1

Answers & Solutions

forforforforfor

JEE (Advanced)-2017

Time : 3 hrs. Max. Marks: 183

CODE

1

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

Ph.: 011-47623456 Fax : 011-47623472

PAPER - 2 (Code - 1)

DATE : 21/05/2017

INSTRUCTIONS

QUESTION PAPER FORMAT AND MARKING SCHEME :

1. The question paper has three parts : Physics, Chemistry and Mathematics.

2. Each part has three sections as detailed in the following table :

Section QuestionType

Number of Questions

Full Marks

Category-wise Marks for Each Question

Partial Marks Zero Marks Negative Marks

MaximumMarksof the

Section

SingleCorrectOption

7 +3If only the bubble corresponding to the correct option

is darkened

— 0If none of the

bubbles is darkened

–1In all other

cases

211

One ormore

correctoption(s)

7 +4If only the bubble(s)

corresponding toall the correct

option(s) is(are)darkened

+1For darkening a bubblecorresponding to each

correct option, provided NO incorrect option is

darkened

0If none of the

bubbles is darkened

–2In all other

cases

282

Compre-hension

4 +3If only the bubblecorresponding to

the correct answeris darkened

— 0In all other

cases

— 123

fgUnh ekè;efgUnh ekè;efgUnh ekè;efgUnh ekè;efgUnh ekè;e

2

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

PHYSICS

[kaM[kaM[kaM[kaM[kaM-1(vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 21)))))

• bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa fliZQ ,d ,d ,d ,d ,d fodYi lgh gSA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lgh mÙkj ds vuq:i cqycqys dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %

iw.kZ vad : +3 ;fn dsoy lgh fodYi ds vuq:i cqycqys dks dkyk fd;k gSA

'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ugha fd;k gSA

½.k vad : –1 vU; lHkh ifjfLFkfr;ksa esaA

1. ,d izlkjh xksys (expanding sphere) dh rkR{kf.kd (instantaneous) f=kT;k R ,oa nzO;eku M vpj jgrs gSA izlkj ds nkSjku

bldk rkR{kf.kd ?kuRo ρ iwjs vk;ru esa ,dleku jgrk gS ,oa vkaf'kd ?kuRo dh nj 1 d

dt

⎛ ⎞ρ⎜ ⎟ρ⎝ ⎠

vpj (constant) gSA bl izlkjh

xksys ds i"B ij ,d fcUnq dk osx v fuEu ds lekuqikrh gksxk

(A) R (B) R3

(C)1

R(D) R2/3

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygy 34

3M R= π ρ

2 340 3

3

dR dR R

dt dt

ρ⎡ ⎤= π ρ +⎢ ⎥⎣ ⎦

ρ ls foHkkftr djus ij

2 3 10 3

dR dR R

dt dt

ρ= + ⋅ρ

2 33

dRR R K

dt= −

dRR

dt∝

2. fp=k }kjk n'kkZ;s lecgqHkqtksa dh Hkqtkvksa dh la[;k n = 3,4,5....... gSA lHkh cgqHkqtksa dk lagfr dsUnz (center of mass) vuqHkwfed

ry ls h Å¡pkbZ ij gSA ;s fcuk fiQlys f{kfrt ry ij izfrxkeh 'kh"kZ (leading vertex) ds pkjksa vkSj ?kw.kZu dj vxzlfjr gks jgs

gSaA izR;sd cgqHkqt ds lagfr dsanz ds js[kkiFk (locus) dh Å¡pkbZ dh vfèkdre o`f¼ Δ gSA rc Δ dh h vkSj n ij fuHkZjrk

fuEu esa ls nh tk,xh

h h h

3

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

(A)2

sinhn

π⎛ ⎞Δ = ⎜ ⎟⎝ ⎠

(B)1

1

cos

h

n

⎛ ⎞Δ = −⎜ ⎟π⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(C)2

sinhn

π⎛ ⎞Δ = ⎜ ⎟⎝ ⎠

(D)2

tan2

hn

π⎛ ⎞Δ = ⎜ ⎟⎝ ⎠

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

gygygygygy lh

π/n

θ

2 n

π πθ = −

sin cos

n

πθ =

sin

hl =

θΔ = l – h

= 1

1sin

h⎡ ⎤−⎢ ⎥θ⎣ ⎦

= 1

1

cos

h

n

⎡ ⎤−⎢ ⎥π⎢ ⎥⎣ ⎦

3. izdk'k fo|qr inkFkZ (photo electric material) ftldk dk;Z iQyu (work funtion) φ0 gS] rjax&nSè;Z

0

hc⎛ ⎞λ λ <⎜ ⎟φ⎝ ⎠

ds izdk'k

ls iznhIr fd;k x;k gSA nzqr izdk'k bysDVªku dh Mh czksXyh (de Broglie) rjax&nSè;Z λd gSA vkifrr izdk'k (incident light) dh

rjax&nSè;Z esa Δλ ds ifjorZu λd ds eku esa Δλ

d dk ifjorZu gksrk gSA rc Δλ

d/Δλ dk vuqikr lekuqikrh gksxk

(A) /d

λ λ (B)2 2/

dλ λ

(C)3/

dλ λ (D)

3 2/

dλ λ

mÙkjmÙkjmÙkjmÙkjmÙkj (D)

gygygygygy2

d

h

hcm

λ =⎛ ⎞− φ⎜ ⎟λ⎝ ⎠

2

d

hc hm⎛ ⎞− φ =⎜ ⎟λ λ⎝ ⎠

2

22

d

hc hm f⎛ ⎞− =⎜ ⎟λ⎝ ⎠ λ

2

2 3

12

d

hm hc d

−⎛ ⎞λ = −⎜ ⎟λ λ⎝ ⎠

3

2

d dd

kd

λ λ=λ λ

4

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

4. tSls dh fpf=kr fd;k x;k gS] ,d lfEer rkjs (symmetric star) ds vkdkj ds pkyd esa vifjofrZr èkkjk I cg jgh gSA ;gk¡

foijhr 'kh"kks± (diametrically opposite vertices) ds chp nwjh 4a gSA pkyd ds dsUnz ij pqEcdh; {ks=k dk eku gksxk

4a

I

(A)I

a

06 3 –1

4

μ ⎡ ⎤⎣ ⎦π

(B)I

a

06 3 1

4

μ ⎡ ⎤+⎣ ⎦π

(C)I

a

03 3 –1

4

μ ⎡ ⎤⎣ ⎦π

(D)I

a

03 2 – 3

4

μ ⎡ ⎤⎣ ⎦π

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygy rkjs vkdkj ds pkyd ywi ds ,d Hkkx dks lefer ls ckgj ekuus ij

T;kferh lsT;kferh lsT;kferh lsT;kferh lsT;kferh ls :

30°

30°

30°

120°

2a

I

O

a

( )ywi dk dsUnz

lHkh 12 le:i Hkkxksa ds dkj.k ywi ds dsUnz ij pqEcdh; {ks=k izoQfr esa ;ksxkRed gSA

∴ BusV = [ ]012 × cos30 cos120

4

I

a

μ ° + °π

= 0

6 3 14

I

a

μ ⎡ ⎤⋅ ⋅ −⎣ ⎦π

5. rhu osDVj ,P Q

��

,oa R�

fp=k }kjk n'kkZ, x, gSaA osDVj R�

ij ,d fcUnq S n'kkZ;k x;k gSA fcUnq P o fcUnq S ds chp dh

nwjh b R�

gSA,P Q

��

,oa S�

osDVjksa ds chp lEcUèk gS

SQ

PbR| |

→

R Q P= −

QS

P

O X

Y

(A) ( )21S b P bQ= − +

� ��

(B) ( )1S b P bQ= − +� ��

(C) ( )1S b P bQ= − +� ��

(D) ( ) 21S b P b Q= − +

� ��

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

5

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy S�

= ˆ| |P b R R+� �

= | || |

RP b R

R+

�

� �

�

= P bR+� �

= ( )–P b Q P+�� �

= (1– )b P bQ+��

6. jkdsV Hkwry ds vfHkyacor lw;Z ,oa i`Foh dks tksM+us okyh js[kk esa lw;Z ls nwj dh rjiQ (radially outward from the direction

of the sun) iz{ksfir fd;k x;k gSA lw;Z iFoh ls 3 × 105 xquk Hkkjh gS ,oa iFoh dh f=kT;k ls 2.5 × 104 xquh nwjh ij fLFkr gSA

i`Foh ds xq:Rokd"kZ.k {ks=k ds fy, iyk;u xfr 11.2 kms–1 gSA jkdsV dks lw;Z ,oa i`Foh fudk; ds xq:Rokd"kZ.k ls eqDr gksus

ds fy, de ls de izkjafHkd osx (νS) dk fudVre eku gS

(iFoh dh pØh; xfr vkSj ifjHkze.k rFkk fdlh vU; xzg dh mifLFkfr dh mis{kk djsa)

(A) vs = 22 km s–1 (B) v

s = 42 km s–1

(C) vs = 62 km s–1 (D) v

s = 72 km s–1

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

gygygygygy Evs

m

M M1 =

S

r R = 2.5 × 10 4

M M2 = 3 × 10

5

KE esa gkfu = PE esa ykHk

⇒ 2 1 21

2s

GM m GM mmv

R r= +

⇒5

2

4

1 × 3 × 10

2 2.5 × 10s

GM G Mv

R R= +

⇒ 2 × × 13s

GMv

R=

= 11.2 × 13 40.4 km/s=

� 42 km/s

7. ,d O;fDr ,d iRFkj dks dq,as esa fxjkrs le; vkSj dq,as dh ryh esa la?kV ls mRiUUk èofu ds le; varjky dk ekiu djds

dq,as dh xgjkbZ dk irk yxkrk gSA og le;karjky ds ekiu esa =kqfV δT = 0.01 lsdsaM ,oa dq,sa dh xgjkbZ L = 20 m ekirk gSA

xq:Rokd"kZ.k Roj.k g = 10 m s–1 ,oa èofu xfr 300 ms–1 nh xbZ gSA δL/L ds ekiu esa fudVre vkaf'kd =kqfV (fractional

error) gS

(A) 0.2%

(B) 1%

(C) 3%

(D) 5%

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

6

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy t1 =

2L

g

t1

t2L

t2 =

L

V

∴ T = t1 + t

2

⇒ T = 2L L

g V+

⇒ ΔT = 2 1 1

2L L

g VL× Δ + Δ

⇒ 0.01 =

1 1 1

3005 2 20L

⎛ ⎞× + Δ⎜ ⎟×⎝ ⎠

⇒ 0.01 = 1 1

20 300L

⎛ ⎞+ Δ⎜ ⎟⎝ ⎠

⇒ 0.01 = (15 1)

