paper_2

A. lkekU; / General :1. ;g iqfLrdk vkidk iz'u&i= gSA bldh eqgj rc rd u rksM+s tc rd fujh{kd ds }kjk bldk funZs'k u fn;k tk;sA

This booklet is your Question Paper. Do not break the seal of this booklet before being instructed to do so by theinvigilator.

2. iz'u&i= dk dksM (CODE) bl i`"B ds ijh nk;sa dkSus ij Nik gSAThe question paper CODE is printed on the right hand top corner of this sheet.

3. dPps dk;Z ds fy, [kkyh i`"B vkSj [kkyh LFkku bl iqfLrdk esa gh gSaA dPps dk;Z ds fy, dksbZ vfrfjDr dkxt ugha fn;k tk;sxkABlank spaces and blank pages are provided in the question paper for your rough work. No additional sheets willbe provided for rough work.

4. dksjs dkxt] fDyi cksMZ] ykWx rkfydk] LykbM :y] dSYdqysVj] dSejk] lsyQksu] istj vkSj fdlh Hkh izdkj ds bysDVkWfud midj.k dhijh{kk d{k esa vuqefr ugha gSaABlank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers and electronicgadgets of any are NOT allowed inside the examination hall.

5. bl iqfLrdk ds fiNys i`"B ij fn, x, LFkku esa viuk uke vkSj QkWeZ uEcj fyf[k,AWrite your name and Form number in the space provided on the back cover of this booklet.

6. mkj i=] ,d ; a=&Js.khdj.k ;ksX; i= (ORS) gS tks fd vyx ls fn;s tk;saxsAThe answer sheet, a machine-readable Optical Response Sheet (ORS), is provided separately.

7. vks-vkj-,l-(ORS) ;k bl iqfLrdk esa gsj&Qsj@fofr u djsa / DO NOT TAMPER WITH/MUTILATE THE ORS OR THIS BOOKLET.8. bl iqfLrdk dh eqgj rksM+us ds i'pkr d`i;k tkp ysa fd blesa 44 i`"B gSa vkSj izR;sd fo"k; ds lHkh 20 iz'u vkSj muds mkj fodYi Bhd

ls i

fo"k; [k.M i`"B la[;kSubject Section Page No.

Hkkx-1 HkkSfrd foKku I(i) dsoy ,d lgh fodYi izdkj 03 - 08Part-1 Physics Only One Option Correct Type

I(ii) vuqPNsn izdkj 09 - 12Paragraph Type

I(iii) lqesyu lwpha izdkj 13 - 18Matching List Type

Hkkx-2 jlk;u foKku I(i) dsoy ,d lgh fodYi izdkj 19 - 23Part-2 Chemistry Only One Option Correct Type



Hkkx-3 xf.kr I(i) dsoy ,d lgh fodYi izdkj 32 - 34Part-3 Mathematics Only One Option Correct Type



Kota/00CT1140042/44

ALL INDIA OPEN TEST/JEE (Advanced)/08-02-2015/PAPER-2

SOME USEFUL CONSTANTSAtomic No. H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16, Cl = 17,

Br = 35, Xe = 54, Ce = 58,

Atomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24,

Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127,

Xe = 131, Ba=137, Ce = 140,


PHYS

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3/44Kota/00CT114004

PART-1 : PHYSICS Hkkx-1 : HkkSfrd foKku

SECTIONI : (i) Only One option correct Type [k.M-I : (i) dsoy ,d lgh fodYi izdkj

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONLY ONE is correct.bl [k.M esa 10 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ls dsoy,d lgh gSA

1. A transverse sinusoidal wave moves along a string in the positive x direction. In figure (I) displacement

of particle at P as a function of time is given and in figure (II) at a particular time t-the snap shot of wave

is shown. The wave velocity (cm/s) and velocity of particle at P (cm/s) will be :

,d vuqizLFk T;koh; rjax ,d jLlh ds vuqfn'k /kukRed x fn'kk esa xfr djrh gSA fp= (I) esa le; ds Qyu ds :i

esa P ij fLFkr d.k ds foLFkkiu dks rFkk fp=&II esa le; t ij rjax ds fp= dks n'kkZ;k x;k gSA rjax osx (cm/s) rFkk P ij

d.k ds osx (cm/s) ds eku gksxsa :

y (cm) y (cm)

2 21 1

t (sec) x (cm)P

4cm2 3

0 0

Figure-I Figure-II

(A) 1 i, 3 j- p (B) 1 i,3 jp (C) 1 i,2 jp (D) 1 i, 2 j- - p

BEWARE OF NEGATIVE MARKINGHAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

Space for Rough Work / dPps dk;Z ds fy, LFkku

4/44

PHYS

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Kota/00CT114004

2. A bob of mass M is suspended by massless string of length L. The horizontal velocity at point A is suchthat the tension at point A is five times the weight of bob. The angle 'q' at which the speed of bob is halfof speed at point A is :-O;eku M okyk ,d xksyd yEckbZ L okyh O;ekughu jLlh }kjk yVdk gqvk gSA fcUnq A ij {kSfrt osx dk eku blizdkj gS fd fcUnq A ij ruko dk eku xksyd ds Hkkj dk ikp xquk gksrk gSA dks.k 'q' ds fdl eku ij xksyd dh pky fcUnqA ij pky dh vk/kh gksxh %&

q

v

v2

A

(A) 60 (B) 30 (C) 120 (D) 903. A glass capillary tube open at both ends is dipped in water, we can see that the water first rises in the tube

and finally remains at rest at certain height as shown in figure. If this capillary tube is cut from B then thediagram of part AB is :- (B is the point where water level intersects the tube)

nksuksa fljksa ls [kqyh dkp dh ,d ds'kuyh dks ty esa Mwcksus ij ;g ik;k tkrk gS fd ty igys uyh esa ij p


PHYS

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5/44Kota/00CT114004

4. Variation of density of solid sphere of radius R with (r)5 is shown in the diagram, where r is the distancefrom centre of the sphere. Moment of inertia of sphere about its symmetric axis is :-

f=T;k R okys Bksl xksys ds ?kuRo esa (r)5 ds lkFk ifjorZu dks fp= esa n'kkZ;k x;k gS] tgk r xksys ds dsU ls nwjh gSA leferv{k ds lkis{k xksys dk tM+Ro vk?kw.kZ gksxk%&

R5r5

r

r0

(A) 5

01 R2

pr (B) 504 R15

pr (C) 504 R3p

r (D) 502 R5p

r

5. A transverse wave travelling in a string of linear mass density 1 is incident on junction point J. The

intensities of reflected and transmitted wave both as a function of 2

1

m m

are plotted. The correct sketch is:

,d vuqizLFk rjax jSf[kd O;eku ?kuRo 1 okyh jLlh esa xfr'khy gS rFkk laf/k fcUnq J ij vkifrr gksrh gSA ijkofrZr rFkk

ikjxfer rjax dh rhozrkvksa dks 21

m m

ds Qyu ds :i esa n'kkZus okyk lgh vkjs[k gksxk %&

J1 2x = 0

(A)

100%

Intensity

2

1

IT

IR

(B)

100%

Intensity

2

1

IR

IT

(C)

400%

Intensity

2

1

IR

IT

100% (D)

100%

Intensity

2

1

IT

IR


6/44

PHYS

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Kota/00CT114004

6. There is a sample of air at standard conditions in the vertical cylinder shown in the figure. The pistonmoves without friction and its mass is same as that of the pan on the other side of the pulley. Some fixed

amount of sand is slowly poured either to the top of the piston or into the pan. The temperature remains

the same. Then :

(A) Displacement of the piston will be greater if sand is poured in the pan

(B) Displacement of the piston will be greater if sand is poured on to the top of the piston.

