for JEE (Advanced)-2020...JEE (ADVANCED)-2 020 (Paper-1) 5 8.,d izdk'k cYc ds fiQykesUV dk i`"Bh;...

1

Questions & Answersforforforforfor

JEE (Advanced)-2020

Time : 3 hrs. Max. Marks: 198

Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005

Ph.: 011-47623456 Fax : 011-47623472

PAPER - 1

DATE : 27/09/2020

PART - I : PHYSICS

[k.M[k.M[k.M[k.M[k.M - 1 (vf/dre vadvf/dre vadvf/dre vadvf/dre vadvf/dre vad : 18)

bl [k.M esa N% (06) ç'u gSaA

çR;sd ç'u ds pkj fodYi gSaA bu pkj fodYiksa esa ls dsoy ,d lgh mÙkj gSA

çR;sd ç'u ds fy, lgh mÙkj ds laxr fodYi dk p;u dhft;sA

çR;sd ç'u ds mÙkj dk ewY;kadu uhps fn, x, vadu ;kstuk ds vuqlkj fd;k tk,xkA

iw.kZ vad : +3 ;fn dsoy lgh fodYi pquk x;k gS;

'kwU; vad : 0 ;fn dksbZ Hkh fodYi ugha pquk x;k gSa (vFkkZr~ ç'u vuqÙkfjr gSa);

½.kkRed vad : –1 vU; lHkh fLFkfr;ksa esaA

1. R f=kT;k dh ,d iqQVckWy dks {kSfrt :i ls j[ks gq, ,d r[rs ij fufeZr r(r < R) f=kT;k ds ,d fNæ ij j[kk x;k gSA r[rsds ,d fljs dks vc bl izdkj Åij mBk;k tkrk gS fd ;g uhps fp=k esa n'kkZ, vuqlkj {kSfrt ls dks.k fufeZr djrs gq, eqM+tkrk gSA iqQVcky ds r[rs ij uhps dh vksj fiQlyuk izkjEHk ugha djus ds fy, dk vfèkdre eku fdls larq"V djrk gS(js[kkfp=k lkadsfrd gS)

2r

r[rk R

JEE (ADVANCED)-2020 (Paper-1)

2

(A)r

sinR

(B)r

tanR

(C)r

sin2R

(D)r

cos2R

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

2. ,Y;qfefu;e (,d vpqEcdh; inkFkZ) ls fufeZr ,d gYdh pdrh dks {kSfrt :i ls j[kk x;k gS rFkk ;g fp=kkuqlkj Lo;a ds v{kds lkis{k ?kw.kZu djus ds fy, Lora=k gSA ,d izcy pqEcd dks blds v{k ls nwj pdrh ds Åij fdlh fcUnq ij ÅèokZèkj :ils j[kk tkrk gSA pqEcd dks pdrh ds v{k ds lkis{k ifjØe.k djkus ij] pdrh (js[kkfp=k lkadsfrd gS)

S

N

(A) pqEcd dh xfr dh foijhr fn'kk esa ?kw.kZu djsxh

(B) pqEcd dh xfr dh leku fn'kk esa ?kw.kZu djsxh

(C) ?kw.kZu ugha djsxh rFkk bldk rkieku vifjofrZr jgsxk

(D) ?kw.kZu ugha djsxh ysfdu bldk rkieku èkhjs&èkhjs c<+sxk

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

3. 20 cm O;kl okys ,d NksVs jksyj dh èkqjh dk O;kl 10 cm gS (uhps ck;ha vksj fp=k ns[ksa)A ;g {kSfrt iQ'kZ ij gS rFkk ,dehVj iSekus dks bldh èkqjh ij bl izdkj LFkkfir fd;k tkrk gS fd iSekus dk ,d fljk èkqjh ds 'kh"kZ ij gksrk gS (nk;ha vksjfp=k ns[ksa)A vc iSekus dks èkhjs ls èkqjh ij bl izdkj èkdsyk tkrk gS rkfd og èkqjh ij fcuk fiQlys xfr djrk gS] rFkk jksyjfcuk fiQlys yq<+duk izkjEHk djrk gSA jksyj }kjk 50 cm nwjh rd xfr djus ds ckn] iSekus dh fLFkfr fdl izdkj fn[kk;hnsxh\ ( js[kkfp=k lkadsfrd gS)

(A)

x = 0 x = 50 cm

(B)

x = 0 x = 75 cm

(C)

x = 0 x = 25 cm

(D)

x = 0 x = 100 cm



3

4. R f=kT;k rFkk N ?ksjksa okyh ,d oÙkh; dq.Myh dk izfrjksèk ux.; gSA js[kkfp=k esa n'kkZ, vuqlkj blds nks fljs nks rkjksa lsla;ksftr gSa rFkk bls mu rkjksa }kjk yVdk;k x;k gS vkSj bldk ry ÅèokZèkj gSA rkjksa dks fLop ls xqtkjrs gq, Q vkos'k okys,d laèkkfj=k ls la;ksftr fd;k x;k gSA dq.Myh Lo;a ds ry ds lekarj ,dleku {kSfrt pqEcdh; {ks=k B

0 esa gSA tc fLop dks

can fd;k tkrk gS] rc laèkkfj=k vR;fèkd de le; esa dq.Myh ls fujkosf'kr gks tkrk gSA le; ds lkFk laèkkfj=k iw.kZr% fujkosf'krgks tkrk gS] dq.Myh }kjk izkIr dks.kh; laosx dk ifjek.k gksxk (ekukfd fujkos'ku le; bruk de gS fd dq.Myh bl le; dsnkSjku eqf'dy ls ?kw.kZu djrh gS)

B0

(A)2

0NQB R

2

(B) NQB

0R2

(C) 2NQB0R2 (D) 4NQB

0R2


5. izdk'k dk ,d lekarj iqat uhps fp=k esa n'kkZ, x;s vuqizLFk&dkV okys ikjn'khZ dk¡p ds ,d VqdM+s ls Vdjkrk gSA fuxZrrjaxkxz dh lgh vkÑfÙk gksxh (js[kkfp=k lkadsfrd gS)

ok;q

çdk’k dk¡p

ok;q

(A) (B)

(C) (D)

mÙkjmÙkjmÙkjmÙkjmÙkj (A)


