JEE Advanced 2019 Paper-1 Physics

®

MNN (Edvebcnd) (ED\EBCND) 8:5< 8:5? MNN

88-:>-8:5<

DETN= 8;-:>-8:5?

@nàry Hesnd Uunstoabs & Saiutoabs ZEZNX - 5 | S^HMNCT = ZF_SOCS ZEZNX-5 = OBSTX^CTOABS TA CEBDODETNS CEBDODETNS •

Uunstoab Zepnr-5 fes tfrnn (:3) perts= Zfysocs, Cfnòstry ebd @etfnètocs.

•

Necf pert fes e tatei nokftnnb (56) qunstoabs dovodnd obta tfrnn (:3) snctoabs (Snctoab-5, Snctoab-8 ebd Snctoab-3)

•

Tatei bu`hnr al qunstoabs ob Uunstoab Zepnr-5 ern Lolty Laur (>4) ebd @exoù` @ergs ern Abn Fubdrnd Nokfty Sox (56<)

Typn al Uunstoabs ebd @ergobk Scfn`ns SNCTOAB-5 (@exoù` @ergs = 58) •

Tfos snctoab cabteobs LA^X (:4) qunstoabs. (:4) qunstoabs.

•

Necf qunstoab fes LA^X aptoabs ABI_ ABN al ABN al tfnsn laur aptoabs os tfn carrnct ebswnr.

•

•

Lar necf qunstoab, cfaasn cfaasn tfn carrnct aptoab carrnspabdobk carrnspabdobk ta tfn carrnct carrnct ebswnr. Ebswnr ta necf qunstoab woii hn nveiuetnd eccardobk ta tfn laiiawobk laiiawobk èrgobk scfn`n = Luii @ergs

=

]nra @ergs

=

Bnketovn @ergs

=

+3 Ol ABI_ tfn carrnct aptoab os cfasnb. : Ol babn al tfn aptoabs os cfasnb (o.n. tfn qunstoab os ubebswnrnd). ubebswnrnd). –5 Ob –5 Ob eii atfnr cesns.

SNCTOAB-8 (@exoù` @ergs = 38) •

Tfos snctoab cabteobs NOKFT (:6) qunstoabs. (:6) qunstoabs.

•

Necf qunstoab fes LA^X aptoabs. ABN AX @AXN TFEB ABN al ABN al tfnsn laur aptoab(s) os (ern) carrnct ebswnr(s).

•

Lar necf qunstoab, cfaasn tfn aptoab(s) carrnspabdobk carrnspabdobk ta (eii) tfn carrnct ebswnr(s). ebswnr(s).

Ebswnr ta necf qunstoab woii hn nveiuetnd eccardobk ta tfn laiiawobk èrgobk scfn`n.

•

Luii @ergs

=

+4 Ol abiy (eii) tfn carrnct aptoab(s) os (ern) cfasnb.

Zertoei @ergs =

+3 Ol +3 Ol eii tfn laur aptoabs ern carrnct hut ABI_ tfrnn aptoabs ern cfasnb.

Zertoei @ergs =

+8 Ol +8 Ol tfrnn ar àrn aptoabs ern carrnct hut ABI_ twa aptoabs ern cfasnb ebd hatf al wfocf ern carrnct.

Zertoei @ergs =

+5 Ol +5 Ol twa ar àrn aptoabs ern carrnct hut ABI_ abn aptoab os cfasnb ebd ot os e carrnct aptoab.

]nra @ergs =

: Ol babn al tfn aptoabs os cfasnb (o.n. tfn qunstoab os ubebswnrnd). ubebswnrnd).

Bnketovn @ergs =

–5 Ob –5 Ob eii atfnr cesns.

Xnsabebcn Nduvnbturns Ioòtnd XNKOSTNXND & CAXZAXETN ALLOCN = CK Tawnr, E-4< & >8, OZOE, Bner Coty @eii, Mfeiewer Xaed, Gate (Xem.) - 384::>

Gbaw ` àrn == s`s XNSA e et ><<;; Zf.Ba. = :;44-8;;;;;;, :;44-8;;;;:: | :;44-8;;;;:: | Taii Lrnn = 56:: 8>6 >>>> | LEV Ba. = +?5-:88-3?5<;888 = +?5-:88-3?5<;888 | Ta G [nhsotn = www.rnsabebcn.ec.ob | N-èoi = cabtectJrnsabebcn.ec.ob | COB == ^6:3:8XM8::;ZIC:84:8? Tfos ssaiutoab w wes d dawbiaed l l ra` X Xnsabebcn MMNN ((ED\EBCND) 8 8:5? S Saiutoab p partei

SNCTOAB-3 (@exoù` @ergs = 56) •

Tfos snctoab cabteobs SOV (:<) qunstoabs. (:<) qunstoabs. Tfn ebswnr ta necf qunstoab os e B^@NXOCEI \EI^N. \EI^N .

•

Lar necf qunstoab, nbtnr tfn carrnct bu`nrocei veiun al tfn ebswnr usobk tfn àusn ebd tfn ab-scrnnb vortuei bu`nr bu`nroc oc gnyped ob tfn piecn dnsokbetnd ta nbtnr tfn ebswnr. Ol tfn bu`nrocei veiun fes àrn tfeb twa dncoèi piecns trubcetn/raubd-all trubcetn/raubd-all tfn veiun ta T[A dncoèi T[A dncoèi piecnd.

•

Ebswnr ta necf qunstoab qunstoab woii hn nveiuetnd eccardobk eccardobk ta tfn laiiawobk èrgobk èrgobk scfn`n = Luii @ergs

=

+3 Ol ABI_ tfn carrnct bu`nrocei bu`nrocei veiun os nbtnrnd. nbtnrnd.

]nra @ergs =

: Ob eii atfnr atfnr cesns. cesns.

Ebswnrobk Uunstoabs = •

Ta sninct tfn aptoab(s), usn tfn àusn ta ciocg ab tfn carrnspabdobk huttab(s) al tfn aptoab(s). aptoab(s).