300L

+ Δ

⇒ ΔL = 0.01 300

16

×

∴ 100L

L

Δ × = 3

10016 20

××

= 1%

[kaM[kaM[kaM[kaM[kaM-2 (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 28)))))

• bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d fodYi lgh gSaA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lkjs lgh mÙkj (mÙkjksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %

iw.kZ vad : +4 ;fn fliQZ lkjs lgh fodYi (fodYiksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk fd;k gSA

vkaf'kd vad : +1 izR;sd lgh fodYilgh fodYilgh fodYilgh fodYilgh fodYi ds vuq:i cqycqys dks dkyk djus ij] ;fn dksbZ xyr fodYi dkyk

ugha fd;k gSA

'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ughaughaughaughaugha fd;k gSA

½.k vad : –2 vU; lHkh ifjfLFkfr;ksa esaA

• mnkgj.k % ;fn ,d iz'u ds lkjs lgh mÙkj fodYi (A), (C) vkSj (D) gSa] rc bu rhuksa ds vuq:i cqycqyksa dks dkyk djus ij

+4 vad feysaxs_ fliQZ (A), (D) ds vuq:i cqycqyksa dks dkyk djus ij +2 vad feysaxsa_ rFkk (A) vkSj (B) ds vuq:i cqycqyksa

dks dkyk djus ij –2 vad feysaxs D;ksafd ,d xyr fodYi ds vuq:i cqycqys dks Hkh dkyk fd;k x;k gSA

7

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

8. ,dleku pqEcdh; {ks=k (uniform magnetic field) B dkxt ds ry ds vfHkyEc fn'kk esa x = 0 ,oa 3

2

Rx = ds chp ds

{ks=k (fp=k esa region 2) esa loZ=k (tSls fd fp=k esa fn[kk;k gS) mifLFkr gSA ,d d.k ftldk vkos'k +Q ,oa laosx p gS] og

x-v{k ds vuqfn'k {ks=k 2 esa fcUnq P1(y = – R) ij ços'k djrk gSA fuEu esa ls dkSu lk(ls) dFku lgh gS@gSa\

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

×

3 /2R

( = – )y R

+Q P1

OP

2

B

x

yRegion 1 Region 2 Region 3

(A)2

3

pB

QR> ds fy, d.k {ks=k 1 (region 1) esa iqu% ços'k djsxk

(B)8

13

pB

QR= ds fy, d.k {ks=k 3 (region 3) esa x-v{k ij fcUnq P

2 ls ços'k djsxk

(C) tc d.k lcls yEcs lEHkoiFk ls {ks=k 2 (region 2) ls {ks=k 1 (region 1) esa iqu% ços'k djrk gS] rc fcUnq P1 vkSj y-v{k

ls lcls nwj fcUnq ds fy, jsf[kd laosx ds ifjek.k esa cnyko / 2p gS

(D) ,d fu;r B ds fy, ,eleku vkos'k Q ,oa ,d leku osx v okys d.kksa ds fy, fcUnq P1 ,oa {ks=k 1 (region 1) esa iqu%

ços'k fcUnq dh nwjh dk varj d.kksa ds æO;eku ds O;qrØekuqikrh gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B)

gygygygygy d.k pqEcdh; {ks=k ds vUnj o`Ùkh; iz{ksi&iFkksa dk vuqlj.k djsxkA pqEcdh; {ks=k osx rFkk laosx ds ifjek.k dks ifjofrZr ugha

dj ldrk gSA

nh?kZre lEHko iFk ds fy,] oÙkh; xfr dh f=kT;k 3

2

R gks ldrh gSA

P2

P1

O

×

y-v{k ls nwjLFk fcUnq ij] laosx Åij dh vksj funsZf'kr gS]

p p2∴ Δ =��

8

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

f=kT;k rFkk p1 o iqu% izosf'kr fcUnq ds eè; nwjh m ds lekuqikrh gS ;fn Q, u, B leku gSaA

d.k {ks=k rd okil ykSVsxk dsoy ;fn ;g v¼Z pØ iw.kZ djrk gSA

Rr

3

2≤

mV R

B

3

2≤

3

2

p R

QB≤

2

3

pB

QR≥

;fn 8 13

;13 8

p p RB r

QR QB= = =

P2

P1

O

θ

rθ

Rr r- cosθ

;g fcUnq P2 ls xqtjrk gS ;fn r – r cosθ = R

R

r

3122

sin13

θ = =

13 51–

8 13

RR

⎛ ⎞ =⎜ ⎟⎝ ⎠

R = R

9. rhu VfeZuyksa ds fcUnqvksa X, Y ,oa Z ds fy, rkR{kf.kd oksYVrk (instantaneous voltage) nh xbZ gS

Vx = V

0 sin ωt,

Vy = V

0sin

2

3t

π⎛ ⎞ω +⎝ ⎠vkSj

0

4sin

3z

V V tπ⎛ ⎞= ω +

⎝ ⎠

,d vkn'kZ oksYVekih (ideal voltmeter) nks fcUnqvksa ds foHkokUrj dk vkj ,e ,l (root mean square, Vrms) eku nsrk gSA

;g oksYVekih fcUnq X ,oa Y ls tksM+k tkrk gS fiQj Y ,oa Z ls tksM+k tkrk gSA bl oksYVekih dk ekiu gksxk@gksaxs

(A)rms

0

3

2=

XYV V (B)

rms

0

1

2=

YZV V

(C)rms

0=

XYV V (D) fdlh Hkh nks fcUnqvksa ds p;u ij fuHkZj ugha djrk

mÙkjmÙkjmÙkjmÙkjmÙkj (A, D)

9

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy VXY

= V0 sin ωt – V

0 t

2sin

3

π⎛ ⎞ω +⎜ ⎟⎝ ⎠

60°

V0

V0

V0

V03

rms

XY

VV

03

2=

VYZ

= V0 0

2 4sin sin

3 3t V t

π π⎛ ⎞ ⎛ ⎞ω + − ω +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ 60°

V0

V03

V0

V0

rms

YZ

VV

03

2=

∴ A, D

10. /ukRed fcUnq vkos'k +Q ,d dkYifud v/Zxksyh; i`"B ftldh f=kT;k R gS] ds ckgj j[kk gS (tSlk fd fp=k esa fn[kk;k x;k

gS)A fuEu esa ls dkSulk(ls) çdFku lgh gS@gSa?

Q

R

(A) v/Zxksyh; ofØr i"B ls xqtjus okys fo|qr ÝyDl (electric flux) dk eku 0

1– 1–2 2

Q ⎛ ⎞⎜ ⎟⎝ ⎠ε gS

(B) ofØr ,oa lery i"B ls xqtjus okyk dqy ÝyDl 0

Q

ε gS

(C) fo|qr {ks=k dk lery i"B ls vfHkyfEcr ?kVd iwjs i"B ij vpy jgsxk

(D) lery i"B dh ifjf/ ,d lefoHko i"B (equipotential surface) gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, D)

gygygygygy oØkdkj lrg rFkk likV lrg ls izokfgr usV ÝyDl = 0

Q

R

R

45º

⇒ φoØkdkj = – φlery

( )0

1 cos2

⎡ ⎤= − − θ⎢ ⎥ε⎣ ⎦

Q

0

11

2 2

⎡ ⎤⎛ ⎞= − −⎢ ⎜ ⎟ ⎥⎝ ⎠ε⎣ ⎦

Q

10

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

ifjfèk ds fcUnq Q ls lenwjLFk gSa

∴ lHkh fcUnq leku foHko ij gksaxsA

∴ fodYi (A) rFkk (D) lgh gSaA

11. nks dyklac/ ,do.khZ (coherent monochromatic) fcUnq lzksr S1 ,oa S

2 ] ftudh rjaxnSè;Z λ = 600 nm gS ,d oÙk ds dsUnz

ds nksuksa vksj lefer voLFkk esa fLFkr gS (tSls fp=k esa fn[kk;k x;k gS)A lzksr S1 o S

2 ds chp dh nwjh d = 1.8 mm gSA bl

O;oLFkk }kjk O;frfdj.k fÚUtsa (interference fringes) izfrorhZ nhIr ,oa vnhIr fpfÙk;ksa (spots) ds :i esa ,d o`Ùk dh ifjf/

ij fn[krh gSA Δθ nks Øekxr nhIr fpfÙk;ksa ds chp dh dks.kh; nwjh (angular separation between two consecutive bright

spots) gSA fuEu esa ls dkSu lk (ls) izdFku lgh gS@gSa\

d

S1

S2

Δθ

P1

P2

(A) P2 ij ,d vnhIr fcUnq cusxk

(B) P2 ij fÚUtksa dk Øe mPpre gksxk

(C) P1 o P

2 ds chp ds izFke oÙkikn (first quadrant) esa dqy djhc 3000 fÚUtsa cusaxh

(D) izFke oÙkikn esa P1 o P

2 rd tkus esa nks Øekxr nhIr fpfÙk;ksa ds chp dh dks.kh; nwjh ?kVrh gS

mÙkjmÙkjmÙkjmÙkjmÙkj (B, C)

gygygygygy d = 1.8 × 10–3 m

= 18 × 10–4 m

P1

P2

S2

S1

d

P

θ

rFkk λ = 6 × 10–7 m

fcUnq P ij iFkkUrj (n'kkZ, vuqlkj)