4

6. ,dleku vuqizLFk dkV {ks=kiQy okyh ,d [kqys fljs okyh U-ufydk esa ty (?kuRo 103kg m–3) fufgr gSA izkjEHk esa izR;sdHkqtk esa ty Lrj vkèkkj ls 0.29 m ij gksrk gSA ?kuRo 800 kg m–3 okys dsjkslhu rsy (,d ty&vfeJ.kh; nzo) dksck;ha Hkqtk esa rc rd feyk;k tkrk gS tc rd dh bldh yEckbZ 0.1 m u gks tk;] tSlk fd uhps lkadsfrd js[kkfp=k esa

n'kkZ;k x;k gSA nksuksa Hkqtkvksa esa nzo dh Å¡pkbZ;ksa dk vuqikr 1

2

h

h

gS

h2

0.1 m

h1

(A)15

14(B)

35

33

(C)7

6(D)

5

4




çR;sd ç'u ds pkj fodYi gSaA bu pkj fodYiksa eas ls ,d ;k ,d ls vf/d lgh mÙkj gS@gSaA

çR;sd ç'u ds fy, (lHkh) lgh mÙkjksa ls lacaf/r fodYi@fodYiksa dk p;u dhft;sA

çR;sd ç'u ds mÙkj dk ewY;kadu uhps nh xbZ vadu ;kstuk ds vuqlkj fd;k tk,xk:

iw.kZ vad : +4 ;fn dsoy lHkh lgh fodYi@fodYiksa dk p;u fd;k x;k gS_

vakf'kd vad : +3 ;fn lHkh pkj fodYi lgh gSa ijUrq dsoy rhu fodYiksa dk p;u fd;k x;k gS_

vakf'kd vad : +2 ;fn rhu ;k vf/d fodYi lgh gSa ijUrq dsoy nks fodYiksa dk p;u fd;k x;k gS rFkk nksuksa lgh

gks_

vkaf'kd vad : +1 ;fn nks ;k vf/d fodYi lgh gSa ijUrq dsoy ,d fodYi dk p;u fd;k x;k gS rFkk og lgh

fodYi gks_

'kwU; vad : 0 ;fn fdlh Hkh fodYi dk p;u ugha fd;k x;k (vFkkZr~ ç'u dk mÙkj ugha fn;k x;k gks);


7. m nzO;eku dk ,d d.k fLFkfrt ÅtkZ V(r) = Fr ds lkFk oÙkh; d{kkvksa esa xfr djrk gS] tgk¡ F èkukRed fu;rkad gS rFkk rewy&fcanq ls bldh nwjh gSA bldh ÅtkZ dh x.kuk cksj ekWMy ds mi;ksx }kjk dh tkrh gSA ;fn d.k dh d{kk dh f=kT;k dks R}kjk fu:fir fd;k tkrk gS rFkk bldh pky rFkk ÅtkZ dks Øe'k% v rFkk E }kjk iznf'kZr fd;k tkrk gS] rc noha d{kk ds fy,(;gk¡ h Iykad fu;rkad gS)

(A) 1/3 2/3R n v nrFkk (B) 2/3 1/3

R n v nrFkk

(C)

1/32 2 2

2

3 n h FE

2 4 m

(D)

1/32 2 2

2

n h FE 2

4 m

mÙkjmÙkjmÙkjmÙkjmÙkj (B, C)


5

8. ,d izdk'k cYc ds fiQykesUV dk i"Bh; {ks=kiQy 64 mm2 gSA fiQykesUV dks Ñf".kdk ds :i esa ekuk tk ldrk gS] nwjh lsns[kus ij ;g rkieku 2500 K ij ,d fcanq lzksr ds leku fofdj.k mRlftZr dj jgk gSA jkf=k esa izdk'k cYc dks 100 m dhnwjh ls izsf{kr fd;k tkrk gSA ekuk izs{kd ds vk¡[kksa dh iqryh 3 mm f=kT;k ds lkFk oÙkkdkj gSA rc

(LVhiQu cksYVteku fu;rkad = 5.67 × 10–8 Wm–2K–4, ohu dk foLFkkiu fu;rkad = 2.90 × 10–3 m-K, Iykad fu;rkad =

6.63 × 10–34 Js, fuokZr esa izdk'k dh pky = 3.00 × 108 ms–1 yhft,)

(A) fiQykesUV }kjk fofdfjr 'kfDr dh ijkl 642 W ls 645 W gS

(B) izs{kd ds ,d us=k ds vanj izos'k djus okyh fofdfjr 'kfDr dh ijkl 3.15 × 10–8 W ls 3.25 × 10–8 W gS

(C) izdk'k dh vfèkdre rhozrk ds laxr rjaxnSè;Z 1160 nm gS

(D) mRlftZr fofdj.k dh vkSlr rjaxnSè;Z dks 1740 nm ysrs gq,] izs{kd ds ,d us=k ds vanj izfr lsd.M izos'k djus okysiQksVkuksa dh dqy la[;k 2.75 × 1011 ls 2.85 × 1011 rd dh ijkl esa gS

mÙkjmÙkjmÙkjmÙkjmÙkj (B, C, D)

9. dHkh&dHkh ek=kdksa dh ,d i¼fr dk fuekZ.k djuk lqfoèkktud gksrk gS rkfd lHkh jkf'k;ksa dks dsoy ,d HkkSfrd jkf'k dsinksa esa O;Dr fd;k tk ldsA bl izdkj dh i¼fr esa] fofHkUu jkf'k;ksa dh foekvksa dks jkf'k X ds inksa esa fuEukuqlkj fn;k x;k gS%[fLFkfr] = [X]; [pky] = [X]; [Roj.k] =[Xp]; [js[kh; laosx] = [Xq]; [cy] = [Xr]A rc

(A) + p = 2(B) p + q – r = (C) p – q + r = (D) p + q + r =

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B)

10. ,dleku fo|qr {ks=k] �

1ˆE 400 3y NC dks ,d {ks=k esa vkjksfir fd;k x;k gSA q èkukRed vkos'k xzg.k fd;s gq, m

nzO;eku ds ,d vkosf'kr d.k dks bl {ks=k esa 62 10 10 ms–1 dh izkjfEHkd pky ls iz{ksfir fd;k tkrk gSA bl d.k dk

mn~ns'; y{; T ls Vdjkus dk gS] tks fd {ks=k ds vanj blds izos'k fcUnq ls 5 m dh nwjh ij gS tSlk fd fp=k esa lkadsfrd :i

ls n'kkZ;k x;k gSA 10q10

m Ckg–1 yhft,A rc

T

u

5m

�

E

(A) d.k T ls Vdjk;sxk] ;fn bls {kSfrt ls 45º dks.k ij iz{ksfir fd;k tkrk gS

(B) d.k T ls Vdjk;sxk ;fn bls {kSfrt ls ;k rks 30º ;k 60º dks.k ij iz{ksfir fd;k tkrk gS