•

Ta dnsninct tfn cfasnb aptoab lar tfn qunstoabs al SNCTOAB-5, SNCTOAB-5 , ciocg ab tfn huttab al tfn cfasnb aptoab ekeob ar ciocg ab tfn Ciner Xnspabsn huttab ta ciner tfn cfasnb aptoab. Ta dnsninct tfn cfasnb aptoab(s) lar tfn qunstoabs al SNCTOAB-8, SNCTOAB-8 , ciocg ab tfn huttab(s) al tfn cfasnb aptoab(s) ekeob ar ciocg ab tfn

•

Ciner Xnspabsn huttab ta ciner eii t fn cfasnb aptoabs. •

Ta cfebkn tfn aptoab(s) al e prnvoausiy ebswnrnd qunstoab al SNCTOAB-5 ebd SNCTOAB-5 ebd SNCTOAB-8 lorst SNCTOAB-8 lorst dnsninct es kovnb ehavn ebd tfnb sninct tfn bnw aptoab(s). Ta ebswnr qunstoabs qunstoabs al SNCTOAB-3, SNCTOAB-3, usn tfn àusn ta ciocg ab bu`hnrs (ebd/ar sy`hais) ab tfn ab–scrnnb vortuei bu`nroc gnyped

•

ta nbtnr tfn bu`nrocei veiun ob tfn specn pravodnd lar ebswnr. Ta cfebkn tfn ebswnr al e qunstoab qunstoab al SNCTOAB-3, SNCTOAB-3 , lorst ciocg ab tfn Ciner Xnspabsn huttab Xnspabsn huttab ta ciner tfn nbtnrnd ebswnr ebd tfnb

•

nbtnr tfn bnw bu`nrocei veiun. Ta èrg e qunstoab ABI_ lar ABI_ lar rnvonw (o.n. wotfaut ebswnrobk ot), ciocg ab t fn @erg lar Xnvonw & Bnxt huttab. Bnxt huttab.

•

•

Ta èrg e qunstoab lar rnvonw (eltnr ebswnrobk ot), ciocg ab @erg lar Xnvonw & Bnxt huttab Bnxt huttab – tfn ebswnrnd qunstoab wfocf os eisa èrgnd lar rnvonw woii hn nveiuetnd.

•

Ta sevn tfn ebswnr, ebswnr, ciocg ab tfn Sevn & Bnxt huttab Bnxt huttab – tfn ebswnrnd qunstoab woii hn nveiuetnd.



| MNN (ED\EBCND) 8:5? | DETN = 8;-:>-8:5? | ZEZNX-5 | @N@AX_ HESND

ZEXT-O = ZF_SOCS SNCTOAB-5 (@exoù` @ergs = 58)

• Tfos snctoab cabteobs LA^X (:4) qunstoabs. (:4) qunstoabs. • Necf qunstoab fes LA^X aptoabs ABI_ ABN al ABN al tfnsn laur aptoabs os tfn carrnct ebswnr. • Lar necf qunstoab, cfaasn cfaasn tfn carrnct aptoab carrnspabdobk carrnspabdobk ta tfn carrnct carrnct ebswnr. • Ebswnr ta necf qunstoab woii hn nveiuetnd eccardobk ta tfn laiiawobk laiiawobk èrgobk scfn`n = Luii @ergs

=

]nra @ergs

=

Bnketovn @ergs

=

+3 Ol ABI_ tfn carrnct aptoab os cfasnb. : Ol babn al tfn aptoabs os cfasnb (o.n. tfn qunstoab os ubebswnrnd). ubebswnrnd). –5 Ob –5 Ob eii atfnr cesns.

Wge@ 5 ¹vl/gdrn ved % 58°

• • • •

5.

hi Wge@ nse ozX7sd oz'u ozX7sd oz'u ozX7sd oz'u ow.g] ved % 'gw^7 ved % Q.g ved

E currnbt cerryobk worn fnets e `ntei rad. Tfn T fn worn pravodns e cabstebt pawnr Z ta tfn rad. Tfn `ntei rad os nbciasnd ob eb obsuietnd cabteobnr. Ot os ahsnrvnd tfet tfn tn`pnreturn (T) ob tfn `ntei rad cfebkns wotf to`n (t) es T(t) 0 T : (5 + θ t5/4) wfnrn θ os e cabstebt wotf eppraproetn do`nbsoab al tn`pnreturn. Tfn fnet cepecoty al `ntei os =

4Z(T( t ) ∘ T: )3

(E) Ebs. Sai.

pgm (:4) oz'u kSE ay ,d k f lad_o ikf `ßgm kSE ds ly, ikf ikf pgm lad_o lb, x, x, kSeE hu pgm lad_ogs lad_ogse nse is dsay ds ly, lb, lb, kq, lad_ogse nsnse is ikf `ßgm is iecl/gr lad_o dgs pqlu,E u,E ds `ßgm dg nw_7ge du luNu 7gstug ds vuq vuqigm kgs xg % +37 lb liU] ikf lad_o kf pqug x7g kSE lb dgsh] Fgf lad_o ukfe pqug x7g kS ¹vLgg]r~ oz 'u vuqßglmr kS°E :7 % –5v ^7 iFgf olmlILglr7gse nseE

θ

4

T:4

(H)

4Z(T( t ) ∘ T: )8

θ

4

T:3

(C)

4Z(T( t ) ∘ T: ) 4

θ

4

T:>

(D)

4Z(T( t ) ∘ T: )

θ 4 T:8

(E) dU 0 FdT dU dT 0 F. dt dt Z 0 F. T: . θ .

5 –3/4 .t 4

4Z 0 t –3/4 . F T: .θ Baw

T – T : 0 T: θ t5/4

t

Sa

∴ F 0

3/4

 T ∘ T:   0   T:θ 

3

4Z(T ∘ T: )3 T:4θ 4



ZEKN # 5


8.

