JEE MAIN EXAMINATION - 2014 QUESTIONS WITH SOLUTIONS [HINDI …€¦ · JEE MAIN EXAMINATION - 2014...

JEE MAIN Examination(2014) (Code - H) (Page # 1)

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[PHYSICS]3. yEckbZ dh , d vfor kU; Mksj h l s c¡/ks nzO; eku m ds , dckc dks , d Å/okZ/kj vk/kkj l s yVdk; k t kr k gSaA ckc Å/okZ/kj i jdks.kh; pky rad/s l s , d {kSfr t oÙk esa ?kw.kZu dj r k gSA fuyacufcUnq i j %(1) dks.kh; l aosx fn' kk esa i fj or Zu' khy gS i j Ur q i fj ek.k esa ugha(2) dks.kh; l aosx nksuksa fn' kk , oa i fj ek.k esa i fj or Zu' khy gSA(3) dks.kh; l aosx l aj f{kr j gr k gSA(4) dks.kh; l aosx i fj ek.k esa i fj or Zu' khy gSa i j Ur q fn' kk esa ughaASol. 1

L

L

L l fn' k fn' kk esa ?kwer k gS fdar q i fj ek.k fu; r j gr k gSA

4. , d Mk; kssM dh /kkj k&oksYVr k l EcU/k I = (e1000V/T – 1)mA l s nh t kr h gSa] t gk¡ V yxkbZ xbZ oksYVr k oksYV esa gS vkSj r ki ekuT fMxzh dSfYou esa gSA ; fn , d fo| kFkhZ 300 K i j 5 mA /kkj k uki r sgq; s eki us esa 0.01 V dh =kqfV dj r k gS] r c /kkj k ds eku esa mA esa=kqfV D; k gksxh\(1) 0.5 mA (2) 0.05 mA(3) 0.2 mA (4) 0.02 mASol. 3

I =

1e T

V1000

mA

TV1000

e = I + 1

log (I + 1) = T

V1000

1I1

× dI = 1000

T × dv

dI = 3001000

× (5 + 1) mA × 0.01

= 0.2 mA5. , d [ kqyh dk¡p dh uyh dks i kj s esa bl i zdkj Mqcks; k t kr kgSa fd i kj s ds Lr j l s 8 cm Åi j dk¡p dh uyh dh yEckbZ gSA uyhds [ kqys fl j s dks vc cUn dj l hy dj fn; k t kr k gS vkSj uyh dksÅ/okZ/kj vfr fj Dr 46 cm l s Åi j mBk; k t kr k gSA uyh esa i kj s dsÅi j ok; q Lr EHk dh yEckbZ vc D; k gksxh\(ok; qea.Myh; nkc = Hg dk 76 cm)(1) 38 cm (2) 6 cm (3) 16 cm (4) 22 cm

1. 10 cm yEckbZ ds , d LVhy ds r kj ds fl j ksa i j t cr ki eku esa of) 100ºC dh t krh gSa r c bl dh yEckbZ fLFkj j [ kus dsfy, fl j ksa i j yxk; k x; k nkc gS %(LVhy dk ; ax i zR; kLFkr k xq.kkad 2 × 1011 N m–2 vkSj j sf[ kd i zl kjxq.kkad 1.1 × 10–5 K–1)(1) 2.2 × 107 i kLdy (2) 2.2 × 106 i kLdy(3) 2.2 × 108 i kLdy (4) 2.2 × 109 i kLdySol. 3

y = 2 × 1011

lf = l0 (1 + t) t = 100° C = 1.1 × 10–5 k–1

lf – l0 = t l = 1.1 × 10–5 × 100= 1.1 × 10–3

y = 3

p1.1 10

2 × 1011 = 3

p1.1 10

p = 2 × 1.1 × 1011 × 10–3

p = 2.2 × 108 Pa

2. , d l qpkyd z-v{k ds l kFk – 1.5 z < 1.5 m i j j [ kk

gS vkSj bl esa - za fn' kk esa fLFkj /kkj k 10.0 A i zokfgr gks j gh gSA ¼fp=k

ns[ ksa½A {ks=k B

= 3.0 × 10–4 e–0.2x ya T ds fy, ] l qpkyd dks

fLFkj pky l s x = 2.0 m, y = 0 m r c 5 × 10–3 s esa xfr dj kusds fy, vko' ; d ' kfDr dh x.kuk dh dhft , A x-v{k i j l ekUr j xfreku ysaA

(1) 14.85 W (2) 29.7 W (3) 1.57 W (4) 2.97 WSol. 4

w = dxe103310 x2.04

= 4. 5 × 10–2 (1 – e–0.4)

P = Tw

= 2.97

JEE MAIN Examination(2014) (Code - H)(Page # 2)

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Sol. 3

8cm

P0

76 × 8 = × pgas

76 8

= pgas

76 8

+ (54 – ) = 76

54 – = 7681

= 76 8

54 – 2 = 76 – 6082 + 22 – 608 = 0

= 222 (22) 4 808

2

= 2

5422 = 16 cm

6. l wph -I (fo| qr pqEcdh; r j ax i zdkj ) dks l wph -II (bul sl Ecf) r @vuqi z; ksfxr ) l s l qesfyr dhft , vkSj l wfp; ksa ds uhps fn; sx; s fodYi ksa esa l s l gh fodYi pqfu; s %

(a) voj Dr r j axs (i)ek¡l i sf' k; ksa dh fodfr

ds bykt ds fy,

(b) j sfM; ks r j axs (ii) i zl kj .k ds fy,

(c) , Dl -fdj .ksa (iii)gfì ; ksa ds vfLFkHkax

dh i gpku ds fy ,

(d) i j kcSaxuh fdj .ksa (iv)okrkoj .k dh vkst ksau

i j r } kj k vo' kks"k.k

l wph-I l wph-II

(a) (b) (c) (d)(1) (iii) (ii) (i) (iv)(2) (i) (ii) (iii) (iv)(3) (iv) (iii) (ii) (i)(4) (i) (ii) (iv) (iii)Sol. 2

7. nks oÙkh; IysVksa] ft uds chp nwjh 5 mm gSa] l s , d l ekUr j i fêdkl a/kkfj =k cuk; k x; k gS ft l ds chp i j koS| qr fLFkj kad 2.2 dk , di j koS| qr j [ kk x; k gS t c i j koS| qr esa fo| qr {ks=k3 × 104 V/m gS] r c /kukRed IysV dk vkos' k ?kuRo yxHkx gksxk%(1) 3 × 104 C/m2

(2) 6 × 104 C/m2

(3) 6 × 10–7 C/m2

(4) 3 × 10–7 C/m2

Sol. 3Q = cv

Q = d

A. r0 V

= AQ

= 0 r.d

V

= 0 r .E= 8.85 × 10–12 × 2.2 × 3 × 104

= 58.41 × 10–8 _~ 6 × 10–7 c/m2

8. , d fo| kFkhZ us , d NM+ dh yEckbZ eki dj 3.50 cm fy[ khAbl dks eki us esa ml us fdl mi dj .k dk i z; ksx fd; k\(1) , d LØw xst ft l ds ofuZ; j Ldsy esa 100 Hkkx gSa vkSj fi p 1mm gSA(2) , d Ldwy xst ft l ds ofuZ; j Ldsy esa 50 Hkkx gSa vkSj fi p1 mmgSA(3) , d ehVj LdsyA(4) , d ofuZ; j dSfyi l Z t gk¡ ofuZ; j Ldsy ds 10 Hkkx eq[ ; Ldsyds 9 Hkkxksa l s feyr s gSa vkSj eq[ ; Ldsy ds 1 cm esa 10 Hkkx gSaASol. 4

ofuZ; j dsfy i j dk vYi r ekad = 10

cm1.0

= 0.01 cmr Fkk 3.50 cm dk U; wur e i kB~; kad 0.01 cm gS

9. i zR; sd nzO; eku M ds pkj d.k t ks fd , d nwl j s l s l ekunwj h i j gSa] , d nwl j s ds vU; ksU; xq: Rokd"kZ.k i zHkko esa f=kT; k R ds , doÙk i j xfr ' khy gSA i zR; sd d.k dh pky gS %