(C) Displacement of the piston will be same in both cases

(D) Displacement of piston is greater or lesser in any case, will depend on the initial volume & pressure

of the gas

fp=kuqlkj ok;q dk ,d uewuk /okZ/kj csyu esa ekud fLFkfr;ksa ij Hkjk gqvk gSA fiLVu fcuk ?k"kZ.k xfr djrk gS rFkk bldk

O;eku f?kjuh ds nwljh vksj yVds gq, iyMs+ ds O;eku ds leku gSA vc jsr dh ,d fuf'pr ek=k dks /khjs&/khjs ;k rks

fiLVu ds ij ;k iyMs+ esa Mkyk tkrk gSA rkieku fu;r cuk jgrk gS] rc %&

(A) fiLVu dk foLFkkiu vf/kd gksxk] ;fn jsr dks iyMs+ esa Mkyk tk,A

(B) fiLVu dk foLFkkiu vf/kd gksxk] ;fn jsr dks fiLVu ij Mkyk tk,A

(C) nksuksa fLFkfr;ksa esa fiLVu dk foLFkkiu leku gksxkA

(D) fiLVu dk foLFkkiu fdlh Hkh fLFkfr esa vf/kd ;k de gksuk] xSl ds izkjfEHkd vk;ru rFkk nkc ij fuHkZj djsxkA



PHYS

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7/44Kota/00CT114004

7. During a coating process, a thin, flat tape of width w is pulled through a channel of length L containinga Newtonian fluid of density r and dynamic viscosity . The fluid is in contact with both sides of thetape. Estimate the force required to pull the tape through the channel if the tape has velocity V and thechannel has height H. You may assume that the tape is much thinner than H.

,d ysiu izf;k ds nkSjku pkSM+kbZ w okyh ,d iryh lery Vsi dks yEckbZ L okys ,d pSuy ls gksdj f[kapk tkrk gS rFkk

bl pSuy ds vUnj ?kuRo r o xfrt ';kurk okyk ,d U;wVksfu;u o Hkjk gqvk gSA ;g o Vsi dh nksuksa lkbMksa ds lkFk

lEidZ esa gSA ;fn Vsi dk osx V rFkk pSuy dh pkbZ H gks rks Vsi dks pSuy ls gksdj f[kapus esa yxs vko';d cy dh

x.kuk dhft,A vki eku ldrs gSa fd ;g Vsi H dh rqyuk esa cgqr vf/kd iryh gSA

LV,F

H

channel of width w filled with a Newtonian fluid

(A) 4 VLw

Hm

(B) 2 VLw

Hm

(C) VLwH

m(D)

VLw2H

m

8. 200 students are taking an examination in a room, and the sounds of pens scratching on paper, sighs,groans, and muttered imprecations has created a more or less continuous sound level of this noise of60dB. Assuming each student contributes equally to this noise and nothing else changes or adds to it,

what will the sound level in the room be when only 50 students are left ? ( 10log 2 0.3= )

200 fo|kFkhZ ,d d{k esa cSBdj ijh{kk ns jgs gSA muds }kjk dkxt ij isu pykus rFkk vkil esa /khjs&/khjs cksyus ds

QyLo:i dejs ds vUnj 60dB ls vf/kd ;k de /ofu Lrj dk yxkrkj 'kksj mRiUu gksrk gSA ekuk bl 'kksj dks mRiUu

djus esa izR;sd fo|kFkhZ dk leku ;ksxnku gksrk gS rFkk blesa dqN Hkh ifjorZu ;k dksbZ vfrfjDr ;ksxnku ugh gksrkA vc ;fn

dejs esa dsoy 50 fo|kFkhZ gh cps jgs rks dejs esa /ofu Lrj D;k gksxk\ ( 10log 2 0.3= )

(A) 50 dB (B) 15 dB (C) 66 dB (D) 54 dB


8/44

PHYS

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Kota/00CT114004


9. The motion of a point like mass can be split into two parts. In the first part its average speed is v1, and in

the second its average speed is v2. For the whole motion the average speed is the geometric mean of the

speeds v1 and v

2, which is 1 2v v v= . Then the ratio of the covered distance in the first part & second

part is :

,d fcUnqor~ O;eku dh xfr dks nks Hkkxksa esa foHkkftr fd;k tk ldrk gSA izFke Hkkx esa bldh vkSlr pky v1 rFkk f}rh;

Hkkx esa vkSlr pky v2 gSA lEiw.kZ xfr ds fy, vkSlr pky v

1 o v

2 dk xq.kkskj ek/; gS vFkkZr~ 1 2v v v= gSA rc izFke o

f}rh; Hkkx esa r; nwjh dk vuqikr gksxk %&

(A) 1

2

vv (B)

2

1

vv (C)

1

2

vv (D)

2

1

vv

10. The working substance of a heat engine is a sample of monatomic ideal gas of specific mass. The gasmay be taken through the cyclic process ABCA or ADEA as shown in the figure. What is the ratio ofthe two efficiencies ?

fdlh "ek batu esa fof'k"V O;eku okys ,dijekf.od vkn'kZ xSl ds uewus dks dk;Zdkjh inkFkZ ds :i esa iz;q fd;k

tkrk gSA bl xSl dks fp=kuqlkj ph; ize ABCA ;k ADEA ls gksdj xqtkjk tk ldrk gSA nksuksa n{krkvksa dk vuqikr

gksxk %&

DE

A

B C

V12V0 V032V0

p0

p

(A) 57 (B)

47 (C)

37 (D)

67


PHYS

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9/44Kota/00CT114004

(ii) Paragraph Type (ii) vuqPNsn izdkj

This section contains 3 paragraphs each describing theory, experiment, data etc. Six questions relateto three paragraphs with two questions on each paragraph. Each question of a paragraph has onlyone correct answer among the four choices (A), (B), (C) and (D).bl [k.M esa flkUrksa] iz;ksxksa vkSj vkdM+ksa vkfn dks n'kkZus okys 3 vuqPNsn gSA rhuksa vuqPNsnksa ls lacaf/kr N% iz'ugSa] ftuesa ls gj vuqPNsn ij nks iz'u gSA vuqPNsn esa gj iz'u ds pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesals dsoy ,d lgh gSA

Paragraph for Questions 11 and 12iz'u 11 ,oa 12 ds fy;s vuqPNsn

Two perfectly elastic identical balls of mass m are connected by a spring of stiffness k so that a dumbbell

like system is formed. That dumbbell lays at rest on a slippery horizontal surface (all the friction forces

can be neglected). Third ball (identical to the ones making up the dumbbell) approaches coaxially the

dumbbell from the left side with velocity v (see figure). Fourth ball (identical to the other ones) lays

coaxially rightwards to the dumbbell. L is the minimum distance between the dumbbell and the right-

most ball for which the final velocity of the latter will be exactly the same, as the initial velocity v

of the left most ball.

O;eku m okyh nks iw.kZr;k izR;kLFk ,dtSlh xsanksa dks k dBksjrk okyh fLizax }kjk tksM+dj ,d MEcyuqek fudk; cuk;k

tkrk gSA ;g MEcy fQlyu ; q {kSfrt lrg ij fojkekoLFkk esa j[kk gqvk gS (lHkh ?k"kZ.k cyksa dks ux.; ekuk tk ldrk

gSA) buds tSlh ,d rhljh xsan fp=kuqlkj ck;h vksj ls MEcy dh vksj lek{kh; :i ls osx v ls vkrh gSA buds tSlh gh

,d pkSFkh xsan MEcy ds nk;h vksj lek{kh; :i ls j[kh gqbZ gSA MEcy rFkk lcls nk;h xsan ds e/; U;wure nwjh L bl izdkj

gS fd ckn okyh xsan dk vfUre osx lcls ck;h vksj dh xsan ds izkjfEHkd osx v ds leku gSALv

