JEE Advanced 2019 Paper-2 Physics

®

DMM (Hnvhlgmn) (HNYHLGMN) 0:89 0:85 DMM

00-:=-0:89

NH^M4 01-:=-0:85

Bmbkry @hsmn Xumstekls & Wkcutekls ZHZMP - 0 | W]@DMG^ 4 ZFUWEGW ZHZMP-0 4 ELW^P]GÊKLW ^K GHLNENH^MW GHLNENH^MW •

Xumstekl phpmr-0 fhs tfrmm (:7) phrts 4 Zfysegs, Gfmbestry hln Bhtfmbhtegs.

•

Mhgf phrt fhs h tkthc ki meaftmml meaftmml (86) qumstekls nevenmn eltk tfrmm eltk tfrmm (:7) smgtekls (Wmgtekl-8, Wmgtekl-0 hln Wmgtekl-7).

•

^kthc lub`mr ki qumstekls qumstekls el Xumstekl el Xumstekl Zhpmr-0 hrm 4 Ieity Ikur (=>) hln Bhxebub Bhros hrm Klm Fulnrmn Meafty Wex (869).

^ypm ki Xumstekls hln Bhroela Wgfmbms WMGÊKL 8 (Bhxebub Bhros 4 70) •

^fes smgtekl gklthels MEAF^ (:6) qumstekls. (:6) qumstekls.

•

Mhgf qumstekl fhs IK]P kptekls KLM KP BKPM ^FHL KLM ki KLM ki tfmsm ikur kptekl(s) es(hrm) gkrrmgt hlswmr(s).

•

Ikr mhgf qumstekl, gfkksm tfm kptekl(s) gkrrmspklnela gkrrmspklnela tk (hcc) tfm gkrrmgt hlswmr(s). hlswmr(s).

Hlswmr tk mhgf qumstekl wecc `m mvhcuhtmn hggkrnela tk tfm ikcckwela bhroela sgfmbm.

•

Iucc Bhros

4

+> Ei klcy (hcc) tfm gkrrmgt kptekl(s) es (hrm) gfksml.

Zhrtehc Bhros 4

+7 Ei +7 Ei hcc tfm ikur kptekls hrm gkrrmgt ùt KLCU tfrmm kptekls hrm gfksml.

Zhrtehc Bhros 4

+0 Ei +0 Ei tfrmm kr bkrm kptekls hrm gkrrmgt ùt KLCU twk kptekls hrm gfksml hln `ktf ki wfegf hrm gkrrmgt.

Zhrtehc Bhros 4

+8 Ei +8 Ei twk kr bkrm kptekls hrm gkrrmgt ùt KLCU klm kptekl es gfksml hln et es h gkrrmgt kptekl.

Tmrk Bhros 4

: Ei lklm ki tfm kptekls es gfksml (e.m. tfm qumstekl es ulhlswmrmn). ulhlswmrmn).

Lmahtevm Bhros 4

‗8 El ‗8 El hcc ktfmr ghsms.

WMGÊKL 0 (Bhxebub Bhros 4 86) •

^fes smgtekl gklthels WEV (:9) qumstekls. (:9) qumstekls. ^fm hlswmr tk mhgf qumstekl es h L]BMPEGHC YHC]M. YHC]M .

•

Ikr mhgf qumstekl, mltmr tfm gkrrmgt lubmreghc vhcum vhcum ki tfm hlswmr usela tfm bkusm hln t fm kl-sgrmml vertuhc lubmreg lubmreg omyphn el tfm pchgm nmsealhtmn tk mltmr tfm hlswmr. Ei tfm lubmreghc vhcum fhs bkrm tfhl twk nmgebhc pchgms, trulghtm/rkuln-kii tfm trulghtm/rkuln-kii tfm vhcum tk ^QK nmgebhc ^QK nmgebhc pchgms.

•

Hlswmr tk mhgf qumstekl qumstekl wecc `m mvhcuhtmn hggkrnela hggkrnela tk tfm ikcckwela bhroela bhroela sgfmbm 4 Iucc Bhros

4

Tmrk Bhros 4

+7 Ei KLCU tfm gkrrmgt lubmreghc lubmreghc vhcum es mltmrmn. mltmrmn. : El hcc ktfmr ktfmr ghsms. ghsms.

Pmsklhlgm Mnuvmlturms Cebetmn PMAEW^MPMN & GKPZKPH^M KIIEGM 4 GA ^kwmr, H->9 & =0, EZEH, Lmhr Gety Bhcc, Dfhchwhr Pkhn, Okth (Phd.) - 70>::=

Olkw b bkrm 44 sbs PMWK h ht =9911 Zf.Lk. 4 :1>>-0111111, :1>>-01111:: | :1>>-01111:: | ^kcc Irmm 4 86:: 0=6 ==== | IHV Lk. 4 +58-:00-75891000 4 +58-:00-75891000 | ^k O Qm`setm 4 www.rmsklhlgm.hg.el | M-bhec 4 gklthgtJrmsklhlgm.hg.el | GEL 44 ]6:7:0PD0::1ZCG:0>:05 ^fes sskcutekl w whs n nkwlckhn i i rkb P Pmsklhlgm DDMM ((HNYHLGMN) 0 0:85 W Wkcutekl p pkrthc


^fes smgtekl gklthels ^QK (:0) Cest-Bhtgf (:0) Cest-Bhtgf smts.

•

Mhgf Cest-Bhtgf smt fhs ^QK (:0) Buctepcm Gfkegm Xumstekls.

•

Mhgf Cest-Bhtgf smt fhs twk cests 4 Cest-E hln Cest-E hln Cest-EE. Cest-EE.

•

Cest-E fhs Cest-E fhs Ikur mltrems mltrems (E),(EE), (EEE) hln (EY) Cest-EE fhs Cest-EE fhs Wex mltrems Wex mltrems (Z),(X), (P ), (W), (^) hln (]).

•

IK]P kptekls IK]P kptekls hrm aevml el mhgf Buctepcm Gfkegm Xumstekl `hsmn kl Cest-E hln Cest-E hln Cest-EE hln Cest-EE hln KLCU KLM ki KLM ki tfmsm ikur kptekls shtesiems tfm gklnetekl hsomn el tfm Buctepcm Gfkegm Xumstekl.

•

Hlswmr tk mhgf qumstekl wecc `m mvhcuhtmn hggkrnela tk tfm ikcckwela ikcckwela bhroela sgfmbm 4 Iucc Bhros

4

+7 Ei KLCU tfm kptekl gkrrmspklnela gkrrmspklnela tk tfm gkrrmgt gkbèlhtekl gkbèlhtekl es gfksml.