(1) GM 1 2 2R

(2) 1 GM 1 2 22 R

(3) GMR

(4) GM2 2R

Sol. 2




(2)(1)

(3) (4)

r

rmv2

= F14 + F24 + F34

= 2

2

r4Gm

+ 2

2

r2Gm

2

= 2

2

r2Gm

2

21

2mvr

= 2

2

r2Gm

2

221

v = Gm(1 2 2)4r

v = 21

)221(r

Gm

10. , d cgr Hkou esa] 40 W ds 15 cYc] 100 W ds 5 cYc]80 W ds 5 i a[ ksa , oa 1 kW dk 1 ghVj gSaA fct yh ds esUl dhoksYVr k 220 V gSA Hkou ds eq[ ; ¶; wt dh U; wur e {ker k gksxh %(1) 12 A (2) 14 A(3) 8 A (4) 10 ASol. 1

P = RV2

R1 = 40

)200( 2

dqy fo| qr /kkj k

= 1R

V × 15 +

2RV

× 5 + 3R

V × 5 +

4RV

× 1

R = V2/P

= 220

1540 +

2205100

+ 220

580 +

2201000

= 11.3626 AU; wur e eku 12 A.

11. , d d.k , d l j y j s[ kk esa l j y vkor Z xfr l s xfr ' khy gSA; g foj kekoLFkk l s i zkj EHk dj i zFke l Sfd.M esa nwj h a vkSj vxys l Sd.M esa nwj h 2a ml h fn' kk esa r ; dj r k gSA r c %(1) xfr dk vk; ke 4a gSA(2) nksyuksa dk vkor Z dky 6gSA(3) xfr dk vk; ke 3a gSA(4) nksyuksa dk vkor Z dky 8gSASol. 2

a

3a

A – A cos () = a ....(1)A – A cos (2) = 3a2A (1 – cos2 ) = 3a ...(2)l ehdj .k (2) dks (1) dk Hkkx nsus i j2 (1 + cos ) = 3cos = 1/2= /3

T2

= /3

T = 6

12. , d NksVs pqEcd dh fuxzkfgr k] t gk¡ yksgpqEcd vpqEcdh; gkst kr k gS] 3 × 103 A m–1 gSA pØksa dh l a[ ; k 100 , oa yEckbZ 10cm dh , d i fj ukfydk l s i zokfgr vko' ; d /kkj k dk eku] ft l l s fdpqEcd i fj ukfydk ds vUnj gksus i j vpqEcdh; gks t k; s] gS %(1) 3 A (2) 6 A(3) 30 mA (4) 60 mASol. 1

fuxzkfgr k 0

B = 3 × 103 A/m

B = 0 (3 × 103) = 0 nI

= 0

1.0

100 I

I = 100

1.0103 3 = 3 A




13. vxzfl r ck; l okyk Mk; ksM+ t ksM+ gS %

(1)

(2)

(3)

(4)

Sol. 3

+2V

( )mPp ( )fuEu

–2V

vxz vfHkufr

14. , d ek/; e esa fo| qr pqEcdh; r j axksa ds l apj .k ds nkSj ku %(1) fo| qr h; Åt kZ ?kuRo pqEcdh; Åt kZ ?kuRo ds cj kcj gSA(2) nksuksa fo| qr h; , oa pqEcdh; Åt kZ ?kuRo ' kwU; gSA(3) fo| qr h; Åt kZ ?kuRo pqEcdh; Åt kZ ?kuRo dk nksxquk gSA(4) fo| qr h; Åt kZ ?kuRo pqEcdh; Åt kZ ?kuRo dk vk/kk gSASol. 1

, d fo| qr pqEcdh; r j ax esa

1/2 0 E2 =

0

2

2B

nksuksa l eku gksr s gS

15. ; gk¡ n' kkZ; s x; s i fj i Fk esa] fcUnq 'C' dks fcUnq 'A' l s r c r dt ksM+s j [ kk t kr k gS t c rd fd i fj i Fk esa i zokfgr /kkj k fLFkj u gks t k, Ar Ri ' pkr ~] vpkud] fcUnq 'C' dks fcUnq 'A' l s gVkdj fcUnq 'B' l s t =0 l e; i j t ksM+ fn; k t kr k gSA t = L/R i j i zfr j ks/k i j oksYVr k dki zsj dRo i j oksYVr k l s vuqi kr gksxk %

(1) –1 (2) 1 e

e

(3) e

1 e(4) 1

Sol. 1t c BC dks t ksM+k t kr k gS] r c L , oa R i fj i Fk es j gt kr s gS

R

– +

+

–L

KVL yxkus i j , VR + VL = 0 VR = –VL

L

R

VV

= – 1

16. f=kT; k R , oa nzO; eku m ds , d , dl eku [ kks[ kys csyu dspkj ksa r j Q , d nzO; ekufoghu Mksj h l s , d nzO; eku 'm' voyafcr gSaA; fn Mksj h csyu i j fQl yr h ugha gSa] r c NksM+s t kus i j nzO; eku fdlRoj .k l s fxj sxk\

(1) 6g5

(2) g (3) 3g2

(4) 2g

Sol. 4mg – T = ma .....(1)TR = I

TR = mR2 aR

T = ma ......(2) T

m

mg – ma = maa = g/2

17. f} i j ek.kqd vkn' kZ xSl dk , d eksy pØh; i zfØ; k ABC l sxqt j r k gS t Sl k fd fp=k esa n' kkZ; k x; k gSA i zfØ; k BC : ) ks"e gSA A,B , oa C ds r ki eku Øe' k% 400K, 800K , oa 600K gSaA l gh dFkupqfu; s %




(1) i zfØ; k AB esa vkUr fj d Åt kZ esa i fj or Zu -350 R gSA(2) i zfØ; k BC esa vkUr fj d Åt kZ esa i fj or Zu -500 R gSA(3) l Ei w.kZ pØh; i zfØ; k esa vkUr fj d Åt kZ esa i fj or Zu 250 R gSA(4) i zfØ; k CA esa vkUr fj d Åt kZ esa i fj or Zu 700 R gSASol. 2

C600

800B

A400

P

V

(1) dUAB = n cv dT

= 1 × 2R5

(400)

= 1000 R(2) dUBC = n cv dT

= 1 × 2R5

(–200)

= – 500 R(3) dUABCA = 0

(4) dUCA = 1 × 2R5

(–200) = – 500 R

18. Å¡pkbZ H dh , d ehukj l s] pky u l s , d d.k dksÅ/okZ/kj Åi j dh vksj Qsadk t kr k gSA d.k dks i Foh rd fxj us esa yxkl e; ml ds mPpr e fcUnq r d i gq¡pus ds l e; dk n xquk gSaA

H, u , oa n ds chp l EcU/k gSA(1) 2g H = nu2(n-2) (2) g H = (n-2)u2

(3) 2g H = n2u2 (4) g H = (n-2)2u2

Sol. 1

u

H

–H = ut – 1/2 g t2

t' = u/g

–H = u

gnu

– 1/2 g 2

gnu

–H = gnu2

– 1/2 gun 22

–H = gnu2

(1 – 21

n)

–2Hg = nu2 (2 – n) 2Hg = nu2 (n – 2)