Δx = S1P – S

2P = d sin θ, tgk¡ θ dks.k n'kkZ, vuqlkj ÅèokZ/j js[kk ls ekik tkrk gSA

pedhyh fÚUt ds fy, gSA d sin θ = mλ ...(i)

fcUnq P1 dsUnzh; mfPp"B dk fcUnq gS

fcUnq P2 ij] iFkkUrj (Δx) = d

;fn P2 pedhyh fÚUt dk fcUnq gS] rc

dd m m 3000= λ ⇒ = =

λlehdj.k (i) dk vodyu djus ij

d cos θ (Δθ) = (Δm) λ = Øekxr pedhyh fÚUt ds fy, fu;r

cos θ ↓ ∴ Δθ ↑ pw¡fd θ, 0 ls 2

π rd ifjofrZr gksrk gSA

11

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

12. nks vkn'kZ izsjd (ideal inductor) L1 ,oa L

2 vkSj ,d izfrjks/ esa (resistance) R dks ,d vpy oksYVrk V ds lzksr ls ,d

fLop S }kjk tksM+k tkrk gS (tSlk fp=k esa fn[kk;k x;k gS)A L1 ,oa L

2 ds chp vU;ksU; izsjdRo (mutual inductance) ugha gSA

izkjaHk esa fLop S [kqyk gSA le; t = 0 ij fLop can fd;k tkrk gS vkSj /kjk cguh 'kq: gksrh gSA fuEu esa ls dkSu lk (ls)

izdFku lgh gS@gSa\

L2

L1

+

–

R

V

S

(A) nh?kZdky ds ckn L1 esa izokfgr /kjk

LV

R L L

2

1 2+ gksxh

(B) nh?kZdky ds ckn L2 esa izokfgr /kjk

LV

R L L

1

1 2+ gksxh

(C) L1 ,oa L

2 esa izokfgr /kjk dk vuqikr gj le; (t > 0) fu;r jgrk gS

(D) t = 0 ij izfrjks/ R esa izokfgr /kjk V

R gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B, C)

gygygygygy cSVjh ls izokfgr vfUre èkkjk = V

R

∴ L1 ls izokfgr èkkjk =

LV

R L L

2

1 2

⎛ ⎞⎜ ⎟+⎝ ⎠

L2 ls izokfgr èkkjk =

LV

R L L

1

1 2

⎛ ⎞⎜ ⎟+⎝ ⎠

t = 0 ij L=kksr ls izokfgr èkkjk = 'kwU;

fdlh le; ij i =

tR

L L

L LV Ve

R R

1 2

1 2

–

0 –

⎛ ⎞⎜ ⎟+⎝ ⎠⎛ ⎞+ ⎜ ⎟

⎝ ⎠

∴ L1 ls izokfgr èkkjk =

Li iL L

2

1

1 2

=+

L2 ls izokfgr èkkjk =

iLi

L L

1

2

1 2

=+

i L

i L

1 2

2 1

=

12

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

13. ,d L yEckbZ dk nz<+ naM (rigid bar) AB viuh ÅèokZ/j fLFkfr ls ?k"kZ.kghu vuqHkwfed ry (frictionless horizontal surface)

ij fp=kkuqlkj fiQly jgk gSA le; ds fdlh {k.k ij naM }kjk ÅèokZ/j ls cuk;k dks.k θ gSA fuEu esa ls dkSu lk (ls) izdFku

lgh gS@gSa\

θ

O

L

A

B

(A) naM dk eè; fcUnq ÅèokZ/j uhps dh vksj (vertically downward) fxjsxk

(B) fcUnq A dk iziFk ijoyf;d (parabolic path) gS

(C) naM vkSj Hkwry ds Li'kZ fcUnq ds pkjksa rjiQ rkR{kf.kd cy;k?kw.kZ (instantaneous torque) sinθ ds lekuqikrh gS

(D) tc naM ÅèokZ/j ls θ dks.k cukrk gS rc naM ds eè; fcUnq dk foLFkkiu mlds vkjafHkd fLFkfr ls (1 – cosθ) ds

lekuqikrh gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, C, D)

gygygygygy fdlh {k.k ij] O ds lkis{k cyk?kw.kZ . sin2

θlmg gS

∴ fodYi (C)

θmg

O

2

l

pw¡fd x-v{k ds vuqfn'k dksbZ ckg~; cy ugha gS blfy, nzO;eku dsUnz ÅèokZèkj :i ls uhps dh vksj fxjsxkA

∴ fodYi (C)

θP x y( , )

2

l

θ

2

l

cosθ2

ly-v{k ds vuqfn'k nzO;eku dsUnz dk foLFkkiu

[ ]1 cos2

= − θl

∴ fodYi (D)

sin , cos2

= − θ = θlx y l

⇒2 2

2

21

⎛ ⎞− + =⎜ ⎟⎝ ⎠x y

l l

⇒ iz{ksi&iFk ijoy; ugha gSA

14. ,d f=kT;k R ,oa nzO;eku M dk ifg;k (wheel) ,d R Å¡pkbZ okys n<+ lksiku (step) ds ry ij j[kk gS (tSls fp=k esa fn[kk;k

x;k gS)A ifg;s dks lksiku ij p<+kus ek=k ds fy, ,d vpj cy ifg;s ds i`"B ij lrr (continuous constant force)

13

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

dk;Zjr gSA dkxt ds i`"B ls vfHkyac fn'kk esa (perpendicular to the plane of the paper) fcUnq Q ls tkus okyh v{k ds

lkis{k cyvk?kw.kZ τ ekfu;sA fuEu esa ls dkSu (lk) ls izdFku lgh gS@gSa\

P Q

R

S

X

(A) ;fn fcUnq P ij Li'khZ; cy (tangential force) yxk;k tk;s rc tSls ifg;k lksiku ij p<+sxk oSls τ lrr ?kVsxk

(B) ;fn fcUnq X ij ifg;s dh ifjf/ ls vfHkyac fn'kk (normal direction) esa cy yxk;k tk;s rc τ vpj jgsxk

(C) ;fn fcUnq P ij ifg;s dh ifjf/ ls vfHkyac fn'kk esa cy yxk;k tk;s rc τ 'kwU; jgsxk

(D) ;fn fcUnq S ij Li'khZ; cy yxk;k tk;s rc τ ≠ 0 gS fdUrq ifg;k lksiku ij dHkh Hkh ugha p<+sxk

mÙkjmÙkjmÙkjmÙkjmÙkj (B,C)

gygygygygy lgh fodYi (B, C) [cy ds ifjek.k dks fu;r ekfu;s]

fodYifodYifodYifodYifodYi (C) ds fy, ds fy, ds fy, ds fy, ds fy, :

vkjksfir cy fcUnq Q ls xqtjrk gSA

blfy, bldk cyk?kw.kZ 'kwU; gSA

fodYifodYifodYifodYifodYi (B) ds fy, ds fy, ds fy, ds fy, ds fy, :

x ij vkjksfir cy ds dkj.k cyk?kw.kZ fu;r jgrk gSA

[kaM[kaM[kaM[kaM[kaM 3 (vf/dre vad(vf/dre vad(vf/dre vad(vf/dre vad(vf/dre vad % % % % % 12)))))

• bl [kaM esa nks vuqPNsn gSaA

• izR;sd vuqPNsn ij vk/kfjr nks iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa fliZQ ,d ,d ,d ,d ,d fodYi lgh gSA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lgh mÙk ds vuq:i cqycqys dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfRk;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%

iw.kZ vad % +3 ;fn dsoy lgh fodYi ds vuq:i cqycqys dks dkyk fd;k gSA

'kwU; vad % 0 vU; lHkh ifjfLFkfr;ksa esaA

vuqPNsnvuqPNsnvuqPNsnvuqPNsnvuqPNsn-1

,d lk/kj.k RC ifjiFk dks nsf[k;s] tSlk fp=k 1 (Figure) esa n'kkZ;k x;k gSaA

çØe 1 (Process 1): t = 0, ij fLop S }kjk ifjiFk iw.kZ fd;k tkrk gS ,oa la/kfj=k iw.kZ :i ls oksYVrk V0 ls vkosf'kr gks tkrk gS (T

>> RC le; rd vkos"k.k pyrk jgrk gS)A bl çØe esa çfrjks/ R ds }kjk dqN fo|qr&ÅtkZ {k; (energy dissipated), ED gksrh gSA

iw.kZ :i ls vkosf'kr la/kfj=k esa lafpr ÅtkZ (stored energy in a charged capacitor) dk eku EC gSA

çØe 2 (Process 2) : ,d vyx çØe esa igys 0

3

V oksYVrk dks vkosf'kr le; T >> RC ds fy, vuqjf{kr fd;k tkrk gSA

rc fcuk la/kfj=k vkos'k foltZu ds le; dks T >> RC ds fy, vuqjf{kr djds oksYVrk dks 02

3

V rd c<+k;k tkrk gSA

14

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

oksYVrk dks V0 rd c<+kus ds fy, ;g çØe ,d vkSj ckj nksgjk;k tkrk gSA la/kfj=k dks vafre oksYVrk V

0 (tSls fd çØe 1

esa gS) rd vkosf'kr fd;k tkrk gSA

;s nksuksa çØe fp=k 2 esa fn[kk, x, gSA

–+

R

C

S

V

Figure 1 Figure 2

Process 1

v

V0

2V0/3

V0/3

Tt

2T

T RC >>

Process 2

15. çØe 1 esa la/kfj=k esa lafpr ÅtkZ EC vkSj çfrjks/ R }kjk ÅtkZ {k; E

D esa lEca/ gS

(A) EC = E

D(B) E

C = E

D In 2

(C) EC =

1

2D

E (D) EC = 2E

D

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygy laèkkfj=k ij vfUre vkos'k = CV