11. Find the minimum distance L :U;wure nwjh L dk eku gS :

(A) mv2k

p (B) v m3 2k

p (C) v m2 2k

p (D) v m4 2k

p

12. Find the final velocity of the centre of mass of the dumbbell :-MEcy ds O;eku dsU dk vfUre osx gksxk %&

(A) 0 (B) v3 (C)

v4 (D) v


10/44

PHYS

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Kota/00CT114004


Graphs that show the variation of stress with strain have the same shape as the force-extension graphs.The gradient of these graphs represents the stiffness of the material, i.e. how difficult the material is tostretch. The structure of natural rubber is like a can of worms, consisting of long chain molecules withoccasional cross-linking between the chains. This is shown in the diagram below.The difference between a forceextension graph and stress-strain graphs for the same material is thatthey have different values and units on the axes.izfrcy rFkk fod`fr ds e/; ifjorZu dks n'kkZus okys vkjs[kksa dh vkd`fr cy&foLrkj vkjs[kksa ds leku gksrh gSA bu vkjs[kksadh izo.krk inkFkZ dh dBksjrk dks n'kkZrh gS vFkkZr~ fdlh inkFkZ dks foLrkfjr djuk fdruk dfBu gS] ;g crkrh gSA izkdfrdjcj dh lajpuk dhM+ksa ls Hkjs ,d ik= ds leku gksrh gS] ftlesa v.kqvksa dh ,d yEch Ja[kyk gksrh gS ftuds e/; la;kstucus gksrs gS] ftls fp= esa n'kkZ;k x;k gSA,d gh inkFkZ ds cy&foLrkj vkjs[k rFkk izfrcy&fodfr vkjs[kksa esa ;g vUrj gksrk gS fd v{kksa ij budh bdkbZ rFkk ekuvyx&vyx gksrs gSaA

When rubber is stretched the stiffness gradually decreases and it becomes relatively easy to stretch as thechains uncoil; once this has happened the rubber is much stiffer.The stress-strain graph for rubber (below) shows that the behaviour as a load is removed is not the sameas that when the load is being increased. This is called hysteresis and the curves are said to make ahysteresis loop. Under stress, the energy absorbed or released by a material is represented by the areabetween the curve and the extension axis of a forceextension graph.jcj dks f[kapus ij dBksjrk /khjs&/khjs de gks tkrh gS rFkk blesa fo|eku la;kstuksa ds [kqyus ls bls foLrkfjr djuk vis{kkd`rvf/kd vklku gks tkrk gSA ,d ckj ,slk ?kfVr gks tkus ij jcj vf/kd dBksj gks tkrk gSAjcj ds fy, uhps iznf'kZr izfrcy fodfr xzkQ ;g n'kkZrk gS fd fdlh yksM dks gVkus rFkk yksM dks c


PHYS

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11/44Kota/00CT114004


;fn fdlh jcj cS.M dks ckj&ckj f[kapk rFkk NksM+k tk, rks ge 'kSfFkY; ds dkj.k mRiUu "ek ds izHkko dks eglwl dj

ldrs gSaA izfrcy&fodfr vkjs[k dk rqY;kadh {ks=Qy izfr ,dkad vk;ru dh tkZ dks n'kkZrk gSA

fdlh inkFkZ dks foLrkfjr djus ij (f[kapus ij) tkZ vo'kksf"kr gksrh gS rFkk yxk;s x;s cy dks gVk ysus ij ;g tkZ eq

gks tkrh gSA jcj }kjk yksfMax ds nkSjku vo'kksf"kr tkZ vuyksfMax dh fLFkfr esa mRlftZr "ek dh rqyuk esa vf/kd gksrh gSA

;g varj 'kSfFkY; ywi ds {ks=Qy }kjk n'kkZ;k tkrk gS ftls izfrcy&fodfr vkjs[k esa Nk;kafdr Hkkx }kjk n'kkZ;k x;k gSA

jcj esa 'kSfFkY; ds izHkko ds dkj.k tkZ blds v.kqvksa esa LFkkukUrfjr gksrh gS ftlds QyLo:i "ek mRiUu gksrh gSA dkj

dk Vk;j ifg;s ds izR;sd ?kw.kZu ds fy, 'kSfFkY; ls gksdj xqtjrk gSA ;fn Vk;j esa gok Hkjh gqbZ gks rks tc Vk;j ds vUnj dh

gok xeZ gks tk,xh rks ;g ckgj fudyus yxsxh ,oa nkc esas of ds dkj.k Vk;j QV tk,xkA13. If a rubber band is hung on a hook and small weights are attached to the bottom of the band one at a time

and then finally the weights are removed, then choose the correct statement :(A) While unloading, removing first weight reduces a length lesser than the length increased while

loading same weight.(B) While unloading removing first weight reduces a length equal to the length increased while loading

same weight.(C) The rubber band is always easier to stretch when being loaded than being unloaded.(D) Less energy is required during the loading than the unloading.

;fn fdlh jcj cS.M dks ,d gqd ls yVdkdj bl cS.M ds fupys fljs ls dqN NksVs Hkkjksa dks (,d ds ckn ,d) tksM nsa

rFkk var esa bu Hkkjksa dks gVk fn;k tk, rks lgh dFku pqfu, %&

(A) Hkkj gVkus ds nkSjku izFke Hkkj dks gVkus ij yEckbZ esa mRiUu deh Hkkj yxkus ds nkSjku leku Hkkj yxkus ij yEckbZ esa

mRiUu of dh rqyuk esa de gksxhA

(B) Hkkj gVkus ds nkSjku izFke Hkkj dks gVkus ij yEckbZ esa mRiUu deh Hkkj yxkus ds nkSjku leku Hkkj yxkus ij yEckbZ esa

mRiUu o`f ds cjkcj gksrh gSA

(C) jcj cS.M lnSo Hkkj yxkus ds nkSjku Hkkj gVkus dh rqyuk esa vf/kd vklkuh ls f[kapk tk ldrk gSA

(D) Hkkj yxkus ds nkSjku Hkkj gVkus dh rqyuk esa de tkZ dh vko';drk gksrh gSA14. Graphs shown below are the hysteresis loop of four dimensionally identical tyres of different companies,

rolling at the same speed. Which one would develope more heat if run for the same time :-

fp= esa vyx&vyx fuekZrk dEiuh ds leku pky ls yq

12/44

PHYS

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Kota/00CT114004



A ring of mass m and radius R is rolling with constant velocity v on a horizontal surface. Young'smodulus of material of ring is y and crosssectional area of the wire by which ring is made is A.

O;eku m rFkk f=T;k R okyh ,d oy; {kSfrt lrg ij fu;r osx v ls yq


PHYS

ICS

13/44Kota/00CT114004


(iii) Matching List Type (iii) lqesyu lwpha izdkj

This Section contains 4 multiple choice questions. Each question has matching lists. The codes for thelists. have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

bl [k.M esa 4 cgqfodYi iz'u gSaA izR;sd iz'u esa lqesyu lwpha gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C) vkSj (D)

gSa ftuesa ls dsoy ,d lgh gSA

17. List-I shows four system of string each of same length, for producing travelling wave or standing wave.In each case velocity of travelling wave on string is same i.e.v. Match each system of list-I with expressionsgiven in list-II describing the energy of the wave.

List-I List-II

(P) A

A

l

(1)2 2 2A v4

m pl

Travelling wave

(Q)A

l

(2)2 2 29 A v

16m p

l

Standing wave of one loop withamplitude of antinode equal to A

(R)A

l

(3)2 2 2A vm pl

Standing wave of one plus half loopwith amplitude of antinode equal to A

(S)A

l

(4)2 2 22 A vm pl

Standing wave of 2 loop withamplitude of antinode equal to A.

