(Chemistry, Mathematics and Physics) · 3 JEE (MAIN)-2016 (Code-F) 6. dkcZu rFkk dkcZu eksuksDlkWbM dh ngu Å"ek;sa Øe'k% –393.5 rFkk –283.5 kJ mol–1 gSaA dkcZu eksuksDlkbM

Time : 3 hrs. M.M. : 360

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Answers & Solutions

forforforforfor

JEE (MAIN)-2016

Important Instructions :

1. The test is of 3 hours duration. The CODE for this Booklet is F.

2. The Test Booklet consists of 90 questions. The maximum marks are 360.

3. There are three parts in the question paper A, B, C consisting of Chemistry, Mathematics and Physics

having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for each correct

response.

4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each

question. ¼ (one-fourth) marks will be deducted for indicating incorrect response of each question. No

deduction from the total score will be made if no response is indicated for an item in the answer sheet.

5. There is only one correct response for each question. Filling up more than one response in each question will

be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 4

above.

6. For writing particulars/marking responses on Side-1 and Side-2 of the Answer Sheet use only Blue/Black

Ball Point Pen provided by the Board.

7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone,

any electronic device, etc. except the Admit Card inside the examination hall/room.

(Chemistry, Mathematics and Physics)

F

Test Booklet Code

2

JEE (MAIN)-2016 (Code-F)

1. ,d xeZ fiQykesaV ls fudyh bysDVªkWu /kjk dks V esu dsfoHkokUrj ij j[ks nks vkosf'kr IysVksa ds chp ls Hkstk tkrkgSA ;fn bysDVªkWu ds vkos'k rFkk lagfr Øe'k% e rFkk m

gksa rks h

dk eku fuEu esa ls fdlds }kjk fn;k tk;sxk\

(tc bysDVªkWu rjax ls lEcfU/r rjaxnSè;Z gS)

(1) 2meV (2) meV

(3) 2meV (4) meV

mÙkjmÙkjmÙkjmÙkjmÙkj (3)

gygygygygy bysDVªkWu dh xfrt ÅtkZ = e × V gS

Mh czksxyh lehdj.k ds vuqlkj

k

h h

2mE 2meV h

2meV

2. esFksukWy esa 2-Dyksjks-2-esfFkyisUVsu] lksfM;e esFkkDlkbM ds lkFkvfHkfØ;k djds nsrh gS%

(a) C H CH C2 5 2

OCH3

CH3

CH3

(b) C H CH C2 5 2

CH2

CH3

(c) C H CH2 5

C

CH3

CH3

(1) (a) rFkk (c) (2) ek=k (c)

(3) (a) rFkk (b) (4) buesa ls lHkh


gygygygygy CH3

CH3

Cl

CH2

CH2

C CH3

MeONa

MeOH

S 1 E N 1

rFkk iFk

+

OMe

+

3. fuEu esa ls dkSu lk ;kSfxd /kfRod rFkk isQjkseSxusfVd (ykSgpqEcdh;) gS\

(1) CrO2

(2) VO2

(3) MnO2

(4) TiO2


gygygygygy CrO2 pqEcdh; {ks=k dh vksj çcy :i ls vkd£"kr gksrk gS

vr% ;g ykSgpqEcdh; gSA

4. fuEu ?kuRo ds ikyhFkhu ds lEcU/ esa fuEu esa ls dkSulk dFku xyrxyrxyrxyrxyr gS\

(1) ;g fo|qr dk ghu pkyd gSA

(2) blesa MkbvkWDlhtu vFkok ijvkDlkbM buhfl;sVj(çkjEHkd) mRçsjd ds :i esa pkfg,A

(3) ;g cdsV (ckYVh)] MLV&fcu] vkfn ds mRiknu esaç;qDr gksrh gSA

(4) blds la'ys"k.k esa mPp nkc dh vko';drk gksrh gSA


gygygygygy fuEu ?kuRo okyh ikWyhFkhu dk la'ys"k.k fuEu çdkj fd;ktkrk gS

nH C = CH2 2

O /1000–2000 atm2

ijkWDlkbM dh lw{eek=kk (,d çkjEHkd ds :i esa) mRçsjd

[ CH2

CH ]2

;g fo|qr dk ghu pkyd gS] vr% blds lUnHkZ esa fodYi(3) xyr gSA

5. ÚkW;UMfyd vf/'kks"k.k lerkih oØ esa x

logm

⎛ ⎞⎜ ⎟⎝ ⎠ rFkk

log p ds chp [khaps x;s js[kh; IykV ds fy, fuEu esa lsdkSulk dFku lgh gS\

(k rFkk n fLFkjkad gSa)

(1)1

n bUVjlsIV ds :i vkrk gSA

(2) ek=k 1

n Lyksi ds :i esa vkrk gSA

(3)1

logn

⎛ ⎞⎜ ⎟⎝ ⎠ bUVjlsIV ds :i esa vkrk gSA

(4) k rFkk 1

n nksuksa gh Lyksi in esa vkrs gSaA


gygygygygy ÚkW;UMfyd vf/'kks"k.k lerki ds vuqlkj:

1

nx

k Pm

<ky =

1n

logx

m

log P

vUr%[k.M = logk

x 1log logP logk

m n

y = m·x + C

PART–A : CHEMISTRY

3


6. dkcZu rFkk dkcZu eksuksDlkWbM dh ngu Å"ek;sa Øe'k%–393.5 rFkk –283.5 kJ mol–1 gSaA dkcZu eksuksDlkbM dhlEHkou Å"ek (kJ esa) çfr eksy gksxh%

(1) 676.5 (2) –676.5

(3) –110.5 (4) 110.5


gygygygygy C(s) + O (g) 2

CO (g) H = – 393.5 kJ mol2

–1

CO(g) + CO (g) H = – 283.5 kJ mol2

–11

2O (g)

2

C(s) + CO(g) H = – 110.5 kJ mol –11

2O (g)

2

– – – +

7. uhps nh xbZ fiQxj esa cqUlu Ýyse dk lokZf/d xeZ Hkkx gS%

jhtu 4

jhtu 3

jhtu 2

jhtu 1

(1) jhtu 2 (2) jhtu 3

(3) jhtu 4 (4) jhtu 1


gygygygygy jhtu "2" cqUlu Tokyk dk lcls xeZ jhtu gksrk gSA

8. fuEu esa ls dkSu lk ,ukbfud fMVjtsaV gS\

(1) lksfM;e ykfjy lYisQV

(2) lsfVyVªkbesfFky veksfu;e czksekbM

(3) fXylfjy vksfy,V

(4) lksfM;e LVhvjsV


gygygygygy lksfM;e ykfjy lYisQV ,ukbfud viektZd

lsfVy VªkbZesfFky veksfu;e czksekbM (/uk;fud (dsVk;fud)i"B lafØ;d)

fXyljkWy vkWfy,V [rsy]

lksfM;e LVhvjsV [lkcqu]

9. 18 g Xyqdksl (C6H

12O

6) dks 178.2 g ikuh esa feyk;k tkrk

gSA bl tyh; foy;u ds fy, ty dk ok"i nkc (torr esa)gksxk

(1) 76.0 (2) 752.4

(3) 759.0 (4) 7.6


gygygygygy s

s

18npº –p 18180

178.2p n 17.82

18

foys;

foyk;d

ty ds lkekU; Doukad ij V.P. = pº = 760 torr

s

s

760 – p 18

p 1782

;k, 1800 ps = 760 × 1782

ps = 752.4 torr

10. lkcqu m|ksx esa HkqDr'ks"k ykb (LisUV ykbZ) ls fXyljkWy iFkddjus ds fy, lcls mi;qDr vklou fof/ gS%

(1) çHkkth vklou

(2) ok"i vklou

(3) lekuhr nkc ij vklou

(4) lkekU; vklou


gygygygygy 1 atm nkc ij fXyljkWy vius DoFkukad rd igq¡pus ls igysgh vi?kfVr gks tkrk gS] vr% bldk vi?kVu jksdus dsfy, bldk vklou lekfur nkc ij fd;k tkrk gSA

11. og Lih'kht] ftlesa N ijek.kq sp ladj.k dh voLFkk esa gS] gksxh%

(1) –

2NO (2) –3NO

(3) NO2

(4)2NO


gygygygygy v.kq@vk;uv.kq@vk;uv.kq@vk;uv.kq@vk;uv.kq@vk;u ladj.kladj.kladj.kladj.kladj.k–

2NO sp2

–

3NO sp2

NO2

sp2

2NO

sp

12. H2O

2 dk fo?kVu ,d çFke dksfV dh vfHkfØ;k gSA ipkl

feuV esa bl çdkj ds fo?kVu esa H2O

2 dh lkUnzrk ?kVdj 0.5

ls 0.125 M gks tkrh gSA tc H2O

2 dh lkUnzrk 0.05 M

igq¡prh gS] rks O2 ds cuus dh nj gksxh

(1) 6.93 × 10–4 mol min–1

(2) 2.66 L min–1 (STP ij)(3) 1.34 × 10–2 mol min–1

(4) 6.93 × 10–2 mol min–1


gygygygygy nj = K[H2O

2] =

0.6930.05

25

O2 cuus dh nj =

1 0.6930.05

2 25

= 6.93 × 10–4 mol min–1

4


13. ,d gh pqEcdh; vk?kw.kZ dk ;qXe gS

[At. No. : Cr = 24, Mn = 25, Fe = 26, Co = 27]