19. Økmu dk¡p

23

l s cus , d i r ys mÙky ysUl dh

Qksdl yEckbZ f gSA t c bl s vi or Zukad 34

, oa 35

okys nks fHkUu nzoksa

esa j [ kdj eki k t kr k gS] r c Qksdl yEckb; k¡ Øe' k f1 , oa f2 gSaAQksdl yEckb; ksa ds chp l gh l EcU/k gSa %(1) f2 > f vkSj f1 _ .kkRed gks t kr k gSA(2) f1 , oa f2 nksuksa _ .kkRed gks t kr s gSA(3) f1 = f2 < f(4) f1 > f vkSj f2 _ .kkRed gks t kr k gSASol. 4

pwafd 4/3 < 3/2 bl fy, f1 > fpwafd 5/3 > 3/2 bl fy, f2 dk fpaâ cnyr k gS

20. r k¡cs] i hr y , oa LVhy dh rhu NM+ksa dks Y- vkdkj l aj puk esa osYMfd; k x; k gSaA i zR; sd NM+ dh vuqi zLFk dkV dk {ks=kQy = 4cm2 gSAr k¡cs dh NM+ ds fl j s dk r ki eku 100°C gSa t cfd i hr y , oa LVhyds fl j s 0°C r ki eku i j j [ ks x; s gSaA r k¡cs] i hr y , oa LVhy dh NM+ksadh yEckbZ; k¡ Øe' k% 46, 13 , oa 12 cms gSaA NM+ksa dks] muds fl j ksadks NksM+dj ] okr koj .k l s Å"eh; j ks/kh fd; k x; k gSA r k¡cs] i hr y , oaLVhy dh Å"ek pkydr k, ¡ Øe' k% 0.92, 0.26 , oa 0.12 CGSbdkbZ gSaA r k¡cs dh NM+ l s i zokfgr Å"ek dh nj gS %(1) 4.8 cal/s (2) 6.0 cal/s(3) 1.2 cal/s (4) 2.4 cal/sSol. 1

100° 0°C

Cu46cmk=0.92

Br13 cmk=0.26T

st, 12 cmk = 0.12

0°C




fdj pksQ ds fu; e l s

1R100T

+ 2

T 0R

+ 3

T 0R

= 0

)46(100T

(0.92) + 13T

(0.26) + 12T

(0.12) = 0

50100T

+ 50T

+ 100T

= 0

2T – 200 + 2T + T = 0T = 40

Cu

dQdt

= 46

)40100( (0.92)(4) = 4.8 cal/s

21. yEckbZ 85 cm ds , d i kbi ds , d fl j s dks cUn dj fn; k t kr kgSa i kbi esa ok; q Lr EHk ds l EHko] i zkd fr d nksyuksa dh og l a[ ; kfudkfy; s ft udh vkofÙk 1250 Hz l s de gSaA ok; q esa /ofu dk osx340 m/s gSA(1) 6 (2) 4 (3) 12 (4) 8Sol. 1

f = L4V

= 210854340

= 100 Hz

100 H, 300 Hz, 500 Hz, 700 Hz, 900 Hz, 1100 Hz = 6

22. , d oÙkkdkj uyh Å/okZ/kj r y esa gSA nks nzo] t ks , d nwl j s l sfefJr ugha gksr s r Fkk ft udk ?kuRo d1 , oa d2 gSa] uyh esa Hkj s x; s gSaAi zR; sd nzo dsUnz i j 90° dk dks.k var fj r dj r k gSaA muds var % i "B

dks t ksM+us okyh f=kT; k Å/okZ/kj l s dks.k cukr h gSA vuqi kr 1

2

dd gSa%

(1) 1 tan1 tan

(2) 1 sin1 cos

(3) 1 sin1 sin

(4) 1 cos1 cos

Sol. 1

R

Rsin

Rcos

R–RcosR-Rsin

RR

R – R sin = d1 (R – R sin ) + d2 (R sin + R cos )d1 (1 – sin ) = d1 (1 – cos ) + d2 (sin + cos )d1 – d1 sin = d1 – d1 cos + d2 (sin + cod )d1 (cos – sin ) = d2 (sin + cos )

2

1

dd

=

sincoscossin

=

tan1tan1

23. , d gj s j ax dk i zdk' k i kuh l s ok; q&t y vUr j ki "B i j ØkfUr ddks.k () l s vki fr r gSA l gh dFku pqfu; sA(1) n' ; i zdk' k dk og Li sDVªe] ft l dh r j axnS/; Z gj s i zdk' k l svf/kd gS] i kuh l s ok; q ds ek/; esa ckgj fudysxkA(2) n' ; i zdkj dk l Ei w.kZ Li sDVªe i kuh l s vfHkyEc l s fofHkUu dks.kksai j ckgj fudysxkA(3) vfHkyEc l s 90° dks.k i j i kuh l s n' ; i zdk' k dk l Ei w.kZ Li sDVªeckgj fudysxkA(4) n' ; i zdk' k dk og Li sDVªe] ft l dh r j axnS/; Z gj s i zdk' k l s degS] i kuh l s ok; q ds ek/; e esa ckgj fudysxkASol. 4

gj k

1

f > fgj k

< gjk

> gj k

T.I.R

24. gkbMªkst u (1H1), M~; wVsfj ; e (1H

2), , d/kk vk; fur ghfy; e(2He4)+ vkSj f} /kk vk; fud yhfFk; e (3Li6)++ l Hkh esa , d bysDVªkWuukfHkd ds pkj ksa vksj gSaA n = 2 l s n = 1 ds bysDVªkWu l aØe.k i jfopkj dhft , A ; fn mRl ft Zr fofdj .k dh r j axnS/; Z Øe' k% 1, 2,3

, oa 4 gSa] r c fuEufyf[ kr l EcU/kksa esa l s dkSu l k yxHkx l gh gS\(1) 1 = 2 = 43 = 94(2) 1 = 22 = 33 = 44(3) 41 = 22 = 23 = 4(4) 1 = 22 = 23 = 4




Sol. 1

hc

= Rc z2

2

22

1 n1

n1

1

z2

1

1 (1)2,

2

1 (1)2,

3

1 (2)2,

4

1 (3)2

1 : 2 : 3 : 4 = 1 : 1 : 41

: 91

25. gkbMªkst u i j ek.kq ds 3 2 l aØe.k ds l axr fofdj .k , d /kkr qi "B i j vki fr r gksdj QksVksbysDVªkWu mRi Uu dj r k gSA ; s bysDVªkWu3×10-4T ds , d pqEcdh; {ks=k esa i zos' k dj r s gSA ; fn bysDVªkWuksa } kj kvuqxkeh vf/kdr e oÙkh; i Fk dh f=kT; k 10.0mm gks] r c /kkr q dkdk; Z Qyu yxHkx gS %(1) 0.8 ev (2) 1.6 ev(3) 1.8 ev (4) 1.1 evSol. 4

r = qBmv

v = m

qBr =

19 4 3

31

1.6 10 3 10 10 109.1 10

= 5.27 × 105

KEmax = 1/2 mv2

= 1/2 × 9.1 × 10–31 × (5.27 × 105)2

= 19

21

106.11036.126

= 78.975 × 10–2

= 0.78 eV

E = 13.6

2

22

1 n1

n1

= 13.6

91

41

= 1.88 ev1.88 = 0.78 + = 1.1 eV

26. , d i "B i j , d nzO; eku m dk CykWd j [ kk gSA i "B dh

Å/okZ/kj vuqi zLFk dkV y = 3x

6 l s nh t krh gSA ; fn ?k"kZ.k xq.kkad 0.5

gS] r c /kj r h l s Åi j og vf/kdre Å¡pkbZ] ft l i j fcuk fQl ys CykWdj [ kk t k l dr k gS] gSa %

(1) 13 m (2)

12

m

(3) 16 m (4)

23 m

Sol. 3

m

f

y = 6x3

dxdy

= 6x3 2

= 2x2

f = mg cos = mg sin = tan

0.5 = 2x2

x = 1

y = 6x3

= 61

m

27. t c , d j cM+ ds NYys dks x nwj h r d r kfur fd; k t kr k gS( r ci fj ek.k F = ax + bx2 , k , d i zR; u; u cy yxr k gS t gk¡ a , oa bfLFkj kad gSA fcuk r kfur j cM+ ds NYys dks L l s r kfur djus esa fd; kx; k dk; Z gS %

(1) 2 3aL bL

2 3 (2)

2 31 aL bL2 2 3

(3) aL2 + bL3 (4) 12

(aL2 + bL3)