Codes :P Q R S

(A) 4 1 2 3(B) 4 2 1 4(C) 2 2 3 1(D) 1 1 2 3

14/44

PHYS

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Kota/00CT114004


lwph-I esa izxkeh ;k vizxkeh rjax mRiUu djus ds fy, leku yEckbZ okyh jLlh ds pkj fudk; n'kkZ;s x;s gSaA izR;sd

izdj.k esa jLlh ij izxkeh rjax dk osx leku vFkkZr~ v gSA lwph&I esa fn,s x, izR;sd fudk; dks lwph&II esa iznf'kZr rjax dh

tkZ ds O;atd ds lkFk lqesfyr dhft,A

lwph-I lwph-II

(P) A

A

l

(1)2 2 2A v4

m pl

izxkeh rjax

(Q)A

l

(2)2 2 29 A v

16m p

l

,d ywi okyh vizxkeh rjax ftlds

izLian dk vk;ke A gSA

(R)A

l

(3)2 2 2A vm pl

,d rFkk vk/ks ywi okyh vizxkeh rjax

ftlds izLian dk vk;ke A gSA

(S)A

l

(4)2 2 22 A vm pl

nks ywiksa okyh vizxkeh rjax

ftlds izLian dk vk;ke A gSACodes :

P Q R S(A) 4 1 2 3(B) 4 2 1 4(C) 2 2 3 1(D) 1 1 2 3


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15/44Kota/00CT114004


18. List-I, shows four system of rod + particle undergoing collision on a smooth horizontal floor. Mass ofparticle & rod in each case is m, & M respectively. In List-II relationships between velocity (v) of centreof rod and angular velocity (w) of the rod just after the collision are given. Choose appropriate option(length of rod is l)lwph-I esa NM + rFkk d.k ls cus pkj fudk; n'kkZ;s x;s gSa tks fpduh {kSfrt lrg ij VDdj djrs gSaA izR;sd fLFkfr esa d.krFkk NM+ dk O;eku e'k% m o M gSA lwph&II esa VDdj ds rqjUr i'pkr~ NM + ds dsU ds osx (v) rFkk NM+ ds dks.kh;osx (w) ds e/; lEcU/k ds ckjs esa n'kkZ;k x;k gSA NM+ dh yEckbZ l gSA

List-I/lwph-I List-II/lwph-II

(P)

v0 e = 1

rest

(1) 3wl

(Q)

v0 e = 12

(2) 2wl

(R)v0

perfectly inelastic collisioniww.kZr;k vizR;kLFk VDdj

(3) 6wl

(S)v0 l4

e= 12

(4)23wl

Codes :P Q R S

(A) 4 3 1 2(B) 2 1 3 2(C) 3 3 3 1(D) 1 2 3 4

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19. Four different situations are shown in list-I. Corresponding to the given situations relation between heatenergy & temperature are shown in list-II. Match the correct list.

List-I List-II(P) A & B are 2 spheres of same size

A B

T0 (1) TA > T

B or T

A = T

B

kept in an isothermal chamber atequilibrium is kept at constanttemperature T

0. A is black body &

B is gray body with emissivity 0.8.(consider steady state)

(Q) A & B are the graphs of spectral

l

El B

A

(2) TA < T

B

emissive power El vs. wave lengthof two black bodies A and B ofsame surface area

(R) A is a solid sphere & B is a thick

A

B(3) Heat energy radiated by

spherical shell. A is connected to a A is greater than Bpower source. Surfaces of A and Bare perfect black bodies (considersteady state)

(S) (1) and (2) are large black body T1 T2

(1) (2)A B

(4) Heat energy radiated by Bsurfaces maintained at temperature is greater than AT

1 and T

2 respectively. A and B are

large plates with emissivity e = 1.(Consider steady state only, T

1 > T

2)

Codes :

P Q R S

(A) 1 4, 2 3 2

(B) 3,1 2,4 3,1 1

(C) 3,1 2 1 1

(D) 3,1 2 3,1 1


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lwph-I esa pkj fofHkUu fLFkfr;k n'kkZ;h x;h gS ftuds laxr "ek tkZ o rkieku esa lEcU/k lwph-II esa fn;s x;s gSA lwph

feyku dhft;sA

lwph-I lwph-II

(P) A rFkk B leku vkdkj okys 2 xksys gSa

A B

T0 (1) TA > T

B or T

A = T

B

ftUgsa fu;r rkieku T0 ij ,d lerkih;

d{k esa lkE;koLFkk esa j[kk x;k gSAA ,d d`".kfi.M gS tcfd B ,d /kwlj

fi.M gS ftldh mRltZdrk 0.8 gSA

(LFkk;h voLFkk ij fopkj djsa)

(Q) fp= esa leku i"Bh; {ks=Qy okys nks (2) TA < T

B

d`".k fi.Mksa A rFkk B dh rjaxnS/;Z

o LiSDVeh mRltZu {kerk El ds e/;nks vkjs[k A o B n'kkZ;s x;s gSaA l

El B

A

(R) fp= esa A ,d Bksl xksyk rFkk B ,d eksVk

A

B(3) A }kjk fofdfjr "ek tkZ

xksyh; dks'k gSA A dks 'kf L=ksr ls tksM+k B dh rqyuk esa vf/kd gSaA

tkrk gSA A o B dh lrgsa iw.kZr;k d`".k

fi.M gSaA (LFkk;h voLFkk ij fopkj djsa)

(S) fp= esa (1) rFkk (2) cM+s d`".k fi.M gSa T1 T2

(1) (2)A B

(4) B }kjk fofdfjr "ek tkZ

ftudh lrgksa dk rkieku e'k% T1 o T

2A dh rqyuk esa vf/kd gSaA

gSA A rFkk B cM+h IysVas gSa ftudh

mRltZdrk e = 1 gSA (dsoy LFkk;h

voLFkk ij fopkj djsa rFkk T1 > T

2 ysa)

Codes :P Q R S

(A) 1 4, 2 3 2

(B) 3,1 2,4 3,1 1

(C) 3,1 2 1 1

(D) 3,1 2 3,1 1

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20. In the given situation, a nonviscous liquid is filled in a cylinder with density rl. The cylinder is rotated

with liquid and linearly accelerated in a manner as shown in list-I. In each case a ball of density rb (r

b < r

l)

density of ball is less than density of liquid, released from rest in the frame of cylinder. If list-II showsthe possible motion of the ball with respect to cylinder just after releasing it, then match the list-Iwith list-II.

uhps nh xbZ fLFkfr esa ?kuRo rl okys ,d v';ku o dks csyu esa Hkjk x;k gSA bl csyu dks o lfgr lwph-I ds vuqlkj

?kqek;k rFkk js[kh; :i ls Rofjr fd;k tkrk gSA izR;sd fLFkfr esa ?kuRo rb (r

b < r

l) okyh ,d xsan dks csyu ds ra= esa

fojkekoLFkk ls NksM+k tkrk gSA xsan dk ?kuRo o dh rqyuk esa de gSA lwph&II esa xsan dks NksMs + tkus ds rqjUr i'pkr~ csyu ds

lkis{k xsan dh laHkkfor xfr dks n'kkZ;k x;k gSA lwph&I dk lwph&II ls feyku dhft,A

List-I/lwph-I List-II/lwph-II

(P) (1)

(Q) (2)

(R) a=g (3)

(S)

a=g

(4) Can not be predicted

Kkr ugha fd;k tk ldrkA

Codes :P Q R S

(A) 3 3 1 4(B) 1 2 2 3(C) 4 2 4 3(D) 1 4 1 3


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PART-2 : CHEMISTRY Hkkx-2 : jlk;u foKku

SECTIONI : (i) Only One option correct Type [k.M-I : (i) dsoy ,d lgh fodYi izdkj

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONLY ONE is correct.

bl [k.M esa 10 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ls dsoy

,d lgh gSA

1. Equal weight of NaCl and KCl are dissolved separately in equal volumes of solutions. Molarity ofthe two solutions will be -

(A) Equal

(B) That of NaCl will be less than that of KCl solution

(C) That of NaCl will be more than that of KCl solution

(D) That of NaCl will be half of than that of KCl solution

NaCl rFkk KCl ds leku Hkkj dks foy;uksa ds leku vk;ruksa esa vyx&vyx ?kksyk x;kA nks foy;uksa dh eksyjrk gksxh -

(A) leku

(B) KCl foy;u dh rqyuk esa NaCl ls de gksxh

(C) KCl foy;u dh rqyuk esa NaCl ls vf/kd gksxh

(D) KCl foy;u dh rqyuk es NaCl ls vkf/k gksxh

2. Moles of K2Cr2O7 used to oxidise 1 mol Fe0.92O to Fe+3 are

1 mol Fe0.92O ls Fe+3 esa vkWDlhdj.k ds fy, mi;ksx fd;s x, K2Cr2O7 ds eksy gSa

(A) 0.92

6(B)

70 1

92 6 (C)

0.76

6(D)

70 1

92 3


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3. Molar enthalpy of combustion of C2H

2(g) , C

graphite and H

2(g) are 1300, 394 and 286 kJ/mole

respectively than calculate Bond enthalpy of CC bond in kJ/mole.