Wb = CV2

Ec =

21

2CV

ED = W

b – ΔE

c

= CV2 – 21

2CV =

21

2CV C D

E E=

16. çØe 2 ds nkSjku çfrjks/ ds }kjk dqy {k; ÅtkZ ED gS

(A)2

0

1

2=

DE CV (B)

2

0

13

2

⎛ ⎞= ⎜ ⎟⎝ ⎠

DE CV

(C)2

0

1 1

3 2

⎛ ⎞= ⎜ ⎟⎝ ⎠

DE CV (D)

2

03=

DE CV

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

gygygygygy ED = W

b – ΔV

= 20 0 0

0 0

2 1–

3 3 3 2

CV V VV CV

⎡ ⎤+ +⎢ ⎥⎣ ⎦

= 20 0 0 0

0

2 3 1–

3 3 2

CV V V VCV

+ +⎡ ⎤⎢ ⎥⎣ ⎦

= [ ] 20

0 0

12 –

3 2

CVV CV =

2

0

2 1–

3 2CV

⎛ ⎞⎜ ⎟⎝ ⎠

=

2

0

6

CV

vuqPNsnvuqPNsnvuqPNsnvuqPNsnvuqPNsn-2

,d o`Ùkkdkj oy; (circular ring) (æO;eku M ,oa f=kT;k R) ,d maxyh ds ifjr /qzr?kw.kZu djrk gS (tSlk fp=k 1 (figure 1).

esa n'kkZ;k x;k gS)A bl çØe esa maxyh oy; ds varfjd i`"B ls ges'kk Li'kZ djrh gSA maxyh ,d 'kadq (cone) ds i`"B dk

vuqjsf[k; iFk dk vuqlj.k djrh gS tSls dh fcUnqfdr js[kk }kjk n'kkZ;k x;k gSA maxyh ,oa oy; ds Li'kZ fcanq ds vuqjsf[k; iFk

dh f=kT;k r gSA maxyh dks.kh; osx ω0 ls ?kw.kZu dj jgh gSA oy; r f=kT;kokys oÙk ds ckgjh i"B ij fiQlyu jfgr ?kw.kZZu (rolls

without slipping) djrk gSA tSlk fp=k 2 (figure 2) esa oy; ,oa maxyh ds Li'kZ fcUnq }kjk n'kkZ;k x;k gSA oy; ,oa maxyh ds

chp ?k"kZ.k xq.kkad (coefficient of friction) μ, ,oa xq:Roh; Roj.k g gSA

15

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

R

R

r

fp=k 1 fp=k 217. oy; dh dqy xfrt mtkZ gS

(A)2 2

0ωM R (B) ( )22

0

1

2ω −M R r

(C) ( )22

0ω −M R r (D) ( )22

0

3

2ω −M R r

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygy 2 21 1

2 2c c

k Mv I= + ω

2 2 2 2

0 0

1 1( )

2 2M R r MR= ω − + ω

2

2 2 2 2

0 0

1 11

2 2

rM R M R

R

⎛ ⎞= ω − + ω⎜ ⎟⎝ ⎠

R r–

V R rC

= ( – )ω0

ω0

r << R

0r

R→

2 2 2 2

0 0

1 1

2 2k M R M R= ω + ω

2 2

0M R= ω

18. U;wure ω0 ftlds de gksrs gh oy; fxj tk;sxk] og gS

(A) ( )μ −g

R r (B) ( )2

μ −g

R r

(C) ( )3

2μ −g

R r (D) ( )2μ −g

R r

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygyMg

N

f

N = Mω2 (R – r)

f = Mg

f ≤ μN

Mg ≤ μMω2 (R – r)

( )0ω =

μ −g

R r

END OF PHYSICS

16

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

CHEMISTRY

[kaM[kaM[kaM[kaM[kaM-1(vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 21)))))

• bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa fliZQ ,d ,d ,d ,d ,d fodYi lgh gSA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lgh mÙkj ds vuq:i cqycqys dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %

iw.kZ vad : +3 ;fn dsoy lgh fodYi ds vuq:i cqycqys dks dkyk fd;k gSA

'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ugha fd;k gSA

½.k vad : –1 vU; lHkh ifjfLFkfr;ksa esaA

19. 'kq¼ ty 273 K vkSj 1 bar ij fgehHkwr (freezes) gksrk gSA 34.5 g ,sFksukWy dks 500 g ikuh esa Mkyus ij foy;u dk fgekad

cny tkrk gSA ty dk fgekad voueu fLFkjkad (freezing point depression constant) 2 K kg mol–1 ysaA uhps fn[kk, fp=k

ok"i nkc (V.P.) dks rkieku (T) ds fo:¼ vkys[kksa dks fu:fir djrs gSaA fuEufyf[kr esa ls fodYi tks fgekad esa cnyko dks

fu:fir djrk gS] gS (,FksukWy dk vk.kfod Hkkj 46 g mol–1)

(A)

Ice

Water

Water + Ethanol

270 273

V.P./bar

1

T/K

(B) Ice

Water

Water + Ethanol

271 273

V.P./bar

1

T/K

(C) Ice

Water

Water + Ethanol

270 273

V.P./bar

1

T/K

(D)

Ice

Water

Water + Ethanol

271 273

V.P./bar

1

T/K

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

gygygygygy ΔTf= 2

f

2 1

W 1000iK

M W

×⎡ ⎤⎢ ⎥×⎣ ⎦

= 34.5 1000

1 246 500

×⎡ ⎤× ⎢ ⎥×⎣ ⎦= 3 K

273 (K) – Tf = 3 (K)

⇒ Tf = 270 K

vkSj rki esa deh ds lkFk V.P. ?kVrk gSA

∴ xzkiQ (C) lgh gSA

20. fuEufyf[kr lsy ds fy,

Zn(s) | ZnSO4(aq) || CuSO

4(aq) | Cu(s)

tc Zn2+ dh lkUnzrk Cu2+ dh lkUnzrk ls 10 xquk gS rks ΔG (in J mol–1) ds fy, O;atd (expression) gS

17

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

[F iSQjkMs fu;rkad gS % R xSl fu;rkad gS : T rkieku gS ; vkSj lsy ds E° dk eku 1.1 V gS]

(A) 1.1F (B) 2.303RT – 2.2F

(C) 2.303RT + 1.1F (D) –2.2F

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

gygygygygy 4 4(aq) (aq)

Zn | ZnSO || CuSO | Cu

ΔG = ΔG° + RT In Q

ΔG = ΔG° + 2.303 RT log Q2

2

[Zn ] 10Q

1[Cu ]

+

+

⎛ ⎞= =⎜ ⎟⎜ ⎟

⎝ ⎠

ΔG°= – nF E°lsy

= – 2F × 1.1

= – 2.2 F

ΔG = – 2.2 F + 2.303 RT log 10

1

G 2.303 RT – 2.2 FΔ =

21. C (xzsiQkbV] graphite) C (ghjk, diamond) cuus dh T = 298 K ij ekud voLFkk fxc dh eqDr ÅtkZ;sa (standard state

Gibbs free energis of formation at T = 298 K)

ΔfG°[C(grapite)] = 0 kJ mol–1

ΔfG°[C(diamond)] = 2.9 kJ mol–1 gSA

ekud voLFkk dk eryc gS fd fn, x, rkieku ij nkc 1 bar gksuk pkfg, vkSj inkFkZ 'kq¼ gksuk pkfg,A C(xzsiQkbV) dk C

(ghjk) esa ifjorZu blds vk;ru dks 2 × 10–6 m3 mol–1 ?kVkrk gSA ;fn C (xzsiQkbV) dk C(ghjk) esa lerkih ifjorZu fd;k

tk; rks og nkc ftl ij C(xzsiQkbV), C(ghjk) ds lkFk lkE;koLFkk esa gS] gS

[mi;ksxh lwpuk % 1 J = 1 kg m2 s–2; 1 pa = 1 kg m–1 s–2; 1 bar = 105 Pa]

(A) 14501 bar (B) 58001 bar

(C) 1450 bar (D) 29001 bar

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygy ΔGº = ΔV·ΔP

⇒ –62900 2 10 P= × Δ

⇒ 6

2900 10P Pa

2

×Δ =

PF–1 = 14500 ckj

⇒ PF = 14501 ckj

22. fuEufyf[kr esa ls dkSulk la;kstu H2 xSl mRikfnr djsxk\

(A) Fe /krq ,oa lkUnz HNO3

(B) Cu /krq ,oa lkUnz HNO3

(C) Zn /krq ,oa NaOH (tyh;) (D) Au /krq ,oa NaCN ok;q dh mifLFkfr esa (tyh;)

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

18

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy Zn + 2NaOH ⎯→ Na2ZnO

2 + H

2

lkUnz HNO3 ds lkFk vk;ju fuf"Ø; cu tkrk gSA

HNO3 ds lkFk dkWij NO

2 eqDr djrk gSA

23. H3PO

2, H

3PO

4, H

3PO

3 vkSj H

4P

2O

6 esa iQkWLiQksjl ijek.kq dh vkWDlhdj.k voLFkk dk Øe gS

(A) H3PO

3 > H

3PO

2 > H

3PO

4 > H

4P

2O

6

(B) H3PO

4 > H

3PO

2 > H

3PO

3 > H

4P

2O

6

(C) H3PO

4 > H

4P

2O

6 > H

3PO

3 > H

3PO

2

(D) H3PO

2 > H

3PO

3 > H

4P

2O

6 > H

3PO

4

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

gygygygygy vkWDlhdj.k voLFkk

H3PO

4P = + 5

H4P

2O

6P = + 4

H3PO

3P = + 3

H3PO

2P = + 1

H3PO

4 > H

4P

2O

6 > H

3PO

3 > H

3PO

2

24. fuEufyf[kr vfHkfØ;k dk eq[; mRikn gSOH

NH2

i) NaNO , HCl, 0°C2

ii) aq.NaOH

(A)