(C) T ls Vdjkus esa d.k }kjk fy;k x;k le; 5

6 s rFkk

5

2 s gks ldrk gS

(D) T ls Vdjkus esa d.k }kjk fy;k x;k le; 5

3 s gS

mÙkjmÙkjmÙkjmÙkjmÙkj (B, C)


6

11. fp=k esa ,d v¼ZoÙkh; èkkfRod ifV~Vdk n'kkZbZ xbZ gS ftldh eksVkbZ t rFkk izfrjksèkdrk gSA bldh vkarfjd f=kT;k R1 o cká

f=kT;k R2 gSA ;fn blds nksuksa fljksa ds eè; oksYVrk V

0 vkjksfir dh tkrh gS rc blesa èkkjk I izokfgr gksrh gSA lkFk gh] ;g

izsf{kr fd;k tkrk gS fd xfreku bysDVªkWuksa ds 'kq¼ v.kqxfrd izHkkoksa ds dkj.k bldh vkarfjd o cká lrgksa ds eè; vuqizLFkoksYVrk V mRiUu gksrh gS (èkkjk ds dkj.k pqEcdh; {ks=k dh fdlh Hkh Hkwfedk dks ux.; ekusa)A rc (js[kkfp=k lkadsfrd gS)

V0

II

R1

R2

V

(A)

0 2

1

V t RI ln

R

(B) cká lrg] vkUrfjd lrg dh rqyuk esa mPp oksYVrk ij gS

(C) cká lrg] vkUrfjd lrg dh rqyuk esa de oksYVrk ij gS

(D) 2V I

mÙkjmÙkjmÙkjmÙkjmÙkj (A, C, D)

12. lkadsfrd fp=k esa n'kkZ, vuqlkj] nks ik=kksa esa iksVsf'k;e ijesaxusV (KMnO4) ds ty foy;u (rkieku T ij) fufgr gS] ftuesa izfr

bdkbZ vk;ru v.kqvksa dh fHkUu&fHkUu lkanzrk n1 o n

2 (n

1 > n

2) gS tcfd n = (n

1 – n

2) << n

1 gSA tc bUgsa de yEckbZ l o

vuqizLFk dkV {ks=kiQy S dh ufydk }kjk la;ksftr fd;k tkrk gS] KMnO4 ufydk ls gksrs gq, ck¡;s ls nk¡;s ik=k esa folfjr gksuk

izkjEHk djrk gSA ekuk v.kqvksa dk laxzg ruq vkn'kZ xSlksa dh Hkk¡fr O;ogkj djrk gS rFkk nksuksa ik=kksa esa buds vkaf'kd nkc esavarj ds dkj.k folj.k gksrk gSA v.kqvksa dh pky v dks izR;sd v.kq ij ';ku cy –v }kjk lhfer fd;k tkrk gS] tgk¡ ,dfu;rkad gSA (n)2 dksVh ds lHkh inksa dks ux.; ekurs gq,] fuEufyf[kr esa ls dkSulk@dkSuls lgh gS@gSa\ (k

B cksYV~teku

fu;rkad gS)

n1

n2S

l

(A) ufydk ds ikj xfr djus okys v.kqvksa ds dkj.k cy nkBTS gS

(B) cy larqyu dk vfHkizk; gS n1vl = nk

BT


7

(C) izfr lsd.M ufydk ds ikj tkus okys v.kqvksa dh dqy la[;k

Bk Tn

Sl

gS

(D) ufydk ls LFkkukUrfjr gksus okys v.kqvksa dh nj le; ds lkFk ifjofrZr ugha gksrh gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B, C)


bl [k.M esa N% (06) ç'u gSaA çR;sd ç'u dk mÙkj ,d vkafdd eku gSA

çR;sd ç'u ds fy,] mÙkj ds lgh vkafdd eku dks ekÅl rFkk vkWu&LØhu opqZvy U;weSfjd dh–iSM ds mi;ksx ls mÙkj çfo"V

djus ds LFkku ij gh çfo"V dhft;sA ;fn vakfdd eku esa nks ls vf/d n'keyo LFkku gks] rks çkIr eku dk nks n'keyo LFkku rd

lfUudVu djsaA

çR;sd ç'u ds mÙkj dk ewY;kadu uhps nh xbZ vadu ;kstuk ds vuqlkj fd;k tk;sxk:

iw.kZ vad : +4 ;fn dsoy lgh vakfdd eku dks çfo"V fd;k x;k gS_

'kwU; vad : 0 vU; lHkh fLFkfr;ksa esaA

13. ,d leku ehVj Ldsy dks viuh foLrkfjr rtZuh vaxqfy;ksa ij {kSfrt :i ls bl izdkj j[ks fd ck;ha vaxqyh 0.00 cm ij gSrFkk nk;ha vaxqyh 90.00 cm ij gSA tc vki nksuksa vaxqfy;ksa dks èkhjs&èkhjs dsUnz dh vksj xfr djkus dk iz;kl djrs gSa] rcizkjEHk esa dsoy ck;ha vaxqyh iSekus ds lkis{k fiQlyrh gS rFkk nk;ha vaxqyh ugha fiQlyrh gSA dqN nwjh dh ckn] ck;ha vaxqyh :dtkrh gS rc nk;ha vaxqyh fiQlyuk izkjEHk djrh gSA rc nk;ha vaxqyh iSekus ds dsUnz (50.00 cm) ls nwjh x

R ij #drh gS rFkk

ck;ha vaxqyh iqu% fiQlyuk izkjEHk djrh gSA ,slk nksuksa vaxqfy;ksa ij ?k"kZ.k cyksa esa varj ds dkj.k gksrk gSA ;fn vaxqfy;ksa rFkkiSekus ds eè; LFkSfrd o xfrd ?k"kZ.k xq.kkad Øe'k% 0.40 rFkk 0.32 gS] rc x

R dk eku (cm esa) _______gSA

mÙkjmÙkjmÙkjmÙkjmÙkj (25.60)

14. tc ty dks ,d Xykl esa lkoèkkuhiwoZd Hkjk tkrk gS] rc ge ty ds i"B ruko ds dkj.k bls Xykl dh fje ds Åij h