Tmrk Bhros 4

: Ei lklm ki tfm kptekls es gfksml (e.m. tfm qumstekl qumstekl es ulhlswmrmn). ulhlswmrmn).

Lmahtevm Bhros 4


Hlswmrela Xumstekls 4 •

^k smcmgt tfm kptekl(s), usm tfm bkusm tk gcego kl tfm gkrrmspklnela ùttkl(s) ki tfm kptekl(s). kptekl(s).

•

^k nmsmcmgt tfm gfksml kptekl(s) ikr tfm qumstekls ki WMGÊKL-8 gcego WMGÊKL-8 gcego kl tfm ùttkl(s) ki tfm gfksml kptekl(s) hahel kr gcego kl tfm Gcmhr Pmspklsm ùttkl Pmspklsm ùttkl tk gcmhr hcc tfm gfksml kptekls.

•

^k nmsmcmgt tfm gfksml kptekl ikr tfm qumstekls ki WMGÊKL-7, WMGÊKL-7 , gcego kl tfm ùttkl ki tfm gfksml kptekl hahel kr gcego kl tfm Gcmhr Pmspklsm ùttkl Pmspklsm ùttkl tk gcmhr tfm gfksml kptekl.

^k gfhlam tfm kptekl(s) ki h prmvekuscy hlswmrmn qumstekl ki WMGÊKL-8 hln WMGÊKL-8 hln WMGÊKL-7 ierst WMGÊKL-7 ierst nmsmcmgt hs aevml h`kvm hln tfml

•

smcmgt tfm lmw kptekl(s) •

^k hlswmr qumstekls ki WMGÊKL-0 usm WMGÊKL-0 usm tfm bkusm tk gcego kl lub`mrs (hln/kr syb`kcs) kl tfm kl-sgrmml vertuhc lubmreg omyphn tk mltmr tfm lubmreghc vhcum el tfm sphgm prkvenmn ikr hlswmr.

•

^k gfhlam tfm hlswmr ki h qumstekl ki WMGÊKL-0 ierst WMGÊKL-0 ierst gcego kl tfm Gcmhr Pmspklsm ùttkl Pmspklsm ùttkl tk gcmhr tfm gkrrmgt hlswmr hln tfml mltmr tfm lmw lubmreghc vhcum.

•

^k bhro h qumstekl KLCU ikr KLCU ikr rmvemw (e.m. wetfkut hlswmrela et). Gcego kl tfm Bhro ikr Bhro ikr Pmvemw & lmxt ùttkl.

^k bhro es qumstekl ikr rmvemw (hitmr hlswmrela et), gcego kl Bhro ikr Pmvemw & Lmxt ùttkl - tfm hlswmrmn qumstekl wfegf es hcsk

•

bhromn ikr rmvemw wecc `m mvhcuhtmn. ^k shvm tfm hlswmr gcego kl tfm Whvm & Lmxt ùttkl, Lmxt ùttkl, tfm hlswmrmn qumstekl wecc `m mvhcuhtmn.

•



| DMM (HNYHLGMN) 0:85 | NH^M 4 01-:=-0:85 | ZHZMP-0 | BMBKPU @HWMN

ZHP^-E 4 ZFUWEGW WMGÊKL 8 (Bhxebub Bhros 4 70)

• ^fes smgtekl gklthels MEAF^ (:6) qumstekls. (:6) qumstekls. • Mhgf qumstekl fhs IK]P kptekls KLM KP BKPM ^FHL KLM ki KLM ki tfmsm ikur kptekl(s) es(hrm) gkrrmgt hlswmr(s). • Ikr mhgf qumstekl, gfkksm tfm kptekl(s) gkrrmspklnela gkrrmspklnela tk (hcc) tfm gkrrmgt hlswmr(s). hlswmr(s). • Hlswmr tk mhgf qumstekl wecc `m mvhcuhtmn hggkrnela tk tfm ikcckwela bhroela sgfmbm. Iucc Bhros

4

+> Ei klcy (hcc) tfm gkrrmgt kptekl(s) es (hrm) gfksml.

Zhrtehc Bhros 4

+7 Ei +7 Ei hcc tfm ikur kptekls hrm gkrrmgt ùt KLCU tfrmm kptekls hrm gfksml.

Zhrtehc Bhros 4

+0 Ei +0 Ei tfrmm kr bkrm kptekls hrm gkrrmgt ùt KLCU twk kptekls hrm gfksml hln `ktf ki wfegf hrm gkrrmgt.

Zhrtehc Bhros 4

+8 Ei +8 Ei twk kr bkrm kptekls hrm gkrrmgt ùt KLCU klm kptekl es gfksml hln et es h gkrrmgt kptekl.

Tmrk Bhros 4

: Ei lklm ki tfm kptekls es gfksml (e.m. tfm qumstekl es ulhlswmrmn). ulhlswmrmn).

Lmahtevm Bhros 4


_ohB 8 ³vi/onrm vhn%

• • • •

8.

70²

`c _ohB msh vo@ (:6) ez'u aWH ezP?sn ez'u ns iy, pod iknUe iknUe il, x, aWhH ù pod iknUeosh msh cs ,n ?o ,n cs vi/on iknUe caf aW³aW h²H ezP?sn ez'u ns iy,R il, il, aq, iknUeosh msh cs caf bÕod ³bÕodosh² cs chgi/or iknUe ³iknUeos h² nos pqiu,H ezP?sn ez'u ns bÕod no mwU?oh nu iuMu ?ostuo ns vuq vuqcod aos xo % ew.oT vhn % +>? il nsky ³cods² caf iknUe ³iknUeosh ² nos pquo x?o aW H vohi'on vhn % +7? il podosh iknUe caf aWh ed]rq nsky rfu iknUeos h nos pq uo x?o aWH vohi'on vhn % +0? il rfu ?o rfu cs v i/on iknUe caf aW ed]rq nsky los iknUeos h nos pquo x?o aW voW voW d loshuos pqus aq, iknUe caf iknUe aWhH vohi'on vhn % +8? il los ?o los cs vi/on iknUe caf aWh ed]rq nsky ,n iknUe nos pquo x?o aW v oWd pquo avo qvo iknUe caf iknUe aWH 'ow ]? vhn % :? il incf Fof iknUe nos uafh pquo x?o aW ³vIooTr~ ez'u vuqÕoidr aW²H [.o vhn % ‗8v ]? cFof eidiCIoir?osh mshH

