcbn skmpoh `pob s`gob`ch   (H) squmro skmpoh s`gob`ch

=6. Fc`t - Zmvmrt's gmw dmy fo roprosobtoh cb vojt`r er`d ms

(M) 9:8

hg r hF cr 

¿

ω   (F) 9

8hF c hg r  ¿

ω   (J) 9

68hg r hF c

¿

ω   (H) 9

8hg r hF c

¿

ω

=:. Xko dmnbotcj ecogh `b tko mxcs `e m g`bn s`gob`ch kmvcbn b  turbs por ubct gobntk mbh jmrrycbn m jurrobt c cs <

(M) 9bc¿   (F)6

9b c¿   (J)6

9bc¿   (H) B`bo `e tkoso

=8. M jurrobt c cs pmsscbn tkr`unk m strmcnkt j`bhujt`r `e cbecbcto gobntk. Xko dmnbotcj ecogh mt m p`cbt sctumtoh mt m hcstmbjo V er`d tkoj`bhujt`r cs <

(M) 96

  c¿

ω(F) 9

66

c

 V

¿

ω(J) 9

:6

c

 V

¿

ω(H) 9

6

c

 V

¿

ω

=?. ^kob jurrobt cs pmssoh tkr`unk m jcrjugmr wcro propmroh er`d m g`bn j`bhujtcbn wcro, tko dmnbotcj ecogh pr`hujoh mt cts jobtro cs F. B`w m g``p kmvcbn tw` turbs cs propmroh er`d tko smdo wcro mbh tko smdo jurrobt cs pmssoh tkr`unk ct. Xko dmnbotcj ecogh mt ctsjobtro wcgg fo <

(M) 8 F   (F)8

 F(J)

6

 F(H) =5 F