Å¡pkbZ rd Hkj ldrs gSaA ty ds cguk izkjEHk djus ls Bhd igys h dh x.kuk djus ds fy,] fje ds Åij ty dh vkÑfÙklkadsfrd fp=k esa n'kkZ, vuqlkj v¼ZoÙkh; fdukjksa okyh h eksVkbZ dh pdrh ds leku gksrh gSA tc bl pdrh ds ry ij tydk nkc vfèkd gks tkrk gS rc blls ;g uqdlku gksrk gS fd i"Bh; ruko ds dkj.k fje ds fudV ty lrg VwV tkrh gSrFkk ty ;gk¡ ls cgus yxrk gSA ;fn ty dk ?kuRo] bldk i"Bh; ruko rFkk xq#Roh; Roj.k Øe'k% 103 kg m–3, 0.07

Nm–1 rFkk 10 ms–2 gS] rc h dk eku (mm esa)_________ gSA

h



8

15. ux.; vrkfur yEckbZ rFkk fLizax fu;rkad k dh fLizax dk ,d fljk ewy fcUnq (0, 0) ij nf<+r gSA èkukRed vkos'k q xzg.kfd;s gq, rFkk m nzO;eku ds ,d fcanq d.k dks blds nwljs fljs ij la;ksftr fd;k tkrk gSA lEiw.kZ fudk; dks ,d fpduh

{kSfrt lrg ij j[kk x;k gSA tc vkos'k q dh vksj bafxr ,d fcanq f}èkzqo ��

p ewyfcUnq ij fLFkj gS] fLiazx l yEckbZ rd rkfur

gks tkrh gS rFkk ,d uohu lkE; fLFkfr izkIr djrh gS (uhps fp=k ns[ksa)A ;fn vc fcanq nzO;eku dks bldh lkE; fLFkfr ls gYdk

lk l << l }kjk foLFkkfir djds NksM+k tkrk gS] rc ;g ik;k tkrk gS fd ;g vkofÙk 1 k

mδ ij nksyu djrk gSA dk eku

________gSA

(0, 0)

p qx

l

y


16. ekuk ,d eksy ghfy;e xSl ,d ik=k esa izkjfEHkd nkc P1 o vk;ru V

1 ij ifjc¼ gSA ;g lerkih; :i ls vk;ru 4V

1 rd

izlkfjr gksrh gSA blds ckn ;g #¼ks"e :i ls izlkfjr gksrh gS rFkk bldk vk;ru 32V1 gks tkrk gSA lerkih; rFkk #¼ks"e

izØeksa ds nkSjku xSl }kjk fd;k x;k dk;Z Wlerkih; rFkk W#¼ks"e gSA ;fn vuqikr W

W

lerkih;

#¼k"s e = f ln2 gS] rc f dk eku ________gSA


17. ,d fLFkj Lofj=k f}Hkqt ,d ikbZi esa ok;q LraHk ds lkFk vuqukn esa gSA ;fn Lofj=k f}Hkqt dks ikbZi ds [kqys fljs ds lkeus rFkkblds lekUrj 2 ms–1 dh pky ls xfr djk;h tkrh gS] rc xfreku Lofj=k f}Hkqt ds lkFk vuqukn gksus ds fy, ikbZi dhyEckbZ dks ifjofrZr fd;k tkuk pkfg,A ;fn ok;q esa èofu dh pky 320 ms–1 gS] rc ikbZi dh yEckbZ esa vko';d izfr'kr

ifjorZu dk U;wure eku __________gSA


18. R f=kT;k dh oÙkh; pdrh i"Bh; vkos'k ?kuRo (r) = 0

r1–

R

σ , xzg.k fd;s gq, gS] tgk¡ 0 ,d fu;rkad gS rFkk r pdrh

ds dsUnz ls nwjh gSA ,d cM+h xksyh; lrg tks vkosf'kr pdrh dks iw.kZr% ifjc¼ djrh gS] ls xqtjus okyk fo|qr ÝyDl 0 gSA

R

4 f=kT;k okyh rFkk pdrh ds lkFk ladsfUnzr vU; xksyh; lrg ls xqtjus okyk fo|qr ÝyDl gSA rc vuqikr

0 dk eku

________gSA



9

PART-II : CHEMISTRY



çR;sd ç'u ds pkj fodYi gSaA bu pkj fodYiksa esa ls dsoy ,d lgh mÙkj gSA

çR;sd ç'u ds fy, lgh mÙkj ds laxr fodYi dk p;u dhft;sA

çR;sd ç'u ds mÙkj dk ewY;kadu uhps fn, x, vadu ;kstuk ds vuqlkj fd;k tk,xkA

iw.kZ vad : +3 ;fn dsoy lgh fodYi pquk x;k gS;

'kwU; vad : 0 ;fn dksbZ Hkh fodYi ugha pquk x;k gSa (vFkkZr~ ç'u vuqÙkfjr gSa);


1. ;fn ,d xSl ds vk.kfod pkyksa dk forj.k uhps n'kkZ;s fp=k ds vuqlkj gS]rks izkf;drk pky] vkSlr rFkk oxZ ekè; ewy pky

Øe'k% gS

(A) 1 : 1 : 1

(B) 1 : 1 : 1.224

(C) 1 : 1.128 : 1.224

(D) 1 : 1.128 : 1

mÙkj (B)

2. fuEu esa ls fdlds tyvi?kVu ij O2 eqDr gksrh gS\

(A) Pb3O

4

(B) KO2

(C) Na2O

2

(D) Li2O

2

mÙkj (B)


10

3. ,d jaxghu tyh; foy;u esa nks /krqvksa X rFkk Y ds ukbVªsV gSaA tc bls NaCl ds tyh; foy;u esa feyk;k tkrk gS] rks

,d liQsn vo{ksi izkIr gksrk gS] ;g vo{ksi xeZ ty esa vkaf'kd :i ls ?kqydj vo'ks"k P rFkk foy;u Q nsrk gSA vo'ks"k P

tyh; NH3 rFkk lksfM;e Fkk;kslkYisQQV ds vkf/D; esa Hkh foys; gSA Q dk xeZ foy;u KI ds lkFk ihyk vo{ksi nsrk gSA X

rFkk Y Øe'k% gS

(A) Ag rFkk Pb (B) Ag rFkk Cd

(C) Cd rFkk Pb (D) Cd rFkk Zn

mÙkj (A)

4. U;weSu iz{ksi.k P, Q, R rFkk S uhps n'kkZ;s x;s gSa:

CH3

CH3

C H2 5

CH3

H C3

HO

P

CH3

H

C H2 5

CH3

H

H

Q

H C3

OH

CH3

H

CH3

C H2 5

HO

C2 5H

R

CH3

CH(CH3 2)

H

OHH

C2 5H

S

fuEu esa ls dkSu ls fodYi leku v.kqvksa dks fu:fir djrs gSa\

(A) P rFkk Q (B) Q rFkk S

(C) Q rFkk R (D) R rFkk S

mÙkj (C)