Sol. 1

W = Fdx

W = Fdx(ax + bx2) dx

W =

L

0

32

3bx

2ax

W =

3bL

2aL 32

28. i kuh dks xeZ dj us i j ] cr Zu dh r yh esa cqycqys cur s gSa vkSjfoyXu gksdj Åi j dh vksj mBr s gSaA cqycqyksa dks f=kT; k R dk xksykeku ysa vkSj cr Zu dh r yh esa oÙkh; Li ' kZ dh f=kT; k r ysaA ; fn r<<RvkSj i kuh dk i "B r uko T gSa] r c cqycyksa ds cl foyXu gksus l s t j ki gys r dk eku gSa %¼i kuh dk ?kuRo w gS½

(1) 2 WgR

T

(2) 2 W3 gR

T

(3) 2 WgR

3T

(4) 2 WgR

6T

Sol. 3

R T

r

34

R3 w g = P (r2) + T (2r) sin

34

R2 w g = RT2

(r2) + T (2r) Rr

34

R3 w g = RT4

r2

r = R2 T3gw

29. /kzqo.k ds vU; ks; yEcor ~ r yksa okys l er y /kzqoh; i zdk' k dh nksi qat A , oa B , d i ksyj k; M+ } kj k t krh gSA ml fLFkfr l s t gk¡ i qat Adh vf/kdr e r hozr k gS ¼vkSj i qat B dh ' kwU; r hozr k gS½ i ksyj k; M dk30° l s ?kw.kZu nksuksa i qat ksa dks , dl eku | qfr eku i zr hr gksr k gSA ; fn

nksuksa i q¡t ksa dh i zkj fEHkd r hozr k, ¡ Øe' k% IA , oa IB gSa] r c A

B

II dk eku

gS %

(1) 1 (2) 13

(3) 3 (4) 32

Sol. 2IA cos2 30° = IB cos2 60°

B

A

II

=

30cos60cos

2

2

= 2

2

)2/3()2/1(

= 4/34/1

= 1/3

30. eku ysa O; kse esa , d fo| qr {ks=k 2E 30x i gSA r c foHkokUr j

VA – VO t gk¡ VO ewyfcUnq i j foHko , oa VA, x = 2m i j foHko gSa]gS %(1) –80 J (2) 80 J(3) 120 J (4) –120 JSol. 1

dv = dr.E

VA – V0 = 2

0

2dxx30

= –

2

0

3

3x30

= – [10x3]= – 10 [8 – 0]VA – V0 = –80 J




[MATHEMATICS]

SECTION – ASingle Correct

31. l er y 2x – y + z + 3 = 0 esa j s[ kk

31x

= 1

3y =

54z

ds i zfr fcac okyh j s[ kk gS%

(A) 3

3x =

15y

= 52z

(B) 33x

= 15y

= 5

2z

(C) 3

3x =

15y

= 52z

(D) 33x

= 15y

= 5

2z

Sol. [1]x 1 y 3 z 4

3 1 5

2 3 4 3x 1 y 3 z 4 22 1 1 4 1 1

x 1 y 3 z 4 22 1 1

x= 1 – 4, y = 3 + 2, z = 4 – 2P' (–3, 5 ,2)j s[ kk l er y ds l ekUr j gSai zfr fcEc j s[ kk dh l ehdj .k

x 3 y 5 z 23 1 5

32. ; fn (1 + ax + bx2) (1 – 2x)18 ds x dh ?kkrksa esa i zl kjesa x3 r Fkk x4 nksuksa dsd xq.kkad ' kwU; gS] r ks (a, b) cj kcjgS%

(A)

3

251,16 (B)

3

251,14

(C)

3

272,14 (D)

3

272,16

Sol. [4](1 + ax + bx2) (1 – 2x)18

x3 dk xq.kkad = 18C3 (–2)3 + a. 18C2 (–2)2

+ b . 18C1(–2)1

= 6528 a612 36b 0

x4 dk xq.kkad = 18C4 (–2)4 + a . 18C3 (–2)3 + b 18C2 (–2)2

= 48960 a.( 6528) b612 0

(16, 2723

) i zkIr dj r s gSaA

33. ; fn a R r Fkk l ehdj .k– 3(x – [x])2 + 2(x – [x]) + a2 = 0(t gk¡ [x] ml cM+s l s cM+s i w.kkZad dks n' kkZr k gS t ks x gS)dk dksbZ i w.kkZadh; gy ugh gS] r ks a ds l Hkh l aHko eku ft lvar j ky esa fLFkr gS] og gS%(A) (–1, 0) (0, 1) (B) (1, 2)(C) (–2, –1)(D) (–, –2) (2, )

Sol. [1]x – [x] = {x} = t [0, 1)–3t2+ 2t + a2 = 0 a2= 3t2 – 2t [0, 1)pwafd l ehdj .k i w.kkZadh; ewy ugha j [ kr h gSa : t 0 a2 (0, 1) a (–1, 0) (0, 1)

34. ; fn accbba

= 2cba gS] r ks cj kcj

gS%(A) 2 (B) 3(C) 0 (D) 1

Sol. [4]Li "V gSa= 1

35. i gyh 50 l e i zkd r l a[ ; kvksa dk i zl j .k gS%

(A) 4

833(B) 833

(C) 437 (D) 4

437

Sol. [2]

50 51 101V 4

6 50

50 51 50 514

50 50 4

= 17 [202 – 153] = 17 × 49 = 833




36. , d i {kh 20 eh- Å¡ps , d Å/okZ/kj [ kaHks ds f' k[ kj i j cSBkgS r Fkk bl dk Hkwfe ds , d fcanq O l s mUu; u dks.k 45º gSA; g i {kh O l s i j s {kSfr t fn' kk esa mM+r k gSA , d l sdaM dsckn] O l s i {kh dk mUu; u dks.k ?kV dj 30º j g t kr k gSAr ks (eh- i zfr l s- esa) i {kh dh pky gS :

(A) 40( 2 – 1) (B) 40( 3 – 2 )

(C) 20 2 (D) 20( 3 – 1)

Sol. [4]

tan30° = 20 1

x 20 3

x + 20 = 20 3

x = 20( 3 1)

37. l ekdy

0

2 dx2xsin4

2xsin41 cj kcj gS &

(A) – 4 (B) 32

– 4 – 4 3

(C) 4 3 – 4 (D) 4 3 – 4 – 3

Sol. [4]

0

x1 2sin dx2

= 3

0

x1 2sin dx2

3

x1 2sin dx2

= 3

03

x xx 4cos x 4cos2 2

= 4cos 0 43 6 4cos 4cos

2 3 6

= 4 3 43

38. dFku ~ (P ~q) gS :(A) p q ds r qY;(B) ~p q ds r qY;(C) , d i qu: fDr (tautology)(D) , d gsRokHkkl (fallacy)

Sol. [1]

p q ~ q p ~ q ~ p ~ qT T F F TT F T T FF T F T FF F T F T

p qTFFT

39. ; fn A , d , sl k 3 × 3 O; wRØe.kh; gS fd AA' = A'A r FkkB = A–1 A' gS, r ks BB' cj kcj gS%(A) 1 + B (B) 1(C) B – 1 (D) (B–1)'

Sol. [2]AA' = A'AB = A–1A'B' = A(A–1)'B . B' = A–1 (A' A) (A–1)'= A–1 (A A') (A–1)1

= (A–1 A) (A') (A')–1

= I

40. l ekdy dxex1x1 x

1x

cj kcj gS :

(A) (x – 1) ce x1x

(B) x ce x

1x

(C) (x + 1) ce x1x

(D) –x ce x

1x

Sol. [2]1 1x xx x1e x e dx

x

...(1)

1xxe

= f(x)

1xxe

2

11x

dx = f'(x)

1 1x+ x+x x

2f(x)

xf '(x)

1e x.e 1 dxx

x f(x) = x . 1x+xe + C




41. ; fn z , d , sl h l fEEJ l a[ ; k gS fd |z| 2 gS, r ks

21z dk U; wur e eku :