Gklsenmr twk pchlm gklvmx cmls ki shbm rhneus ki gurvhturm hln rmirhgtevm elnmx l 8 hln l0 rmspmgtevmcy. lkw gklsenmr twk ghsms 4 mouo los cmryosÕoy yWhcosh nf kÖro i2o^?o,s i2o^?o,sh cmou rIoo buns buns v ekrTuoh n Öm'o% l8 rIoo l0 aWhH

iuMu losi CIoir?osh e d ikpod nfit?s

4

P

l8 l0

P

Ghsm ‗ E 4 Qfml l 8 2 l0 2 l, tfml mquevhcmlt ikghc cmlatf ki cmls es i : Ghsm-EE 4 Qfml l 8 2 l, l0 2 l + ∉l, tfml mquevhcmlt ikghc cmlatf ki cmls es i 2 i : + ∉i : ^fml gkrrmgt kptekls hrm 4 iCIoir ‗ E 4 tg l8 2 l0 2 l, aos ros yWhcosh nf rqU? Xosnc lwdf i : aWH

iCIoir-EE 4 tg l8 2 l, l0 2 l + ∉l aos , ros yWhcos h nf rqU? Xos nc lwdf rg caf iknUeos n h o p?u ndos 4 (H) Ei ∉l/l < :, tfml ∉i :/i : 3 : (@) |∉i :/i :| 3 |∉l/l|

i 2 i : + ∉i : aWH



ZHAM # 8


(G) Ei l 2 8.=, ∉l 2 8: ‗7 hln i : 2 0: gb tfml | ∉i :| 2 :.:0 gb (N) (H) ?il ∉l/l < :, aos ros ∉i :/i : 3 :

Hls. Wkc.

(@) |∉i :/i :| 3 |∉l/l| (G) ?il l 2 8.=, ∉l 2 8:7 rIoo i : 2 0: gb ros |∉i :| 2 :.:0 gb (N) (HG) 8 8 0(l ∐ 8)  8 8  .....(8) 2 (l ∐ 8) ∐  ⇐ 2 i 8 P  P ∜  i :

 8 8  2 (l + ∉l ∐ 8) ∐   P ∜  8 (l ∐ 8)  8  2 + (l + ∉l ∐ 8)  i : + ∉i : P  P  8 0l + ∉l ∐ 0 2 i : + ∉i : P 0(l ∐ 8) i + ∉i : P (8)/(0) ⇐ : 2 + ∉l ∐ 0 0 l i : 8 i 0

.....(0)

P 8+

∉i :

∉i :

2

i :

i :

∉i : 0:

∐∉l ( 0l + ∉l ∐ 0)

2∐

⇐

0(l ∐ 8) 0l + ∉l ∐ 0

2

8: ∐7 7 + 8: ∐7 ∐ 0 ∉i : 2 ‗ 0 Ñ 8: ‗0

|∉i :| 2 :.:0 gb

0.

El UNWM bklkgfrkbhteg ceaft ki whvmcmlatf 9:: lb elgenmlt ki scets hs sfkwl el ieaurm. /?Tn o ,nk.ofT? ezno'o ip2oouqcod i}iCyY ed voeirr aosro aWH UNWM msh 9:: lb rdhxlW/?T Z W8

θ K W0 N28b Ei W8W0 2 7bb, KZ 2 88 bb tfml KZ 2 88 bb ?il W8W0 2 7bb, (H) Ei

θ2

:.79

(@) Ei

θ2

:.79

ϊ ϊ

rg

nmarmm tfml nmstrugtevm eltmrihgms ht pkelt Z nmarmm tfml gklstrugtevm eltmrihgms ht pkelt K



ZHAM # 0


(G) Ei θ 2 : tfml gklstrugtevm eltmrihgms ht K (N) Irelam wentf nmpmlns hl θ :.79 iBxzf aos ros ig]lq ig]lq Z ed ik]?ocf (H) ?il θ 2

ϊ

(@) ?il

K?irnd.o aos xoH

:.79

iBxzf aos ros K ed cMeos"of K?irnd.o aosxo ϊ aosxoH (G) ?il θ 2 : aos ros K ed cMeos"of K?irnd.o aos (N) iÒ]t poWB+o`T θ ed iuFoT d ndsxfH Hls. Wkc.

θ2

(H@G)

Z

W8W0 2 n

y

θ

ζ

K

n nselθ

nselθ

N

∉x 2 nselθ + nselζ ζ θ 4 sbhcc hlacm LosYo nos.o ∉x 2 nθ +

selζ ~ thlζ 2

y `

ny N

7bb Ñ 88bb 2 75::lb ϊ 86: 8 ο 9::lb 75:: l, 2 (0l ∐ 8) 2 (0l ∐ 8) Ñ 0 0 l21 nmstrugtevm elimrmlgm fhppmlmn ikuo'of K?irnd.o (H) ∉x 2 7bb Ñ

:.79

Ñ

(@) ∉x 2 7bb Ñ

:.79

Ñ

ϊ

ϊ

ϊ 86:

9:: lb 2 lο l28 gklstrugtevm eltmrimrmlgm

+

+ : 2 9::lb

cMeos"of ?irnd.o

(G) ∉x 2 : Wk gklstrugtevm eltmrimrmlgm cMeos"of

K?irnd.o (N) Irelam wentf nkms lkt nmpmln kl θ. iÒ]t poW B +o`Te idkirTr uafh aos xf H



ZHAM # 7


7.

H uleikrb reaen rkn ki bhss b & cmlatf c es rmcmhsmn irkb vmrteghc pksetekl kl rkuaf surihgm wetf suiiegemlt iregtekl ikr ckwmr mln lkt tk scep hs sfkwl el ieaurm. Qfml rkn bhoms hlacm 9:º wetf vmrteghc tfml ieln gkrrmgt hctmrlhtevm/s b éK?mou rIoo c yMgo`T nf lj3+ LB+ Í/koT/od cs _oq dldf cra ed Los B+f torf aWH iXcyus cs dosnus ns iy?s ;o"oT.o

e?oTEr aWH tg LB+ Í/koT/od cs

9:º nos.o

guorf aWH ros

b,

Hls. Wkc.

0a

θ2

(H)



υ2

(@)

7a 0

(G) L 2

ba 89

(N) hrhnehc 2

7a >

(@GN)

/>

9:º

 gks

hGBhv

/0

9:º/0

K trmht hs felamn

∉O + ∉] 2 : 8 Ε : υ0 0

2 ∐∉]

8 b 0 0 7

   υ0 2 ∐ ∐ ba  >  

υ2

7a 0

⇐

hrhnehc 2

⇐

ώ 2 Ε:θ

υ0

ba

θ 2



0

hv

0

2

7a  0 0

sel 9:º

b

⇐





0

2

2

7a >

7 7a >

7

    2  θ  sel 9:º + υ0 gks 9:´ 0  0 

7 7a 7 6 0 5a 9a + hv 2 89 89 ba ‗ L 2 bh v ba L2 89 hv 2

+

7a 6



ZHAM # >


>.