Ob e cepoiiery tuhn al redous :.8 `` tfn wetnr rosns up ta fnokft al ;.> c` wotf ebkin al cabtect nquei ta znra. Ol ebatfnr cepoiiery wotf se`n redous hut al dollnrnbt ètnroei doppnd ob tfn se`n ioquod. Tfn fnokft al wetnr reosnd ob cepoiiery woii hn, ol ebkin al cabtect hnca`ns <:º. Io'g] dgs.g ds igLg ;.> c` Î¡pgh] rd Î¡om df vgsm `Hrg kSE 7lb v^7 :.8 `` l0gT7g df ds'guyf nse oguf 'gw^7 Io'g]

ingu l0gT7g df ds 'guyf ltidg obgLg] obgLg] lFgû kSP dgs oguf nse @ qcgs7g tg7s rgs ds'guyf nse p9+s kq7s oguf df Î¡pgh] D7g kgsxf 1 7lb Io'g] dgs.g <:º kgsE Ebs. Sai.

(E) ;.> c` (H) 5> c` (C) Ol X 0 :.8 `` lar twa cepoiiery pweld bgsugse ds'guly7gse df l0gT7g X 0 :.8 `` kS Es ob 5st cesn vr% ozLgn f 0 ;.> c` Xfυk T0 ( ζ 0 :) 8 cas ζ 0 ;.> Û 5: –8 0 :.:;> B/` Baw ob 8 bd cesn

(C) 3.;> c`

(D) 3: c`

lILglr nse

vc l}rf7 lILglr ns e Xf5υk T0 ( ζ 0 <:) 8 cas ζ 8 cas <: Û ;.> Û 5: ∘8 f5 0 :.8 Û 5: ∘3 Û 5: 3 Û 5: ;.> Û 5: ∘8 8 0 3.;> Û 5: –8 ` 0 3.;> c` Eitnrbetn = Xfυk T0 8 cas ζ ;.> f' 0 5:: cas <: f' 0 3.;> c`

0

3.

E se`pin se` pin al 5? G 4: dosobtnkretns obta twa bucino Ce & Er wotf dncey cabstebt

ηCe 0 4.> Û 5: –5: S –5 ebd

η Er 0 0 :.> Û 5: –5: S –5 rnspnctovniy. Tfn to`n eltnr wfocf ??% al 5? G 4: knts dnceynd os = 4: la1gl\r kgsdm bgs uglFgdgse Ce rLgg Er nse laFgDr kgsrg kS ltuds la1g\u lu7rged Ön'g% ηCe 0 4.> Û 5: –5: 5? G SE ak in7 D7g kgsxg ltids o'pgr~ 5? G 4: , ??%l aFgDr kgs tgrg kSE S –5 rLgg η Er 0 0 :.> Û 5: –5: S –5k Ebs.

(E) <.8 Û 5:? snc (H) ηCe

Sai.

(H*) ?.8 Û 5:? snc

Ce

(C) ;.8 Û 5:? snc

(D) 4.8 Û 5:? snc

:

G

η Er

Er

:

t0: dB dt

0 ∘(η5 + η 8 ) Û B



ZEKN # 8


 B    0 ∘(η5 + η 8 )t  B:   B:   0 > Û 5: ∘5: t 8.3 Û iak5:   B: / 5::  8.3:3 Û 8 0t > Û 5: ∘5: iakn

8.3:3 Û :.4 Û 5: 5: 0 t t 0 ?.8 Û 5: ? snc 4.

Cabsodnr e spfnrocei kesnaus ciaud al èss dnbsoty υ(r) ob e lrnn specn wfnrn r os tfn redoei dostebcn lra` ots cnbtrn. Tfn kesnaus ciaud os èdn al pertocins al nquei èss ` àvobk ob corcuier arhots ehaut tfnor ca`àb cnbtrn wotf tfn se`n gobntoc nbnrky G. Tfn larcn ectobk ab tfn pertocins os tfnor ùtuei krevotetoabei larcn. Ol υ(r) os cabstebt wotf to`n. Tfn pertocin bu`hnr dnbsoty b(r) 0 υ(r)/` os = (k 0 ubovnrsei krevotetoabei cabstebt) n Dq r vgdg'g nse υ(r) ìA7ngu 1guXa dg ,d xgsygdgm xSif7 cgby df d_oug dmse E tkg¡ r ds^ì is l0gT7f7 bwmf kSE

xSif7 cgby ingu ìA7ngu ` ds d.ggse is lnydm cug kS tgs `Fg7lu"H ds^ì ds igos{g ajßggdgm oLggse nse ingu xlrt Îtg] G i sxlr'gfy kSE d.ggse om yxus agyg cy v^7gs^7 xq=Xaf7 cy kSE 7lb υ(r) in7 ds igLg lu7r kS rgs d.ggse dg ieW7gXnd 1guXa b(r) 0 υ(r)/` os = (K 0 iga]l0gd xq=Xaf7 lu7rge lu7rged ) (E) Ebs. Sai.

3G 8

8

ϊr ` K

(H)

G 8

8

8ϊr ` K

(C)

G 8

8

ϊr ` K

(D)

G 8

<ϊr ` 8 K

(H)

K@` r 8

0 0

`v 8 r 8  5

  `v 8  r  8 

⇘

K@`

⇘

8Gr K` 8G dr d@ 0 K` 8G dr 4ϊr 8dr υ 0 K` G υ 0 8ϊK`r 8

⇘ ⇘ ∴

r 8

0

8G r

@0



ZEKN # 3


Eitnrbetovn.