(A) 25

ds cj kcj gSA

(B) var j ky (1, 2) esa fLFkr gSA

(C) 25

l s fuj ar j cM+k gSA

(D) 23

l s fuj ar j cM+k gS i j Ur q 25

l s de gSA

Sol. [2]|z| 2

1 1 1| z | z | z |2 2 2

min

1 3Z2 2

42. ; fn g Qyu f dk O; wRØe gS r Fkk f'(x) = 5x11

gS, r ks

g'(x) cj kcj gS%(A) 1 + x5 (B) 5x4

(C) 5)}x(g{11

(D) 1 + {g(x)}5

Sol. [4]f(g(x)) = xf'(g(x)) g'(x) = 1

g'(x) = 1

f '(g(x))

g'(x) = 5

11

1 (g(x))

1 + (g(x))5

43. ; fn 0, f(n) = n + n r Fkk

)4(f1)3(f1)2(f1)3(f1)2(f1)1(f1)2(f1)1(f13

= K(1– )2 (1 – )2 ( – )2 gS, r ks K cj kcj gS%

(A) (B) 1

(C) 1 (D) –1

Sol. [1]f(n) = n + n

3

1 1 1 1 11 1 1

1 1 1

= 2 2

1 1 1 1 1 11 11 1

= (1 – )2 ( – )2 ( – 1)2

k 1

44. ekuk fk(x) = k1

(sink x + cosk x) gS] t gk¡ x R

r Fkk k 1 gS] r ks f4(x) – f6(x) cj kcj gS%

(A) 61

(B) 31

(C) 41

(D) 121

Sol. [4]

f4(x) – f6(x) = 14

(sin4x + cos4x) – 16

(sin6 x + cos6 x)

= 14

(1 – 2sin2x cos2x) – 16 (1 – 3 sin2x cos2x)

= 1 1 3 2 14 6 12 12

45. ekuk r Fkk l ehdj .k px2 + qx + r = 0, p 0 ds

ewy gSA ; fn p, q, r l ekar j Js<+h esa gS r Fkk 1

+ 1

=

4 gS] r ks | – | dk eku gS%

(A) 961

(B) 9172

(C) 934

(D) 9132




Sol. [4]

fn; k x; k gSa fd = –qp =

rp

p, q, r l ekUr j Js<h , r c

q – p = r – q 2q r p ...(1)

i qu% 1 1 4

= 4

q 4r ...(2)

l ehdj .k (1) o (2) l s– 8r = r + p

p 9r ...(3)

vc, | – | = 2( ) 4

= 2q 4pr|p |

= 2 216r 36r

|9r |

= 52 2 139 9

46. ekuk A r Fkk B nks , sl h ?kVuk, ¡ gSa fd )BA(P = 61

,

P (A B) = 41

r Fkk P( A ) = 41

gS t cfd A ?kVuk

A ds i wj d dks n' kkZr k gSA r ks ?kVuk, ¡ A r Fkk B :(A) i j Li j vi ot hZ r Fkk Lor a=k gSA(B) l el EHkkoh gSa i j Ur q Lor a=k ugha gSA(C) Lor a=k gS i j Ur q l el EHkkoh ugha gSA(D) Lor a=k gSa r Fkk l el EHkkoh gSaA

Sol. [3]

1P(A B)6

1P(A B)4

1P(A)4

Li "V gSa fd P(A)= 34

r Fkk P(A B) = 56

P(A) + P(B) – P(A B) = 56

34

+ P(B) – 1 54 6

P(B) = 5 3 16 4 4

= 13

P(A B) = 14

P(A) . P(B) = 3 1 14 3 4

bl fy, Lor a=k

P(A) P(B) bl fy, l Ei zkf; d ?kVuk, ¡ ugha gSa

47. ; fn f r Fkk g, [0, 1] esa vodyuh; Qyu gSa t ksf(0) = 2 = g(1), g(0) = 0 vkSj f(1) = 6 dks l ar q"Vdj r s gS] r ks fdl h c ]0, 1[ ds fy, %(A) 2f'(c) = g'(c)(B) 2f'(c) = 3g'(c)(C) f'(c) = g'(c)(D) f'(c) = 2g'(c)

Sol. [4]2g'(c) = f'(c)

= 2 g(1) g(0) f(1) f(0)

1 0 1 0

= 22 0 6 2

1 1

4 = 4

48. ekuk fdl h l e; t i j t hfor [ kj xks' kksa dh t ul a[ ; k vody

l ehdj .k dt

)t(dp =

21

p(t) – 200 } kj k fu; af=kr gSA

; fn p(0) = 100, gS] r ks p(t) cj kcj gS%(A) 400 – 300 et/2 (B) 300 – 200 e–t/2

(C) 600 – 500 et/2 (D) 400 – 300 e–t/2




Sol. [1]

2dp(t) dtp(t) 400

2 log|p(t) – 400| = t + c ...(1)t = 0, p = 100

2 log (300) = C

l ehdj .k (1) l s2log|p(t) – 400| = t + 2 log (300)|p(t) – 400| = et/2 . elog(300)

t /2p(t) 400 e (300)

49. ekuk C , d oÙk gS ft l dk dsanz (1, 1) i j gS r Fkk f=kT; k= 1 gSA ; fn T dsUnz (0, y) okyk oÙk gS t ks ewy fcaanq l sgksdj t kr k gS r Fkk oÙk C dks cká : i l s Li ' kZ dj r k gS] r ksT dh f=kT; k cj kcj gS%

(A) 23

(B) 23

(C) 21

(D) 41

Sol. [4]

C1C = 1 + y(1 – 0)2 + (1 – y)2 = (1 + y)2

1 + 1 – 2y + y = 1 + y2 + 2y4y = 1

1y4

50. A = {(x, y) : x2 + y2 1 r Fkk y2 1 – x} ds } kj ki znÙk {ks=k dk {ks=kQy gS%

(A) 2

+ 34

(B) 2

– 34

(C) 2

– 32

(D) 2

+ 32

Sol. [1]

A1 = 21

01 x dx

A1 = 2 0 2

12t dt

A1 = 4 . 13

42 3

{k=skQy

51. ekuk a, b, c r Fkk d ' kwU; sr j l a[ ; k, ¡ gSA ; fn j s[ kkvksa4ax + 2ay + c = 0 r Fkk 5bx + 2by + d = 0 dki zfrPNsn fcanq pkSFks prqFkkZa' k esa gS rFkk nksuksa v{kksa l s l enwj LFkgS] r ks%(A) 2bc – 3ad = 0 (B) 2bc + 3ad = 0(C) 3bc – 2ad = 0 (D) 3bc + 2ad = 0

Sol. [3]4ax + 2ay + c = 05bx + 2by + d = 0ekuk i zfr PNsnh fcUnq (, – ) gSa4a – 2a + c = 0

= – c2a

....(1)

5b – 2b + d = 0

= – d3b

....(2)

– c d2a 3b

3bc 2ad3bc – 2ad = 0

52. ekuk PS , d f=kHkqt dh ekf/; dk gS ft l ds ' kh"kZ P(2, 2),Q(6, –1) r fkk R(7, 3) gSA (1, –1) l s gksdj t kus okyhj s[ kk] t ks PS ds l ekar j gS] dk l ehdj .k gS%(A) 4x – 7y – 11 = 0 (B) 2x + 9y + 7 = 0(C) 4x + 7y + 3 = 0 (D) 2x – 9y – 11 = 0




Sol. [2]PS dk <ky

m = 2 1 1

13 922 2

m = 29

j s[ kk dh l ehdj .k

y + 1 = 29

(x – 1)

9y + 9 = 2x + 22x + 9y + 7 = 0

53. 2

2

0x x)xcossin(Lim

dk eku gS%

(A) 2

(B) 1

(C) – (D) Sol. [4]

2x 0

sin( c'x)limx

2

2 2x 0

sin( c x) (1 cx)lim (1 cx)( c x) x

= 1 . . 12

. 2

=

54. ; fn X = {4n – 3n – 1) : n N} r FkkY = {9 (n – 1) : n N} gS] t gk¡ N, i zkd r l a[ ; kvksadk l eqPp; gS] r ks X Y cj kcj gS%(A) N (B) Y – X(C) X (D) Y

Sol. [4]x : 4n – 3n –1x : (1 + 3)n – 3n – 1x : 1 + 3n + nC2 3

2 + nC3 33 + ........ –3n–1

x : 9 {nC2 + nC3 3 + ......} ...(1)r Fkk y : 9 (n – 1) ...(2)l ehdj .k (1) o (2) l s