OH

Cl

(B)

O Na– +

N Cl2

(C)

OH

N = N

(D)

OHN = N

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

gygygygygy

+

OH

N = N

NaNO + HCl2

aq.NaOH

OH

N NCl+ –≡

OH

N N≡

O–

N = N

O

H

NH2

0°C

19

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

25. fuEufyf[kr ;kSfxdksa esa {kkjdrk dk Øe gS

NH

H C3

NH2

I

N NH

II

HN N

III

NH2

H N2

NH

IV

(A) II > I > IV > III (B) IV > II > III > I

(C) IV > I > II > III (D) I > IV > III > II

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

gygygygygy

NH2

H N2

NH

IV

nks NH2 lewg ds }kjk vuqukn ds dkj.k NH ds 'N' ij bysDVªkWu ?kuRo c<+rk gSA

NH

NH2CH

3

dsoy ,d

= NH

–NH2 lewg ds lkFk vuqukn ds dkj.k

ij bysDVªkWu ?kuRo esa of¼ de gksrh gS

Nsp

2

N ;g ,dkadh ;qXe miyC/ ugha jgrk D;ksafd ;g,jksesfVd "k"Vd esa Hkkx ysrk gSA 'N'

C sp2

nksuksa rjiQ ls tqM+k gSAIII

H

N

N ;g ,dkadh ;qXe ,jksesfVdrk esa Hkkx ugha ysrkA vr% vf/d miyC/ jgrk gSAvkSj ,d rjiQ 'N' sp C

3 ls ca/k gSAII

H

∴ IV > I > II > III

[kaM[kaM[kaM[kaM[kaM-2 (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 28)))))

• bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d fodYi lgh gSaA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lkjs lgh mÙkj (mÙkjksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %

iw.kZ vad : +4 ;fn fliQZ lkjs lgh fodYi (fodYiksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk fd;k gSA

vkaf'kd vad : +1 izR;sd lgh fodYilgh fodYilgh fodYilgh fodYilgh fodYi ds vuq:i cqycqys dks dkyk djus ij] ;fn dksbZ xyr fodYi dkykugha fd;k gSA

'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ughaughaughaughaugha fd;k gSA

½.k vad : –2 vU; lHkh ifjfLFkfr;ksa esaA

• mnkgj.k % ;fn ,d iz'u ds lkjs lgh mÙkj fodYi (A), (C) vkSj (D) gSa] rc bu rhuksa ds vuq:i cqycqyksa dks dkyk djus ij+4 vad feysaxs_ fliQZ (A), (D) ds vuq:i cqycqyksa dks dkyk djus ij +2 vad feysaxsa_ rFkk (A) vkSj (B) ds vuq:i cqycqyksadks dkyk djus ij –2 vad feysaxs D;ksafd ,d xyr fodYi ds vuq:i cqycqys dks Hkh dkyk fd;k x;k gSA

20

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

26. i"B xq.kksa (surface properties) ds ckjs esa lgh dFku gS(gSa)

(A) vf/'kks"k.k (Adsorption), fudk; dh ,UVªkih ?kVus vkSj ,UFkSYih ?kVus ds lkFk gksrk gS

(B) ,Fksu vkSj ukbVªkstu ds Økafrd rkieku (critical temperatures) Øe'k% 563 K vkSj 126 K gSaA ,d fn, x;s rkieku ij

lfØf;r pkjdksy dh leku ek=k ij ,Fksu dk vo'kks"k.k ukbVªkstu dh vis{kk vf/d gksxk

(C) ckny ,d beY'ku izdkj dk dksykbM gS ftlesa nzo ifjf{kIr çkoLFkk (dispersed phase) gS vkSj xSl ifj{ksi.k ekè;e

(dispersion medium) gS

(D) dksykbZMh d.kksa dh czkÅuh xfr d.kksa ds lkbt ij fuHkZj ugha gksrh ijUrq foy;u dh ';kurk (viscosity) ij fuHkZj djrh gSa

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B)

gygygygygy vf/'kks"k.k Å"ek{ksih çØe gS rFkk blesa ,UVªkWih esa deh gksrh gSA

H 0, S 0Δ < Δ <fudk; fudk;

ØkfUrd rki (Tc) vf/d gksus ij vUrjvk.kfod vkd"kZ.k cy vf/d gksaxsA

∴ vf/'kks"k.k dk ifjek.k vf/d gksrk gSA

27. ifjos'k (surroundings) ds lkFk lkE;koLFkk esa ,d ik=k esa gks jgh ,d vfHkfØ;k ds fy,] ,UVªkWih esa cnyko ds vuqlkj blds

lkE;koLFkk fLFkjkad K ij rkieku ds çHkko dk o.kZu ,sls fd;k tkrk gS

(A) rkieku c<+us ds lkFk Å"ek{ksih (exothermic) ds lkE;koLFkk fLFkjkad K eku ?kVrk gS D;ksafd fudk; dh ,aVªksih esa cnyko

/ukRed gS

(B) rkieku c<+us ds lkFk Å"ek'kks"kh (endothermic) vfHkfØ;k ds lkE;koLFkk fLFkjkad K eku c<+rk gS D;ksafd ifjos'k dh çfrdwy

,aVªksih esa cnyko ?kVrk gS

(C) rkieku c<+us ds lkFk Å"ek'kks"kh (endothermic) vfHkfØ;k ds lkE;koLFkk fLFkjkad K eku c<+rk gS D;ksafd fudk; dh ,aVªksih

esa cnyko ½.kkRed gS

(D) rkieku c<+us ds lkFk Å"ek{ksih (exothermic) vfHkfØ;k ds lkE;koLFkk fLFkjkad K eku ?kVrk gS D;ksafd ifjos'k dh vuqdwy

,aVªksih esa cnyko ?kVrk gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B, D)

gygygygygy vfHkfØ;k vxz fn'kk esa Å"ek'kks"kh gks ;k Å"ek{ksih gks] rki of¼ ds dkj.k ifjos'k ls fudk; esa Å"ek çfo"V gksrh gSA Å"ek'kks"kh

fn'kk esa blds dkj.k fudk; dh ,UVªkWih ifjorZu /ukRed rFkk ifjos'k dh ΔS ½.kkRed gksxhA

28. ,d f}v.kqd vfHkfØ;k esa f=kfoe foU;klh ?kVd (steric factor) P dk çk;ksfxd eku 4.5 fu/kZfjr fd;k x;kA fuEufyf[kr esa ls

lgh fodYi gS(gSa)

(A) f=kfoe foU;klh ?kVd ds eku ls vfHkfØ;k dh lfØ;.k ÅtkZ (activation energy) vçHkkfor jgrh gS

(B) vkofÙk ?kVd (frequency factor) dk ç;ksfxd eku vkjhfu;l lehdj.k }kjk vuqekfur eku ls T;knk gS

(C) D;ksafd P = 4.5 gS] tc rd çHkkoh mRçsjd dk mi;ksx uk fd;k tk,] vfHkfØ;k vkxs ugha c<+sxh

(D) vkjhfu;l lehdj.k }kjk vuqekfur eku vkofÙk ?kVd (frequency factor) ds çk;ksfxd eku ls T;knk gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B)

gygygygygy f=kfoe foU;klh ?kVd A

A= çk;ksfxd

ifjdfyr

f=kfoe foU;klh ?kVd = 4.5

bldk vfHkçk; gS] Açk;ksfxd > Aifjdfyr

[,slk çrhr gksrk gS fd vfHkfØ;k d.kksa dh VDdj vis{kk vf/d rhozrk ls gksrh gSA vr% f=kfoe foU;klh ?kVd dk fl¼kUr

fn;k x;k gSA ]

21

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

29. uqfDyvksfiQfyd izfrLFkkiu vfHkfØ;kvksa (nucleophilic substitution reactions) ds lUnHkZ esa fuEufyf[kr ;kSfxdksa ds fy, lghdFku gS (gSa)

Br

I

Br

II III

H – C Br3C –

CH3

CH3

Br

IV

CH3

(A) I vkSj III SN1 fØ;kfof/ dk vuqlj.k djrs gSa

(B) I vkSj II SN2 fØ;kfof/ dk vuqlj.k djrs gSa

(C) ;kSfxd IV ds foU;kl (configuration) dk izrhiu (inversion) gksrk gS

(D) I, III vkSj IV ds fy, vfHkfØ;kf'kyrk dk Øe gS% IV > I > III

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B, C)

gygygygygy tc ekè;e vR;Ur /qzoh; rFkk çksfVd gSA vr% I o III, SN1 dk ikyu djsaxsA

vr% (A) lgh gS

(B) I o II, SN2 dk ikyu djsaxs] tc ekè;e /qzoh; vçksfVd gks rFkk ukfHkdLusgh mPp lkUnzrk esa çcy gksA

fodYi (C) lgh gS

Br NuNu

–

S 2N

SN2 dh fLFkfr esa çrhiu

(D) SN1 o S

N2 nksuks ifjfLFkfr;ksa ds fy, xyr gSA

30. fuEufyf[kr esa ls lgh dFku gS (gSa)

(A) Al(CH3)3 dh f}r;h lajpuk (dimeric structure) esa f=kdsUnz&nks bysDVªkWu vkca/ gS

(B) BH3 dh f}r;h lajpuk (dimeric structure) esa f=kdsUnz&nks bysDVªkWu vkca/ gS

(C) AlCl3 dh f}r;h lajpuk (dimeric structure) esa f=kdsUnz&nks bysDVªkWu vkca/ gS