⇘

\8 wfnrn @ 0 tatei èss upta redous (r) 0 r r 8 tkg¡ @ ìA7ngu @ 0 (r) l0gT7g rd dqy ìA7ngu K@(r )

G

@(r) 0

K@` 8r

0

8Gr K`

⇘

d@ (r)

⇘

υ0 υ

⇘

`

8G K` G

dr 0 υd\ 0 υ4ϊr 8dr

K8ϊr 8` G

0

8ϊK`8r 8

SNCTOAB-8 (@exoù` @ergs = 38)

• Tfos snctoab cabteobs NOKFT (:6) qunstoabs. (:6) qunstoabs. • Necf qunstoab fes LA^X aptoabs. ABN AX @AXN TFEB ABN al ABN al tfnsn laur aptoab(s) os (ern) carrnct ebswnr(s). • Lar necf qunstoab, cfaasn tfn aptoab(s) carrnspabdobk carrnspabdobk ta (eii) tfn carrnct ebswnr(s). ebswnr(s). • Ebswnr ta necf qunstoab woii hn nveiuetnd eccardobk ta tfn laiiawobk èrgobk scfn`n. Luii @ergs

=

+4 Ol abiy (eii) tfn carrnct aptoab(s) os (ern) cfasnb.

Zertoei @ergs =

+3 Ol +3 Ol eii tfn laur aptoabs ern carrnct hut ABI_ tfrnn aptoabs ern cfasnb.

Zertoei @ergs =

+8 Ol +8 Ol tfrnn ar àrn aptoabs ern carrnct hut ABI_ twa aptoabs ern cfasnb ebd hatf al wfocf ern carrnct.

Zertoei @ergs =

+5 Ol +5 Ol twa ar àrn aptoabs ern carrnct hut ABI_ abn aptoab os cfasnb ebd ot os e carrnct aptoab.

]nra @ergs =

: Ol babn al tfn aptoabs os cfasnb (o.n. tfn qunstoab os ubebswnrnd). ubebswnrnd).

Bnketovn @ergs =

–5 Ob –5 Ob eii atfnr cesns.


• • • •

hi Wge@ nse vgH (:6) oz'u kSE ozX7sd oz'u ds ly, pgm lad_o lad_o lb, x, kSeE hu pgm lad_ogse nse is ,d 7g ,d is vl/gd lad_o ikf kS¹kS e°E ozX7sd oz'u ds ly,P lb, lb, kq, lad_ogse nse is ikf `ßgm ¹`ßgmgse° is iecl/gr lad_o ¹lad_ogs e° dgs pqlu,E ozX7sd oz'u ds `ßgm dg nw_7ge du luNu 7gstug ds vuq vuqigm kgs xg % ow.g] ved % +47 lb dsay ¹igms° ikf lad_o ¹lad_ogse ° dgs pqug x7g kS E vgel'gd ved % +37 lb pgmgse lad_o ikf kSe om^rq dsay rfu lad_ogs e dgs pq ug x7g kSE vgel'gd ved % +87 lb rfu 7g rfu is v l/gd lad_o ikf kS om^rq dsay bgs lad_ogs e dgs pqug x7g kS vgS vgS m bgseugs pqus kq, lad_o ikf lad_o kSeE vgel'gd ved % +57 lb bgs 7g bgs is vl/gd lad_o ikf kSe om^rq dsay ,d lad_o dgs pqug x7g kS v gSm pqug kvg qvg lad_o ikf lad_o kSE 'gw ^7 ved % :7 lb ldif Fgf lad_o dgs ukfe pqug x7g kS ¹vLgg]r~ oz'u vuqßglmr kS°E Q.g ved % –5v ^7 iFgf olmlILglr7gse nseE



ZEKN # 4


>.

E tfob spfnrocei obsuietobk sfnii al redous X cerons e ubolarìy dostrohutnd cferkn sucf tfet tfn patnbtoei et ots surlecn os \ :. E fain wotf sèii erne ε4ϊX8 (ε 995) os èdn ob tfn sfnii wotfaut nllnctobk tfn rnst al tfn sfnii. [focf abn al tfn laiiawobk os carrnct. X l0gT7g dg ,d oryg vpgyd WggsWgys xgsys om vgas'g hi ozdgm is vgasl'gr kS ld hidf irk om aS|qr laFga

ε4ϊX8 ( ε 995) {gs0gUy dg ,d Bgs\g Bsb hi xgsys om hi ozdgm is cug7g x7g kS ld 'gs"g Fggx df lILglr volmalr] r kSE luNulylWgr nse is dgS uis dLgu ikf kgs kgsexsE \: kSE



(E) Tfn èkbotudn al N et e paobt iacetnd ab e iobn pessobk tfraukf tfn fain ebd sfnii's cnbtrn ab e εv : dostebcn 8X lra` tfn cnbtrn al spfnrocei sfnii woii hn rnducnd hy 8X (H) Zatnbtoei et tfn cnbtrn al sfnii os rnducnd hy 8 εv:.  εv : (C) Tfn èkbotudn al N et tfn cnbtrn al sfnii rnducnd hy 8X 5 (D*) Tfn retoa al patnbtoei et tfn cnbtrn al tfn sfnii ta tfet al tfn paobt et X lra` cnbtrn tawerds tfn 8 5∘ ε fain woii hn 5 ∘ 8ε  εv : om aS|qr {gs0g N dg olmng.g is (E) xgsys ds ds^ì rLgg Bsb is xqtmus agyf ds ^ì is 8X bwmf om lILgr lc^bq om 8X

dn kgs tg7sxgE (H) xgsys ds ds^ì om aS|qr laFga laFga 8εv: is dn kgs tg7sxgE. εv : (C) xgsys ds ds^ì om aS|qr {gs 0g dg olmng.g is dn kgs tg7sxgE (D) xgsys Ebs. Sai.

ds ds^ì om aS|qr laFga rLgg lBì

8X 5 is X bwmf 8

5∘ ε

ds^ì df vgs m lc^bq om aS |qr laFga dg vuq vuqogr

5 ∘ 8ε

(D) X

E

X/8

H C

dq

0

U 4ϊX 8

dE

0

Uε

Kovnb \ et surlecn GU \: 0 X \ et C GU GεU ∘ \C 0 0 \: (5 – ε) X X \ et H GU G(εU) ∘ \H 0 0 \: (5 – 8ε) X X/8 \C 5∘ ε

∴

\H

0

5 ∘ 8ε

N et E



ZEKN # >


N E 0

GU ( 8X)8

∘

GεU X8

0

GU 4X 8

∘

ε\: X

ε\:

Sa rnducnd hy N et C G (εU ) NC 0 X8

0

X

ε\: X

ε\:

sa obcrnesnd hy

X

Ebs. (D) <.