5. fuEu esa ls fdl lajpuk dk IUPAC uke

3-,Fkkbfuy-2-gkbMªkWDlh-4-esfFkygsDl-3-bZu-5-vkbukWbd vEy gS\

(A)

OH

CO H2 (B)

OH

HO C2


11

(C)

OH

CO H2 (D)

CO H2

OH

mÙkj (D)

6. D-,fjFkzkst dk fiQ'kj iz{ksi.k uhps n'kkZ;k x;k gSA

CH OH2

CHO

OHH

OHH

dkWyedkWyedkWyedkWyedkWye-I esa D-,fjFkzkst rFkk blds leko;fo;ksa dks P, Q, R, rFkk S ds :i esa n'kkZ;k x;k gSA dkWyedkWyedkWyedkWyedkWye-II ls D-,fjFkzkst ds lkFk

P, Q, R, rFkk S ds lgh lEca/ dk p;u dhft,A

dkWyedkWyedkWyedkWyedkWye-I dkWyedkWyedkWyedkWyedkWye-II

P.OHOH

HHOOHC

H 1. vizfrfcEc f=kfoe leko;o

Q.

OH

OH

H

HHO

OHC

2. le:i

R.

OHH

OHOH

H

OHC

3. izfrfcEc leko;o

S.

OH

H

OH

HHO

OHC

(A) P 2, Q 3, R 2, S 2

(B) P 3, Q 1, R 1, S 2

(C) P 2, Q 1, R 1, S 3

(D) P 2, Q 3, R 3, S 1

mÙkj (C)


12



çR;sd ç'u ds pkj fodYi gSaA bu pkj fodYiksa eas ls ,d ;k ,d ls vf/d lgh mÙkj gS@gSaA

çR;sd ç'u ds fy, (lHkh) lgh mÙkjksa ls lacaf/r fodYi@fodYiksa dk p;u dhft;sA

çR;sd ç'u ds mÙkj dk ewY;kadu uhps nh xbZ vadu ;kstuk ds vuqlkj fd;k tk,xk:

iw.kZ vad : +4 ;fn dsoy lHkh lgh fodYi@fodYiksa dk p;u fd;k x;k gS_

vakf'kd vad : +3 ;fn lHkh pkj fodYi lgh gSa ijUrq dsoy rhu fodYiksa dk p;u fd;k x;k gS_

vakf'kd vad : +2 ;fn rhu ;k vf/d fodYi lgh gSa ijUrq dsoy nks fodYiksa dk p;u fd;k x;k gS rFkk nksuksa lgh

gks_

vkaf'kd vad : +1 ;fn nks ;k vf/d fodYi lgh gSa ijUrq dsoy ,d fodYi dk p;u fd;k x;k gS rFkk og lgh

fodYi gks_

'kwU; vad : 0 ;fn fdlh Hkh fodYi dk p;u ugha fd;k x;k (vFkkZr~ ç'u dk mÙkj ugha fn;k x;k gks);


7. Å"ekxfrdh eas] fd;k x;k P – V dk;Z fuEu izdkj fn;k tkrk gS

extw dVP .

,d fo'ks"k izØe ls xqtjus okys fudk; ds fy, fd;k x;k dk;Z fuEu gS

2

RT aw dV .

V b V

mijksDr lehdj.k fdl ij ykxw gksrk gS\

(A) og fudk; tks ok.Mj okYl voLFkk lehdj.k dks larq"V djrk gS\

(B) og izØe tks mRØe.kh; rFkk lerkih; gS

(C) og izØe tks mRØe.kh; rFkk :¼ks"e gS

(D) og izØe tks fu;r nkc ij vuqRØe.kh; gS

mÙkj (A,B,C)

8. ;kSfxd I-V ds lanHkZ esa, lgh dFku@dFkuksa dk p;u dhft,A

H

I

H

II

H

IV

H H

V

H CH3

III


13

(A) ;kSfxd I dh vEyrk la;qXeh {kkj esa foLFkkuhdj.k ds dkj.k gS

(B) ;kSfxd IV dk la;qXeh {kkj ,sjkseSfVd gS

(C) ;kSfxd II esa -NO2 izfrLFkkih gksus ij ;g vf/d vEyh; gks tkrk gS

(D) ;kSfxdksa dh vEyrk dk Øe I > IV > V > II > III gS

mÙkj (A,B,C)

9. uhps n'kkZ;s x;s vfHkfØ;k vuqØe esa Q, R, rFkk S eq[; mRikn gSaA

H C3

H C3

CH3

H C3 CH

3

O

O

O

AlCl3

Q

(i) Zn-Hg/HCl

(ii) H PO3 4

R

(i) CH MgBr

(ii) H O

3

3

+

(iii) H SO /2 4

S

P

lgh lajpuk okyk gS

(A) S ;

H C3

H C3

CH3 H C

3 CH3

CH3

gS

(B) Q ;

H C3

H C3

CH3 H C

3 CH3

OHO C2

gS

(C) R;

H C3

H C3

CH3 H C

3 CH3

O

gS

(D) S;

H C3

H C3

CH3 H C

3 CH3

H C3 gS

mÙkj (B, D)


14

10. fuEu esa ls lgh dFku@dFkuksa dk p;u dhft,k

(A) [FeCl4]– dh prq"iQydh; T;kfefr gksrh gS

(B) [Co(en)(NH3)2Cl

2]+ ds 2 T;kferh; leko;o gksrs gSa

(C) [Co(en)(NH3)2Cl

2]+ dh vis{kk [FeCl

4]– dk pØ.k ek=k pqEcdh; vk?kw.kZ vf/d gksrk gS

(D) [Co(en)(NH3)2Cl

2]+ esa dksckYV vk;u dk ladj.k sp3d2 gS

mÙkj (A,C)

11. gkbiksDyksjkbV] DyksjsV rFkk ijDyksjsV vk;uksa ds lanHkZ esa lgh dFku@dFkuksa dk p;u dhft,

(A) gkbiksDyksjkbV vk;u izcyre la;qXeh {kkj gS

(B) dsoy DyksjsV vk;u dh vk.kfod vkÑfr Cl ds ,dkadh bysDVªkWu ;qXe }kjk izHkkfor gksrh gS

(C) gkbiksDyksjkbV rFkk DyksjsV vk;u vlekuqikru ij leku vk;uksa okys leqPp; nsrs gSa

(D) gkbiksDyksjkbV vk;u vkWDlhÑr gksdj lYiQkbV vk;u nsrk gS

mÙkj (A,B,D)