Bklkhtkbeg ahs H fhvela = bkcm es bexmn wetf nehtkbeg ahs @ fhvela 8 bkcm el gklthelmr ki vkcubm Y :. Y Lkw tfm vkcubm ki bexturm es gkbprmssmn tk : `y hneh`hteg prkgmss. Eletehc prmssurm hln tmbpmrhturm > 7.0 ki ahs bexturm es Z : hln ^:. _aevml 0 2 5.0R Gfkksm gkrrmgt kptekl 4 (H)

ηbex 2 8.9

(@) Ielhc prmssurm es `mtwmml 5Z: hln 8:Z:

(G) |Q.N| 2 87P^ : Wkc.

ηbex 2

Q2

(N) Hvmrham ^rhlschteklhc oelmteg mlmray

l8GZ8 + l0GZ 0 l8G Y8 + l0G Y 0

2

6 =

Z8Y8 ∐ Z0 Y0

η ∐8

 Y  Z:Y:6/= 2 Z0  :   > 

6/=

Z0 2 5.0Z:

Z: Y: Q2 =.

∐ 5.0Z: 7/=

Y: > 2 ‗87P^:

^fm aevml hrrhlambmlt es rmcmhsmn irkb rmst wfml sprela es el lhturhc cmlatf. Bhxebub mxtmlsekl el sprela nurela tfm bktekl es x :. h8, h0 hln h7 hrm hggmcmrhtekls ki tfm `ckgos. Bhom tfm gkrrmgt kptekls h8 0b

h0 b

h7 0b

(@) x : 2

(H) h0 ‗ h8 2 h8 ‗ h7

(G) Ymckgety ki 0b gkllmgtmn tk sprela wfml mcklahtekl es (N) hggmcmrhtekl h 8 ht

x: >

es

>ba 7o x: 0

es v

2

x: 0

7o 8>b

7ox : >0b

Wkc.



ZHAM # =

| DMM (HNYHLGMN) 0:85 | NH^M 4 01-:=-0:85 | ZHZMP-0 | BMBKPU @HWMN h8 0b

h8 h0 b

h7 0b

0h8 2 h0 + h7 h8 ‗ h7 2 h0 ‗ h8 ikr ktfmr kptekls usm b mquevhcmlt

bmq b 0b

^ a'

2

0^ a'

0(0b)(b) 0b + b

2

bmq. 2

2

>b 7

2

6b 7

6b 7 >b(0b) b + 0b

0b

6b/7

8 0 6ba ox : 2 x: 0 7 89ba x : 2 7o Yx :

2 v bhx 2

0

h x: >

2

x: >

w0

x: 0

2

w

2

x:

o

0

0b +

x : 7o > 8>b

2

6b 7

2

x:

7o

0

8>b

7ox : >0b



ZHAM # 9


9.



H nepkcm ki Nepkcm bkbmlt p 2

p:

( ˉe + dˉ ). es pchgmn ht kreael. Lkw h uleikrb mxtmrlhc mcmgtreg iecmn ht

0 bhaletunm M: es hppcemn hckla nermgtekl ki nepkcm. ^wk pkelts H hln @ hrm cyela kl h mquepktmltehc surihgm ki rhneus P gmltmrmn ht kreael. H es hckla hxehc pksetekl ki nepkcm hln @ es hckla mquhtkrehc pksetekl. ^fmrm gkrrmgt kptekl hrm 4

(H) Lmt mcmgtreg iemcn ht pkelt H es 7M :

(@) Lmt mcmgtreg iemcn ht pkelt @ es Tmrk 8/ 7

 op  (G) Phneus ki mquhtkrehc surihgm P 2  :   M : 

8/ 7

 0op:   (N) Phneus ki mquhtkrehc surihgm P 2   M:   

Hls.

(H@G)

Wkc.

 op  Mlmt Wfkucn `m ⊭ tk surihgm sk 7 2 M: ⇐ r 2  :  r  M : 

8/ 7

op :

(M H)Lmt 2

0op : r 7

+ M: 2 7M:

(M@)Lmt 2 : M:

0op : r 7

0op : r 7

+ M:

Z:



ZHAM # 1


1.

H irmm fynrkaml htkb hitmr h`skrèla h pfktkl ki whvmcmlatf

οh amts mxgetmn irkb sthtm l 2 8 tk l 2 >.

Ebbmnehtmcy hitmr mcmgtrkl dubps tk l 2 b sthtm `y mbettela h pfktkl ki whvmcmlatf bkbmltub ki htkb num tk tfm h`skrptekl hln tfm mbessekl hrm

οm. Cmt gfhlam el

∉Zh hln ∉pm rmspmgtevmcy. Ei οh/οm 2 8/=.

Qfegf ki tfm ikcckwela es gkrrmgt

,n Ckr]2o ao`Bª ostu edmo.oq ,n οh rdhxlW/?T ns ezno'o n.o nos vk'oosi"or ndus ns gol vkCIoo bÕositr aosro aWH `cns rqd]r gol `ysNYªoQu

l2b

l28

l 2 > msh cs l

vkCIoo msh ,n οm rdhxlW/?T ns ez no'o n.o nos bPcitT r ndus ns

gol nwl toro aWH mouo in vk'oos"o.o voW d bPctTu nf kta cs edmo.oq ns chksx msh eidkrTu Öm'o% ∉Zh voW d ∉pm aWhH ?il οh/οm 2 8/= H iuMuiyi_or msh cs noWu cP? aW (H) b 2 0 (@) ∉Zh/∉Zm 2 8/0 (G) οm 2 >86 lb (N) Phtek ki O.M. ki mcmgtrkl el tfm sthtm l 2 b tk l 2 8 es ³

vkCIoo Hls.

Wkc.

l 2 b rIoo l 2 8 msh

xirt ÍtoTvosh no vuq eor

³ aWH

(HN)

ο h M > ∐ M8 2 2 ο m M > ∐ Mb

8 89 8 8 ∐ 0 89 b 8∐

2

8 =

kl skcvela b20 m 2

O0 O8 6.