E cferknd sfnii al redous X cerrons e tatei cferkn U. Kovnb ό es tfn liux al ninctroc lonid tfraukf e ciasnd cyiobdrocei surlecn al fnokft f, redous r & wotf ots cnbtnr se`n es tfet al tfn sfnii. Fnrn cnbtnr al cyiobdnr os e paobt ab tfn exos al tfn cyiobdnr wfocf os nquodostebt lra` ots tap & hatta` surlecns. [focf al tfn laiiawobk ern carrnct. U (E) Ol f 2 8X & r 2 X tfnb ό 0

ξ:

6X 3X & r 0 tfnb ό 0 : > > U 4X (C) Ol f 2 8X & r 0 tfnb ό 0 >ξ : > (H) Ol f 9

U 3X tfnb ό 0 >ξ : >

(D) Ol f 2 8X & r 0 Ebs. Sai.

(EHD) (e) f 2 8X

r2X r

X U

ό0

U

ξ:

cineriy lra` Keuss' Iew

(h) suppasn f 0

6X >

r0

3X >



ZEKN # <


3X/>

4X/>

ό0: sa lar f 9

6X

ό 0 :

>

(C) lar f 0 8X

r0

4X >

4X/> >3½ X

Sfednd cferkn 0 8 ϊ (5 – cas>3½) Û U

∴

0

∴

qnbciasnd 0

∴

ό 0

∴

lar f 2 8X r 0

> 8U >

8U >ξ : 4X >

(d) iogn aptoab C lar f 0 8X r 0 0 qnbciasnd 0 8 Û 8ϊ (5 – cas3;½)

∴

U 4ϊ

ό 0

∴ ό 0

8U >ξ :

3X > U

4ϊ

0

U >

U >ξ :



ZEKN # ;


;.

[focf stetn`nbts os/ern carrnct = Z 6:¾L >\ 3:ℬ

S5

C4 S8 C5

5:¾L 3:¾L ;:ℬ

Ebs. Sai.

C8 3:ℬ

6:¾L C3

5:\ 5::ℬ

U (E) Et to`n t 0 :, tfn S 5 os ciasnd obstebtebnaus currnbt ob tfn ciasnd corcuot woii hn 8> È (H) Tfn gny S 5 os gnpt ciasnd lar iabk to`n sucf tfet cepecotars ern luiiy cferknd. Baw gny S 8 os ciasnd et tfos to`n tfn obstebtebnaus currnbt ecrass 3: ℬ rnsostar hntwnnb Z & U woii hn :.8E. (C) Ol gny S5 os gnpt ciasnd lar iabk to`n sucf tfet cepecotars ern luiiy cferknd tfn vaitekn ecrass C 5 woii hn 4\. (D) ol S5 os gnpt ciasnd lar iabk to`n sucf tfet cepecotars ern luiiy cferknd tfn vaitekn dollnrnbcn hntwnnb Z & U woii hn5:\. (EC)

Must eltnr ciasobk al swotcf cferkn ab C os znra. ∴ Xnpiecn eii cepecotars wotf worn. o

>\ 3:ℬ

;:ℬ 5::ℬ >

0

>

0 8>È ;: + 5:: + 3: 8:: Baw S5 os gnpt ciasnd lar iabk to`n corcuot os ob stnedy stetn o0

Z –q q >\ –q 6:¾L 6:¾L 5:¾L q U ?

+

?

+

?

∘> 0 : 5: 6: 6: 5:? 0> 6: ∴ q 0 4: ¾C ∴ \ ecrass C5 0 4:/5: 0 4 vait Baw must eltnr ciasobk al S 8 cferkn ab necf cepecotar rnèob se`n



ZEKN # 6


–4: 4: : 6:¾L :3:¾L

4: 5: ¾L y –4:

> 3:ℬ x–y

4:

3:ℬ

;:

5:\ x

–4:

5::ℬ

G\I –5: + x Û 3: + 4:/5: + y Û ;: 0 : 3:x + ;:y 0 < ....(5) 4: 4: ∘ + > + (x – y) 3: ∘ + (x – y) Û 5:: – 5: + x Û 3: 0 : 6: 6: 5<:x – 53:y – < 0 : ....(8) y 0 ?5: x 0 :.:> e`p. 6.

E keiveba`ntnr al r nsostebcn 5: af` ebd èxoù` ` exoù` currnbt al 8 ¾ E os cabvnrtnd obta vait`ntnr al rebkn 5::`\ ebd wfnb cabvnrtnd obta e``ntnr tfnb rebkn os 5È. [fnb tfnsn vait`ntnr ebd e``ntnr ern cabbnctnd hy e (odnei) hettnry ob snrons wotf e rnsostebcn al X 0 5::: ℬ, tfnb ,d /ggmgngof dg oz lrmgs/g 5: vgsn rLgg ow .g] la{gs o ds vga'7d /ggmg 8¾ E kSE hi /ggmgngof dgs luNu nse olmalr] olmalr]r dmus

ds ly, ldrus ozlrmgs/g df vga'7drg kgsxf

Ebs. Sai.

(E) `nesurnd veiun al X os hntwnnb ?;6 ℬ ebd ??<ℬ (H) rnsostebcn al vait`ntnr 5: >ℬ (C) sfubt rnsostebcn os 8:` ℬ (D) Ol tfn odnei hettnry os rnpiecnd hy bab odnei hettnry wotf obtnrbei rnsostebcn al > ℬ tfnb X woii hn 25::: ℬ (EC)

Οk

Xk K

v 0 5:: Û 5:-3v v 0 Ok(Xk + X) 5: ∘5

0 Xk +X 8 Û 5: ∘< > Û 5:4 0 Xv X\ \ X E E 5:::ℬ

ξ O0OÛ

5:—3



ZEKN # ?