12. /uk;u M rFkk Í.kk;u X ;qDr ;kSfxd ds ?kuh; ,dd dksf"Bdk dh lajpuk uhps n'kkZ;h x;h gSA Í.kk;u dh rqyuk esa

èkuk;u dh vk;fud f=kT;k de gSA lgh dFku@dFkuksa dk p;u dhft,A

M X

(A) ;kSfxd dk ewykuqikrh lw=k MX gS

(B) /uk;u M rFkk Í.kk;u X dh leUo; T;kfefr fHkUUk&fHkUUk gS

(C) M-X ca/ yEckbZ o ?kuh; ,dd dksf"Bdk dh dksj yEckbZ dk vuqikr 0.866 gS

(D) /uk;u M o Í.kk;u X dh vk;fud f=kT;k dk vuqikr 0.414 gS

mÙkj (A,C)


15


bl [k.M esa N% (06) ç'u gSaA çR;sd ç'u dk mÙkj ,d vkafdd eku gSA

çR;sd ç'u ds fy,] mÙkj ds lgh vkafdd eku dks ekÅl rFkk vkWu&LØhu opqZvy U;weSfjd dh–iSM ds mi;ksx ls mÙkj çfo"V

djus ds LFkku ij gh çfo"V dhft;sA ;fn vakfdd eku esa nks ls vf/d n'keyo LFkku gks] rks çkIr eku dk nks n'keyo LFkku rd

lfUudVu djsaA

çR;sd ç'u ds mÙkj dk ewY;kadu uhps nh xbZ vadu ;kstuk ds vuqlkj fd;k tk;sxk:

iw.kZ vad : +4 ;fn dsoy lgh vakfdd eku dks çfo"V fd;k x;k gS_

'kwU; vad : 0 vU; lHkh fLFkfr;ksa esaA

13. ,d 'kaDokdkj ÝykLd esa 5 .00 mL 0.10 M vkWDlsfyd vEy foy;u fy;k x;k gS bldk fiQukWYÝFksyhu lwpd dk mi;ksx

djds C;wjsV ls NaOH ds lkFk vuqekiu fd;k tkrk gSA ik¡p iz;ksxksa ds fy, LFkk;h gYdk xqykch jax izdV gksus ds fy,

vko';d NaOH dk vk;ru lkj.kh esa fn;k x;k gSA NaOH foy;u dh eksyjrk esa lkUnzrk D;k gS\

NaOH (mL)

1 12.5

2 10.5

3 9.0

4 9.0

5 9.0

iz; kxs la[;k dk vk;ru

mÙkj (0.10)

14. 1000 K ij vfHkfØ;k A � B ij fopkj dhft,A le; t ij fudk; ds rki esa 2000 K rd of¼ dh x;h rFkk fudk;

dks lkE; izkIr gksus fn;k tkrk gSA lEiw.kZ iz;ksx ds nkSjku A dk vkaf'kd nkc 1 ckj ij vuqjf{kr j[kk x;kA uhps B ds

vkaf'kd nkc o le; ds eè; xzkiQ n'kkZ;k x;k gSA 1000 K o 2000 K ij vfHkfØ;k dh ekud fxCl ÅtkZ dk vuqikr D;k

gS\

115

100

50

10

t

mÙkj (0.25)


16

15. ekud ifjfLFkfr;ksa 1 ckj rFkk 298 K eas dk;Z djus okys 70% n{krk okys gkbMªkstu-vkWDlhtu bZa/u lsy ij fopkj dhft,A

bldh lsy vfHkfØ;k fuEu gS

2 2 2

1H (g) O (g) H O(l)

2

1.0 × 10–3 eksy H2(g) ds iz;qDr gksus ij lsy ls izkIr fd;s x;s dk;Z dk mi;ksx ,d rkih; :i ls dqpkyd ik=k esa 1.00

eksy ,dyijek.kqd vkn'kZ xSl dks laihfMr djus esa fd;k tkrk gSA vkn'kZ xSl ds rki esa ifjorZu (K esa) D;k gS\

nksuksa v/Z lsyksa ds fy, ekud vip;u foHko uhps fn;s x;s gSaA

o

2 2O (g) 4H (aq) 4e 2H O(l), E 1.23 V,

o

22H (aq) 2e H (g), E 0.00 V.

F = 96500 C mol–1, R = 8.314 J mol–1 K–1 dk mi;ksx dhft,A

mÙkj (13.32)

16. ,syqfefu;e o lYÝ;wfjd vEy dh vfHkfØ;k ij ,syqfefu;e lYisQV rFkk gkbMªkstu izkIr gksrs gSaA 300 K rFkk 1.0 atm nkc ij

izkIr gkbMªkstu xSl dk vk;ru (L esa) D;k gksxk tcfd vfHkfØ;k esa 5.4 g ,syqfefu;e rFkk 50.0 mL 5.0 M lYÝ;wfjd vEy

la;ksx djrs gSa\ (,syqfefu;e dk eksyj nzO;eku = 27.0 g mol–1, R = 0.082 atm L mol–1 K–1)

mÙkj (6.15)

17. 238

92U ds jsfM;ks,fDVo {k; esa ,YiQk d.k o chVk d.kksa ds mRltZu ij 206

82Pb izkIr gksrk gSA ,d pV~Vku esa izkjEHk esa

68 × 10–6 g 23892U gSA ;fn 238

92U dk 206

82Pb esa jsfM;ks,fDVo {k; ds nkSjku mRlftZr ,YiQk d.kksa dh la[;k rhu v/Z vk;q

esa Z × 1018 gks] rks Z dk eku D;k gS\

mÙkj (1.2)

18. uhps nh x;h vfHkfØ;k eas] ;kSfxd P ls ,d vk;fud eè;orhZ ds }kjk ;kSfxd Q izkIr gksrk gSA

P

C H6 5

C H6 5

CO CH2 3

C H6 5

Q dh vlarIrrk dh dksfV D;k gS\

mÙkj (24.00)


17

PART-III : MATHEMATICS

[ k.M - 1 (vf/ dre vad : 18)

bl [ k.M esa N% (06) ç' u gSaA

çR;sd ç' u ds pkj fodYi gSaA bu pkj fodYi ksa esa l s dsoy ,d l gh mÙkj gSA

çR;sd ç' u ds fy, l gh mÙkj ds l axr fodYi dk p;u dhft ; sA

çR; sd ç' u ds mÙkj dk ewY; kadu uhps fn, x, vadu ; kst uk ds vuql kj fd; k t k, xkA

i w.kZ vad : +3 ; fn dsoy l gh fodYi pquk x; k gS;