(D) BCl3 dh yqbZl vEyrk AlCl

3 ls vf/d gS

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B, D)

gygygygygye

–

B B

H

H

H

H

H

H

e–

e–

e–

blesa nks 3c-2e cU/ gSa

2AlCl3

⎯→ Al

Cl Cl

Cl Cl

Al

Cl

Cl

blesa dksbZ 3c-2e cU/ ugha gSA

Al

CH3

CH3

CH3

CH3

Al

CH3

CH3

blesa nks 3c-2e cU/ gSA

vkSj BCl3 ,d AlCl

3 dh vis{kk çcy yqbZl vEy gSA

22

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

31. dsoy mHk;/ehZ (amphoteric) vkWDlkbMksa okyk (okys) fodYi gS(gSa)

(A) Cr2O

3, BeO, SnO, SnO

2(B) Cr

2O

3, CrO, SnO, PbO

(C) NO, B2O

3, PbO, SnO

2(D) ZnO, AI

2O

3, PbO, PbO

2

mÙkjmÙkjmÙkjmÙkjmÙkj (A, D)

gygygygygy ZnO, Al2O

3, PbO, PbO

2, Cr

2O

3, BeO, SnO o SnO

2 mHk;/ehZ vkWDlkbM gSaA

NO mnklhu vkWDlkbM gS

CrO {kkjh; vkWDlkbM gS

B2O

3 vEyh; vkWDlkbM gS

32. ;kSfxd P vkSj R ds vkstksuhdj.k (ozonolysis) djus ij Øe'k% Q vkSj S mRiUu gksrs gSaA mRikn Q vkSj S dk vk.kfod lw=k

C8H

8O gSA Q dh dSfutkjks vfHkfØ;k (Cannizzaro reaction) gksrh gS ijUrq gkyksiQkseZ vfHkfØ;k (haloform reaction) ugha gksrh]

tcfd S dh gkyksiQkseZ vfHkfØ;k gksrh gS ijUrq dSfutkjks vfHkfØ;k ugha gksrhA

(i)

i) O /CH CI3 2 2

ii) Zn/H O2

Q(C H O)

8 8

P

(ii)

i) O /CH CI3 2 2

ii) Zn/H O2

S(C H O)

8 8

R

P vkSj R ds mfpr la;kstu okyk fodYi Øe'k% gS(gSa)

(A) H C3 and

CH3

(B)H C

3

CH3

and CH

3

CH3

H C3

(C)

H C3

CH3

CH3

and CH

3

CH3

CH3

(D) H C3 and

CH3

H C3

mÙkjmÙkjmÙkjmÙkjmÙkj (A, B)

gygygygygy CH3

(i) O /CH Cl

(ii) Zn/H O

3 2 2

2

CH3

C – H + H – C – H

O O

dsfutkjks vfHkfØ;k nsrk gS

O /CH Cl

Zn/H O

3 2 2

2

C

gkyksiQkWeZ vfHkfØ;knsrk gS

C

CH2

CH3 CH

3

+ H – C – H

O O

O /CH Cl

Zn/H O

3 2 2

2

C – H

CH3 CH

3

+ CH – C – H3

O O

CH3

dsfutkjks vfHkfØ;k nsrk gS

O /CH Cl

Zn/H O

3 2 2

2

C

CH3

O

CH3

CH3

CH3 CH

3

+

CH3 CH

3

O

gkyksiQkWeZ vfHkfØ;knsrk gS

23

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

[kaM[kaM[kaM[kaM[kaM 3 (vf/dre vad(vf/dre vad(vf/dre vad(vf/dre vad(vf/dre vad % % % % % 12)))))

• bl [kaM esa nks vuqPNsn gSaA

• izR;sd vuqPNsn ij vk/kfjr nks iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa fliZQ ,d ,d ,d ,d ,d fodYi lgh gSA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lgh mÙk ds vuq:i cqycqys dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfRk;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%

iw.kZ vad % +3 ;fn dsoy lgh fodYi ds vuq:i cqycqys dks dkyk fd;k gSA

'kwU; vad % 0 vU; lHkh ifjfLFkfr;ksa esaA

vuqPNsnvuqPNsnvuqPNsnvuqPNsnvuqPNsn 1

MnO2 dh mifLFkfr esa KCIO

3 dk rkiu djus ij ,d xSl W curh gSA W dh vf/D; ek=k lisQn iQkLiQksjl ds lkFk

vfHkfØ;k djds X nsrh gSA X dh 'kq¼ HNO3 ds lkFk vfHkfØ;k Y vkSj Z nsrh gSA

33. W vkSj X Øe'k% gSa

(A) O3 vkSj P

4O

6

(B) O2 vkSj P

4O

6

(C) O2 vkSj P

4O

10

(D) O3 vkSj P

4O

10

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

34. Y vkSj Z Øe'k% gSa

(A) N2O

3 vkSj H

3PO

4(B) N

2O

5 vkSj HPO

3

(C) N2O

4 vkSj HPO

3(D) N

2O

4 vkSj H

3PO

3

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

ç- l- ç- l- ç- l- ç- l- ç- l- (33) ooooo (34) ds gyds gyds gyds gyds gy

gygygygygy 2[MnO ]

3 2(W)

2KClO 2KCl 3O⎯⎯⎯⎯→ +

2 4 4 10(X)

5O P P O+ →

4 10 3 2 5 3(X) (Z)

P O 4HNO 2N O 4HPO+ → +

vuqPNsnvuqPNsnvuqPNsnvuqPNsnvuqPNsn 2

(C2H

5)2O esa ;kSfxd P dh CH

3MgBr dh vf/drk ds lkFk vfHkfØ;k ds mijkUr ty Mkyus ij Q feyrk gSA ;kSfxd Q

H2SO

4 ds lkFk 0°C ij foospu djus ij R nsrk gSA CH

2Cl

2 esa R dh futZyh; AlCl

3 dh mifLFkfr esa CH

3COCl ds lkFk

vfHkfØ;k ds mijkUr ty Mkyus ij ;kSfxd S mRiUu gksrk gSA [;kSfxd P esa Et ,fFky xzqi gSA]

(H C) C3 3

CO Et2

P

Q R S

24

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

35. mRikn S gS

(A)

(H C) C3 3

H C3

CH3

COCH3

(B)(H C) C

3 3CH

3

COCH3

(C)

H COC3

(H C) C3 3

H C3 CH

3

(D)

HO S3

(H C) C3 3

O CH3

COCH3

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

36. Q ls R vkSj R ls S vfHkfØ;k,¡ gSa

(A) futZyhdj.k vkSj izQhMy&ØkÝV~ ,sflfydj.k (Friedel-Crafts acylation)

(B) ,sjksesfVd lYiQksuSlu vkSj izQhMy&ØkÝV ,sflfydj.k (Friedel-Crafts acylation)

(C) izQhMy&ØkÝV~ ,fYdyhdj.k (Friedel-Crafts alkylation), futZyhdj.k vkSj izQhMy&ØkÝV~ ,sflfydj.k (Friedel-Crafts acylation)

(D) izQhMy&ØkÝV ,fYdyhdj.k (Friedel-Crafts alkylation) vkSj izQhMy&ØkÝV ,sflyhdj.k (Friedel-Crafts acylation)

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

ç- l- ç- l- ç- l- ç- l- ç- l- (35) ooooo (36) ds gyds gyds gyds gyds gy

C(CH )3 3

C(CH )3 3

C(CH )3 3

C(CH )3 3

C(CH )3 3

C(CH )3 3

C(CH )3 3

C – OEt CH –C–CH3 3

CH –C–CH3 3

CH3

CH3

C(CH )3 2

C(CH )3 2

CH MgBr (C H ) O3 2 5 2

(vkf/D;)

O OMgBr

O–HO

– +

H O2

H SO2 4

/

0°C

( ),fYdyhdj.k

HH

–H O ( )2

futZyhdj.k(Q)

(P)

(R)

(S)

CH3

CH3

CH –C–Cl/AlCl

( )

3 3

,flyhdj.k

O

COCH3

25

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

MATHEMATICS

[kaM[kaM[kaM[kaM[kaM-1(vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 21)))))

• bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa fliZQ ,d ,d ,d ,d ,d fodYi lgh gSA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lgh mÙkj ds vuq:i cqycqys dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %fdlh ,d ds vuqlkj fn;s tk,saxs %

iw.kZ vad : +3 ;fn dsoy lgh fodYi ds vuq:i cqycqys dks dkyk fd;k gSA

'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ugha fd;k gSA

½.k vad : –1 vU; lHkh ifjfLFkfr;ksa esaA

37. leryksa 2x + y – 2z = 5 ,oe~ 3x – 6y – 2z = 7 ds yEcor~ vkSj fcUnq (1, 1, 1) ls xqtjus okys lery dk lehdj.k gS

(A) 14x + 2y – 15z = 1

(B) 14x – 2y + 15z = 27

(C) 14x + 2y + 15z = 31

(D) –14x + 2y + 15z = 3

mÙkjmÙkjmÙkjmÙkjmÙkj (C)

gygygygygy lery dk visf{kr lehdj.k

1 1 1

02 1 2

3 6 2

x y z− − −=−

− −

⇒ –14(x – 1) – 2(y – 1) + (–15)(y – 1) = 0

⇒ 14 2 15 31x y y+ + =

38. ekuk fd O ewyfcUnq (origin) gS ,oe~ PQR ,d LosfPNd f=kHkqt (arbitrary triangle) gSA fcUnq S bl izdkj gS fd

OP OQ OR OS OR OP OQ OS OQ OR OP OS⋅ + ⋅ = ⋅ + ⋅ = ⋅ + ⋅���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ����

rc fcUnq S f=kHkqt PQR dk gS

(A) dsUnzd (Centroid)