S

K OkXk 0 (O – Ok)S S0

8 Û 5: ∘< Û 5:

5: ∘3 ∘ 8 Û 5: ∘< S 0 8 Û 5:—> Û5:3 ⇘ 8 Û 5:—8 ⇘ 8:`ℬ

8: Û 5: ∘3 Û 5: X E 0 0 8: Û 5: –3 5: ?.



Cabductobk worn al perehaioc sfepn, obotoeiiy y 0 x 8 os àvobk wotf vniacoty v

0 v : ˌo ob e bab-ubolar`

  y θ  èkbntoc lonid H 0 H: 5 +   gˌ es sfawb ob lokurn. Ol \ :, H:, I & H ern +vn cabstebts & ∌ό os patnbtoei     I   

dollnrnbcn dnvniap hntwnnb tfn nbds al worn, tfnb carrnct stetn`nbt(s) os/ern 

y

H

I 

v

A

0 v : ˌo

I

5 H: \:I lar θ 0 : 8 4 (H) | ∌ό |0 H : \:I lar θ 0 8 3 (C) |∌ό| os prapartoabei ta tfn inbktf al worn pramnctnd ab y-exos (E) | ∌ό |0

(D) |∌ό| rnèobs se`n ol tfn perehaioc worn os rnpiecnd hy e streokft worn, y 0 x, obotoeiiy al inbktf

omay7gdgm

y 0 x8

dg pgyd rgm asx



v

  y   gˌ nse lp0gguqigm   I     ∌ό rgm ds limgse om `Xoû laFgag^rm kgs rgs ikf

0 v : ˌo is vin=o pqNcdf7 {gs0g

xlr'gfy kSE 7lb \:, H:, I a H /gugXnd lu7rged ,ae lad_oJlad_ogse dg p7u dflt, &

8



H 0 H : 5 + 

θ 



y

H

I 

v

A

0 v : ˌo

I



ZEKN # 5:


(E) | ∌ό |0

5

H: \:I , θ 0 : ds ly, 8 4 (H) | ∌ό |0 H : \:I , θ 0 8 ds ly, 3 z{gso (C) |∌ό|, y-v{g om rgm df yNcgh] ds o

ds inguqogrf kgsxf (D) |∌ό|, volmalr]r mksxg 7lb omay7gdgm rgm dgs 8 yNcgh] ds if/gs rgm kSE Ebs. Sai.

y0x

ds }gmg ozlrILgglor ld7g tgrg

(HCD) y H

H I

y 0 x8 dy \:

A

\: x

  

Lar ceicuietobk tfn àtoabei n`l ecrass tfn inbktf al tfn worn, int us pramnct worn sucf tfet H, v,  hnca`ns ùtueiiy artfakabei. Tfus

  y θ  dξ 0 Hv: dy 0 H : 5 +    \: dy   I   I   y θ  ξ 0 H : 5 +    \: dy     I   :  5  0 H: \:I 5 +   θ + 5

∧

n`l ob iaap os prapartoabei ta I lar kovnb veiun al lar θ0: 7 ξ 0 8H:\:I  5 4 θ08 7 ξ 0 H:\:I 5 +  0 H:\:I  3 3

θ.

tfn inbktf al tfn pramnctoab al tfn worn y 0 x al inbktf

8 I ab tfn y-exos os I tfus tfn ebswnr rnèob

ubcfebknd Tfnrnlarn, ebswnr os H,C,D

5:.

Ol ob e fypatfntocei systn` ol tfn ebkuier à`nbtu` ebd èss ern do`nbsoabinss. Tfnb wfocf al tfn laiiawobk os trun. (E) Tfn iobner à`nbtu` verons es I –5 (H) Tfn nbnrky verons es I –8 (C) Tfn pawnr verons es I –4 (D) Tfn larcn verons es I –>



ZEKN # 55


7lb ,d dg_olud ludg7 nse dgs .gf7 ieas x vgSm ìA7ngu langkfu kSe rgs luNulylWgr nse dgSu igJis lad_o lad_o ikf kSJkSeE (E) msWgf7 ieasx I –5 ds vuqigm olmalr]r kgs rg kSE (H) Îtg] I –8 ds vuqigm olmalr]r kgsrf kSE (C) 'glDr I –4 ds vuqigm olmalr]r kgs rf kSE (D) cy I –> ds vuqigm olmalr]r kgs rg kSE Ebs. Sai.

(EHC) W@ P 0 W@essP 0 W@:I:T:P WMP 0 WEbkuier à`nbtu`P 0 W@I 8T –5P WIP 0 WInbktfP Baw 7 W@I 8T –5P 0 W@:I:T:P ∴ WI8P 0 WTP Zawnr WZP 0 W@IT –8 . IT –5P 0 W@I8T –3P 0 WI8 I –

Ebs.

(E), (H), (C)

Sai.

W@ P 0 W ìA7nguP 0 W@:I:T:P WMP 0 W dgs.gf7

ieasxP 0 W@I8T –5

WIP 0 W yNcgh]P

vc 7 W@I8T –5P 0 W@:I:T:P ∴ WI8P 0 WTP

'glDr WZP 0 W@IT –8 . IT –5P 0 W@I8T –3P 0 WI8 I –



ZEKN # 58


Îtg]/ dg7] W[P0

W@IT –8 . IP 0 WI8 I –4P 0 WI –8P

cy WLP 0 W@IT –8P 0 WI . I –4P 0 WI –3P msWgf7 ie asx WpP 0 W@IT –5P 0 WI . I –8P WpP 0 WI –5P Ebs. (E), (H), (C) 55.

\–T doekre` lar b ài àbaetaòc kes os kovnb hniaw =

Cfaasn tfn carrnct stetn`nbt =

(E)

∌U5↘ 8 5 0 ∌U3 ↘ 4 8

(H)

∌U5↘ 8 > 0 ∌U8 ↘ 3 3

(C) [arg dabn ob cycioc pracnss os ∌[ 0

bXT: 8

(D) Tfnrn ern abiy edoehetoc ebd osacfaroc pracnssns ern obvaivnd. Ebs.