(1) [Cr(H2O)

6]2+ rFkk [Fe(H

2O)

6]2+

(2) [Mn(H2O)

6]2+ rFkk [Cr(H

2O)

6]2+

(3) [CoCl4]2– rFkk [Fe(H

2O)

6]2+

(4) [Cr(H2O)

6]2+ rFkk [CoCl

4]2–


gygygygygy v;qfXer bysDVªkWuksa dh la[;k leku gksus ij pqEcdh; vk?kw.kZleku gksxk

/krq vk;u/krq vk;u/krq vk;u/krq vk;u/krq vk;u v;qfXer bysDVªkWuv;qfXer bysDVªkWuv;qfXer bysDVªkWuv;qfXer bysDVªkWuv;qfXer bysDVªkWu

[Cr(H2O)

6]2+ Cr2+ 4

[Fe(H2O)

6]2+ Fe2+ 4

[Cr(H2O)

6]2+ ,oa [Fe(H

2O)

6]2+ dk pqEcdh; vk?kw.kZ

leku gSA

14. fn;s x;s ;kSfxd dk fujis{k foU;kl gS

H

H

OH

Cl

CO H2

C3

H

(1) (2S, 3R) (2) (2S, 3S)

(3) (2R, 3R) (4) (2R, 3S)


gygygygygyH

H

OH

Cl

CH H2O

C3

H

1

2

(1) ij

3

2

4 1

1

4

2 3

;g 'S' foU;kl gS

(2) ij

2

3

4 1

1

4

3 2

;g 'R' foU;kl gS

15. rkieku 298 K ij] ,d vfHkfØ;k A + B ��⇀↽�� C + D

ds fy, lkE; fLFkjkad 100 gSA ;fn izkjfEHkd lkUnzrk lHkhpkjksa Lih'kht esa ls izR;sd dh 1 M gksrh] rks D dh lkE;lkUnzrk (mol L–1 esa) gksxh %

(1) 0.818 (2) 1.818

(3) 1.182 (4) 0.182


gygygygygy A B C D �

çkjEHk esa : 1 1 1 1

Q = 1

Q < keq

lkE; vxz fn'kk esa foLFkkfir gksxk

A B C D �

lkE; : 1–x 1–x 1+x 1+x

2

2

2

(1 x)10

(1 x)

1 x

1 x

= 10

1 + x = 10 – 10x

11x = 9

x = 9

11 = 0.818

vr% 'D' dh lkE; lkUnzrk = 1.818 M gSA

16. izQkWFk ÝyksVs'ku fofèk }kjk fuEu esa ls og dkSu lk v;LdlokZfèkd :i ls lkfUnzr fd;k tk ldrk gS\

(1) flMsjkbV (2) xSysuk

(3) eSykdkbV (4) eSXusVkbV


gygygygygy lYiQkbM v;Ldksa dk lkUnz.k ÚkWFk ÝyksVs'ku }kjk fd;k tkrk gSA

vr% xSysuk (PbS) dk lkUnz.k ÚkWFk ÝyksVs'ku }kjk fd;k tkrk gSA

17. 300 K rFkk 1 atm nkc ij] 15 mL xSlh; gkbMªksdkcZu dsiw.kZ ngu ds fy, 375 mL ok;q ftlesa vk;ru ds vkèkkjij 20% vkWDlhtu gS] dh vko';drk gksrh gSA ngu dsckn xSlsa 330 mL ?ksjrh gSA ;g ekurs gq, fd cuk gqvkty nzo :i esa gS rFkk mlh rkieku ,oa nkc ij vk;ruksadh eki dh xbZ gS rks gkbMªksdkcZu dk iQkewZyk gS%

(1) C3H

8

(2) C4H

8

(3) C4H

10

(4) C3H

6


5


gygygygygy C3H

8(g) + 5O

2(g) 3CO

2(g) + 4H

2O(l)

vr% 1 mL gkbMªksdkcZu ds ngu ds fy, vko';d O2 dk

vk;ru = 5 mL.

vr% 15 mL gkbMªksdkcZu ds ngu ds fy, vko';d O2 dk

vk;ru = 75 mL (vFkkZr~, 375 mL ok;q dk 20%)

NOTE : ysfdu blds fy,] ngu ds ckn xSlksa dk dqy vk;ru330 mL ds ctk; 345 mL gksuk pkfg,A

18. og ;qXe ftuesa iQkLiQksjl ijek.kqvksa dh iQkeZy vkWDlhdj.kvoLFkk +3 gS] gS%

(1) ik;jksiQkLiQksjl rFkk gkbiksiQkLiQksfjd ,flM

(2) vkFkksZsiQkLiQksjl rFkk gkbiksiQkLiQksfjd ,flM

(3) ik;jksiQkLiQksjl rFkk ik;jksiQkLiQksfjd ,flM

(4) vkFkksZsiQkLiQksjl rFkk ik;jksiQkLiQksjl ,flM


gygygygygy vkWFkksZiQkWLiQksjl vEy H3PO

3 rFkk ik;jksiQkWLiQksjl vEy H

4P

2O

5

ds iQkWLiQksjl ijek.kqvksa dh iQkeZy vkWDlhdj.k voLFkk +3 gSA

19. fuEu esa ls dkSulk dkWEIysDl izdkf'kd leko;ork iznf'kZrdjsxk\(1) cis[Co(en)

2Cl

2]Cl (2) trans[Co(en)

2Cl

2]Cl

(3) [Co(NH3)4Cl

2]Cl (4) [Co(NH

3)3Cl

3]

(en = ethylenediamine)


gygygygygy Co

Cl

Cl

en

en

blesa lefer ry ugha gS] vr% ;g çdkf'kd lfØ; gSA

20. ruq rFkk lkUnz ukbfVªd ,flM ds lkFk ftad dh vfHkfØ;k}kjk Øe'k% mRiUu gksrs gSa%

(1) NO2 rFkk NO (2) NO rFkk N

2O

(3) NO2 rFkk N

2O (4) N

2O rFkk NO

2


gygygygygy 4Zn + 10HNO3(ruq) 4Zn(NO

3)2

+ N2O + 5H

2O

Zn + 4HNO3(lkUnz) Zn(NO

3)2 + 2NO

2 + 2H

2O

21. ty ds lEcU/ esa fuEu dFkuksa esa ls dkSulk ,d xyr xyr xyr xyr xyr gS\

(1) ty] vEy rFkk {kkjd nksuksa gh :i esa dk;Z dj ldrk gSA

(2) blds la?kfur izkoLFkk esa foLrh.kZ var%v.kqd gkbMªkstuvkcU/ gksrs gSaA

(3) Hkkjh ty }kjk cuk ciZQ lkekU; ty esa Mwcrk gSA

(4) izdk'kla'ys"k.k esa ty vkDlhdr gksdj vkDlhtu nsrk gSA


gygygygygy ty esa vUrjk.kfod gkbMªkstu vkcU/ gksrk gSA

HO

HO

H

H

OH

H

( )ty esa

O

H

H

H

O

HO

H

H

H

OH

( )ciZQ esa

OH

H

22. Hkwfexr >hy ls izkIr ty izfrn'kZ esa ÝyksjkbM] ysM] ukbVªsVrFkk vk;ju dh lkUnzrk Øe'k% 1000 ppb, 40 ppb,

100 ppm rFkk 0.2 ppm ikbZ xbZA ;g ty fuEu esa lsfdldh mPp lkUnzrk ls ihus ;ksX; ugha gS\

(1) ysM (2) ukbVªsV

(3) vk;ju (4) ÝyksjkbM


gygygygygy is; ty esa ukbVªsV dh vf/dre lhek 50 ppm gSA

is; ty esa ukbVªsV ds vkf/D; ds dkj.k Cyw csch fl.Mªksegks ldrk gSA

ÝyksjkbM dh vuq'kaflr lhek = 10 ppm

ysM dh vuq'kaflr lhek = 50 ppb.

vk;ju dh vuq'kaflr lhek = 0.2 ppm.