80>:: Ñ > 279>1 87.9

2

80 0

0

2

8 >

Hs oelmteg mlmray es prkpkrteklhc tk

8 l0

El h gycelnmr h fmhvy pestkl es bkvela wetf spmmn v hs sfkwl neharhb hln ahs es ieccmn elsenm et. H ahs bkcmgucm es bkvela wetf spmmn v : tkwhrns bkvela pestkl. ^fml wfegf ki tfm ikcckwela es gkrrmgt (Hssubm v 3333 v:

∉ 

) hln gkccesekl es mchsteg) Z

Y:

Y 

(H) gfhlam el spmmn hitmr gkccesekl es 0Y (@) gfhlam es spmmn hitmr gkccesekl es 0v : (G) rhtm ki gkccesekl es (N) Qfml pestkl es ht

∉ 

Y 



0

ets oelmteg mlmray wecc `m ikur tebms



ZHAM # 6


Hls. Wkc.

(H)

Y:

Y

@mikrm Gkccesekl

Y: + 0Y

Y

Hitmr Gkccesekl ^fmrmikrm gfhlam el spmmn 2 (0Y + Y : ‗ Y:) 2 0Y WMGÊKL 0 (Bhxebub Bhros 4 86)

• ^fes smgtekl gklthels WEV (:9) qumstekls. (:9) qumstekls. ^fm hlswmr tk mhgf qumstekl es h L]BMPEGHC YHC]M. YHC]M . • Ikr mhgf qumstekl, mltmr tfm gkrrmgt lubmreghc vhcum vhcum ki tfm hlswmr usela tfm bkusm hln tfm kl-sgrmml vertuhc vertuhc lubmreg omyphn el tfm pchgm nmsealhtmn tk mltmr tfm hlswmr. Ei tfm lubmreghc vhcum fhs bkrm tfhl twk nmgebhc pchgms, trulghtm/rkuln-kii tfm trulghtm/rkuln-kii tfm vhcum tk ^QK nmgebhc ^QK nmgebhc pchgms.

• Hlswmr tk mhgf qumstekl qumstekl wecc `m mvhcuhtmn hggkrnela hggkrnela tk tfm ikcckwela bhroela bhroela sgfmbm 4 Iucc Bhros

4

+7 Ei KLCU tfm gkrrmgt lubmreghc lubmreghc vhcum es mltmrmn. mltmrmn.

Tmrk Bhros 4

: El hcc ktfmr ghsms. ghsms.

_ohB 0 ³vi/onrm vhn% 86² • `c _ohB ms h L% (:9) ez 'u aWH ez P?sn ez'u no bÕod ,n ch_?oPmn mou (L]BMPEGHC YHC]M) aWh H • ezP?sn ez'u ns bÕod ns caf ch_?oPmn mou nos mobt+ (bkusm) voWd voQu&CÖfu (kl‗sgrmml) kpTqvy ]?qmsidn nfesB (vertuhc lubmreg omyphn) ns á?osx cs bÕod ns iy, ipi]ar CIoou ed ltT ndshH ?il ch_?oPmn mou msh los cs hnYs JdobhB voQX (trulghtm/rkuln-kii) vi/on l'omyk CIoou aWR ros ch_?oPmn mou nos l'omyk ns los CIoouos h rn Yªns ndshH • ezP?sn ez 'u ns bÕod no mwU?oh nu iuMu ?ostuo ns vuqcod aos xo %& ew.oT vhn % +7 ?il ltT in?o x?o ch _?oPmn mou (Lubmreghc vhcum)a f caf bÕod aW H

'ow]? vhn % 5.

Ei i 2

]? :v

cFof eidiCIoir?osh mshH

θyˉe + 0θx dˉ ghcguchtm tfm wkro nklm ei h phrtegcm bkvms hckla phtf hs sfkwl el neharhb. 8

H

@ N

G

:.= M :.=

Hls.

‗:.1=



ZHAM # 5




Wkc.



nw 2 I.n r nw 2 θynx + 0θxny H← @ y 2 8, ny 2 : w H← @ 2

∯

8

∯

θynx 2 θ.8 nx 2 θ :

∯

: .=

@ ← G x 2 8, nx 2 : w @ ← G 2 0θ.8 ny 8

2 ∐0θ(:.= ) 2 ∐θ

: .=

G ← N y 2 :.= ny 2 : w G ← N 2

∯ θynx 8

2

θ.

8 0

∯

: .=

nx

8

2∐

θ >

N ← M x 2 :.= nx 2 : w N←M 2 0θ

∾ w 2 θ ∐ θ ∐

θ >

∐

θ 0

2∐

∯

8 xny 2 0θ. 0

:

∯

ny 2

:.=

∐

θ 0

7θ >

Aevml θ 2 8 7 Q2 ∐ > 8:.

El h aevml gerguet elnugtkr ki C 2 8bF hln rmsesthlgm P 2 8 ℩ hrm gkllmgtmn el smrems tk mlns ki twk phrhccmc gklnugtela rkns hs sfkwl. Lkw h rkn ki cmlatf 8: gb es bkvmn wetf gklsthlt vmckgety ki 8 gb/s el bhalmteg iemcn @ 2 8^. Ei rkn sthrts bkvela ht t 2 : tfml gurrmlt gurrmlt el gerguet hitmr 8 beccesmgkln es ‗7 ‗8 x Ñ 8: H. ^fml vhcum ki x es 4 (aevml m 2 :.71)

Wkc.

m 2 v Ñ @ , n



( )

←

2 8: ∐0 Ñ 8Ñ 8: ∐8

ν 2 8: ‗7 vkct e2

8: ∐7 (8 ∐ m ∐8 ) 8

e 2 8: ‗7 (8‗ :.71) E 2 :.97 bH



ZHAM # 8:


88.

H presb es sfkwl el tfm ieaurm wetf presb hlacm 1=º hln rmirhgtevm elnmx 7 . H ceaft rhy elgenmlts kl h surihgm ht elgenmlt hlacm ζ. Ktfmr ihgm es gkhtmn wetf h bmneub ki rmirhgtevm elnmx l . Ikr ζ ≮ 9:º rhy suiimrs tkthc eltmrlhc rmicmgtekl ieln vhcum ki l 0.

nos.o rIoo 7 vekrTuohn no iez^m ip2oouqcod il_oo?o x?o aWH ezno'o rdhx `c ed ζ nos.o ed voeirr aosrf aWH lwcdf rdX l vekrTuohn nf ,n eryf iXUm yxo?f x`T aWH aW H ζ ≮ 9:º ns i y?s ?il ezno'o no ew.oT 0 vohridn edokrTu aos ros l aosxoH 1=º iez^m

1=º

ζ

Gkhtela

l PE 2 7

Wkc.