(HC)



ZEKN # 53


Sai.

(E)

∌U5↘8 BCZ ∌T5↘8 T 0 0 : 08 ∌U3↘4 BCZ ∌T3↘4 T: / 8

(H)

∌U5↘8 BCZ ∌T5↘8 C > 0 0 Z 0 ∌U8↘3 BC \ ∌T8↘3 C \ 3

(C) [ cycin 0 Z:\: 0 bX

 T:   8  W^sobk paobt ba. 4P  

(D) [rabk es ba edoehetoc pracnss os obvaivnd 58. X

X F

F

b

b

F

b

x x x Eppernbt dnptf lar paobt ahmnct x ob eii tfrnn cesns ern F 5, F 8 & F3 rnspnctovniy wfnb snnb lra` ehavn kovnb F 0 3: c`, b 0 5.> & X 0 3 `, tfnb bf x7f iFgf lILglr7gse ds ly7s Îom is bsWgus om lc^bq x df vgFggif xkmgh] Ön'g% F5, F8 rLgg F3 kSE F 0 3: c`,

Ebs. Sai.

b 0 5.> rLgg X 0 3 `, rgs (E) :.6 9 F8 – F5 9 :.? (H) F8 2 F5 (H,C) Cesn-O =

F

(C) F8 2 F3

(D) F3 2 F5

b

x F 0 3: c` b 0 3/8



ZEKN # 54


⇘

F5 0 F/b

3: Û 8 3

0 8: c`

Cesn-OO = X F

b

x X 0 3:: c` b 8 b5 b 8 v

∘

5 ∘ F8 F8

0

u

∘

0

X

3

∘ 8 Û 3:

<::

8? Cesn-OOO = X F

∘ b5

0

3 8 ∘ 3:: 5∘

0 8:.<64 c`

b x

b8 v

∘

b5 u

0

b8

∘ b5 X

7

5 ∘ F3

∘

3

∘ 8 Û 3:

0

3 8 7F 3 3::

5∘

0

<:: 35

0 5?.3>4 c`

SNCTOAB-3 (@exoù` @ergs = 56)

• Tfos snctoab cabteobs SOV (:<) qunstoabs. (:<) qunstoabs. Tfn ebswnr ta necf qunstoab os e B^@NXOCEI \EI^N. \EI^N . • Lar necf qunstoab, nbtnr tfn carrnct bu`nrocei veiun veiun al tfn ebswnr usobk tfn àusn ebd tfn ab-scrnnb vortuei vortuei bu`nroc gnyped ob tfn piecn dnsokbetnd ta nbtnr tfn ebswnr. Ol tfn bu`nrocei veiun fes àrn tfeb twa dncoèi piecns trubcetn/raubd-all trubcetn/raubd-all tfn veiun ta T[A dncoèi T[A dncoèi piecnd.

• Ebswnr ta necf qunstoab qunstoab woii hn nveiuetnd eccardobk eccardobk ta tfn laiiawobk èrgobk èrgobk scfn`n = Luii @ergs

=

]nra @ergs =

+3 Ol ABI_ tfn carrnct bu`nrocei bu`nrocei veiun os nbtnrnd. nbtnrnd. : Ob eii atfnr atfnr cesns. cesns.


• hi Wge@ ns e B%(:<)o z'u kS E ozX7sd oz'u dg `ßgm ,d ie W7gXnd ngu (B^@NXOCEI \EI^N) kSeE qvy uqnslmd • ozX7sd oz'u ds` ßgm ds ikf ieW7gXnd ngu dgs ng`t (àusn) vgSm vg[u&IÖfu (ab–scrnnb) ap]vy dfos@ (vorteui bu`nroc gnyped) ds ë7gsx is `ßgm ds ly, lpl^kr ILggu om bt] dmseE 7lb ieW7gXnd ngu nse bgs is vl/gd b'gnya ILggu kS P rgs ieW7gXnd ngu dgs b'gnya ds b gs ILggugse rd \ªeds\Jmgè@ vg[U (trubcetn/raubdall) dms eE • ozX7sd oz 'u ds `ßgm dg nw_7ge du luNu 7gstug ds vuqigm kgs xg %& ow.g] ved % +3 7lb bt] ld7g x7g ie W7gXnd ngu (Bu`nrocei veiun)k f ikf `ßgm kS E 'gw^7 ved % :v ^7 iFgf olmlILglr7gse nseE



ZEKN # 5>


53.

Cabsodnr tfn laiiawobk buciner lossoab rnectoab Xe 88<

Xb888

+ 8 Fn 4 + U.

66 6< Ob tfos lossoab rnectoab. Gobntoc nbnrky al redoetoab ob gn\ ob tfos rnectoab.

ε-pertocin nòttnd os 4.44 @n\. Lobd tfn nbnrky nòttnd es γ –

 Xe 88<   0 88<.::> eù  66     Xb888   0 888.::: eù `   6<     4  `  Fn  0 4.::: eù.  8  `

Sai. @ess dnlnct ∌` 0 88<.::> – 888.::: – 4.::: 0 :.::> eù U veiun 0 :.::> Û 435.> 0 4.<>> @n\ G.N ε ` 0 Xb G.NXb `ε

∴ Eisa

54.

Ebs. Sai.

`ε

4 Û 4.44 0 :.:6 @n\ 888

⇘

G.NXb 0

∴

Nbnrky al γ – Zfatab 0 4.<>> – (4.44 + :.:6) 0 :.53> @n\ 0 53> Gn\

`Xb

. G.Nε 0

B doninctrocs ern obtraducnd ob snrons ob e cepecotar al tfocgbnss D. Necf doninctroc fevn wodtf d 0 D/B & doninctroc cabstebt al ` tf doninctroc os kovnb hy G ` 0 G(5 + `/B)= WB ≧ 5:3, Erne al pietns 0 EP Gξ: E Bnt cepecotebcn os kovnb hy . Lobd veiun al ε. εDb8 5 dx

x

D

x `

0

D B

dx dx dx  5  0 0 0 `   x   C  G ` ξ : E Gξ E  Gξ : E 5 +  : 5 +  B   D 

d

5 C nq

D

Ddx  5  0 d  0  C  : Gξ : E(D + x )

∧

∧



ZEKN # 5<


5

0

C nq

C nq

5>.