Given : DHsub

(Cgraphite

) = 715 kJ/mole

DHBE

(HH) = 436 kJ/mole

DHBE

(CH) = 413 kJ/mole

(A) 415 (B) 610 (C) 1215 (D) 814

C2H

2(g) , C

xzsQkbV rFkk H

2(g) ds ngu dh eksyj , sUFksYih;k e'k% 1300, 394 rFkk 286 kJ/mole gS] rc CC

cU/k dh cU/k ,sUFksYih kJ/mole esa Kkr dhft,A

fn;k gS : DHsub

(Cgraphite

) = 715 kJ/mole

DHBE

(HH) = 436 kJ/mole

DHBE

(CH) = 413 kJ/mole

(A) 415 (B) 610 (C) 1215 (D) 814

4. For the following two equation occuring in separate closed container value of equilibrium constant issame, starting with same number of mole A

A B + C ..(1)A 2B ..(2)

Which of the following statement is correct -

(A) Extent of reaction for reaction (1) & (2) is same

(B) Extent of reaction for reaction (1) is greater than reaction (2)

(C) Extent of reaction for reaction (1) is less than reaction (2)

(D) None of the above

izFkd&izFkd cUn ik=ksa esa A ds leku eksyksa ls izkjEHk fuEu nks vfHkf;kvksa ds fy;s lkE ; fu;rkad ds eku leku gaSA B + C ..(1)A 2B ..(2)

fuEu esa ls dkSuls dFku lgh gS -

(A) vfHkf;k (1) rFkk (2) ds fy, vfHkf;k dh ek=k leku gS

(B) vfHkf;k (1) ds fy, vfHkf;k dh ek=k] vfHkf;k (2) dh rqyuk esa vf/kd gksrh gS

(C) vfHkf;k (1) ds fy, vfHkf;k dh ek=k ] vfHkf;k (2) dh rqyuk esa de gksrh gS

(D) mijksDr esa ls dksbZ ugha



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5. Identify species in which oxidation number of all sulphur atoms are same :

og Lih'kht igpkfu,sa ftlesa lHkh lYQj ijek.kqvksa dh vkWDlhdj.k la [;k leku gS :

(A) H2S

2O

3(B) H

2S

2O

4(C) H

2S

2O

5(D) H

2S

3O

6

6. The ionization energy of Li+ is about ................. as compared to ionization energy of Be+ :

(A) Four times larger (B) 1

2 times smaller (C) Similar (D)

2

3 times smaller

Be+ dh vk;uu tkZ dh rqyuk esa Li+ dh vk;uu tkZ yxHkx ................. gSa :

(A) pkj xquk vf/kd (B) 1

2 xquk de (C) leku (D)

2

3 xquk de

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7. Which hybridisation scheme is observed in the formation of boron tri-fluoride :

(A) 2px 2 yp 2 zp

2s

HybridisationE

(B)

2px 2 yp 2 zp

2s

HybridisationE

(C) 2px 2 yp 2 zp

2s

HybridisationE

(D) 2px 2 yp 2 zp

2s

HybridisationE

cksjkWu VkbZyksjkbM ds fuekZ.k esa] fuEu esa ls dkSulh ladj.k Ldhe izsf{kr dh xbZ gS :

(A) 2px 2 yp 2 zp

2s

ladj.kE

(B) 2px 2 yp 2 zp

2s

ladj.kE

(C) 2px 2 yp 2 zp

2s

ladj.kE

(D) 2px 2 yp 2 zp

2s

ladj.kE


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8. Identify correct heat of hydrogenation order ?

gkbMkstuhdj.k dh "ek dk lgh e igpkfu,s&

(A) < (B) OHHO

(C)

OH OH

Cl

>

Cl(D)

COOH

>Me

NO2Me

COOH

MeCN

Me

10. Identify correct basic strength order ?{kkjh; lkeF;Z dk lgh e igpkfu,s&

(A)

NH2 NH2

> (B)

NH2 NH2

Me

>Me

(C) HN

NH

>HN

NH

NH (D) OH > NH2


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(ii) Paragraph Type

(ii) vuqPNsn izdkjThis section contains 3 paragraphs each describing theory, experiment, data etc. Six questions relateto three paragraphs with two questions on each paragraph. Each question of a paragraph has onlyone correct answer among the four choices (A), (B), (C) and (D).

bl [k.M esa flkUrksa] iz;ksxksa vkSj vkdM+ksa vkfn dks n'kkZus okys 3 vuqPNsn gSA rhuksa vuqPNsnksa ls lacaf/kr N% iz'u

gSa] ftuesa ls gj vuqPNsn ij nks iz'u gSA vuqPNsn esa gj iz'u ds pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa

ls dsoy ,d lgh gSA


In a H-like species there are two energy levels A and B above the ground state having principal quantumnumbers of n1 and n2 respectively. A sample of this H-like species has all atoms/ions in excited levelsA or B only and none in any other energy level. Energy of level B is greater than that of level Aand a total of 15 different lines are emitted from this sample on returning to ground state out of which6 lines are emitted due to electronic transitions between the levels n1 and n2 only. Also energy differencebetween levels n2 and n1

, En2 En1 = 4.53 eV.

,d H-ds leku Lih'kht esa nks tkZ Lrjksa A rFkk B, tks vk| voLFkk ls ij gS] dh eq[; Dok.Ve la[;k,sa e'k%

n1 rFkk n2 gSA bl H-ds leku Lih'kht ds ,d uewus esa lHkh ijek.kq@vk;u dsoy mksftr voLFkkvksa A ;k B esa

gS vkSj vU; fdlh tkZ Lrj ds ugha gSA Lrj B dh tkZ Lrj A dh tkZ ls vf/kd gS vkSj vk | voLFkk esa ykSVus

ij bl uewus ls mRlftZr dqy 15 fHkUu js[kkvksa esa ls mRlftZr 6 js[kk,sa dsoy n1 rFkk n2 Lrjksa ds e/; bysDVk suh;

lae.k ds dkj.k gksrh gS n2 rFkk n1Lrjks a ds e/; tkZ vUrj En2 En1 = 4.53 eV gksrk gSA

11. The correct option is -

lgh fodYi gS-

(A) n2 = 2, n1 = 5 (B) n2 = 6, n1 = 3 (C) n2 = 5, n1 = 2 (D) n2 = 3, n1 = 6

12. Calculate minimum wavelength in the above transition -

mijksDr lae.k eas U;wure rjaxnS/;Z dh x.kuk dhft,-

(A) H

43R (B) H

98R (C) H

90011R (D) H

3635R



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25/44Kota/00CT114004

Paragraph for Questions 13 and 14

iz'u 13 ,oa 14 ds fy;s vuqPNsnThe outer shell contains one or more bond pairs of electrons, but it may also contain unshared pairs ofelectrons (lone pairs). Bond pairs and lone pairs are taken as valence shell electron pair to decide shape& bond angle of molecules, since all electron pairs take up some space, and since all electron pairs repeleach other. Repulsion is minimized if the electron pairs are orientated in space as far apart as possible.