Gkhtela

1=º

ζ

(1= ‗ g) g PE 2 7

Ikr ^.E.P ht gkhtela iXUm

ed

^.E.P ns

l

2 sel g 7 Hppcela slmcc's chw ht ierst surihgm selg 2

iy?s

ezIom cra ed Cusy ns iu?m cs

sel ζ 2 7 sel(1= ‗ g ) ikr cebetela gklnugtekl, ht ζ 2 9:º cfmo]r

7 sel(1= ‗ g )

sel9: 2

7 0 8 0

iCIoir ns iy?s iy?s , ζ 2 9:º ed

2 7 sel(1= ∐ g )

2 sel(1= ∐ g )

sel 7: 2 sel(1= ∐ g ) 7: 2 1= ‗ g g 2 >=º

l 7 l0

2

2

8 0

7 2 8.=: 0



ZHAM # 88


80.

Zmrimgtcy rmicmgtela berrkr ki bhss B bkultmn kl h sprela gklstetutm h sprela bhss systmb ki hlauchr >ϊB℩ 2 8: 0> b ∐0 wfmrm f es pchlo gklsthlt. L pfktkls ki whvmcmlatf ο 2 6ϊ Ñ irmqumlgy ℩ sugf tfht f ‗9 8: b streoms tfm berrkr sebucthlmkuscy ht lkrbhc elgenmlgm sugf tfht tfm berrkr amts nespchgmn `y 8 ½b. Ei tfm vhcum ki L es x Ñ 8: 80, tfml ieln vhcum ki x. ,n iCezhx&éK?mou iuno? guoro aWR itcnf itcnf vokjiÕo ℩ `c B éK?mou no ,n iCezh x ed d_oo aqvo ew.oT edokrTn leT.o ,n

eznod aW in

>ϊB℩ f

2 8: 0> b ∐0 tao¡ f Eyohn iu?rohn aWH rdhxlW/?T ο 2 6ϊ Ñ 8: ‗9 b ns L ezno'o n.o ,n coIo 8 ½b

yMgkr~ il'oo msh leT.o ed `c eznod Yndors aWh in leT.o ros x no mou Oor nfit?s nfit?sH

ikCIooier aos toro aWH ?il

L

no mou

x Ñ 8:80,

aW

Ceaft

Berrkr Hls.

8

Wkc.

Bkbmltub trhlsimrrmn kl berrkr leT.o

0Lf

ο

nos CIoouo]ridr CIoouo]ridr chksx

0Lf

ο

2 BY(bmhl pksetekl)

Y(bmhl pksetekl) 2 ℩ H

(wfmrm tao¡ H H 2 8 ½B)

0Lf

(wfmrm tao¡ ο 2 6ϊ Ñ 8: ‗9)

ο

2

2 B℩ H

B℩(8: ∐9 )ο B℩6ϊ Ñ 8: ∐9 Ñ 8: ∐9 L2 2 0f 0f >ϊB℩ Ñ 8: ∐80 L2 f 2 8:0> Ñ 8: ‗80 L 2 8 Ñ 8:80 x28

87.

H phrtegcm es prkdmgtmn wetf spmmn v : ht hl hlacm ζ ( ζ ≪ 5:º) wetf fkrezklthc hln et `kulgm ht shbm hlacm wetf fkrezklthc. Ei hvmrham vmckgety ki dkurlmy es :.6 v : wfmrm v: es hvmrham vmckgety ki ierst prkdmgtecm tfml θ es. ,n n.o nos {oWirt cs ζ (ζ ≪ 5:º) nos.o ed v: poy cs Xshno x?o aW H ?a {oWirt cs cmou nos.o cs bLyro aWH

?il cMew.oT xir no voWcr ksx

Wkc.

Ikr ierst prkdmgtecm ezIom

:.6 v: aWR

tao¡

v: eays

ez{osE? xir no voWcr ksx aW ros θ aosxo4.

ez{os E? ns iy?s



ZHAM # 80


3Y<2

P

2 ]x 2 v: ^ Ikr dkurlmy xir ns loWdou

0u x8u y8 3 Y <8‗l 2

P8 + P 0

+ .... + Pl 2 ^8 + ^0 + ...... + ^l

+

a

0u y8 a

0u x 0 u y 0

+

a 0u y 0 a

+ ...... + + ......

0u x l u y l a

0u y l a

8 + 8 + 8 + ..... 8   θ0 θ> θ 0l  2 :.6 v: ]x   8 + 8 + 8 + .... + 8   θ θ 0 θ l    8 v:  8 ∐ 8  θ 0    8    8 ∐ 8   θ 

     2 :.6v :

θ 2 :.6 8+ θ θ 2 > 8>.

hvhech`cm skkl

WMGÊKL 7 (Bhxebub Bhros 4 80)

• ^fes smgtekl gklthels ^QK (:0) Cest-Bhtgf (:0) Cest-Bhtgf smts. • Mhgf Cest-Bhtgf smt fhs ^QK (:0) Buctepcm Gfkegm Xumstekls. • Mhgf Cest-Bhtgf smt fhs twk cests 4 Cest-E hln Cest-E hln Cest-EE. Cest-EE. • Cest-E fhs Cest-E fhs Ikur mltrems mltrems (E),(EE), (EEE) hln (EY) Cest-EE fhs Cest-EE fhs Wex mltrems Wex mltrems (Z),(X), (P ), (W), (^) hln (]). • IK]P kptekls IK]P kptekls hrm aevml el mhgf Buctepcm Gfkegm Xumstekl `hsmn kl Cest-E hln Cest-E hln Cest-EE hln Cest-EE hln KLCU KLM ki KLM ki tfmsm ikur kptekls shtesiems tfm gklnetekl hsomn el tfm Buctepcm Gfkegm Xumstekl.