' kwU; vad : 0 ; fn dksbZ Hkh fodYi ugha pquk x; k gSa (vFkkZr~ ç' u vuqÙkfjr gSa);

½.kkRed vad : –1 vU; l Hkh fLFkfr ; ksa esaA

1. ekuk a, b f}?kkr cgqi n x2 + 20x – 2020 ds fofHkUu okLr fod ewyksa dks fu: fi r djr s gSa rFkk ekuk c, d f}?kkr cgqi n

x2 – 20x + 2020 ds fofHkUu l fEeJ ewyksa dks fu: fi r djrs gSaA rc

ac(a – c) + ad(a – d) + bc(b – c) + bd(b – d)

dk eku gS

(A) 0 (B) 8000

(C) 8080 (D) 16000

mÙkj (D)

2. ; fn i Qyu f : , f(x) = |x|(x – sinx) }kjk i fjHkkf"kr gS] r c fuEu esa l s dkSul k dFku l R; gS\

(A) f is one-one, but NOT onto (B) f is onto, but NOT one-one

f , dSdh gS] i jUrq vkPNknd ugha gS f vkPNknd gS] i jUrq ,dSdh ugha gS

(C) f is BOTH one-one and onto (D) f is NEITHER one-one NOR onto

f , dSdh ,oa vkPNknd nksuksa gSa f u r ks ,dSdh gSa vkSj u vkPNknd gS

mÙkj (C)

3. ekuk i Qyu f : , oa g : ,

f(x) = ex – 1 – e–|x – 1| rFkk x–1 1–x1g(x) (e e )

2 }kjk i fjHkkf"kr gSa]

rc i zFke prqFkk±'k esa oØksa y = f(x), y = g(x) o x = 0 }kjk i fjc¼ Hkkx dk {ks=ki Qy gS

(A) –112 – 3 e – e

2(B) –11

2 3 e – e2

(C) –112 – 3 e e

2(D) –11

2 3 e e2

mÙkj (A)


18

4. ekuk a, b o / ukRed okLr fod l a[ ; k, ¡ gSA ekuk P, i joy; y2 = 4x ds ukfHkyEc dk ,d fl jk fcanq gS rFkk ekuk nh?kZoÙk

2 2

2 2

x y1

a b fcanq P l s xqt jr k gSA ; fn fcanq P i j i joy; o nh?kZoÙk dh Li ' kZ js[ kk, ¡ , d nwl js ds yEcor~ gSa] r c nh?kZoÙk

dh mRdsUnzrk gS

(A)1

2(B)

12

(C)13

(D)25

mÙkj (A)

5. ekuk C1 o C2 nks vfHkur fl Dds gSa t cfd bUgsa ,d ckj mNkyus i j i zkIr gsM dh i zkf; drk, ¡ Øe' k% 23

o 13

gS] ekuk

, C1 dks Lora=k : i l s nks ckj mNkyus i j i zkIr gsM dh l a[ ; k gS rFkk ekuk , C2 dks nks ckj Lora=k : i l s mNkyus i j gsMdh l a[ ; k gS] r c f}?kkr cgqi n x2 – x + ds ewy okLr fod ,oa l eku gksus dh i zkf;drk gS

(A)4081

(B)2081

(C)12

(D)14

mÙkj (B)

6. ekuk {ks=k

x,y : 0 x 0 y 2sin(2x)2

rFkk

esa l Hkh vk; r fLFkr gSa ft udh ,d Hkqt k x-v{k i j gSA rc ml vk; r dk {ks=ki Qy dkSul k gS ft l dk , sl s l Hkh vk; r ksa esa l svf/ dre i fjeki gks\

(A)32

(B)

(C)2 3

(D)

32

mÙkj (C)

[ k.M - 2 (vf/ dre vad : 24)

bl [ k.M esa N% (06) ç' u gSaA

çR;sd ç'u ds pkj fodYi gSaA bu pkj fodYi ksa eas l s , d ; k , d l s vf/ d l gh mÙkj gS@gSaA

çR;sd ç'u ds fy, (l Hkh) l gh mÙkjksa l s l acaf/ r fodYi @fodYi ksa dk p; u dhft ; sA

çR; sd ç' u ds mÙkj dk ewY; kadu uhps nh xbZ vadu ; kst uk ds vuql kj fd; k t k, xk:i w.kZ vad : +4 ; fn dsoy l Hkh l gh fodYi @fodYi ksa dk p; u fd; k x; k gS_vakf' kd vad : +3 ; fn l Hkh pkj fodYi l gh gSa i jUrq dsoy rhu fodYi ksa dk p; u fd; k x; k gS_

vakf' kd vad : +2 ; fn rhu ; k vf/ d fodYi l gh gSa i jUrq dsoy nks fodYi ksa dk p; u fd; k x; k gS rFkk nksuksa l ghgks_

vkaf' kd vad : +1 ; fn nks ; k vf/ d fodYi l gh gSa i jUrq dsoy ,d fodYi dk p; u fd; k x; k gS rFkk og l ghfodYi gks_

' kwU; vad : 0 ; fn fdl h Hkh fodYi dk p; u ugha fd; k x; k (vFkkZr~ ç' u dk mÙkj ugha fn; k x; k gks);

½.kkRed vad : –2 vU; l Hkh fLFkfr ; ksa esaA


19

7. ekuk i Qyu f : , f(x) = x3 – x2 + (x – 1)sin x }kjk i fjHkkf"kr gS rFkk ekuk g : , d LoSfPNd i Qyu gSA

ekuk fg : , (f g)(x) = f(x)g(x) }kjk i fjHkkf"kr , d xq.ku i Qyu gSA rc fuEu esa l s dkSul k@l s dFku l R; gS@gSa\

(A) ; fn g, x = 1 i j l r r gS] r c f g, x = 1 i j vodyuh; gS

(B) ; fn f g, x = 1 i j vodyuh; gS] r c g, x = 1 i j l r r gS

(C) ; fn g, x = 1 i j vodyuh; gS] r c f g, x = 1 i j vodyuh; gS

(D) ; fn f g, x = 1 i j vodyuh; gS] r c g, x = 1 i j vodyuh; gS

mÙkj (A, C)

8. ekuk M okLr fod vo; oksa okyh ,d 3 × 3 O; qRØe.kh; vkO; wg gS rFkk ekuk I, 3 × 3 rRl ed vkO; wg dks n' kkZrk gSA ; fnM–1 = adj (adj M), r c fuEu esa l s dkSul k@l s dFku l nSo l R; gS@gSa

(A) M = I (B) det M = 1 (C) M2 = I (D) (adj M)2 = I

mÙkj (B, C, D)