23. gok ds vkf/D; esa Li, Na vkSj K ds ngu ij cuus okyheq[; vkDlkbMsa Øe'k% gSa%

(1) LiO2, Na

2O

2 rFkk K

2O

(2) Li2O

2, Na

2O

2 rFkk KO

2

(3) Li2O, Na

2O

2 rFkk KO

2

(4) Li2O, Na

2O rFkk KO

2


gygygygygy Li eq[;r% vkWDlkbM nsrk gS] Na ijkWDlkbM rFkk K

lqijkWDlkbM nsrk gSA

24. Fkk;ksy xzqi ftleas mifLFkr gS] og gS%

(1) flfLVu(Cystine) (2) flLVhu(Cysteine)

(3) esFkkbvksuhu (4) lkbVkslhu


gygygygygy (– SH) Fkk;ks lewg flLVhu (Cysteine) esa ik;k tkrk gSA

HS – CH – CH – COOH2

NH2

6


25. xSYoukbts'ku fuEu esa ls fdlds dksV ls gksrk gS\(1) Cr (2) Cu

(3) Zn (4) Pb


gygygygygy xSYouhdj.k dksV Zn dh ijr gksrh gSA

26. fuEu ijek.kqvksa esa fdldh çFke vk;uu ÅtkZ mPpre gS\(1) Na (2) K

(3) Sc (4) Rb


gygygygygy Sc, d-CykWd dk rRo gS ftldk Zeff

mPp gksrk gSA vr%bldh vk;uu ,UFkSYih mPp gksrh gSA

27. gkiQeku czksekekbM fuEuhdj.k vfHkfØ;k esa NaOH rFkk Br2

ds ç;qDr eksyksa dh la[;k çfreksy vehu ds cuus esa gksxh%

(1) pkj eksy NaOH rFkk nks eksy Br2

(2) nks eksy NaOH rFkk nks eksy Br2

(3) pkj eksy NaOH rFkk ,d eksy Br2

(4) ,d eksy NaOH rFkk ,d eksy Br2


gygygygygy R – C – NH2

O

+ Br2 + 4NaOH

RNH2 + Na

2CO

3 + 2NaBr + 2H

2O

vfHkfØ;k ls ;g vklkuh ls dgk tk ldrk gS fd vfHkfØ;kesa 4 eksy NaOH ,oa 1 eksy Br

2 ç;qDr gksrh gSA

28. leku vk;ru (V) ds nks cUn cYc] ftuesa ,d vkn'kZ xSlçkjfEHkd nkc p

i rFkk rki T

1 ij Hkjh xbZ gS] ,d ux.;

vk;ru dh iryh V~;wc ls tqM+h gS tSlk fd uhps ds fp=kesa fn[kk;k x;k gSA fiQj buesa ls ,d cYc dk rki c<+kdjT

2 dj fn;k tkrk gSA vfUre nkc p

f gS%

p,Vi

T1

p,Vi

p,Vf

p,Vf

T1

T1

T2

(1)1

i

1 2

T2p

T T

⎛ ⎞⎜ ⎟⎝ ⎠

(2)2

i

1 2

T2p

T T

⎛ ⎞⎜ ⎟⎝ ⎠

(3)1 2

i

1 2

TT2p

T T

⎛ ⎞⎜ ⎟⎝ ⎠

(4)1 2

i

1 2

TTp

T T

⎛ ⎞⎜ ⎟⎝ ⎠


gygygygygy çkjEHk esa eksyksa dh la[;k = vUr esa eksyksa dh la[;k

i i f f

1 1 1 2

p V p V p V p V

RT RT RT RT

i

f

1 1 2

2p 1 1p

T T T

⎛ ⎞ ⎜ ⎟

⎝ ⎠

i 1 2

f

1 1 2

2p T Tp

T T T

⎛ ⎞⎜ ⎟⎝ ⎠

2

f i

1 2

Tp 2p

T T

⎛ ⎞ ⎜ ⎟⎝ ⎠

29. çksihu dh HOCl (Cl2 + H

2O) ds lkFk vfHkfØ;k ftl

eè;orhZ ls gksdj lEiUu gksrh gS] og gS%(1) CH

3 – CH+ – CH

2 – Cl

(2) CH3 – CH(OH) –

2CH

+

(3) CH3 – CHCl –

2CH

+

(4) CH3 – CH+ – CH

2 – OH


gygygygygy CH =CH – CH + Cl2 3

+

CH – CH – CH2 3

+

vf/d LFkk;h eè;orhZ

CH – CH – CH2 3

+

Cl

Cl

CH – CH – CH2 3

+OH–

CH – CH – CH2 3

Cl OHCl

30. uhps nh xbZ vfHkfØ;k ds fy, mRikn gksxk%

1. NBS/h

2. H O/K CO

2 2 3

X

(1)

OH

(2)

O

(3)

CO H2

(4)


gygygygygyNBS/h

vf/d LFkk;h

NBS

Br

H O/K CO2 2 3

O –

H

7


PART–B : MATHEMATICS

31. ;fn ,d leprqHkqZt dh nks Hkqtk,¡] js[kkvksa x – y + 1 = 0

rFkk 7x – y – 5 = 0 dh fn'kk esa gSa rFkk blds fod.kZ

fcUnq (–1, –2) ij izfrPNsn djrs gSa] rks bl leprqHkqZt dk

fuEu esa ls dkSu&lk 'kh"kZ gS\

(1) (–3, –8) (2)1 8,

3 3

⎛ ⎞⎜ ⎟⎝ ⎠

(3)10 7

,3 3

⎛ ⎞ ⎜ ⎟⎝ ⎠

(4) 3, 9


gygygygygy Hkqtkvksa dk izfrPNsnh fcUnq

A B

CD

M

(–1, –2)

(1, 2)

x – y + 1 = 0

rFkk 7x – y – 5 = 0

x = 1, y = 2

AM dh izo.krk = 4

2 = 2

BD dk lehdj.k : y + 2 = x

1( 1)

2− +

x + 2y + 5 = 0

x +2y + 5 = 0 rFkk 7x – y – 5 = 0 gy djus ij

x = 1

3, y =

8

3−

1 8,

3 3

⎛ ⎞−⎜ ⎟⎝ ⎠

32. ;fn ,d vpjsrj lekarj Js<+h dk nwljk] 5 oka rFkk 9 oka

in ,d xq.kksÙkj Js<+h esa gSa] rks ml xq.kksÙkj Js<+h dk lkoZ

vuqikr gS %

(1)4

3(2) 1

(3)7

4(4)

8

5


gygygygygy a + d, a + 4d, a + 8d xq-Js- esa gSa

(a + 4d)2 = (a + d) (a + 8d)

a2 + 8ad + 16d2 = a2 + 9ad + 8d2

8d2 = ad a

d = 8

lkoZ vuqikr = a d

a d

4+

+

= 8 4 4

8 1 3

+=

+

33. ekuk ijoy; y2 = 8x dk P ,d ,slk fcUnq gS tks o`Ùk

x2 + (y + 6)2 = 1, ds dsUnz C ls U;wure nwjh ij gS] rks

ml oÙk dk lehdj.k tks C ls gksdj tkrk gS rFkk ftldk

dsUnz P ij gS] gS

(1) x2 + y2 – x + 4y – 12 = 0

(2)2 2

2 24 04

xx y y

(3) x2 + y2 – 4x + 9y + 18 = 0

(4) x2 + y2 – 4x + 8y + 12 = 0


gygygygygy ekuk ijoy; dk vfHkyEc

(0, –6) C

P(2 , –4 )m m2

y = mx – 4m – 2m3

(0, – 6) bl ij fLFkr gS

– 6 = – 4m – 2m3

m3 + 2m – 3 = 0

(m – 1) (m2 + m + 3) = 0

m = 1

fcUnq P: (2m2, –4m)

= (2, – 4)

oÙk dk lehdj.k

(x – 2)2 + (y + 4)2 = (4 + 4)

x2 + y2 – 4x + 8y + 12 = 0

8


34. jSf[kd lehdj.k fudk;

x + y – z = 0

x – y – z = 0

x + y – z = 0

dk ,d vrqPN gy gksus ds fy, %

(1) dk rF;r% ,d eku gSA

(2) ds rF;r% nks eku gaSA

(3) ds rF;r% rhu eku gSaA

(4) ds vuar eku gSaA


gygygygygy 1 1

1 1 0

1 1

λ −

λ − − =

−λ

1( + 1) – (– 2 +1) + 1(– –1) = 0

3 –+ + 1 – – 1 = 0

3 – = 0

(2 – 1) = 0

= 0, = ±1

ds rF;r% rhu eku gS

35. ;fn 1

( ) 2 3 , 0f x f x xx

⎛ ⎞ ⎜ ⎟⎝ ⎠

g S ] rF k k

{ : ( ) ( )}S x R r x f x gS_ rks S

(1) esa dsoy ,d vo;o gSA

(2) esa rF;r% nks vo;o gSaA

(3) esa nks ls vf/d vo;o gSaA

(4) ,d fjDr leqPp; gSA


gygygygygy f x f xx

1( ) 2 3

⎛ ⎞+ =⎜ ⎟⎝ ⎠

f f xx x

1 32 ( )

⎛ ⎞ + =⎜ ⎟⎝ ⎠

3f(x) = x

x

63−

f(x) = x

x

2⎛ ⎞−⎜ ⎟⎝ ⎠

f(–x) = x

x

2− +

f(x) = f(–x)

x

x

2− = x

x

2− +

x

x

42 − = 0

x = 2±

36. ekuk 1

lim 2 2

01 tan

x

xp x gS] rks log p cjkcj gS %

(1) 1 (2)1

2

(3)1

4(4) 2


gygygygygy p = ( )1

2 2

0

lim 1 tanx

x

x+

→

+

= 2

0

1lim tan

2x

x

xe

→

=

2

lim 1 tan

0 2

x

x x

e

⎛ ⎞⎜ ⎟→ ⎝ ⎠

= e

1

2

logp = 1

2

37. dk og ,d eku ftlds fy, 2 3 sin

1 2 sin

i

i

iw.k Zr%

dkYifud gS] gS

(1)6

(2)