(B) ifjoÙkdsUnz (Circumcentre)

(C) vUr%dsUnz (Incentre)

(D) yEcdsUnz (Orthocenter)

mÙkjmÙkjmÙkjmÙkjmÙkj (D)

26

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy OP OQ OR OS OR OP OQ OS OQ OR OP OS⋅ + ⋅ = ⋅ + ⋅ = ⋅ + ⋅���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ���� ����

OP OQ OR OS OR OP OQ OS⋅ + ⋅ = ⋅ + ⋅���� ���� ���� ���� ���� ���� ���� ����

⇒ ( ) ( ) 0OP OQ OR OS OR OQ⋅ − + ⋅ − =���� ���� ���� ���� ���� ����

RQ

P

S

⇒ ( ) 0RQ OP OS⋅ − =���� ���� ���� �

⇒ 0RQ SP⋅ =���� ���� �

⇒ RQ SP⊥���� ����

rFkk blh izdkj ls OR OP OQ OS OQ OR OP OS⋅ + ⋅ = ⋅ + ⋅���� ���� ���� ���� ���� ���� ���� ����

ls

SR PQ⊥���� ����

∴ S yEcdsUnz gS

39. ;fn y = y(x) vodyuh; lehdj.k (differential equation) ( ) ( ) 1

8 9 4 9 , 0x x dy x dx x

−

+ = + + > dks lUrq"V djrk

gS ,oe~ ( )0 7y = gS] rc y(256) =

(A) 3 (B) 9

(C) 16 (D) 80

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygy pw¡fd,

8 9 4 9

dxdy

x x x

=+ ⋅ + +

lekdyu djus ij,

4 9y x c= + + +

x = 0 ij, 7y = ⇒ c = 0

blfy,] 4 9y x= + +

x = 256 ij, y = 3

40. ;fn :f →� � ,d bl izdkj dk f}vodyuh; (twice differentiable) iQyu gS fd lHkh x ∈� ds fy;s f ′′(x) > 0, ,oe~

1 1, (1) 1

2 2f f

= = gS] rc

(A) (1) 0f ≤′ (B)1

0 (1)2

f< ≤′

(C)1

(1) 12

f< ≤′ (D) (1) 1f >′

mÙkjmÙkjmÙkjmÙkjmÙkj (D)

27

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy ( ) 0f x′′ > , 11

22f⎛ ⎞ =⎜ ⎟⎝ ⎠

rFkk f(1) = 1

( )f x′ lnSo o/Zeku gksrk gS 1

11/2

1/2

B

A1

(1)2

(1)1

12

f f

f

⎛ ⎞− ⎜ ⎟⎝ ⎠′ >

−

(1) 1f ′ >

B ij Li'kZ js[kk dh izo.krk > thok AB dh izo.krk

41. ,sls fdrus 3 × 3 vkO;wg M gSa ftudh izfof"V;k¡ (entries) {0, 1, 2} esa gSa ,oe~ MT M dh fod.khZ; izfof"V;ksa (diagonal entries)

dk ;ksx 5 gS\

(A) 126 (B) 198

(C) 162 (D) 135

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

gygygygygy ekuk 1 1 1 1 2 3

2 2 2 1 2 3

3 3 3 1 2 3

,

T

a b c a a a

M a b c M b b b

a b c c c c

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= =⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

fod.kZ izfof"V;ksa dk ;ksxiQy = ( )3

2 2 2

1

5i i i

i

a b c

=

+ + =∑

∴ lEHko fLFkfr;k¡ (,d 2, ,d 1 rFkk lkr 'kwU;) ;k (ik¡p 1 rFkk pkj 0)

9! 9!72 126 198

7! 5!4!= + = + =

42. ekuk fd S = {1, 2, 3, ..., 9} gSA k = 1, 2, ..., 5 ds fy;s] ekuk fd Nk, leqPp; S ds mu mileqPp;ksa dh la[;k gS ftuesa

izR;sd mileqPp; esa 5 vo;o gSa ,oe~ bu vo;oksa esa fo"ke vo;oksa dh la[;k k gSA rc N1 + N

2 + N

3 + N

4 + N

5 =

(A) 210 (B) 252

(C) 125 (D) 126

mÙkjmÙkjmÙkjmÙkjmÙkj (D)

gygygygygy mileqPp;ksa dh visf{kr la[;k

= 5C1 × 4C

4 + 5C

2 × 4C

3 + 5C

3 × 4C

2 + 5C

4 × 4C

1 + 5C

5 × 4C

0

= 5 + 40 + 60 + 20 + 1

= 126

oSdfYid fof/oSdfYid fof/oSdfYid fof/oSdfYid fof/oSdfYid fof/

(1 + x)5(1 + x)4 esa x5 dk xq.kkad

= 9C5

= 126

28

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

43. ;g ik;k x;k gS fd ;knfPNd (randomly) :i ls p;fur rhu v½.kkRed iw.kk±d (non-negative integers) x, y ,oe~ z lehdj.kx + y + z = 10 dks lUrq"V djrs gSaA rc z ds le (even) gksus dh izkf;drk (probability) gS

(A)36

55

(B)6

11

(C)1

2

(D)5

11

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

gygygygygy x + y + z = 10

n(s) = 10+3–1C3–1

= 12C2 =

12 1166

2

× =

ekuk z = 2n, tgk¡ n = 0, 1, 2, 3, 4, 5

x + y + 2n = 10

x + y = 10 – 2n

,sls dqy gy 5

0

(11 2 ) 36n

n

== − =∑

P(E) = 36 6

66 11=

[kaM[kaM[kaM[kaM[kaM-2 (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad (vf/dre vad : 28)))))

• bl [kaM esa lkrlkrlkrlkrlkr iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d,d ;k ,d ls vf/d fodYi lgh gSaA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lkjs lgh mÙkj (mÙkjksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfr;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %fdlh ,d ds vuqlkj fn;s tk,axs %

iw.kZ vad : +4 ;fn fliQZ lkjs lgh fodYi (fodYiksa) ds vuq:i cqycqys (cqycqyksa) dks dkyk fd;k gSA

vkaf'kd vad : +1 izR;sd lgh fodYilgh fodYilgh fodYilgh fodYilgh fodYi ds vuq:i cqycqys dks dkyk djus ij] ;fn dksbZ xyr fodYi dkykugha fd;k gSA

'kwU; vad : 0 ;fn fdlh cqycqys dks dkyk ughaughaughaughaugha fd;k gSA

½.k vad : –2 vU; lHkh ifjfLFkfr;ksa esaA

• mnkgj.k % ;fn ,d iz'u ds lkjs lgh mÙkj fodYi (A), (C) vkSj (D) gSa] rc bu rhuksa ds vuq:i cqycqyksa dks dkyk djus ij+4 vad feysaxs_ fliQZ (A), (D) ds vuq:i cqycqyksa dks dkyk djus ij +2 vad feysaxsa_ rFkk (A) vkSj (B) ds vuq:i cqycqyksadks dkyk djus ij –2 vad feysaxs D;ksafd ,d xyr fodYi ds vuq:i cqycqys dks Hkh dkyk fd;k x;k gSA

29

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

44. ;fn sin(2 )

1

sin( ) sin ( ) ,

x

x

g x t dt−= rc

(A) 22

gπ − = − π′ (B) 2

2g

π − = π′

(C) 22

gπ = π′ (D) 2

2g

π = − π′

mÙkjmÙkjmÙkjmÙkjmÙkj (fn;k x;k dksbZ Hkh fodYi lgh ugha gSfn;k x;k dksbZ Hkh fodYi lgh ugha gSfn;k x;k dksbZ Hkh fodYi lgh ugha gSfn;k x;k dksbZ Hkh fodYi lgh ugha gSfn;k x;k dksbZ Hkh fodYi lgh ugha gS)

gygygygygy ( )( ) ( )( )1 1( ) 2cos2 cossin sinsin2 sing x x xx x− −′ = −

∴ 02

gπ⎛ ⎞′ =⎜ ⎟

⎝ ⎠, 0

2g

π⎛ ⎞′ =−⎜ ⎟⎝ ⎠

fn;k x;k dksbZ Hkh fodYi lgh ugha gS

45. ekuk fd α ,oe~ β bl izdkj dh v'kwU; okLrfod la[;k;sa (non-zero real numbers) gaS fd 2(cosβ – cosα) + cosα cosβ = 1.

rc fuEu esa ls dkSu lk(ls) lR; gS(gSa)\

(A) tan 3 tan 02 2

α β + = (B) 3 tan tan 02 2

α β + =

(C) tan 3 tan 02 2

α β − = (D) 3 tan tan 02 2

α β − =

mÙkjmÙkjmÙkjmÙkjmÙkj (A, C)

gygygygygy pw¡fd 2(cosβ – cosα) = 1 – cosα ⋅ cosβ

2cos 1cos

2 cos

β − − β

;ksxkUrjkuqikr dk iz;ksx djus ij

1 cos 1 cos3

1 cos 1 cos

− α − β⎛ ⎞⇒ = ⎜ ⎟+ α + β⎝ ⎠

2 2tan 3 tan 0

2 2

α β

blfy,, tan 3 tan 02 2

α β+ =

;k

tan 3 tan 02 2

α β− =

46. ;fn :f →� � bl izdkj dk vodyuh; (differentiable) iQyu gS fd lHkh x ∈�ds fy;s f′(x) > 2f(x), ,oe~ f(0) = 1 gS]rc

(A) (0, ∞) esa f(x) oèkZeku (increasing) gS (B) (0, ∞) esa f(x) ßkleku (decreasing) gS

(C) (0, ∞) esa f(x) > e2x (D) (0, ∞) esa f ′(x) < e2x

mÙkjmÙkjmÙkjmÙkjmÙkj (A, C)