• Hlswmr tk mhgf qumstekl wecc `m mvhcuhtmn hggkrnela tk tfm ikcckwela ikcckwela bhroela sgfmbm 4 Iucc Bhros

4


Tmrk Bhros 4


Lmahtevm Bhros 4


_ohB 7 ³vi/onrm vhn% 80² • `c _ohB msh los (:0) cwpf&cqm y s u (Cest-Bhtgf) csY~c (smts) aWH • ezP?sn cwpf&cqmsyu cs Y (smt) msh los (:0) ,noi/on iknUe á'u (Buctepcm Gfkegm Xumstekl) aWH



ZHAM # 87


p f-EE • ezP?sn cwpf&cqmsyu cs Y msh los cwip?o¡ aW % cwpf-E voWd cwpf • cwpf-Em sh pod áiki"Y?o¡ (E),(EE),(EEE) voWd (EY) aW ,kh cwpf-EE msh L% áiki"Y?o¡ (Z),(X),(P),(W),(^) voWd (])a WH ,noi/on iknUe á'u msh cwpf -E voW d cwpf-EEe d vo/ooidr pod iknUeosh msh cs nsky ,n iknUe af ,noi/or • ezP?sn ,noi/on

iknUe á'u nf 'orT nos ewdo ndro aW H • ezP?sn ez 'u ns bÕod no mwU?oh nu iuMu?ostuo nsv uqcod aos xo%& ew.oT vhn % +7? il icXT caf iknUe af pquo x?o aWhH 'ow]? vhn % :? il nos`T Fof iknUe uafh pquo x?o aW ³vIooTr~ ez'u vuqÕoidr aW²H [.o vhn % ‗8v ]? cFof eidiCIoir?osh msh

Bhtgf tfm gkcubl H shb pcm ki bklkhtkbeg ahs ulnmrakms neiimrmlt tfmrbknylhbeg prkgmss. X 2 Fmht aevml tk tfm ahs, Q 2 Qkro nklm `y tfm ahs, ] 2 Gfhlam el eltmrlhc mlmray ki tfm ahs. 8=.

^fm shbpcm ki bklkhtkbeg ahs ulnmrakms h prkgmss hs rmprmsmltmn `y Z-Y arhpf (ei Z:Y: 2 8/7 P^ :) tfml Z 7

0Z:

Z:

8

0 Y

(Z) Q 8 ← 0 2 8/7 P^ : (P) ]8 ← 0 2 P^:/0

Wkc.

Y: 0Y: (X) X8 ← 0 ← 7 2 88/9 P^ : (W) Q 8 ← 0 ← 7 2 8/7 P^ :

Qfegf ki tfm ikcckwela kptekls hrm gkrrmgt (H) Z, X, P, W hrm gkrrmgt (@) Klcy Z, X hrm gkrrmgt (G) Klcy P, W hrm gkrrmgt (N) Klcy Z, P, W gkrrmgt Q 8 ‗ 0 2 Z:Y: 2 8/7 P^ : i i X0 ‗ 7 2 lGY∉^ 2 l P∉^ 2 0Y:Z: 2 iZ:Y: 2 P^: 0 0 = =  i  X8 ‗ 0 2 lGZ∉^ 2 l + 8P∉^ 2 .Z:Y: 2 P^: 0 9  0  Q 8 ‗ 0 ‗ 7 2 8/7 P^ : ]8 ‗ 0 2 lGY∉^

7 2 l P^: 0 2

P^: 0



ZHAM # 8>


89.

H shbpcm ki bklkhtkbeg ahs ulnmrakms h prkgmss hs rmprmsmltmn `y ^-Y arhpf (ei Z:Y: 2 8/7 P^ :) tfml ,n edmo.kf? xWc ns umw umwus no pÖf? ezÖm ^-Y xzoX }odo ip2o msh ezli'oTr aW ( ?il Z:Y: 2 8/7 P^ :) ros ^ 7

0^:

^:

8

0 Y

Y:

8 P^: l 0 7

(Z) Q 8 ← 0 2

(P) ]8 ← 0 2 :

0Y:

(X) X8 ← 0 ← 7 2 (W) Q 8 ← 0 ← 7 2

P^: 9 P^: 7

(0l(0) + 7) l0

Qfegf ki tfm ikcckwela kptekl hrm gkrrmgt4

iuMu msh cs n oWuco iknUe caf aW (H) Z, X hrm elgkrrmgt

(@) P, W hrm elgkrrmgt

(G) Z, X, W hrm elgkrrmgt

(N) lklm ki tfmsm

(H) Z, X vcP?

(@) P, W vcP?

(G) Z, X, W

aW

vcP? aW

Hls.

(N)

Wkc.

Q 8 ‗ 0 2 lP^ : l 0

h s (N) ùms c

aW

nos`T uafh

X8 ‗ 0 ‗ 7 2 X8 ‗ 0 + X0 ‗ 7 2 nQ8 ‗ 0 + n]0 ‗ 7 2

P^:

2

P^:

7

7

l0 + l

l0 +

i 0

P^:

87 P^: 70

]8 ‗ 0 2 : Q 8 ‗ 0 ‗ 7 2

8 P^: l0 + : 7



ZHAM # 8=


81.

Cmlatf ki strela ki h buseghc elstrubmlt es vhremn irkb C k tk 0Ck el > neiimrmlt ghsms. Qerm es bhnm ki neiimrmlt bhtmrehcs ki bhss pmr ulet cmlatf ½, 0½, 7½, >½ rmspmgtevmcy. Ikr ierst ghsm (strela-8) cmlatf es C k, 7C k rn ^mlsekl es ^ k tfml iulnhbmlthc irmqumlgy es i k, ikr smgkln ghsm cmlatf ki tfm strela es (7 0 =Ck tf Fhrbkleg), ikr tfern ghsm cmlatf ki tfm strela es (= Fhrbkleg) hln ikr tfm ikurtf ghsm cmlatf ki tfm > 1C k strela es (8>tf fhrbkleg). Ei irmqumlgy ki hcc es shbm tfml tmlsekl el strelas el tmrbs ki ^ k wecc `m4 > ko| ?h2o nf dCcf Ck cs 0Ck rn > iFo]u&iFo]u iCIoir?osh ns vuqcod eidkirTr aosrf aWH rod iFo]u&iFo]u eloIoos¸ no

guo aqvo aW itcnf `no`T yMgo`T no éK?mou Öm'o% ½, 0½, 7½, >½ aWH ezIom Iom iCIoir ( dCcf-8) ns iy?s yMgo`T ruok

^k

aos ros mwy vokj iÕo

dCcf nf yMgo`T

=C k >

(=tf

i k ezoEr

aos rf aW, i}rf? iCIoir msh dCcf nf yMgo`T

chuolf) rIoo prqIoT iCIoir msh dCcf nf yMgo`T

cmou aos ros diCc?os diCc?osh msh ruok no mou

^k ns

elosh msh a osxo

Wtrela dCcf-8

(Z)

(@)

Wtrela dCcf -0

(X)

(G)

Wtrela dCcf -7

(P)

^k

(N)

Wtrela dCcf ->

(W)

^k

(^) Z, (@) P, (G) ^, (N) C 2 Ck, ^ 2 ^ k, i 2 i k i 8 2 Ghsm 0.