1 3sin

4

⎛ ⎞⎜ ⎟⎝ ⎠

(3)1 1

sin3

⎛ ⎞⎜ ⎟⎝ ⎠

(4)3


gygygygygy i i

i i

2 3 sin 1 2 sin

1 2 sin 1 2 sin

+ θ + θ×

− θ + θ

= 'kq¼ dkYifud

2 – 6sin2 = 0 sin2 = 1

3

sin =

1

3±

38. ml vfrijoy;] ftlds ukfHkyac dh yEckbZ 8 gS rFkk ftldsla;qXeh v{k dh yackbZ mldh ukfHk;ksa ds chp dh nwjh dhvk/h gS] dh mRdsUnzrk gS %

(1)4

3(2)

2

3

(3) 3 (4)4

3


9


gygygygygy. fn;k gS 2

28, 2

bb ae

a

2

b e

a

ge tkurs gSa fd 2 2 2( 1)b a e

22

21

be

a

22

14

ee ,

2 4

3e

2

3e

39. ;fn la[;kvksa 2,3, a rFkk 11 dk ekud fopyu 3.5 gS] rksfuEu esa ls dkSu&lk lR; gS\

(1) 3a2 – 32a + 84 = 0 (2) 3a2 – 34a + 91 = 0

(3) 3a2 – 23a + 44 = 0 (4) 3a2 – 26a + 55 = 0


gygygygygy izlj.k = 2 = ( )x

x

n

22

1Σ

−

ekud fopyu

= a a

22 2 2 22 3 11 2 3 11

4 4

+ + + + + +⎛ ⎞− ⎜ ⎟⎝ ⎠ = 3.5

a a

22134 16

4 4

+ +⎛ ⎞− ⎜ ⎟⎝ ⎠ = (3.5)2

( ) ( )a a a2 2 2

4 134 16 32

16 16

+ + +

− = (3.5)2

536 + 4a2 – 256 – a2 – 32a = 196

3a2 – 32a + 84 = 0

40. lekdy 12 9

5 3 3

2 5

( 1)

x xdx

x x

∫ cjkcj gS %

(1)

10

25 3

2 1

xC

x x

(2)

5

25 3

2 1

xC

x x

(3)

10

25 3

2 1

xC

x x

(4)

5

25 3

1

xC

x x

tgk¡ C ,d LosPN vpj gSA


gygygygygy ( )x x

dxx x

12 9

2 3

2 5

1

+

+ +∫

=

dxx x

x x

3 6

3

2 5

2 5

1 11

⎛ ⎞+⎜ ⎟⎝ ⎠

⎛ ⎞+ +⎜ ⎟⎝ ⎠

∫

x x2 5

1 11+ + = t

dxx x3 6

2 5⎛ ⎞− −⎜ ⎟⎝ ⎠ = dt

= dt

t3

−

∫ = Ct2

1

2+

= C

x x

3

2 5

1

1 12 1

+⎛ ⎞+ +⎜ ⎟⎝ ⎠

=

( )x

C

x x

10

25 3

2 1

+

+ +

41. ;fn js[kk 3 2 4

,2 1 3

x y z lery lx + my – z = 9

esa fLFkr gS] rks l2 + m2 cjkcj gS%

(1) 18 (2) 5

(3) 2 (4) 26


gygygygygy js[kk lery ds vfHkyEc ds yEcor~ gS

�( ) �( )2 3 0i j k l i m j k� � � �

− + • + − =

2l – m – 3 = 0 ...(i)

(3, –2, –4) lery ij fLFkr gS

3l – 2m + 4 = 9

3l – 2m = 5 ...(ii)

(i) rFkk (ii) gy djus ij

l = 1, m= –1

l2 + m2 = 2

42. ;fn 0 2x gS] rks x ds mu okLrfod ekuksa dh la[;k tks

lehdj.k cos x + cos 2x + cos 3x + cos 4x = 0 dks larq"V

djrs gSa] gS

(1) 5 (2) 7

(3) 9 (4) 3


10


gygygygygy cosx + cos2x + cos3x + cos4x = 0

x c x x5 3 52cos cos 2cos cos 0

2 2 2 2⋅ + ⋅ =

x xx

52cos 2cos cos 0

2 2× ⋅ =

x = ( ) ( )

( )n k

r

2 1 2 1, , 2 1

5 2

+ π + π

+ π ,

tgk¡ n, k, 0 x < 2

vr% x = 3 2 9 3, , , , , ,

5 5 5 5 2 2

π π π π π π

π

43. {k s= k 2 2 2( , ) : 2 4 , 0, 0x y y x x y x x y rFkk

dk {ks=kiQy (oxZ bdkbZ;ksa esa) gS %

(1)8

3 (2)

4 2

3

(3)2 2

2 3

(4)4

3


gygygygygy

(2, 0)

(2, 2)

{ks=kiQy = xdx

22

0

22

4

π ⋅

− ∫

= x

23

2

0

22

3π − ⋅ =

8

3π −

44. ekuk ,a b

��

rFk k c�

rhu , sl s ek= kd lfn'k g S a fd

3

2a b c b c

� ��

gSA ;fn ,b c�

�

ds lekarj ugha

gS] rks a�

rFkk b�

ds chp dk dks.k gS %

(1)2

(2)

2

3

(3)5

6

(4)

3

4


gygygygygy ( )a b c× ×

� � �

= ( ) ( )a c b a b c

� � � � � �

i i− = ( )3

2b c� �

+ rFk k

rqyuk djus ij

a b⋅

� �

= 3

2−

cos = 3

2−

= 5

6

π

45. 2 bdkbZ yach ,d rkj dks nks Hkkxksa esa dkV dj mUgsa Øe'k%x bdkbZ Hkqtk okys oxZ rFkk r bdkbZ f=kT;k okys o`Ùk ds:i esa eksM+k tkrk gSA ;fn cuk;s x;s oxZ rFkk oÙk ds {ks=kiQyksadk ;ksx U;wure gS] rks %

(1) (4 ) x r (2) x = 2r

(3) 2x = r (4) 2x = ( + 4)r


gygygygygy rkj dh yEckbZ = 2

r

x

fn;k gS fd 4x + 2r = 2

2x + r = 1 ...(i)

A = x2 + r2 = r

r

2

21

2

− π⎛ ⎞ + π⎜ ⎟⎝ ⎠

dA

dr =

rr

12 2

2 2

− π π⎛ ⎞ ⎛ ⎞− + π⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

vf/dre rFkk U;wure ds fy, dA

dr = 0

(1 – r) = 4r

1 = 4r + r ...(ii)

(i) rFkk (ii) ls

2x + r = 4r + r

x = 2r

46. fcanq (1, –5, 9) dh lery x – y + z = 5 ls og nwjh tksjs[kk x = y = z dh fn'kk esa ekih xbZ gS] gS %

(1) 10 3 (2)10

3

(3)20

3(4) 3 10


11


gygygygygy

P

Q

(1, –5, 9)

L: x = y = z

js[kk PQ dk lehdj.k :

js[kk PQ ij ,d x fcUnq Q ( + 1, – 5. + 9) gS

∵ fcUnq Q lery, : x – y + z = 5 ij fLFkr gS](+ 1) – (– 5) + + 9 = 5

+ 10 = 0

= – 10

fcUnq Q ] (– 9, – 15, – 1) gS

PQ = 2 2 2(1 9) ( 5 15) (9 1) 10 3+ + − + + + =

47. ;fn ,d oØ y = f(x) fcanq (1, –1) ls gksdj tkrk gS rFkkvody lehdj.k y(1 + xy)dx = x dy dks larq"V djrk

gS] rks 1

2

⎛ ⎞⎜ ⎟⎝ ⎠

f cjkcj gS %

(1)4

5 (2)

2

5

(3)4

5(4)

2

5


gygygygygy ydx – xdy = –y2xdx

2

ydx xdyxdx

y

x

d xdxy

⎛ ⎞ ⎜ ⎟⎝ ⎠

nksuksa vksj lekdyu djus ij

2

2

x xc

y

;g (1, –1) ls xqtjrk gS

1 1

12 2

c c ⇒

blfy,,

21

2 2

x x

y

2

2

1

xy

x

2

2

1

xy

x

i.e., 1 4

2 5

⎛ ⎞ ⎜ ⎟⎝ ⎠

f

48. ;fn 2

2 41 , 0⎛ ⎞ ⎜ ⎟⎝ ⎠

n

x

x x

ds izlkj esa inksa dh la[;k

28 gS] rks bl izlkj esa vkus okys lHkh inksa ds xq.kkadksa dk;ksx gS %

(1) 2187 (2) 243

(3) 729 (4) 64


gygygygygy inksa dh la[;k 2n + 1 gS tks fo"ke gS] ijUrq ;g 28 nh xbZgS ;fn ge (x + y + z)n ysrs gSa rc inksa dh la[;kn + 2C