ck dks'k esa bysDVkWuksa ds ,d ;k vf/kd ca/k ; qXe gks ldrs gSa ysfdu blesa bysDVkWuksa ds vlkf>r ; qXe Hkh gks ldrs

gSA ca/k ;qXeksa rFkk ,dkdh bysDVkWu ; qXeksa dks la;ksth dks'k bysDVkWu ;qXe ds :i esa ekuk tkrk gS tks v.kqvksa dh vkd`fr

rFkk ca/k dks.k fu/kkZfjr djrs gS] D;ksafd lHkh bysDVkWu ;qXe dqN LFkku ?ksjrs gS rFkk lHkh bysDVkWu ; qXe ,d nwljs dks

izfrdf"kZr djrs gSA ;fn f=foe esa vfHkfoU;kflr bysDVkWu ;qXe ,d&nwljs ls vf/kdre laHkkfor nwjh ij gksa rks izfrd"kZ.k

dks de fd;k tk ldrk gSA

13. F M F- - bond angles are 101.6 and 173.1 observed in :

fuEu esa ls fdlesa F M F- - ca/k dks.k e'k% 101.6 rFkk 173.1 izsf{kr fd;s x;s gSa :(A) ClF

3(B) SF

4(C) BrF

5(D) IF

7

14. Select correct statement about the molecules under both situation having either sp3d (TBP) or sp3d2

hybridisation :

(A) AB4 type molecule are always planar

(B) Must use dx2y2

orbital in hybridisation

(C) AB5 type molecules are always non polar

(D) If central atom have two lone pairs, molecule must be planar

lgh dFku pqfu;s tc v.kq nksuksa ifjfLFkfr;ksa esa ] ;k rks sp3d (TBP) ;k sp3d2 ladj.k j[krk gks :

(A) AB4 izdkj ds v.kq ges'kk leryh; gksrs gS

(B) ladj.k esa dx2y2

d{kd iz;ksx fd;k tkuk pkfg;s

(C) AB5 izdkj ds v.kq ges'kk v/kzqoh ; gksrs gS

(D) ;fn dsUh; ijek.kq ij nks ,dkdh bysDVkWu ; qXe mifLFkr gSa rks v.kq leryh; gksuk pkfg;s


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OH

COOHAqueousNaHCO3

Organic Layer

Aqueous Layer

OrganicLayer

AqueousLayer

(Compound - C)

(Salt - B)

(Salt - A)Mixture of

3-compoundsin hexane

AqueousNaOH

OH

COOH tyh;NaHCO3

dkcZfud ijr

tyh; ijr (;kSfxd ) - C

(yo.k ) - AgsDlsu esa ;kSfxdksa

dk feJ.k3-

NaOH

(yo.k ) - B

dkcZfudijr

tyh;ijr

tyh;

15. Identify salt 'A' ?

yo.k 'A' igpkfu,s&

(A)

O Na+

(B)

COO Na+

(C)

Na+

(D) All of these (mijksDr lHkh)

16. Identify compound 'C' ?

;kSfxd 'C' igpkfu,s&

(A)

OH

(B)

COOH

(C) (D)

OH

COOHSpace for Rough Work / dPps dk;Z ds fy, LFkku


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This Section contains 4 multiple choice questions. Each question has matching lists. The codes for thelists. have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.bl [k.M esa 4 cgqfodYi iz'u gSaA izR;sd iz'u esa lqesyu lwpha gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C) vkSj (D)gSa ftuesa ls dsoy ,d lgh gSA

17. It is known that C(g) and H2(g) react to give C

2H

2 (g) and/or C

2H

4 (g) depending upon the ratio in which

C(g) & H

2(g)

are taken. Given that C

2H

2(g) may

react with H

2(g) to give C

2H

4(g) and C

2H

4(g) may react

with C(g) to give C2H

2(g). Formation of 1 mole of C

2H

4(g) requires 60 units of energy and formation of

1 mole of C2H

2(g) releases 60 units of energy. From this information match List-I

(representing composition of gases taken) with List-II (representing the observation).

List-I List-II(composition of gases) (observation)

(P) 80 L C(g) and 30 L H2(g) (1) contraction by 33.6 L

(same temperature and pressure)

(Q) 33.6 L of C(g) and H2(g) taken at 1 atm and 273 K (2) contraction by 30 L

in a ratio such that max. release of energy is observed

(R) 22.4 L of C(g) and 30 L of H2(g) (3) contraction by 60 L


(S) 20L of C(g) and more than 22.4 L of H2(g) (4) contraction by 22.4 L


Codes :P Q R S

(A) 3 2 1 4

(B) 3 4 1 2

(C) 2 4 1 3

(D) 2 1 4 3

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;g Kkr gS fd C(g) rFkk H2(g) vfHkf;k djds C2H2 (g) rFkk@;k C2H4 (g) nsrs gaS ] ;g fy;s x, C(g) rFkk H2(g) ds

vuqikr ij fuHkZj djrk gS rFkk fn;k gS C2H

2(g), H

2(g) ds lkFk vfHkf;k djds

C

2H

4(g)

ns ldrk gSA rFkk

C

2H

4(g),

C(g) ds lkFk vfHkf;k djds C2H

2(g) ns ldrk gSA ,d eksy C

2H

4(g)

ds fuekZ.k ds fy, tkZ ds 60 bdkbZ dh

vko';drk gksrh gS rFkk 1 eksy C2H

2(g) ds fuekZ.k esa 60 bdkbZ tkZ eqDr gksrh gSA bl lwpuk ds vk/kkj ij lwpha -II

(izs{k.kksa dks iznf'kZr djrs gS) ds lkFk lwpha-I (yh xbZ xSlksa ds la?kVu dks iznf'kZr djrk gS) dks lqesfyr dhft;saA

lwpha-I lwpha-II

(xSlks a dk Lka?kVu) (izs{k.k)

(P) 80 yhVj C(g) rFkk 30 yhVj H2(g) (leku rki rFkk nkc) (1) 33.6 yhVj ls ladqpu

(Q) 1 atm rFkk 273 K ij C(g) rFkk H2(g) ds 33.6 yhVj feJ.k (2) 30 yhVj ls ladqpu

dks bl vuqikr esa fy;k tk;s fd vf/kdre tkZ eqDr gks

(R) 22.4 yhVj C(g) rFkk 30 yhVj H2(g) (leku rki rFkk nkc) (3) 60 yhVj ls ladqpu

(S) 20 yhVj C(g) rFkk H2(g) ds 22.4 yhVj ls vf/kd (4) 22.4 yhVj ls ladqpu

(leku rki rFkk nkc)

Codes :

P Q R S

(A) 3 2 1 4

(B) 3 4 1 2

(C) 2 4 1 3

(D) 2 1 4 3



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18. Match the List-List-I List-II

(P) Angular probability is independent of q & f (1) 5d

(Q)

r

4R

p22

(2) 5P

(R) Two maxima in 4pr2R2 vs r graph. (3) 4(s)

(S)

r

Yr (4) 3P

lwpha lqqesyhr dhft,] rFkk lgh dwV dk p;u dhft;s&

lwpha-I lwpha-II

(P) dks.kh; izkf;drk q rFkk f ls Lora= gksrh gS (1) 5d

(Q)

r

4R

p22

(2) 5P

(R) 4pr2R2 vs r o esa s nks mfPPk"B gS (3) 4(s)

(S)

r

Yr (4) 3P

Codes :P Q R S

(A) 3 4 1 2

(B) 3 4 2 1

(C) 3 1 4 2

(D) 2 3 4 1

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19. List-I List-II

Radius of atom and (Element)

its most stable ion respectively (in pm unit)

(P) 186, 102 (1) Li

(Q) 72, 133 (2) F

(R) 160, 72 (3) Mg

(S) 152, 76 (4) Na

lwph-I lwph-II

ijek.k q rFkk blds lokZf/kd LFkk;h (rRo)

vk;u dh e'k % f=T;k (pm bdkbZ es a)

(P) 186, 102 (1) Li

(Q) 72, 133 (2) F

(R) 160, 72 (3) Mg

(S) 152, 76 (4) Na

Codes :

P Q R S

(A) 4 2 3 1

(B) 4 1 3 2

(C) 3 2 4 1

(D) 1 4 3 2


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20. List-I List-II(Compounds)