9. ekuk S l Hkh l fEeJ l a[ ; kvksa z dk l eqPp; gS t ks |z2 + z + 1| = 1 dks l arq"V djrh gSa] r c fuEu esa l s dkSul k@l s dFkul R; gS@gSa\

(A) l Hkh 1 1

z S z 2 2

ds fy, (B) l Hkh z S z 2 ds fy,

(C) l Hkh 1 1

z S z2 2

ds fy, (D) l eqPp; S ds Bhd pkj vo; o gSa

mÙkj (B, C)

10. ekuk x, y o z / ukRed okLr fod l a[ ; k,a gSaA ekuk x, y o z , d f=kHkqt dh Hkqt kvksa dh yEckbZ; k¡ gSa t ks bl ds Øe' k% dks.kX, Y o Z ds l Eeq[ k gSaA ; fn

X Z 2ytan tan

2 2 x y z

r c fuEu esa l s dkSul k@l s dFku l R; gS@gSa\

(A) 2Y = X + Z (B) Y = X + Z

(C)x x

tan2 y z

(D) 2 2 2x z y xz

mÙkj (B, C)

11. ekuk L1 o L2 l j y j s[ kk, ¡ 1 2x 1 y z 1 x 1 y z 1

L : L :1 1 3 3 1 1

o

gSaA ekuk l j y j s[ kk

x y 1 zL :

l m 2

js[ kkvksa L1 o L2 okys r y esa fLFkr gSa vkSj L1 o L2 ds i zfrPNsnh fcanq l s xqt jrh gSA ; fn js[ kk L,

js[ kkvksa L1 o L2 ds eè; U;wu dks.k dks l ef}Hkkft r djrh gS] rc fuEu esa l s dkSul k@l s dFku l R; gS@gSa\

(A) – = 3 (B) l + m = 2 (C) – = 1 (D) l + m = 0

mÙkj (A, B)


20

12. fuEu esa l s dkSul h vl fedk, ¡ l R; gS@gSa\

(A)1

0

3xcos x dx

8

(B)1

0

3x sinx dx

10

(C)1 2

0

1x cosx dx

2

(D)1 2

0

2x sinx dx

9

mÙkj (A, B, D)

[ k.M - 3 (vf/ dre vad : 24)

bl [ k.M esa N% (06) ç' u gSaA çR; sd ç'u dk mÙkj , d vkafdd eku gSA

çR; sd ç' u ds fy, ] mÙkj ds l gh vkafdd eku dks ekÅl rFkk vkWu&LØhu opqZvy U; weSfjd dh–i SM ds mi ; ksx l s mÙkj çfo"Vdjus ds LFkku i j gh çfo"V dhft ; sA ; fn vakfdd eku esa nks l s vf/ d n' keyo LFkku gks] r ks çkIr eku dk nks n' keyo LFkku rdl fUudVu djsaA

çR; sd ç' u ds mÙkj dk ewY; kadu uhps nh xbZ vadu ; kst uk ds vuql kj fd; k t k; sxk:

i w.kZ vad : +4 ; fn dsoy l gh vakfdd eku dks çfo"V fd; k x; k gS_

’ kwU; vad : 0 vU; l Hkh fLFkfr ; ksa esaA

13. ekuk m, 1 32y yy3log 3 3 3 dk U; wure l aHkkfor eku gS] t gk¡ y1, y2, y3 okLr fod l a[ ; k, ¡ gSa ft uds fy, y1 + y2 +

y3 = 9, ekuk M] (log3x1 + log3x2 + log3x3) dk vf/ dre l aHkkfor eku gS] t gk¡ x1, x2, x3 / ukRed okLr fod l a[ ; k,a gSaft l ds fy, x1 + x2 + x3 = 9. r c log2(m3) + log3(M2) dk eku gS______

mÙkj (8)

14. ekuk a1, a2, a3, ... l ekUr j Js<+h esa / ukRed i w.kk±dksa dk ,d vuqØe gS ft l dk l koZ vUr j 2 gS rFkk ekuk b1, b2, b3, ...

xq.kksÙkj Js<+h esa / ukRed i w.kk±dksa dk ,d vuqØe gS ft l dk l koZ vuqi kr 2 gSA ; fn a1 = b1 = c, r c c ds mu l Hkh l aHkkforekuksa dh l a[ ; k Kkr dhft , ft l ds fy, l fedk

2(a1 + a2 + ... + an) = b1 + b2 + ... + bn

fdl h / ukRed i w.kk±d n ds fy, oS/ gS ______

mÙkj (1)

15. ekuk f : [0, 2] , f(x) (3 – sin(2 x))sin x – – sin 3 x4 4

}kjk i fjHkkf"kr i Qyu gS]

; fn , [0, 2] bl i zdkj gSa fd {x [0, 2] : f(x) 0} = [, ], r c – dk eku _____gS

mÙkj (1)


21

16. , d f=kHkqt PQR esa, ekuk

a QR, b RP c PQ rFkk , ; fn

a 3,

aa (c – b)b 4

c (a – b) a b

rFkk

r c 2

a b dk eku gS

mÙkj (108)

17. okLr fod xq.kkadksa okys cgqi nksa g(x) ds fy, ekuk mg, g(x) ds fofHkUu okLr fod ewyksa dh l a[ ; k dks n' kkZrk gSA ekuk S okLr fodxq.kkadksa okys cgqi nksa dk l eqPp; gS t ks

S = {(x2 – 1)2(a0 + a1x + a2x2 + a3x3) : a0, a1, a2, a3 } }kjk i fjHkkf"kr gS

,d cgqi n f ds fy, ] ekuk f o fØe' k% bl ds i zFke o f}rh; dksfV vodyt dks n' kkZrs gSaA rc f fm m dk U; wure

l aHkkfor eku Kkr dhft , t gk¡ f S gS _____

mÙkj (5)

18. ekuk e i zkdr y?kqx.kd ds vk/ kj dks n' kkZrk gSA okLr fod l a[ ; k a dk eku ft l ds fy, nk; ha l hek

1–1x

ax 0

(1– x) – elim

x

, d v&' kwU; okLr fod l a[ ; k ds cjkcj gS] gS_____

mÙkj (1)

for JEE (Advanced)-2020...JEE (ADVANCED)-2 020 (Paper-1) 5 8.,d izdk'k cYc ds fiQykesUV dk i`"Bh;...

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Transcript of for JEE (Advanced)-2020...JEE (ADVANCED)-2 020 (Paper-1) 5 8.,d izdk'k cYc ds fiQykesUV dk i`"Bh;...