2 = 28 gS

vr% n = 6

6

2 60 1 2 62

2 41 ......a a x a x a x

x x

⎛ ⎞ ⎜ ⎟⎝ ⎠

xq.kkadksa dk ;ksxiQy x = 1 }kjk Kkr fd;k tk ldrk gS

(1 – 2 + 4)6 = 36 = 729

blfy, ijh{kd ds iwNs x;s iz'u ds vuqlkj fodYi 3 lghgks ldrk gSA

49.1 1 sin

( ) tan , 0,1 sin 2

⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

xf x x

x ij fopkj dhft,A

y = f(x) ds fcanq 6

x ij [khapk x;k vfHkyac fuEu fcanq

ls Hkh gksdj tkrk gS %

(1)2

0,3

⎛ ⎞⎜ ⎟⎝ ⎠

(2) , 06

⎛ ⎞⎜ ⎟⎝ ⎠

(3) , 04

⎛ ⎞⎜ ⎟⎝ ⎠

(4) (0, 0)


gygygygygy 1 1 sin( ) tan

1 sin

xf x

x

=

2

1

2

cos sin2 2

tan

cos sin2 2

⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟⎝ ⎠

x x

x x

= 1

tan tan4 2

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

x

12


= 4 2

x

1

( )2

f x rFkk , ( )6 3

x f x ij

blfy, vfHkyEc dk lehdj.k

22 2

3 6 3y x y x

⎛ ⎞ ⇒ ⎜ ⎟⎝ ⎠

50. x R ds fy, ( ) | log2 sin | f x x rFkk g(x) = f(f(x))

gSa] rks %

(1) g(0) = cos(log2) gSA

(2) g(0) = –cos(log2) gSA

(3) x = 0 ij gvodyuh; gS rFkk g(0) = –sin(log2) gSA

(4) x = 0 ij gvodyuh; ugha gSA


gygygygygy ( ) ( ( )) | log2 sin | log2 sin ||g x f f x x

AZ x = 0

g(x) = f(f(x)) = log2 – sin(log2 – sinx)

g(x) = cos(log2 – sinx)x – cosx

g (0) = cos(log2)

51. ekuk nks vufHkur N% iQydh; ikls A rFkk B ,d lkFkmNkys x;sA ekuk ?kVuk E

1 ikls A ij pkj vkuk n'kkZrh

gS] ?kVuk E2 ikls B ij 2 vkuk n'kkZrh gS rFkk ?kVuk E

3

nksuksa iklksa ij vkus okyh la[;kvksa dk ;ksx fo"ke n'kkZrh gS]rks fuEu esa ls dkSu&lk dFku lR; ughalR; ughalR; ughalR; ughalR; ugha gS\

(1) E2 rFkk E

3 Lora=k gSaA

(2) E1 rFkk E

3 Lora=k gSaA

(3) E1, E

2 rFkk E

3 Lora=k gSaA

(4) E1 rFkk E

2 Lora=k gSaA


gygygygygy 1

1( )

6P E

2

1( )

6P E

P(E1 E

2) = P(A, 4 rFkk B, 2 n'kkZrk gS)

= 1 2

1( ). ( )

36P E P E

blfy, E1, E

2 Lora=k gSa

blh izdkj E1 E

2 E

3 =

vr% P(E1 E

2 E

3) P(E

1. P(E

2). P(E

3)

vr% E1, E

2, E

3 Lora=k ugha gSa

52. ;fn 5

3 2

⎡ ⎤ ⎢ ⎥⎣ ⎦

a bA rFkk A.adj A = A AT g S a ] rk s

5a + b cjkcj gS %

(1) 5 (2) 4

(3) 13 (4) –1


gygygygygy A - adj A = IAI = A.AT

adj A = AT

2 5 3

3 5 2

b a

a b

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

5a = 2, b = 3

blfy,, 5a + b = 5

53. c wy s d s O; atd (Boolean Expression)

( ) ( ) ∼ ∼p q q p q dk lerqY; gS %

(1) p q (2) p q

(3) ∼p q (4) ∼ q q


gygygygygy ( ) ( )p q q p q ∼ ∼

= ( ) ( ) ( )p q q q p q ∼ ∼

= ( ) ( )p q t p q ∼

= ( ) ( )p q p q

= ( ) ( )p q p p q q

= ( )t p q

= p q

54. x ds mu lHkh okLrfod ekuksa dk ;ksx tks lehdj.k

2

4 602

5 5 1

x x

x x dks larq"V djrs gSa gS %

(1) –4 (2) 6

(3) 5 (4) 3


13


gygygygygy x2 – 5x + 5 = 1

x = 1, 4

;k x2 – 5x + 5 = – 1

x = 2, 3

;k x2 + 4x – 60 = 0

x = –10, 6

x = 3 vLohdk;Z gksxk pwafd L.H.S. = –1 gS

vr% x ds ekuksa dk ;ksxiQy = 1 + 4 + 2 – 10 + 6 = 3

55. mu o`Ùkksa ds dsUnz] tks o`Ùk x2 + y2 – 8x – 8y – 4 = 0

dks ckâ; :i ls Li'kZ djrs gSa rFkk x-v{k dks Hkh Li'kZdjrs gSa] fLFkr gSa %

(1) ,d nh?kZoÙk ij tks oÙk ugha gSA

(2) ,d vfrijoy; ijA

(3) ,d ijoy; ijA

(4) ,d oÙk ijA


gygygygygy

6 k

(4, 4) ( )h k1

( = )r k

x v{k

f=kT;k = 16 16 4 6

(6 + k)2 = (h – 4)2 + (k – 4)2

h x, k y izfrLFkkfir djus ij

(y + 6)2 – (y – 4)2 = x2 – 8x + 16

(2y + 2) (10) = x2 – 8x + 16

20y + 20 = x2 – 8x + 16

x2 – 8x – 20y – 4 = 0

dsUnz ijoy; ij fLFkr gSA

56. 'kCn SMALL ds v{kjksa dk iz;ksx djds] ik¡p v{kjksa okyslHkh 'kCnksa (vFkZiw.kZ vFkok vFkZghu) dks 'kCndks'k ds Øekuqlkjj[kus ij] 'kCn SMALL dk LFkku gS %

(1) 59 oka (2) 52 oka

(3) 58 oka (4) 46 oka


gygygygygy A ls vkjEHk gksus okys 'kCn 4!

122!

L ls vkjEHk gksus okys 'kCn = 4! = 24

M ls vkjEHk gksus okys 'kCn 4!

122!

SA ls vkjEHk gksus okys 'kCn3!

32!

SL ls vkjEHk gksus okys 'kCn = 3! = 6

vxyk 'kCn SMALL gS

jSad = 12 + 24 + 12 + 3 + 6 + 1 = 58

57.

1

2

( 1)( 2)...3lim

⎛ ⎞⎜ ⎟⎝ ⎠

n

nn

n n n

n

cjkcj gS %

(1)2

27

e

(2)2

9

e

(3) 3 log3 – 2 (4)4

18

e


gygygygygy

1

( 1)( 2)( 3)....( 2 )lim

. . .....

n

n

n n n n np

n n n

⎡ ⎤ ⎢ ⎥⎣ ⎦

2

1

1log lim log

n

nr

n rp

n n

⎛ ⎞ ⎜ ⎟⎝ ⎠

∑

=

2

0

log(1 )x dx∫

= 2

2

0

0

1.log(1 )

1

xx dx dx

x

∫

=

2

0

12log3 1

1dx

x

⎡ ⎤⎛ ⎞⎢ ⎥ ⎜ ⎟⎢ ⎝ ⎠ ⎥⎣ ⎦∫

= 20

2log3 log(1 )x x

= 2 log3 – (2 – log3]

logp = 3 log3 – 2

log273log3 2

2 2

27ep e

e e

14


58. ;fn Js.kh

2 2 2 2

23 2 1 41 2 3 4 4 .....,5 5 5 5

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

ds izFke

nl inksa dk ;ksx 16

5m gS] rks m cjkcj gS %

(1) 101 (2) 100

(3) 99 (4) 102


gygygygygy2 2 2

23 2 11 2 3 4 .......5 5 5

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

= 16

5m

2 2 2

8 12 16 20 16....10 =

5 5 5 5 6m

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

in

2

2 2 2 24[2 3 4 5 ...... 10 ]

5

⎛ ⎞ ⎜ ⎟⎝ ⎠

in = 16

5m

2

2 2 2 24[2 3 4 ....... 11 ]

5

⎛ ⎞ ⎜ ⎟⎝ ⎠

= 16

5m

2

2 2 2 2 24[1 2 3 ....... 11 1 ]

5

⎛ ⎞ ⎜ ⎟⎝ ⎠

16

5 m

2

4 11.12.23 161

5 6 5m

⎛ ⎞ ⎡ ⎤ ⎜ ⎟ ⎢ ⎥⎝ ⎠ ⎣ ⎦

(fn;k gS)

16 16

[22.23 1]25 5

m

1(505)