(P) HClO4

(1) Compound show intramolecular H-bonding

(Q)

OHNO2

(2) Conjugate base form equivalent resonating structures

(R) EtOH (3) Compound not soluble in aqueous NaOH

(S) CH2 = CH

2(4) Compound not soluble in NaNH

2

lwph-I lwph-II

(;k Sfxd)

(P) HClO4

(1) ;kSfxd vUr% vkf.od H-cU/ku n'kkZrk gSA

(Q)

OHNO2

(2) la;qXeh {kkj lerqY; vuquknh lajpuk, cukrk gSA

(R) EtOH (3) ;kSfxd tyh; NaOH esa foys; ugha gksrk gSaA

(S) CH2 = CH

2(4) ;kSfxd NaNH

2 esa foys; ugha gksrk gSaA

Codes :P Q R S

(A) 2 1 3 4

(B) 2 3 1 4

(C) 3 4 1 2

(D) 3 1 2 4

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PART-3 : MATHEMATICS

Hkkx-3 : xf.krSECTIONI : (i) Only One option correct Type [k.M-I : (i) dsoy ,d lgh fodYi izdkj

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONLY ONE is correct.bl [k.M esa 10 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesa ls dsoy,d lgh gSA

1. There are two groups with no common person. Group-I has 4 women and 3 men and Group-II has3 women and 4 men. The number of ways in which 3 men and 3 women can be seleceted so that

each selection has 3 people from each group, is -

nks lewg gSa ftuesa dksbZ Hkh O;fDr mHk;fu"B ugha gSA lewg-I esa 4 fL=;k ,oa 3 iq#"k rFkk lewg-II esa 3 fL=;k ,oa 4 iq#"k gSaA3 iq#"kksa rFkk 3 fL=;ksa ds p;u ds rjhdksa dh la[;k rkfd izR;sd p;u esa izR;sd lewg ls 3 O;fDr gks] gksxh -

(A) 485 (B) 502 (C) 452 (D) 5024

2. The minimum value of expression 3sec2x + cot6 x is -O;atd 3sec2x + cot6 x dk U;wure eku gksxk -

(A) 7 (B) 8 (C) 5 (D) 4

3. Sum of all possible values of x such that x,[x] and {x} are in A.P. is -(where [.] and {.} denotes greatest integral function & fractional part function respectively)

x ds lHkh lEHko ekuksa dk ;ksxQy rkfd x,[x] rFkk {x} lekUrj Js.kh esa gksa] gksxk -(tgk [.] rFkk {.} e'k% egke iw.kkd Qyu rFkk fHkUukRed Hkkx Qyu dks n'kkZrs gksa)

(A) 0 (B) 3 (C) 4

3(D)

3

24. A certain function has property that (3x) = 3(x) " x R+. Also (x) = 1 |x 2|, 1 < x < 3.

The value of (2001) is -

fdlh Qyu dk xq.k/keZ (3x) = 3(x) " x R+ gSA lkFk gh (x) = 1 |x 2|, 1 < x < 3 gSArc (2001) dk eku gksxk -

(A) 200 (B) 107 (C) 186 (D) 199



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5. The complete solution set of the equation 2

1 1x 1 xsin sin x42

- - + - p

= +

is -

lehdj.k 2

1 1x 1 xsin sin x42

- - + - p

= +

dk iw.kZ gy leqPp; gksxk -

(A) [1,0] (B) [0,1] (C) 1

1,2

-

(D) 1

,12

6. Given circles w1 & w2 intersects at X & Y. Let l1 be a line through the centre of w1 and intersecting w2at points P and Q and let l2 be the line through centre of w2 intersecting w1 at points R and S.

Let w1 x2 + y2 2x 2y + 1 = 0,

w2 x2 + y2 4x 4y + 4 = 0

If P,Q,R,S are concyclic with centre of circle passing through them is (a,b), then

( ) ( )1 1tan tan 1- -a + b + a + b - is equal to -

fn, x, o`k w1 rFkk w2 ,d nwljs dks X rFkk Y ij izfrPNsn djrs gaSA ekuk js[kk l1, w1 ds dsU ls xqtjrh gS rFkk w2 dksfcUnqvksa P rFkk Q ij izfrPNsn djrh gS rFkk ekuk js[kk l2, w2 ds dsU ls xqtjrh gS rFkk w1 dks fcUnqvksa R rFkk S ijizfrPNsn djrh gSA

ekuk w1 x2 + y2 2x 2y + 1 = 0,

w2 x2 + y2 4x 4y + 4 = 0 gSA

;fn P, Q, R rFkk S, fcUnq (a,b) ls xqtjus okys o`k ds dsU ds leph; gks] rks ( ) ( )1 1tan tan 1- -a + b + a + b -dk eku gksxk -

(A) tan11 (B) 1 3tan

2-

(C) tan18 (D) 12tan3

-


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7. Consider : [2,2] [4,4], ( ) ( )x | x |, x 1

xsgn x ; x 1

= - =

(where sgn denotes signum function).

Number of solutions of the equation (x) = 1(x) is-

ekuk : [2,2] [4,4], ( ) ( )x | x |, x 1

xsgn x ; x 1

= - =

(tgk sgn flXue Qyu dks n'kkZrk gS)

lehdj.k (x) = 1(x) ds gyksa dh la[;k gksxh -

(A) 2 (B) 3 (C) 4 (D) 5

8. : R {1} (0, ), ( )x

1 x x e -= is-

(A) one-one onto (B) one-one into (C) many-one onto (D) many-one into

: R {1} (0, ), ( )x

1 x x e -= gksxk -

(A) ,dSdh vkPNknd (B) ,dSdh vUr%{ksih (C) cgq,dSdh vkPNnd (D) cgq,dSdh vUr%{ksih

9. Consider a grid as shown in figure having 8 blocks of dimension 1 1. Each block is to be painted witheither blue or red colour. In how many ways this can be done if atleast one block of dimension 2 2 is

to be painted red completely ?

ekuk fp= esas n'kkZ;s x;s fxzM esa 1 1 ds 8 CykWd gSaA izR;sd CykWd dks ;k rks uhys ;k yky jax ls iksrk tkrk gSA fdrusrjhdksa ls ;g fd;k tk ldrk gS] ;fn 2 2 dk ,d CykWd iw.kZr;k yky jax ls iksrk x;k gks\

1 1 1

1

1

1

(A) 37 (B) 36 (C) 39 (D) 40

10. The number of solutions of the equation sinx cosx + sinx + cosx = 2 in [0,p] is -[0,p] esa lehdj.k sinx cosx + sinx + cosx = 2 ds gyksa dh la[;k gksxh -

(A) 0 (B) 1 (C) 2 (D) 4


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(ii) Paragraph Type (ii) vuqPNsn izdkj

This section contains 3 paragraphs each describing theory, experiment, data etc. Six questions relateto three paragraphs with two questions on each paragraph. Each question of a paragraph has onlyone correct answer among the four choices (A), (B), (C) and (D).bl [k.M esa flkUrksa] iz;ksxksa vkSj vkdM+ksa vkfn dks n'kkZus okys 3 vuqPNsn gSA rhuksa vuqPNsnksa ls lacaf/kr N% iz'ugSa] ftuesa ls gj vuqPNsn ij nks iz'u gSA vuqPNsn esa gj iz'u ds pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesals dsoy ,d lgh gSA


iz'u 11 ,oa 12 ds fy;s vuqPNsn

2 2 2 2x y x y x y y xE , x, y R

2

+ + + + - + -= . Let E attains its minimum value of at x = a; y = b.