9 dk xaq.kt vr % X Y Y

55. nh?kZoÙk x2 + 3y2 = 6 ds dsanz l s bl dh fdl h Li ' kZ j s[ kki j [ khaps x, yac ds i kn dk fcanq i Fk gS%(A) (x2 – y2)2 = 6x2 + 2y2

(B) (x2 – y2)2 = 6x2 – 2y2

(C) (x2 + y2)2 = 6x2 + 2y2

(D) (x2 + y2)2 = 6x2 – 2y2

Sol. [3]

nh?kZoÙk 2 2x y 16 2

; fn yEc dk i kn (h,k) gSa r cj s[ kk dh l ehdj .k xh + ky = k2 + h2

is y = hk

x + 2 2k h

k

vc ; fn ; g Li ' kZ j s[ kk gSa r c Li ' kZr k dk i zfr cU/kc2 = a2m2 + b2

2 2k hk

= 2h6

k

+ 2

22 2

2

k h

k

=

2

26h 2k

(k2 + h2)2 = 6h2 + 2k2

(x2 + y2)2 = 6x2 + 2y2

56. r hu /kukRed l a[ ; k, a c<+r h xqa.kksÙkj Js<+h esa gSA ; fn blxq.kksÙkj Js<+h dh chp okyh l a[ ; k nqxquh dj nh t k, ] t ks ubZcuh l a[ ; k, a l ekar j Js<+h esa gks t kr h gSA xq.kksÙkj Js<+h dkl koZvuqi kr gS%

(A) 2 + 3 (B) 3 + 2

(C) 2 – 3 (D) 2 + 3Sol. [4]

a, ar, ar2 xq.kksÙkj Js<h esa gSaa, 2ar, ar2 l ekUr j Js<h esa gSa

2ar = 2a ar

2

4r = 1 + r2

r2 – 4r + 1 = 0

r = 4 16 4

2

r = 4 2 3

2

r =2 3

bl fy, r = 2 + 3 xq.kksÙkj Js<h esa gksxk




57. ; fn (10)9 + 2(11)1 (10)8 + 3(11)2 (10)7

+..... ... + 10(11)9 = k(10)9 gS] r ks k cj kcj gs%

(A) 10121

(B) 100441

(C) 100 (D) 110Sol. [3]

109 + 2.111 108 + 3.112 107 ---- + 10.119

S = 109 (1+2 111

10

+ 3. 211

10

+ ..... + 10911

10

)

S111

10

= 109 (111

10

+ 2211

10

+ 3311

10

+.......101011

10

)

11s 110

=109 1 2 9 1 01 1 1 1 1 1 1 1

1 1 01 0 1 0 1 0 1 0

= 109

10

10111 1

1110 1011 10110

S

10 1091 11 1110 1 10 10

10 10 10

= 109 1010 1011 111

10 10

S . 1

10

= 109 (–10)

S = 100. 109

bl fy, K = 100

58. nks j s[ kk, ¡] ft uds fnd~&dksT; k] l ehdj .kksa1 + m + n = 0 r Fkk l2 = m2 + n2 dks l ar q"V dj r s gSa]ds chp dk dks.k gS :

(A) 3

(B) 4

(C) 6

(D) 2

Sol. [1]l + m + n = 0l2 – m2 – n2 = 0(m + n)2 – m2 – n2 = 0mn = 0

m = 0 ; k n = 01.l + 1.m + 1.n = 0, 1.l + 1.m + 1.n = 00.l + 1.m + 0.n = 0, 0.l + 0.m + 1.n = 0

l m n1 1 1 1 1 11 0 0 0 0 1

,

l m n1 1 1 1 1 10 1 1 0 0 0

l m n1 0 1

; k

l m n1 1 0

Cos = 1 0 02 2

Cos = 12

= 3

59. i j oy; ksa y2 = 4x r Fkk x2 = – 32y nksuksa dks Li ' kZ dj usokyh j s[ kk dh i zo.kr k gS :

(A) 21

(B) 23

(C) 81

(D) 32

Sol. [1]y2 = 4x, x2 = –32yLi ' kZ j s[ kk dh l ehdj .k] Li ' kZ j s[ kk dh l ehdj .k

y = mx + 1m

, y = mx + 8m2

1m

= 8m2

m = 12

60. ; fn x = – 1 r Fkk x = 2f(x) = log |x| = x2 + x ds pj efcanq gSa] r ks :(A) d (B) d(C) d (D) d

Sol. [3]

f'(x) = 2 x 1x

x i j = –1, 2 f'(x) = 0 – – 2+ 1 = 0 ....(1)

2

+ 4 + 1 = 0 .... (2)

= 2, = 12

JEE MAIN Examination(2014) (Code - #) (Page # 9)



[CHEMISTRY]61. NO dkSu&l k fuEu xq.k i znf' kZr ugha dj r k gS\

(1) ; g vkWDl ht u l s ; ksx dj ukbVªkst u MkbZvkWDl kbMcukrk gSA(2) bl dh cU/k dksfV 2.5 gSA(3) xSl h; voLFkk esa i zfr pqEcdh; gSA(4) ; g , d mnkl hu vkWDl kbM gSA

Sol. 3(1) NO + 1/2 O2

NO2

(2) NO dk ca/k Øe 2.5 gSA(3) ; g xSl h; voLFkk esa vuqpqEcdh; gSA(4) ; g mnkl hu vkWDl kbM gSA

62. ; fn Z l ai hM+u xq.kd gks r ks de nkc i j okaMjokYl l ehdj .kdks fy[ kk t k l dr k gS %

(1) Z = 1 – RTPb

(2) Z = 1 + RTPb

(3) Z = 1 + PbRT

(4) Z = 1 – VRT

a

Sol. 4, d eksy xSl ds fy, okW.Mj okWy l ehdj .k ds vuql kj

2

aP (V b) RTV

fuEu nkc i j vk; r u mPp gksxkA b dks ux.; eku l dr s gSAvr %,

2

aP (V) RTV

aPV RTV

Z = PVRT

= 1 – a

VRT

63. /kkr q t ks vi us yo.kksa ds t yh; foy; uksa ds bySDVªkysfl l¼fo| qr vi ?kVu½ l s i zkIr ugha gks l dr h gS %(1) Cu(2) Cr(3) Ag(4) Ca

Sol. 4

22 2H o /H Ca / Ca

Eº Eº

Ca vf/kd fo| qr /kuh gS vr % t yh; foy; u i z; qDr ughagks l dr kA

64. , d oS| qr vi ?kV~; esa 0.2 M foy; u dk i zfr j ks/k 50 gSAbl foy; u dk fof' k"V pkydRo 1.4 S m–1 gSA bl h fo| qrvi ?kV~; ds 0.5 M foy; u dk i zfr j ks/k 280 gSA fo| qrvi ?kV~; ds 0.5 M foy; u dh eksyj pkydr k S m2

eksy –1 esa gksxh %(1) 5 × 103

(2) 5 × 102

(3) 5 × 10–4

(4) 5 × 10–3

Sol. 3

R = a

50 = 1

1.4 a

170ma

R = a

280 = 1 70

= 0.25 Sm–1

= 0.25 × 10–2 –1 - cm–1

m

1000c

=

–21000 0.25 100.5

= 5 –1-cm2 mole–1

= 5 × 10–4 S-m2 mol–1

65. CsCl dk; dsfUnzr ?kukdj t kyd esa fØLVfyr gksr k gSA

; fn fdukj s dh yEckbZ 'a' gks r ks fuEu l w=kksa esa l s dkSu&l kBhd gksxk\

(1) Cs Cl3r r a2

(2) Cs Clr r 3a

(3) Cs Clr r 3a

(4) Cs Cl3ar r2

JEE MAIN Examination(2014) (Code - #)(Page # 10)