5m

m = 101

59. ;fn lehdj.k x2 + y2 – 4x + 6y – 12 = 0 }kjk iznÙk ,doÙk dk ,d O;kl ,d vU; oÙk S, ftldk dsUnz (–3, 2)

gS] dh thok gS] rks oÙk S dh f=kT;k gS %

(1) 5 3

(2) 5

(3) 10

(4) 5 2


gygygygygy

C2(–3, 2)

5

A

C1

(+2, –3)

50

Eq. x2 + y2 – 4x + 6y – 12 = 0

C1; (2, –3),

1 4 9 12 5r

C2 = (– 3, 2)

2 2

1 2 5 5 50C C

rc, 2 2

2 5 ( 50) 75 5 3C A

60. ,d O;fDr ,d ÅèokZ/j [kaHks dh vksj ,d lh/s iFk ij ,dleku pky ls tk jgk gSA jkLrs ij ,d fcUnq A ls og [kaHks dsf'k[kj dk mUu;u dks.k 30° ekirk gSA A ls mlh fn'kk esa10 feuV vkSj pyus ds ckn fcUnq B ls og [kaHks ds f'k[kj dkmUu;u dks.k 60° ikrk gS] rks B ls [kaHks rd igq¡pus esa mlsyxus okyk le; (feuVksa esa) gS

(1) 10 (2) 20

(3) 5 (4) 6


gygygygygy

60°30°

AB10v

h

x

ekuk pky = V bdkbZ@feuV

tan3010

h

v x

tan60h

x

1

510 3

⇒ x

x v

v x

vr%] le; = 5 feuV

15


PART–C : PHYSICS

61. 20 M YkEckbZ dh ,dleku Mksjh dks ,d n`<+ vk/kj lsyVdk;k x;k gSA blds fupys fljs ls ,d lw{e rjax&Lianpkfyr gksrk gSA Åij vk/kj rd igq¡pus esa yxus okykle; gS (g = 10 m/s2 ysa)

(1) 2 s (2) 2 2 s

(3) 2 s (4) 2 2s


gygygygygyT

dx xg

dt

00

Ltdxdt

xg∫ ∫

t = 2 2 s

62. ,d HkkjksÙkksyd Hkkj dks igys Åij vkSj fiQj uhps rd ykrkgSA ;g ekuk tkrk gS fd fliQZ Hkkj dks Åij ys tkus esadk;Z gksrk gS vkSj uhps ykus esa fLFkfrt ÅtkZ dk âkl gksrkgSA 'kjhj dh olk ÅtkZ nsrh gS tks ;kaf=kdh; ÅtkZ esa cnyrh

gSA eku ysa fd olk }kjk nh xbZ ÅtkZ 73.8 10 J

izfr kg Hkkj gS] rFkk bldk ek=k 20% ;kaf=kdh; ÅtkZ esacnyrk gSA vc ;fn ,d HkkjksÙkksyd 10 kg ds Hkkj dks1000 ckj 1 m dh Å¡pkbZ rd Åij vkSj uhps djrk gS

rc mlds 'kjhj ls olk dk {k; gS % ( 29.8msg

ysa)

(1) 6.45 × 10–3 kg (2) 9.89 × 10–3 kg

(3) 12.89 × 10–3 kg (4) 2.45 × 10–3 kg


gygygygygy ekuk x kg olk dk {k; gksrk gS] rc

x × 3.8 × 107 × 20

100 = 10 × 9.8 × 1000

x = 12.89 × 10–3 kg

63. m nzO;eku dk ,d fcanq d.k ,d [kqjnjs iFk PQR (fp=knsf[k;s) ij py jgk gSA d.k vkSj iFk ds chp ?k"kZ.k xq.kkad gSA d.k P ls NksM+s tkus ds ckn R ij igq¡p dj :d

tkrk gSA iFk ds Hkkx PQ vkSj QR ij Pkyus esa d.k }kjk[kpZ dh xbZ ÅtkZ,¡ cjkcj gSaA PQ ls QR ij gksus okysfn'kk cnyko esa dksbZ ÅtkZ [kpZ ugha gksrhA

rc vkSj nwjh x(= QR) ds eku yxHkx gSa Øe'k%

P

h = m2

30° R

{kSfrt lrg Q

(1) 0.2 vkSj 3.5 m

(2) 0.29 vkSj 3.5 m

(3) 0.29 vkSj 6.5 m

(4) 0.2 vkSj 6.5 m


gygygygygy PQ ds vuqfn'k ?k"kZ.k }kjk fd;k x;k dk;Z

= QR ds vuqfn'k ?k"kZ.k }kjk fd;k x;k dk;Z

mg cossin30º

h = mg x

x = 3.5 m

vc, dk;Z ÅtkZ izes; ds vuqlkj

mgh = wf(PQ) + w

f(QOR)

Since, wf(PQ) = w

f(QR)

mg(2) = 2 × mg cos 30° sin30º

h

= 0.29

64. nks ,dleku rkj A o B izR;sd dh yEckbZ I esa leku/kjk I izokfgr gSA A dks eksM+dj R f=kT;k dk ,d o`ÙkvkSj B dks eksM+dj Hkqtk a dk ,d oxZ cuk;k tkrk gSA;fn B

A rFkk B

B Øe'k% o`Ùk ds dsUnz rFkk oxZ ds dsUnz

ij pqEcdh; {ks=k gSa] rc vuqikr A

B

B

B gksxk%

(1)

2

16 2

(2)

2

16

(3)

2

8 2

(4)

2

8


16


gygygygygy A ds fy, B ds fy,

2R = L 4a = L

R = 2

L

a =

4

L

0

2A

iB

R

04 sin sin

4 / 2 4 4B

iB

a

⎡ ⎤ ⎛ ⎞ ⎜ ⎟⎢ ⎥ ⎝ ⎠⎣ ⎦

vc

2

8 2

A

B

B

B

65. ,d xSYosuksehVj ds dkby dk izfrjks/ 100 gSA 1 mA

/kjk izokfgr djus ij blesa iQqy&Ldsy fo{ksi feyrk gSAbl xSYosuksehVj dks 10 A ds ,ehVj esa cnyus ds fy;s tksizfrjks/ yxkuk gksxk og gS%

(1) 2 (2) 0.1

(3) 3 (4) 0.01


gygygygygy Ig = 10–3 A

Rg = 100

RS ('kaV izfrjks/) =

( )0.01

g g

g

I R

I I

66. nwj fLFkr 10 m Å¡ps isM+ dks ,d 20 vko/Zu {kerk okysVsfyLdksi ls ns[kus ij D;k eglwl gksxk\

(1) isM+ 10 xquk ikl gS (2) isM+ 20 xquk Å¡pk gS

(3) isM+ 20 xquk ikl gS (4) isM+ 10 xquk Å¡pk gS


gygygygygy VsfyLdksi ess vko/Zu dh ifjHkk"kk ls oLrq izs{kd dks20 xquk fudV fn[kkbZ nsxhA

67. rk¡ck rFkk vekfnr (undoped) flfydku ds izfrjks/ksa dhmuds rkieku ij fuHkZjrk] 300-400 K rkieku varjky esa]ds fy;s lgh dFku gS %

(1) rk¡ck ds fy;s js[kh; c<+ko rFkk flfydku ds fy,pj?kkrkadh c<+ko

(2) rk¡ck ds fy;s js[kh; c<+ko rFkk flfydku ds fy;spj?kkrkadh ?kVko

(3) rk¡ck ds fy, js[kh; ?kVko rFkk flfydku ds fy;s js[kh;?kVko

(4) rk¡ck ds fy;s js[kh; c<+ko rFkk flfydku ds fy;s js[kh;c<+ko


gygygygygy /krqvksa ds fy, izfrjks/ rki esa o`f¼ ij c<+rk gSA vekfnrSi ds fy,, izfrjks/ rki esa deh ij ?kVrk gSA

68. lgh dFku pqfu;s

(1) vk;ke ekMqyu esa mPp vkofÙk dh okgd rjax dh vkofÙkesa cnyko èofu flXuy ds vk;ke ds vuqikrh gS

(2) vkofÙk ekMqyu esa mPp vkofÙk dh okgd rjax ds vk;keesa cnyko èofu flXuy ds vk;ke ds vuqikrh gS

(3) vkofÙk ekMqyu esa mPp&vkofÙk dh okgd rjax dh vk;keesa cnyko èofu flXuy dh vkofÙk ds vuqikrh gS

(4) vk;ke ekMqyu esa mPp&vkofÙk dh okgd rjax ds vk;keesa cnyko èofu flXuy ds vk;ke ds vuqikrh gS


gygygygygy vk;ke ekWMwyu dh ifjHkk"kk lsA

69. nks jsfM;ks/ehZ rRo A rFkk B dh v¼Zvk;q Øe'k% 20 min

rFkk 40 min gSaA çkjEHk esa nksuksa ds uewuksa esa ukfHkdksa dhla[;k cjkcj gSA 80 min ds mijkUr A rFkk B ds {k;gq, ukfHkdksa dh la[;k dk vuqikr gksxk(1) 4 : 1 (2) 1 : 4

(3) 5 : 4 (4) 1 : 16


gygygygygy A dh T1/2

= 20 feuV

B dh T1/2

= 40 feuV

80 feuV ckn

0

AN

N({kf;r)