30

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy ( ) 2 ( ) 0f x f x′ − >

2 2( ) 2 ( ) 0x xe f x e f x

− −′⋅ − ⋅ >

( )2 0( )xd

e f xdx

− > ⇒ 2 ( )xe f x

− ⋅ o/Zeku iQyu gSA

2 ( ) 1xe f x

− ⋅ > lHkh (0, )x ∈ ∞ ds fy,

2( ) xf x e>

∵2( ) 2 ( ) 0x

f x f x e′ > > >

∴ f(x) o/Zeku gS

rFkk] ( ) (0)( )

0

f x ff x

x

−′ =−

⇒ ( ) 1

( )f x

f xx

−′ =

i.e., 2( ) (0, 1)xf x e x′ > ∀ ∈

2 (1, )xe x< ∀ ∈ ∞

47. ekuk fd x ≠ 1 ds fy;s] 1 (1 1 ) 1

( ) cos1 1

x xf x

x x

− + − ⎛ ⎞= ⎜ ⎟− ⎝ − ⎠A rc

(A)1

lim ( ) 0x

f x−→= (B)

1lim ( )

x

f x−→ dk vfLrRo ugha gS (does not exist)

(C)1

lim ( ) 0x

f x+→= (D)

1lim ( )

x

f x+→ dk vfLrRo ugha gS (does not exist)

mÙkjmÙkjmÙkjmÙkjmÙkj (A, D)

gygygygygy1 (1 |1 |) 1

( ) cos|1 | 1

x xf x

x x

− + − ⎛ ⎞= ⎜ ⎟− ⎝ − ⎠

1

1 (1 1) 1lim cos

( 1) 1x

x x

x x+→

− + − ⎛ ⎞⎜ ⎟− ⎝ − ⎠

2

1

1 1lim cos

( 1) 1x

x

x x+→

− ⎛ ⎞⎜ ⎟− ⎝ − ⎠

1

1lim – (1 )cos

1x

x

x+→

⎛ ⎞+ ⎜ ⎟⎝ − ⎠

= –2 o 2 ds eè; fLFkr ,d la[;k

vr%] lhek vfLrRo esa ugha gS

1

1 (1 (1 )) 1lim cos

(1 ) 1x

x x

x x−→

− + − ⎛ ⎞⎜ ⎟− ⎝ − ⎠

1

1 (2 ) 1lim cos

(1 ) 1x

x x

x x−→

− − ⎛ ⎞⎜ ⎟− ⎝ − ⎠

1

1lim(1 )cos 0

1x

x

x→

⎛ ⎞− =⎜ ⎟⎝ − ⎠

31

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

48. ;fn

cos(2 ) cos(2 ) sin(2 )

( ) cos cos sin

sin sin cos

x x x

f x x x x

x x x

= − − , rc

(A) (–π, π) esa dsoy rhu fcUnqvksa ij f ′ (x) = 0 gS

(B) (–π, π) esa rhu ls vfèkd fcUnqvksa ij f ′ (x) = 0 gS

(C) x = 0 ij f(x) dk vfèkdre (maximum) gS

(D) x = 0 ij f(x) dk U;wure (minimum) gS

mÙkjmÙkjmÙkjmÙkjmÙkj (B, C)

gygygygygy1 1 2

C C C→ −

0 cos2 sin2

( ) 2cos cos sin

0 sin cos

x x

f x x x x

x x

= − −

⇒ ( ) 2cos (cos2 cos sin sin2 )f x x x x x x= −

⇒ ( ) 2cos cos3f x x x= ; (f(0) = 2, x = 0 ij vf/dre)

⇒ ( ) cos4 cos2f x x x= +

( ) 2sin2 (4cos2 1)f x x x′ = − +

⇒ sin2 0x = ;k 1cos2

4x = −

2 0, , x = π − π

0, , 2 2

xπ π= − rFkk

1cos2

4x = − , (–π, π) esa 4 gy nsrk gS

∴ gyksa dh dqy la[;k = 7

49. ;fn js[kk x = α {ks=k (region) ( ){ }2 3, : ,0 1R x y x y x x= ∈ ≤ ≤ ≤ ≤� ds {ks=kiQy dks nks cjkcj Hkkxksa esa foHkkftr djrh gS]

rc

(A)1

02

< α ≤

(B)1

12

< α <

(C) 4 22 4 1 0α − α + =

(D) 4 24 1 0α + α − =

mÙkjmÙkjmÙkjmÙkjmÙkj (B, C)

32

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

gygygygygy1

3 3

0

( ) ( )x x dx x x dx

α

α

− = −∫ ∫

⇒1

2 4 2 4

04 2 4

x x x x

α

α=− −

α

⇒2 4 2 41 1

2 4 2 4 2 4

xα ⎛ ⎞⎛ ⎞ α α− = −− −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

(0, 0)O (1, 0)

y x = 3

y

x

x = α

y x =

⇒4

2 10

2 4

α − α + =

⇒ 4 22 4 1 0α − α + =

ekuk 4 2( ) 2 4 1f α = α − α +

(0) 1 0f = > , 11

082

f⎛ ⎞ = >⎜ ⎟⎝ ⎠

(1) 1 0f = − <

∴1

, 12

⎛ ⎞α ∈ ⎜ ⎟⎝ ⎠

50. ;fn 98

1

1

1,

( 1)

k

kk

kI dx

x x

+=

+=+ rc

(A) I > loge99 (B) I < log

e99

(C)49

50I < (D)

49

50I >

mÙkjmÙkjmÙkjmÙkjmÙkj (B, D)

gygygygygy I = 198

1

( 1)( 1)

k

k k

dxk

x x

+

=

+ +

198 98

1 1

1( 1) log ( 1) log log

1 2 1

k

k kk

x k kk k

x k k

+

= =

+ = + = + − + + +

{ }98

1

1( 1)log log log( 1) log

2 1k

k kk k k k

k k=

+ = + − + + − + +

( )99 199log log log99 log1

100 2

= − + −

9999log log2 log (99)

100e

⎛ ⎞= + +⎜ ⎟⎝ ⎠

33

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

[kaM[kaM[kaM[kaM[kaM 3 (vf/dre vad(vf/dre vad(vf/dre vad(vf/dre vad(vf/dre vad % % % % % 12)))))

• bl [kaM esa nks vuqPNsn gSaA

• izR;sd vuqPNsn ij vk/kfjr nks iz'u gSaA

• çR;sd iz'u ds pkjpkjpkjpkjpkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa fliZQ ,d ,d ,d ,d ,d fodYi lgh gSA

• izR;sd iz'u ds fy, vks-vkj-,l- ij lgh mÙk ds vuq:i cqycqys dks dkyk djsaA

• izR;sd iz'u ds fy, vad fuEufyf[kr ifjfLFkfRk;ksa esa ls fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%fdlh ,d ds vuqlkj fn;s tk,axs%

iw.kZ vad % +3 ;fn dsoy lgh fodYi ds vuq:i cqycqys dks dkyk fd;k gSA

'kwU; vad % 0 vU; lHkh ifjfLFkfr;ksa esaA

vuqPNsn vuqPNsn vuqPNsn vuqPNsn vuqPNsn 1

ekuk fd O ewyfcUnq (origin) gS ,oe~ , , OX OY OZ

���� ���� ����

Øe'k% f=kHkqt PQR dh Hkqtk;sa , , QR RP PQ

���� ���� ����

, dh fn'kkvksa esa rhu ,dd

lfn'k (unit vectors) gSaA

51. | |OX OY× =���� ����

(A) sin (P + Q) (B) sin 2R

(C) sin (P + R) (D) sin (Q + R)

mÙkjmÙkjmÙkjmÙkjmÙkj (A)

gygygygygy QR RPOX OY

pq

×× =���� ����

���� ����

sinpq R

pq=

sin( )P Q= +

52. ;fn f=kHkqt PQR ifjorhZ gS (if the triangle PQR varies), rc cos( ) cos( ) cos( )P Q Q R R P+ + + + + dk U;wure eku (minimum

value) gS

(A)5

3− (B)

3

2−

(C)3

2(D)

5

3

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

gygygygygy cos(P + Q) + cos(Q + R) + cos(R + P) = –(cosP + cosQ + cosR)

cosP + cosQ + cosR dk vf/dre eku = 3

2

vr% –(cosP + cosQ + cosR) dk U;wure = 3

2−

vuqPNsnvuqPNsnvuqPNsnvuqPNsnvuqPNsn 2

ekuk fd p, q iw.kk±d gS ,oe~ α, β lehdj.k x2 – x – 1 = 0 ds ewy gSa] tgk¡ α ≠ β gSA n = 0, 1, 2, ... , ds fy, ekuk fda

n = pαn + qβn gSA

rF;rF;rF;rF;rF;: ;fn a ,oe~ b ifjes; la[;k;sa (rational numbers) gSa ,oe~ 5 0a b+ = gS] rc a = 0 = b gSA

34

JEE (ADVANCED)-2017 (PAPER-2) CODE-1

53. a12

=

(A) 11 10a a− (B) 11 10

a a+

(C) 11 102a a+ (D) 11 10

2a a+

mÙkjmÙkjmÙkjmÙkjmÙkj (B)

gygygygygy α2 – α – 1 = 0 ⇒ α12 = α11 + α10 ...(i)

rFkk β12 = β11 + β10 ...(ii)

(i) dks p ls ,oa (ii) dks q ls xq.kk djus ij rFkk ;ksx djus ij, a12

= a11

+ a10

54. ;fn a4 = 28, rc p + 2q =

(A) 21 (B) 14

(C) 7 (D) 12

mÙkjmÙkjmÙkjmÙkjmÙkj (D)

gygygygygy a4 = 28

4 4

1 5 1 528

2 2

p q⎛ ⎞ ⎛ ⎞+ −+ =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⇒ 56( ) 24 5( ) 28 16p q p q+ + − = ×

⇒ p = q = 4

END OF MATHEMATICS