0

D Gξ : E

Gξ : E Db8

b8

. Tfnrnlarn ε 0 5

Ol et ebkin ζ tfn iokft tegns èxoù` to`n ta trevni ob aptocei lohnr. Tfnb tfn èxoù` to`n os x Û 5: –6, ceicuietn x.

7lb dgs.g ζ om oz dg'g df ldm.g ozdgl'gd r^rq is xqtmus nsnse vl/gdrn in7 ysrf kgs rgs vl/gdrn in7 in7 D7g kgsxg Y b5

b5 0 5.44

b8

b8 0 5.>

ζ ?.< ` Ebs. Sai.

x0>

d

ζc

x

ζ

?.< ` 5.> sob ζc 0 5.44 sob ?:½ 5.44 84 0 sobζC 0 5.>: 8> x 84 ∴ sobζC 0 0 d 8> 8>x d0 84

∴ tatei inbktf trevni hy iokft ozdg'g }gmg r7 df x7f x7f dq y bwmf 0

∴ t 0

0

S

 C     b8 

0

8> Û ?.< 0 5:` 84

5: 3 Û 5: 6 5.>

5 Û 5: ∘; 0 > Û 5: –6 8

t 0 >:bs t 0 > Û 5: –6



ZEKN # 5;


5<.

Tfn saurcn S5 os et rnst. Tfn ahsnrvnr ebd tfn saurcn S 8 ern àvobk tawerds S 5 es sfawb ob lokurn. Tfn raal hnets ahsnrvnd hy tfn ahsnrvnr ol hatf saurcns fevn lrnqunbcy 58: Fz ebd spnnd al saubd 33: `/s ob os i zgsr S5 lILgm kSE ozs{gd rLgg rLgg iz gsr S8, izgsr S5 df rmU lp0gguqigm xlr'gfy xlr'gfy kSE ozs{gd }gmg ozsl{gr laIo^b vgaj vgajlßg D7g

kgsxfE 7lb bgsugse izgsr df vgajlßg7g¡

58: Fz rLgg

/alu df pgy pgy

5:6 g`/` 0 3: `s –5

Xnst

S5

33: `/s kSe S8

6::

3;º

<:: >3º

5: `/s

ahsnrvnr

Ebs. Sai.

6.58 ar 6.53 Spnnd al saubd

/alu df pgy 0 33: `/s

Ceicuietn hnet laIo^b

vgaj lßg l rnq rnq 5:6 g`/` 0 3: `s –5

Xnst

S5

6::

S8 3;º

<:: >3º

5: `/s

ahsnrvnr

l h 0 58:

5;.

 33: + 5: cas >3º   33: + 5:   33: ∘ 3: cas 3;º  ∘  33:  0 58:    

 33< 34   3:< ∘ 33  0 6.586 Fz  

E wnokft al 5:: B os suspnbdnd hy twa worns èdn hy stnni ebd cappnr es sfawb ob lokurn inbktf al stnni worn os 5 ` ebd cappnr worn os

3` . Lobd retoa al cfebkn ob inbktf al cappnr worn ( ∌c) ta cfebkn

ob inbktf al stnni worn ( ∌s). Kovnb _aubk's àduius = _ stnni 0 8 Û 5: 55 B/`8, _cappnr 0 0 5 Û 5:55 B/` 8. I\fy rLgg rgNcs ds bgs rgmgse om lp0gguqigm 5:: B dg Fggm y\dg7g x7g kSE I\fy ds rgm df yNcgh] yNcgh] 5 ` rLgg

rgNcs df 3` kSE rgNcs df yNcgh] ns e olmar]u (∌c) rLgg I\fy df yNcgh] nse olmar] u (∌s) dg vuqogr Ggr dflt7sE lb7g kS 7ex ozX7gILgrg 7gILgrg xq.gged= _stnni 0 8 Û 5:55 B/` 8, _cappnr 0 0 5 Û 5:55 B/` 8. <:½

3:½ Cappnr

Stnni 5`

Stnni

3`

5: gk



ZEKN # 56


Sai. Ts

Tc

<:½

3:½

5:: B

Ts

0 Tc

8

Ts 0

3 8

3 Tc

∌ c  Tc    c   _s   5   3   8 Û 5:55            0      0     08 55 ∌ s  Ts    s   _c   3   5   5Û 5:  56.

Ebs. Sai.

Eb aptocei hnbcf, ta `nesurn tfn lacei inbktf al inbs, os 5.> ` iabk ebd eb d ab tfn hnbcf èrgs ern wotf 5 c`. Baw e inbs os piecnd et ;> c` ebd pob typn ahmnct os piecnd et 4> c` èrgs ab tfn specobk 4 hnbcf. Ol ots oèkn os lar`nd et 53> c` lobd èxoù` passohin nrrar ob ceicuietoab al lacei inbktf. (5.36 & 5.3?)

u 0 (x8 – x5) 0 ;> – 4> 0 3: c` 5 5 5 ∌u 0 ∌x 8 + ∌x5 0 + 0 c` 4 4 8 v 0 (x3 – x8) 0 53> – ;> 0 <: c` 5 5 5 ∌v 0 ∌x 3 + ∌x 8 0 + 0 c` 4 4 8 5 5 5

∴ ∘ v 5

+

u 5

0

0

l 5

<: 3: l ∴ l 0 8: c` ∘dv ∘du + 8 Eisa, v8 u

0

∘dl l 8

5 5  dv du   5 0 l  8 + 8  0 8:  8 + 8  l 3:  8 u   <: v dl  5 5  >: Û 5:: 0 5:  +  0 0 5.36 & 5.3? (hatf) ∴ l  3< ?  3<

⇘

dl



ZEKN # 5?

JEE Advanced 2019 Paper-1 Physics

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