41

12

⎛ ⎞ ⎜ ⎟⎝ ⎠

…(1)

0

BN

N({kf;r)

21

12

⎛ ⎞ ⎜ ⎟⎝ ⎠

…(2)

5

4

A

B

N

N

70. n eksy vkn'kZ xSl ,d çØe A B ls xqtjrh gS (fp=knsf[k;s)A bl çØe ds nkSjku mldk vf/dre rkieku gksxk

V

B

A

P

2P0

P0

2V0

V0

(1)0 0

3

2

P V

nR(2)

0 09

2

P V

nR

(3)0 0

9P V

nR(4)

0 09

4

P V

nR

17



gygygygygy 0

0

0

3P

P V PV

2

0 0

0

3

P v P v

TV nR nR

…(1)

Tvf/dre ds fy,

0dT

dv

0

3

2v v …(2)

(1) o (2) ds iz;ksx ls

Tvf/dre0 09

4

P V

nR

71. ,d vkdZ ySEi dks izdkf'kr djus ds fy;s 80 V ij 10 A

dh fn"V /kjk (DC) dh vko';drk gksrh gSA mlh vkdZdks 220 V (rms) 50 Hz izR;korhZ /kjk (AC) ls pykus dsfy;s Js.kh esa yxus okys izsjdRo dk eku gS

(1) 0.08 H (2) 0.044 H

(3) 0.065 H (4) 80 H


gygygygygy 8 VR

I

P = 800 W

10 A 8 314 L

(220)2 = (10×8)2 + (314×L×10)2

L = 0.065 H

72. nksuksa fljksa ij [kqys ,d ikbi dh ok;q esa ewy&vkofÙk f gSAikbi dks ÅèokZ/j mldh vk/h yEckbZ rd ikuh esa Mqck;ktkrk gSA rc blesa cps ok;q&dkye dh ewy vkofÙk gksxh

(1)3

4

f(2) 2f

(3) f (4)2

f


gygygygygy Mqckus ls igys] 2

vf

L

Mqckus ds ckn]4

2

vf f

L

73. ,d fiu&gksy dSejk dh yEckbZ L gS rFkk fNnz dh f=kT;k a

gSA ml ij rjaxnSè;Z dk lekUrj izdk'k vkifrr gSA fNnzds lkeus okyh lrg ij cus LikWV dk foLrkj fNnz dsT;kferh; vkdkj rFkk foorZu ds dkj.k gq, foLrkj dk dqy;ksx gSA bl LikWV dk U;wure vkdkj b

min rc gksxk tc

(1) a L rFkk 2

min

2b

L

⎛ ⎞ ⎜ ⎟⎜ ⎟⎝ ⎠

(2) a L rFkk min4b L

(3)

2

aL

rFkk min4b L

(4)

2

aL

rFkk 2

min

2b

L

⎛ ⎞ ⎜ ⎟⎜ ⎟⎝ ⎠


gygygygygyQ

a

sinL

L La

Lb a

a

b ds U;wure gksus ds fy,, a L min

2b L

74. la/kfj=kksa ls cus ,d ifjiFk dks fp=k esa fn[kk;k x;k gSA,d fcUnq&vkos'k Q (ftldk eku 4 F rFkk 9 F okysla/kfj=kksa ds dqy vkos'kksa ds cjkcj gS) ds }kjk 30 m nwjhij oS|qr&{ks=k dk ifjek.k gksxk%

3 F

8 V

9 F

4 F

2 F

–+

(1) 360 N/C (2) 420 N/C

(3) 480 N/C (4) 240 N/C


gygygygygy Cnet

= 5 F

Qnet

= 5 × 8 = 40

Q4 F

= 24

Q9 F

= 18

Q = Q4 F

+ Q9 F

= 42 C

4 –6

2

9 10 42 10420 N/C

30 30

kQE

r

18


75. fuEu izfr DokaVe oS|qr&pqEcdh; fofdj.kksa dks mudh ÅtkZds c<+rs gq, Øe esa yxk;sa

A : uhyk izdk'k B : ihyk izdk'k

C : X&fdj.ksa D : jsfM;ks rjax

(1) A, B, D, C (2) C, A, B, D

(3) B, A, D, C (4) D, B, A, C


gygygygygy fo|qr pqEcdh; LiSDVªe ds vuqlkj D, B, A, C

76. nks pqEcdh; inkFkZ A rFkk B ds fy;s fgLVsjsfll&ywi uhpsfn[kk;s x;s gSa %

B

H

(A)

B

H

(B)

bu inkFkks± dk pqEcdh; mi;ksx fo|qr&tsusjsVj ds pqEcd]VªkUliQkWeZj dh ØksM ,oa fo|qr&pqEcd dh ØksM vkfn ds cukusesa fd;k tkrk gSA rc ;g mfpr gS fd

(1) A dk bLr seky fo|qr&pqEcd es a rFkk B dkfo|qr&tsusjsVj esa fd;k tk,

(2) A dk bLrseky VªkUliQkWeZj esa rFkk B dk fo|qr&tsusjsVjeas afd;k tk,

(3) B dk bLrseky fo|qr&pqEcd rFkk VªkUliQkWeZj nksuksa esafd;k tk,

(4) A dk bLrseky fo|qr&tsusjsVj rFkk VªkUliQkWeZj nksuksa esafd;k tk,


gygygygygy fo|qr pqEcdkas] fo|qr tujsVj rFkk VaªkliQkWeZj ds fy, ÅtkZgkfu de gksuh pkfg,A blfy, (B) iz;qDr fd;k tkukpkfg,A

77. ,d isUMqye ?kM+h 40ºC rkieku ij 12 s izfrfnu /heh gkstkrh gS rFkk 20ºC rkieku ij 4 s izfrfnu rst gks tkrhgSA rkieku ftl ij ;g lgh le; n'kkZ;sxh rFkk isUMqyedh /krq dk js[kh;&izlkj xq.kkad () Øe'k% gSa

(1) 60°C; = 1.85 × 10–4/°C

(2) 30°C; = 1.85 × 10–3/°C

(3) 55°C; = 1.85 × 10–2/°C

(4) 25°C; = 1.85 × 10–5/°C


gygygygygy1

(40 ) 86400 12 s2

T ...(1)

1( 20) 86400 4

2T ...(2)

(1) dk (2) ls Hkktu dj gy djus ij

T = 25°C

78. f=kT;k a rFkk b ds nks ,d&dsUnzh xksyksa ds (fp=k nsf[k;s)

chp ds LFkku esa vk;ru vkos'k&?kuRo A

r gS] tgk¡

A fLFkjkad gS rFkk r dsUnz ls nwjh gSA xksyksa ds dsUnz ij,d fcUnq&vkos'k Q gSA A dk og eku crk;sa ftlls xksyksads chp ds LFkku esa ,dleku oS|qr&{ks=k gksa %

a

b

Q

(1) 2 22 ( )

Q

b a (2) 2 2

2

( )

Q

a b

(3)2

2Q

a(4)

22

Q

a


gygygygygy

a

rdr

r = a ij] 2a

kQE

a

,d xksys dks r = r ij yhft,A

(a r b )

dq = 4r2drA

r

r = a ls r = r rd q

2 24 2 [ ]

r

a

q A rdr A r a ∫

19


r = a ls r = b rd vkos'k

q = 2A[b2 – a2]

vc, r = b ij {ks=k 2 2

2

0

2 [ ]

4b

A b a QE

b

gSA

vc, Ea = E

b ls,

22

QA

a

79. ,d iz;ksx djds rFkk i – xzkiQ cukdj ,d dk¡p ls cusfizTe dk viorZukad fudkyk tkrk gSA tc ,d fdj.k dks35ºC ij vkifrr djus ij og 40ºC ls fopfyr gksrh gSrFkk ;g 79ºC ij fuxZe gksrh gSA bld fLFkfr esa fuEu esals dkSulk eku viorZukad ds vf/dre eku ds lcls iklgS\

(1) 1.6 (2) 1.7

(3) 1.8 (4) 1.5


gygygygygy fn;s x;s vkadMas ls, A = i + e – = 74°, = 40°

vc,

sin sin2 2

sin sin2 2

mA A

A A

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

sin57

1.39sin37

⇒

fudVre eku 1.5 gSA

80. ,d Nk=k ,d ljy&vkorZ&nksyd ds 100 vko`fÙk;ksa dkle; 4 ckj ekirk gS vkSj mudks 90 s, 91 s, 95 s vkSj92 s ikrk gSA bLrseky dh xbZ ?kM+h dk U;wure vYika'k1 s gSA rc ekis x;s ekè; le; dks mls fy[kuk pkfg;s%

(1) 92 5.0 s

(2) 92 1.8 s

(3) 92 3 s

(4) 92 2 s


gygygygygy 1 2 3 4

4

T T T TT

1 2 3 4| | | | | | | |

4

T T T T T T T TT

= 1.5 s 2s (pwafd vYirekad 1s gSA)

vfUre mÙkj 92 ± 2s gSA

81. fp=k (a), (b), (c), (d) ns[kdj fu/kZfjr djsa fd ;s fp=k Øe'k%fdu lsehdUMDVj fMokbZl ds vfHky{kf.kd xzkiQ gSa\