C2 i 0 2

Ghsm 7.

C2

i 7 2

8

^k

0C :

½

>

0 (8>tf

(7rn

chuolf), rjrf? iCIoir msh

chuolf) H ?il cFof vokj iÕo?o¡

4

(H)

Wkc. (H) Ghsm 8.

1C k

7C k

Ck ,

^k

^k 0

0

89 7^k 89

W

7C k 0 7 7C 0Ñ k 0 =C k

^0 0½

2 i k ⇐ i k 2

8

^0

0C k

½

0

^7

7C k

½

⇐ ^0 2

^k

⇐ ^7 2

7^k

0

> = =C 0Ñ k >

^7 7½

2 i k ⇐ i k 2

89



ZHAM # 89


^fes smgtekl gklthels ^QK (:0) Cest-Bhtgf (:0) Cest-Bhtgf smts.

•

Mhgf Cest-Bhtgf smt fhs ^QK (:0) Buctepcm Gfkegm Xumstekls.

•

Mhgf Cest-Bhtgf smt fhs twk cests 4 Cest-E hln Cest-E hln Cest-EE. Cest-EE.

•

Cest-E fhs Cest-E fhs Ikur mltrems mltrems (E),(EE), (EEE) hln (EY) Cest-EE fhs Cest-EE fhs Wex mltrems Wex mltrems (Z),(X), (P ), (W), (^) hln (]).

•

IK]P kptekls IK]P kptekls hrm aevml el mhgf Buctepcm Gfkegm Xumstekl `hsmn kl Cest-E hln Cest-E hln Cest-EE hln Cest-EE hln KLCU KLM ki KLM ki tfmsm ikur kptekls shtesiems tfm gklnetekl hsomn el tfm Buctepcm Gfkegm Xumstekl.

•

Hlswmr tk mhgf qumstekl wecc `m mvhcuhtmn hggkrnela tk tfm ikcckwela ikcckwela bhroela sgfmbm 4 Iucc Bhros

4


Tmrk Bhros 4


Lmahtevm Bhros 4


Hlswmrela Xumstekls 4 •

^k smcmgt tfm kptekl(s), usm tfm bkusm tk gcego kl tfm gkrrmspklnela ùttkl(s) ki tfm kptekl(s). kptekl(s).

•

^k nmsmcmgt tfm gfksml kptekl(s) ikr tfm qumstekls ki WMGÊKL-8 gcego WMGÊKL-8 gcego kl tfm ùttkl(s) ki tfm gfksml kptekl(s) hahel kr gcego kl tfm Gcmhr Pmspklsm ùttkl Pmspklsm ùttkl tk gcmhr hcc tfm gfksml kptekls.

•

^k nmsmcmgt tfm gfksml kptekl ikr tfm qumstekls ki WMGÊKL-7, WMGÊKL-7 , gcego kl tfm ùttkl ki tfm gfksml kptekl hahel kr gcego kl tfm Gcmhr Pmspklsm ùttkl Pmspklsm ùttkl tk gcmhr tfm gfksml kptekl.

^k gfhlam tfm kptekl(s) ki h prmvekuscy hlswmrmn qumstekl ki WMGÊKL-8 hln WMGÊKL-8 hln WMGÊKL-7 ierst WMGÊKL-7 ierst nmsmcmgt hs aevml h`kvm hln tfml

•

smcmgt tfm lmw kptekl(s) •

^k hlswmr qumstekls ki WMGÊKL-0 usm WMGÊKL-0 usm tfm bkusm tk gcego kl lub`mrs (hln/kr syb`kcs) kl tfm kl-sgrmml vertuhc lubmreg omyphn tk mltmr tfm lubmreghc vhcum el tfm sphgm prkvenmn ikr hlswmr.

•

^k gfhlam tfm hlswmr ki h qumstekl ki WMGÊKL-0 ierst WMGÊKL-0 ierst gcego kl tfm Gcmhr Pmspklsm ùttkl Pmspklsm ùttkl tk gcmhr tfm gkrrmgt hlswmr hln tfml mltmr tfm lmw lubmreghc vhcum.

•

^k bhro h qumstekl KLCU ikr KLCU ikr rmvemw (e.m. wetfkut hlswmrela et). Gcego kl tfm Bhro ikr Bhro ikr Pmvemw & lmxt ùttkl.

^k bhro es qumstekl ikr rmvemw (hitmr hlswmrela et), gcego kl Bhro ikr Pmvemw & Lmxt ùttkl - tfm hlswmrmn qumstekl wfegf es hcsk

•

bhromn ikr rmvemw wecc `m mvhcuhtmn. ^k shvm tfm hlswmr gcego kl tfm Whvm & Lmxt ùttkl, Lmxt ùttkl, tfm hlswmrmn qumstekl wecc `m mvhcuhtmn.

•




Ghsm >.

C2

1C k > 8> 1C 0Ñ k >

i > 2

86.

^> >½

2 i k ⇐ i k 2

0

^>

Ck

½

⇐ ^> 2

^k 89

^fm irmm cmlatf ki hcc ikur strela es vhremn irkb C : tk 0C:. Ieln tfm bhxebub iulnhbmlthc irmqumlgy ki 8, 0, 7, > el tmrbs ki i : (tmlsekl es shbm el hcc strelas) cFof pod diCc?osh nf mqNr yMgo`T C: cs 0C: rn torf aWH 8, 0, 7, > nf vi/onrm mwy vokj iÕo i : ns elos msh aosxfH ( cFof

diCc?osh msh ruok cmou aWH)

(H)

Wtrela (½) dCcf-8

(Z)

8

(@)

Wtrela (0½) dCcf -0

(X)

8 0

(G)

Wtrela (7½) dCcf -7

(P)

(N)

Wtrela (>½) dCcf ->

(W)

(^) (]) Wkc.

8 0 8 7 8 89 7 89

(H) Z, (@) P, (G) W, (N) X Iulnhbmlthc irmqumlgy es bhxebub wfml cmlatf es belebub e.m. C :, m y w vokjiÕo bc cm? vi/onrm aosrf aW tg yMgo`T iuMurm aW v IooTr~ C:,

Ghsm 8. C 2 Ck, ^ 2 ^ k, i 2 i k i 8 2

8

^k

0C :

½

Ghsm 0.

i 0 2

Ghsm 7.

i 7 2

Ghsm >.

i > 2

8 C:

^0 0½

2

i k

8

^0

i k

C:

7½

2

8 C:

^0 >½

2

i k 0

0 7



ZHAM # 81

JEE Advanced 2019 Paper-2 Physics

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