Sol. 1Cl– , SC cukr k gSACs+ ?ku ds dsUnz i j t kr k gSA

–3ar r2

66. 0.500 M C2H5OH(t y h; ), 0.100 MMg3(PO4)2(t yh; ), 0.250 M KBr(t yh; ) vkSj 0.125M Na3PO4(t yh; ) foy; uksa dks 25ºC i j /; ku nhft ; sAl Hkh uedksa dks i zcy bySDVªksykbV ekur s gq, fuEu dFkuksa esal s dkSu&l k dFku ; FkkFkZ gS\(1) 0.125 M Na3PO4(t yh; ) dk vkl ekfVd nkc

mPpr e gksxkA(2) 0.500 M C2H5OH(t yh; ) dk vkl ekfVd nkc

mPpr e gksxkA(3) bl l c ds fy, vkl ekfVd nkc ds eku l eku gksxkA

(4) 0.100 M Mg3(PO4)2(t yh; ) dk vkl ekfVd nkc

mPpr e gksxkASol. 3

i ic0.5 M C2H5OH (aq.) 1 0.50.10 M Mg3 (PO4)2 5 0.50.25 M KBr 2 0.50.125 M Na3PO4 4 0.5l Hkh l eku v.kql a[ ; d xq.k/keZ j [ kr s gSA

67. fuEu fdu vfHkfØ; kvksa esa H2O2 , d vi pk; d dk dke

dj r k gS\(a) H2O2 + 2H+ + 2e– 2H2O(b) H2O2 – 2e– O2 + 2H+

(c) H2O2 + 2e– 2OH–

(d) H2O2 + 2OH– –2e– O2 + 2H2O(1) (a), (c)(2) (b), (d)(3) (a), (b)(4) (c), (d)

Sol. 2D; ksafd vi pk; d gS

01 –

22 2H O O 2e

(b) & (d)

68. ; kSfxdksa CH3Cl, CH3CH2Cl, (CH3)2CHCl vkSj(CH3)3CCl dk SN2 fØ; k esa fØ; k dj .k dk mfpr Lr j

Øe gksr k gS %(1) CH3CH2Cl > CH3Cl > (CH3)2CHCl > (CH3)3CCl(2) (CH3)2CHCl > CH3CH2Cl > CH3Cl > (CH3)3CCl(3) CH3Cl > (CH3)2CHCl > CH3CH2Cl > (CH3)3CCl(4) CH3Cl> CH3CH2Cl > (CH3)2CHCl > (CH3)3CCl

Sol. 4SN2

SN2 dh fØ; k' khyr k 1

f=kfoe ck/kkSN2 dh vksj fØ; k' khyr k dk Øe gSCH3Cl > CH3–CH2–Cl > (CH3)2CH–Cl > (CH3)3C–Cl

69. M3+ /kkrq vk; u dk pkj , d i dM+h fyxSaMksa] L1, L2, L3 vkSj

L4 ds l kFk v"V Qydh; l adj yky] gj s] i hys vkSj uhys

LFkyksa l s r j axnS/; kZsa dk Øekuql kj vo' kks"k.k dj r k gSA pkj

fyxSaM+ksa dh ' kfDr dk c<+r k Øe gS %(1) L3 < L2 < L4 < L1

(2) L1 < L2 < L4 < L3

(3) L4 < L3 < L2< L1

(4) L1 < L3 < L2 < L4

Sol. 4

(a) Li sDVªks j l k; fud Js.kh ds vuql kj vf/kd vo' kks"k.k

vkofÙk gksus i j fyxs.M i zcy gksxkA

V I B G Y O R

EL1 < L3 < L2 < L4

(yky) (gj k) (i hyk) (uhyk)

70. ukbVªkst u ds vkdyu ds fy, 1.4 xzke dkcZfud ; kSfxd

t sYMkWy fof/k ds vuql kj vi fpr fd; k x; k r Fkk eqDr gq,

veksfu; k dks 60 feyh 10M

l Y¶; wfj d vEy esa vo' kksf"kr

fd; k x; kA vf/k' ks"k vEy ds i w.kZ mnkl huhdj .k ds fy, 20

feyh 10M

l ksfM; e gkbMªkWDl kbM dh vko' ; dr k gqbZA ; kSfxd

esa ukbVªkst u dh i zfr ' kr r k gS %(1) 3 % (2) 5 %(3) 6 % (4) 10 %




Sol. 41.4 gm NH3

2 4M M60mL H SO 20mL NaOH10 10

ekuk x % N

x1.4 1 20 1 60100 1 214 10 1000 10 1000

14 100x (0.012 – 0.002)1.4

= 10 %

71. l kUnz.k C i j vkSj vuUr r uqr k i j NaCl foy; u dh

bfDooySUV pkydrk dks C vkSj ekur s gq, mudk vki l h

l EcU/k fy; k t k l dr k gS %

(B , d fLFkj vad gS)

(1) C = – (B) C

(2) C = + (B) C

(3) C = + (B) C

(4) C = – (B) C

Sol. 1

c = — CB

72. vfHkfØ; k SO2(g) + 21

O2(g) SO3(g), ds fy, Kp =

KC (RT)x gksxk t cdh l c l wpd v{kj l kekU; vFkZ j [ kr s

gSa r ks vkn' kZj : i r k ekur s gq, x dk eku gksxk %(1) 1/2(2) 1(3) –1(4) – 1/2

Sol. 4

SO2(g) 21 O (g)2

SO3(g)

Kp = Kc (RT)ng

ng = 1 – (1 + 21

) = 21–

Kp = Kc (RT)–1/2

73. vfHkfØ; k l sV]

CH3COOH LiAlH4 A PCl5 B Alc. KOH C,

esa fØ; k Qy C gksr k gS %

(1) bFkkbZyhu

(2) , fl Vkby Dyksj kbM

(3) , sfl V, sfYMgkbM

(4) , fl fVyhuSol. 1

CH3–CH2–OH

CH3–CH2–Cl

CH2=CH2 (bFkkbZfyu)

74. l ksfM; e QSukDl kbM dh mPp nkc vkSj 125°C i j CO2 l s

vfHkfØ; k djus i j t ks ; kSfxd i zkIr gksrk gS ml ds , fl fVys' ku

i j fØ; k Qy C gksr k gSA

ONa

+ CO2 B C125º H+

5 Atm Ac O2

cM+h ek=kk esa fØ; k Qy C gksxk (

(1) COOCH3

OH

(2)

OCOCH3

COOH

(3) COOH

OCOCH3

(4)

OH

COCH3

COCH3

Sol. 3




75. , sfyQSfVd i zk; ej h , ehu dks Dyksj ksQkeZ vkSj , Fkkuksfyd

i ksVSf' k; e gkbMªkDl kbM ds l kFk xje djus i j cuk vkj xSfud; kSfxd gksr k gS %

(1) , d , sfYdy fl ; kukbM(2) , d , sfYdy vkbl ksfl ; kukbM

(3) , d , sYdkuksy(4) , d , sYdsuMk; ksy

Sol. 2

R—NH2 + CHCl3 +KOH R–NC

1º-, ehu Dyksj ksQkWeZ , fYdy vkbl ks l k; ukbM; g dkfcZy , ehu vfHkfØ; k ; k vkbl ks l k; ukbM i j h{k.k gSA

76. CsI3 v.kq ds fy, ; FkkFkZ dFku gksxk %(1) bl esa Cs3+ vkSj I– vk; u gksr s gSA

(2) bl esa Cs+, I– vkSj I2 t kyd gksr s gSA

(3) ; g , d l gl a; kst dh v.kq gSA(4) bl esa Cs+ vkSj I3

– vk; u gksr s gSASol. 4

CsI3 Cs+ + I3–

77. l ehdj .k t ks l ar qfyr gS vkSj ; FkkFkZ fØ; k Qyksa dh l wpd gS]

gSa %

(1)[Mg(H2O)6]2+ + (EDTA)4– NaOH dk vkf/kD;

[Mg(EDTA)]2+ + 6H2O(2) CuSO4 + 4KCN K2[Cu(CN)4] + K2SO4

(3) Li2O + 2KCl 2LiCl + K2O(4) [CoCl(NH3)5]

+ + 5H+ CO2++5NH4++ Cl–

Sol. 1; g vfHkfØ; k dBksj t y esa Mg2+ dk i r k yxkus ds fy,i z; qDr gksr h gSA

78. fuEu esa l s fdl v.kq ds fy; s cgqr l hek r d 0 gksxk?