I

V

(a)

I

V

(b)

I

V

(c)

vizdkf'kr

izdkf'kr(d)

izfrjks/

izdk'k dh rhozrk

(1) thuj Mk;ksM] lk/kj.k Mk;ksM] LDR (ykbZV fMisUMsUVjsftLVsUl)] lksyj lsy

(2) lksyj lsy] LDR (ykbZV fMisUMsUV jsftLVsUl)] thujMk;ksM] lk/kj.k Mk;ksM

(3) thuj Mk;ksM] lksyj lsy] lk/kj.k Mk;ksM] LDR (ykbVfMisUMsUV jsftLVsUl)

(4) lk/kj.k Mk;ksM] thuj Mk;ksM] lksyj lsy] LDR (ykbZVfMisUMsUV jsftLVsUl)


gygygygygy lwpuk ij vk/kfjr iz'uA

82. ,d iQksVks&lsy ij rjaxnSè;Z izdk'k vkifrr gSA mRlftZr

bysDVªkWu dh vf/dre xfr v gSA ;fn rjaxnSè;Z 3

4

λ gks

rc mRlftZr bysDVªkWu dh vf/dre xfr gksxh%

(1)

1

24

3v⎛ ⎞< ⎜ ⎟⎝ ⎠

(2)

1

24

3v⎛ ⎞= ⎜ ⎟⎝ ⎠

(3)

1

23

4v⎛ ⎞= ⎜ ⎟⎝ ⎠

(4)

1

24

3v⎛ ⎞> ⎜ ⎟⎝ ⎠


gygygygygy 21

2

hcmv

...(i)

2143 2

hcmv

...(ii)

(ii) – 4

3 (i) ls,

3

=

2 21 1 4

2 2 3mv mv

1

22 2

1 1

4 4

3 3V V V V

⎛ ⎞ ⇒ ⎜ ⎟⎝ ⎠

20


83. ,d d.k A vk;ke ls ljy&vkorZ nksyu dj jgk gSA tc

;g vius ewy&LFkku ls 2

3

A ij igq¡prk gS rc vpkud

bldh xfr frxquh dj nh tkrh gSA rc bldk u;k vk;kegS%

(1) 3A (2) 3A

(3)7

3

A(4) 41

3

A


gygygygygy2

2 2 5 A

3 3

AA

⎛ ⎞ ⎜ ⎟⎝ ⎠

vc, 3 5 A

3V

vc,

2

2 2 7

3 3

A AV A A

⎛ ⎞ ⇒ ⎜ ⎟⎝ ⎠

84. fp=k esa Hkqtk a dk oxZ x-y ry esa gSA m nzO;eku dk,d d.k ,dleku xfr] v ls bl oxZ dh Hkqtk ij pyjgk gS tSlk fd fp=k esa n'kkZ;k x;k gSA

a

a

a

a

v

v

v

v

A B

CDy

xO

45°

R

rc fuEu esa ls dkSulk dFku] bl d.k ds ewy fcUnq ds

fxnZ dks.kh; vk?kw.kZ L

→

ds fy, xyr gS\

(1) L

→

= ˆ

2

Rmv a k

⎡ ⎤−⎢ ⎥

⎣ ⎦, tc d.k C ls D dh vksj py

jgk gSA

(2) L

→

= ˆ

2

Rmv a k

⎡ ⎤+⎢ ⎥

⎣ ⎦, tc d.k B ls C dh vksj py

jgk gSA

(3) L

→

= ˆ

2

mvR k , tc d.k D ls A dh vksj py jgk

gSA

(4) L

→

= ˆ

2

mvR k−

, tc d.k A ls B dh vksj py

jgk gSA

mÙkjmÙkjmÙkjmÙkjmÙkj (1, 3)

gygygygygy fodYi 1 eas, lgh L�

, ˆ

2

Rmv a k

⎡ ⎤⎢ ⎥⎣ ⎦

gksuk pkfg,] tc

d.k C ls D dh vksj py jgk gSA

fodYi 3 eas, lgh L�

, ˆ

2

mvRk

gksuk pkfg,A

85. ,d vkn'kZ xSl mRØe.kh; LFkSfrd&dYi izØe ls xqtjrhgS rFkk mldh eksyj&mQ"ek&/kfjrk C fLFkj jgrh gSA ;fnbl izØe esa mlds nkc P o vk;ru V ds chp laca/ PVn

= constant gSA (CP rFkk C

V Øe'k% fLFkj nkc o fLFkj

vk;ru ij mQ"ek /kfjrk gS) rc ‘n’ ds fy;s lehdj.k gS%

(1) n = P

V

C C

C C

−

−

(2) n = P

V

C C

C C

−

−

(3) n = V

P

C C

C C

−

−

(4) n = P

V

C

C


gygygygygy1

V

RC C

n

1V

RC C

n

vFkok 1 1

P P

R nRC C R C C

n n ⇒

P

V

C Cn

C C

86. ,d LØw xst dk fip 0.5 mm gS vkSj mlds o`Ùkh;&Ldsyij 50 Hkkx gSaA blds }kjk ,d iryh vY;qehfu;e 'khVdh eksVkbZ ekih xbZA eki ysus ds iwoZ ;g ik;k x;k fdtc LØw&xst ds nks tkWoksa dks lEidZ esa yk;k tkrk gS rc45 oka Hkkx eq[; Ldsy ykbZu ds laikrh gksrk gS vkSj eq[;Ldsy dk 'kwU; (0) eqf'dy ls fn[krk gSA eq[; Ldsy dkikB;kad ;fn 0.55 mm rFkk 25 oka Hkkx eq[; Ldsy ykbZuds laikrh gks] rks 'khV dh eksVkbZ D;k gksxh\

(1) 0.80 mm

(2) 0.70 mm

(3) 0.50 mm

(4) 0.75 mm


21


gygygygygy 'kwU; =kqfV = o`Ùkh; Ldsy dk –5 izHkkx

oÙkh; Ldsy dk 1 izHkkx

=–2

0.510 mm = 0.01 mm

50

'kwU; =kqfV = –5 × 10–2 = –0.05 mm

'kwU; la'kks/u = + 0.05 mm

iBu = 0.5 + 25 × 0.01 + 0.05 = 0.80 mm

87. nks 'kadq dks muds 'kh"kZ O ij tksM+dj ,d jksyj cuk;k x;kgS vkSj mls AB rFkk CD jsy ij vlefer j[kk x;k gS (fp=knsf[k;s)A jksyj dk v{k CD ls yEcor gS vkSj O nksuksa jsyds chpksachp gSA gYds ls /dsyus ij jksyj jsy ij bl çdkjyq<+duk vkjEHk djrk gS fd O dk pkyu CD ds lekUrjgS (fp=k nsf[k;s)A pkfyr gks tkus ds ckn ;g jksyj

B D

O

A C

(1) nk;ha vksj eqM+sxk

(2) lh/k pyrk jgsxk

(3) ck;sa rFkk nk;sa Øe'k% eqM+rk jgsxk

(4) ck¡;ha vksj eqM+sxk


gygygygygy jksyj ck;ha vksj eqMsxk pwafd ?k"kZ.k cy ihNs dh fn'kk esa iVjhAB ij mRiÂ gksXkkA

88. ,d xsV esa a, b, c, d buiqV gSa vkSj x vkÅViqV gSA rcfn;s x;s Vkbe&xzkiQ ds vuqlkj xsV gS

d

c

b

a

x

(1) AND

(2) OR

(3) NAND

(4) NOT


gygygygygy OR xsV pawfd vkÅViqV 1 gS] tc dksbZ ,d buiqV 1 gSA

89. mHk;fu"B&mRltZd foU;kl ds fy, rFkk ds chp fuEuesa ls dkSulk lEcU/ xyrxyrxyrxyrxyr gS\ rFkk fpUg lkekU;eryc okys gSa

(1)1

(2)

1

(3)

2

21

(4)1 1

1

mÙkjmÙkjmÙkjmÙkjmÙkj (1, 3)

gygygygygy Ie = I

b + I

c

1e b

c c

I I

I I

1 11

vFkok]1

90. i`Foh dh lrg ls 'h' Å¡pkbZ ij ,d mixzg o`Ùkkdkj iFkij pDdj dkV jgk gS (i`Foh dh f=kT;k R rFkk h<<R)AiFoh ds xq:Ro {ks=k ls iyk;u djus ds fy;s bldh d{kh;xfr esa vko';d U;wure cnyko gS% (ok;qeaMyh; izHkko dksux.; yhft,A)

(1) gR

(2) / 2gR

(3) ( 2 1)gR

(4) 2gR


gygygygygy0

V gR

2e

V gR

( 2 1)V gR

� � �

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(Chemistry, Mathematics and Physics) · 3 JEE (MAIN)-2016 (Code-F) 6. dkcZu rFkk dkcZu eksuksDlkWbM dh ngu Å"ek;sa Øe'k% –393.5 rFkk –283.5 kJ mol–1 gSaA dkcZu eksuksDlkbM