2 2 2 2x y x y x y y xE , x, y R

2

+ + + + - + -= gSA ekuk x = a; y = b ij E U;wure eku izkIr djrk gSA

11. Minimum value of E is-E dk U;wure eku gksxk -

(A) 1

8- (B)

1

4- (C) 0 (D)

1

2-

12. The distance of the point P(a,b) from the line x + y = 0 is-fcUnq P(a,b) dh js[kk x + y = 0 ls nwjh gksxh -

(A) 0 (B) 1

2(C) 2 (D) 1


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Consider the circle S x2 + y2 2x + 4y 11 = 0 & line L 3x 4y 1 = 0. Let line L = 0 cuts

circle S = 0 in points A and B.

ekuk o`k S x2 + y2 2x + 4y 11 = 0 rFkk js[kk L 3x 4y 1 = 0 gSA ekuk js[kk L = 0, o`k S = 0

dks fcUnqvksa A rFkk B ij dkVrh gSA

13. Angle of intersection between the S = 0 & L = 0 is-

S = 0 rFkk L = 0 ds e/; izfrPNsn dks.k gksxk -

(A) 30 (B) 45 (C) 60 (D) 90

14. The locus of centre of variable circle passing through points A and B is-

fcUnqvksa A rFkk B ls xqtjus okys pj o`k ds dsU dk fcUnqiFk gksxk -

(A) 4x + 3y + 2 = 0 (B) 4x + 3y 2 = 0 (C) 4x 3y + 2 = 0 (D) 4x 3y + 10 = 0



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Let P(x) be a quadratic polynomial with real coefficients satisfying

x2 2x + 2 < P(x) < 2x2 4x + 3 " x R and P(11) = 181

ekuk P(x) okLrfod xq.kkadksa okyk ,d f}?kkr cgqin gS] tks

x2 2x + 2 < P(x) < 2x2 4x + 3 " x R dks lUrq"V djrk gS rFkk P(11) = 181 gSA

15. P(16) has value -

P(16) dk eku gksxk -

(A) 400 (B) 401 (C) 405 (D) 406

16. The number of solution(s) of the equation P(sin1x) = P(cos1x) is-

lehdj.k P(sin1x) = P(cos1x) ds gyksa dh la[;k gksxh -

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


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This Section contains 4 multiple choice questions. Each question has matching lists. The codes for thelists. have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

bl [k.M esa 4 cgqfodYi iz'u gSaA izR;sd iz'u esa lqesyu lwpha gSA lwfp;ksa ds fy, dksM ds fodYi (A), (B), (C) vkSj (D)

gSa ftuesa ls dsoy ,d lgh gSA

17. Consider the function (x) = cos(sin1(tan(cos1x))).Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II(P) If number of integers in the domain of (x) is l, (1) 4

then l + 7 is(Q) If number of integers in the range of (x) is m, (2) 9

then m + 5 is(R) If number of solutions of equation ((x)) = (x) is k, (3) 3

then k + 1 is

(S) If number of integers in domain of ((x)) is 't', (4) 7

then t + 2 is

ekuk Qyu (x) = cos(sin1(tan(cos1x))) gSA

lwph-I dks lwph-II ls lqesfyr dhft, rFkk lwfp;ksa ds uhps fn, u, dksM dk iz;ksx djds lgh mkj pqfu;s %

lwph-I lwph-II(P) ;fn (x) ds izkUr esa iw.kkdksa dh la[;k l gks] rks l + 7 gksxk (1) 4(Q) ;fn (x) ds ifjlj esa iw.kkdksa dh la[;k m gks] rks m + 5 gksxk (2) 9(R) ;fn lehdj.k ((x)) = (x) ds gyksa dh la[;k k gks] rks k + 1 gksxk (3) 3(S) ;fn ((x)) ds izkUr esa iw.kkdksa dh la[;k t gks] rks t + 2 gksxk (4) 7

Codes :P Q R S

(A) 2 4 3 1(B) 2 4 1 1(C) 1 4 3 2(D) 3 4 1 2


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18. Let ( ) ( ) ( )( )

n kn

k 0

1 .k n 1 !P n 1

k 1 k! n 1 k !

-

=

- ++ =

+ + - .Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) P(8) (1)3

4

(Q) P(7) (2)4

5(R) P(9) (3) 1

(S) P(11) (4)5

6

ekuk ( ) ( ) ( )( )

n kn

k 0

1 .k n 1 !P n 1

k 1 k! n 1 k !

-

=

- ++ =

+ + - gSAlwph-I dks lwph-II ls lqesfyr dhft, rFkk lwfp;ksa ds uhps fn, u, dksM dk iz;ksx djds lgh mkj pqfu;s %

lwph-I lwph-II

(P) P(8) (1)3

4

(Q) P(7) (2)4

5(R) P(9) (3) 1

(S) P(11) (4)5

6Codes :

P Q R S(A) 1 2 4 3(B) 2 1 3 4(C) 3 1 2 4(D) 4 3 1 2

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19. Let O be the origin & A (4,0). Let P(x,y) be a variable point and POA = a & PAO = b. PointP moves such that (tana) (tanb) = 1 as shown in figure

a b

P(x,y)

A(4,0)O

Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) If greatest value of ( ) ( )2 2x 2 y 8- + - is M, then M

5 is (1) 2

(Q) If least value of ( ) ( )- + -2 2x 2 y 8 is m, then m is (2) 8(R) If greatest value of x + y is G, then (G 2)2 is (3) 6

(S) If least value of x + y is L, then (L 2)2 is (4) 10

ekuk O, ewyfcUnq rFkk A (4,0) gSA ekuk P(x,y) ,d pj fcUnq rFkk POA = a rFkk PAO = b gSA fp=kuqlkjfcUnq P bl izdkj xfr djrk gS fd (tana) (tanb) = 1 gSA

a b

P(x,y)

A(4,0)O


lwph-I lwph-II

(P) ;fn ( ) ( )2 2x 2 y 8- + - dk vf/kdre eku M gks] rks M

5 gksxk (1) 2

(Q) ;fn ( ) ( )- + -2 2x 2 y 8 dk U;wure eku m gks] rks m gksxk (2) 8(R) ;fn x + y dk vf/kdre eku G gks] rks (G 2)2 dk eku gksxk (3) 6

(S) ;fn x + y dk U;wure eku L gks] rks (L 2)2 dk eku gksxk (4) 10Codes :

P Q R S(A) 1 3 4 2(B) 1 3 2 2(C) 3 1 2 4(D) 1 4 3 2


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20. Let a1 = 50 and a

1, a

2, ...... a

n be a sequence of number satisfying the rule n(a

n a

n+1) = n3 + n2 a

n.

Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) 16a16 (1) 16

(Q) a11

(2) 50

(R) a10

(3) 55

(S) 12a

12(4) 70

ekuk a1 = 50 rFkk a

1, a

2, ...... a

n la[;kvksa dk ,d vuqe gS] tks fu;e n(a

n a

n+1) = n3 + n2 a

n dks lUrq"V

djrk gSA


lwph-I lwph-II

(P) 16a16 (1) 16

(Q) a11

(2) 50

(R) a10

(3) 55

(S) 12a

12(4) 70

Codes :P Q R S

(A) 4 3 2 1(B) 4 3 1 2(C) 2 1 3 4(D) 2 1 4 3

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D. vadu ;kstuk / Marking scheme :

12. [kaM-I (i, ii & iii) ds gj iz'u esa dsoy lgh mkjksa (mkj) okys lHkh cqycqyksa (cqycqys) dks dkyk djus ij 3 vad vkSj dksbZ Hkh cqycqyk

dkyk ugha djus ij 'kwU; (0) vad iznku fd;k tk;sxkA vU; lHkh fLFkfr;ksa esa .kkRed ,d (1) vad iznku fd;k tk;sxkA

For each question in Section-I (i, ii & iii) , you will be awarded 3 marks if you darken all the bubble(s) corresponding to

only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases minus one (1) mark will be awarded

13. g = 10 m/s2 iz;qDr djsa ] tc rd fd vU; dksbZ eku ugha fn;k x;k gksA

Take g = 10 m/s2 unless otherwise stated.

Name of the Candidate / ijh{kkFkhZ dk uke

I have read all the instructions and shall abide by them.eSusa lHkh vuqns'kksa dks i

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