(a)

Cl

Cl

(b)

CN

CN

(c)

OH

OH

(d)

SH

SH(1) dsoy (c)(2) (c) vkSj (d)(3) dsoy (a)(4) (a) vkSj (b)

Sol. 2

(a) (b)

(c) (d)




79. j l k; fudr k fj Dr vfHkfØ; k 2A + B C + D, esa r hui Fkd i z; ksxksa esa 298 K i j fuEu xfr d vkadM+s i zkIr fd; sx; sA

3

3

3

104.2M1.0M2.0102.1M2.0M1.0102.1M1.0M1.0

)SLmol(

CofformationofrateInitial

)B(ionConcentrat

Initial

)A(ionConcentrat

Initial

i zkj fEHkd l kanz.k

i zkj fEHkd l kanz.k

cuus dh i zkj fEHkdnj ¼eksy ½(A) (B)

CL S– –

vfHkfØ; k ds fy; s C cuus dk nj fu; e gksxkA

(1) dtdc

= k[A] [B]2

(2) dtdc

= k[A]

(3) dtdc

= k[A] [B]

(4) dtdc

= k[A]2 [B]

Sol. 22A + B C + D(1) & (3) [A]1

(1) & (2) [B]º r = k[A]1

80. buesa l s vfHkfØ; kvksa dk dkSu&l k Øe ; FkkFkZ : i esa yksgs vkSj

bl ds ; kSfxdksa dh j k; k; fud vfHkfØ; kvksa dks fu: fi r dj r kgS\

(1) Fe Cl ,heat2 FeCl3 heat, air FeCl2

Zn Fe

(2) Fe O heat2, Fe3O4 CO, 600ºC FeO

CO, 700ºC Fe

(3) Fe dil H SO2 4 FeSO4 H SO2 4, 2O Fe2(SO4)3

heat Fe

(4) Fe O heat2, FeO dil H SO2 4 FeSO4

heat FeSol. 2

Fe Heat

O2 Fe3O4 Cº600

CO FeO Cº700

CO Fe

(FeO + Fe2O3); g vfHkfØ; k okR; k Hkêh esa i z; qDr gksr h gSA

81. t yh; foy; u esa , ehuksa dh {kkj h; i zofÙk ds vuql kjfuEufyf[ kr ksa esa l s fdl ds fy, pKb dk eku de l s de

gksxk\(1) (CH3)3N(2) C6H5NH2(3) (CH3)2NH(4) CH3NH2

Sol. 3

foLFkkfud r , dkdh ; qXe bysDVªkWu

(U; wur e {kkj h; )t yh; foy; u esa {kkj h; l keF; Z dk Øe

{kkj h; l keF; Z Kb bpk

1

(CH3)2NH vf/kd {kkj h; gSA vr % ; g U; wur e pKb j [ kr kgSA

82. fuEu {kkj ksa esa l s dkSu , d DNA esa ugha i k; k t kr k?(1) l kbVksl hu(2) FkkbZehu(3) D; wuksyhu(4) , fMuhu

Sol. 3

(D; wuksyhu)

D; wuksyhu DNA esa mi fLFkr ugha gksr k gSAl kbVksl hu] FkkbZehu rFkk , fMuhu DNA esa mi fLFkr gksrss gSA

83. : fcfM; e i j ek.kq (Z = 37) ds fy; s l a; kst h bySDVªkWuksa dsmfpr pkj DokUVe uEcj ksa dk l sV gksr k gS ?(1) 5, 1, 1 + 1/2(2) 5, 0, 1, + 1/2(3) 5, 0, 0, + 1/2(4) 5, 1, 0, + 1/2

Sol. 3

84. 1,1,1-VªkbDyksj ksbZFksu dks fl Yoj i kmMj ds l kFk fØ; kdjus i j l cl s cM+h ek=kk esa cuk vkj xSfud ; kSfxd gksr k gSA?(1) 2 C; qVkbu(2) 2 - C; qVhu(3) , fl fVyhu(4) bZFkhu




Sol. 1

CH3—CC—CH3 + 6AgCl2-butyne

85. uhps dqN v) Z l sy vfHkfØ; k, nh xbZ gSAMn2+ + 2e– Mn : Eº = – 1.18 V2(Mn3 + e– Mn2+) : Eº = + 1.51 V3 Mn2+ Mn + 2Mn3+ ds fy; s Eº gksxkA(1) – 0.33 V ; vfHkfØ; k ugh gksxh(2) – 0.33 V ; vfHkfØ; k gksxh(3) – 2.69 V ; vfHkfØ; k ugh gksxh(4) – 2.69 V ; vfHkfØ; k gksxh

Sol. 3Mn2+ + 2e– Mn ; Eº = – 1.18 V2Mn3+ + 2e– 2Mn2+ ; Eº = +1.51 V(1) – (2)Mn2+ + 2e– + 2Mn2+ 2Mn3+ + 2e–1 + MnEº = – 1.18 – 1.51 ( n l eku gS) Eº = – 2.69 V(3) vfHkfØ; k i zkIr ugha gksxh gSA

86. , d fo' ks"k xSl h; feJ.k esa vkWDl ht u vkSj ukbVªkst u ds

nzO; ekuksa dk vuqi kr % 1 : 4 gSa A feJ.k esa budh v.kql a[ ; kvksa dk vuqi kr gksxkA(A) 1 : 8 (B) 3 : 16(C) 1 : 4 (D) 7 : 32

Sol. 4O2 : N2

nzO; eku 1 : 4

eksy321

:284

7 : 32

87. buesa l s fdl dks dUMSUl s' ku cgqyd ekuk t k; sxk ?(A) VSQykWu (B) , sfØyksukbVªkby

(C) MSdjku (D) fu; ksfi zuSol. 3

Vsfj yhu ; k MsØksu

–nH O2 ( )l a?kuu

(Msdj ku)

Msdj ku ds vykok vU; l Hkh ; ksxkRed cgqyd gSA

88. fuEu vkDl ks vEyksa ds fy, vEy ' kfDr dk ; FkkFkZ ?kVrk Øegksxk %(A) HClO4 > HClO3 > HClO2 > HOCl(B) HClO2 > HClO4 > HClO3 > HOCl(C) HOCl > HClO2 > HClO3 > HClO4(D) HClO4 > HOCl > HClO2 > HClO3

Sol. 1ClO4

– (vf/kd vuqukn LFkk; h )

89. , FksukWy ds i w.kZ Toyu ds fy; sC2H5OH(l) + 3O2(g) 2CO2(g) + 3H2O(l),ce dsyksj hehVj esa ekfi r Åt kZ 25ºC i j 1364.47 kJmol–1 gSA vkn' kZr k ekur s gq, Toyu dh , UFkSYi h CH,gksxh A(R = 8.314 kJ mol–1)(A) –1460.50 kJ mol–1

(B) –1350.50 kJ mol–1

(C) –1366.95 kJ mol–1

(D) –1361.95 kJ mol–1

Sol. 3H = U + ngRT= – 1364.47 + (–1) × 8.314 × 10–3 × 298= –1364.47 – 2.47= – 1366.95 kJ mol–1

90. R – CH2 – OH R – CHO esa cnyus dk l cl s vf/kd

mi ; qDr vfHkdkj d gksr k gSA(A) CrO3

(B) PCC (fi fj Mhfu; e Dyksj ksØksesV)(C) KMnO4(D) K2Cr2O7

Sol. 2

R—CH2—OH

PCC (fi j hfMfu; e Dyksj ks ØksesV) nqcZy vkWDl hdkjd gSA

JEE MAIN EXAMINATION - 2014 QUESTIONS WITH SOLUTIONS [HINDI …€¦ · JEE MAIN EXAMINATION - 2014...

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Transcript of JEE MAIN EXAMINATION - 2014 QUESTIONS WITH SOLUTIONS [HINDI …€¦ · JEE MAIN EXAMINATION - 2014...