allen paper 2

i;k bu fun sZ'kks a dks /;ku ls i

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

Hkkx-1 HkkSfrd foKku I(i) ,d ;k vf/kd lgh fodYi izdkj 03 - 06Part-1 Physics One or More Option Correct Type

I(ii) vuqPNsn izdkj 07 - 08Paragraph Type

I(iii) lqesyu lwpha izdkj 09 - 12Matching List Type

IV iw.kkd eku lgh izdkj (0 ls 9) 13 - 14Integer Value Correct Type (0 to 9)

Hkkx-2 jlk;u foKku I(i) ,d ;k vf/kd lgh fodYi izdkj 15 - 18Part-2 Chemistry One or More Option Correct Type




Hkkx-3 xf.kr I(i) ,d ;k vf/kd lgh fodYi izdkj 27 - 29Part-3 Mathematics One or More Option Correct Type




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 masse s : 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,

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Boltzmann constant k = 1.38 1023 JK1

Coulomb's law constant pe9

0

1 = 9104

Universal gravitational constant G = 6.67259 1011 Nm2 kg2 Speed of light in vacuum c = 3 108 ms1 StefanBoltzmann constant s = 5.67 108 Wm2K4 Wien's displacement law constant b = 2.89 103 mK Permeability of vacuum 0 = 4p 107 NA2

Permittivity of vacuum 0 = 20

1cm

Planck constant h = 6.63 1034 Js

Kota/00CT214006

ALL INDIA OPEN TEST/JEE (Advanced)/10-05-2015/PAPER-2

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

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

PART-1 : PHYSICS Hkkx-1 : HkkSfrd foKku

SECTIONI : (i) One or more options correct Type [k.M-I : (i) ,d ;k vf/kd lgh fodYi izdkj

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONE or MORE are correct.bl [k.M esa 8 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls ,d ;kvf/kd lgh gSA

1. AB is a linear object placed along optical axis as shown in figure. Tick the incorrect statement(s)-(A) The length of image is smaller than the length of object.(B) The length of image is larger than the length of object.(C) The length of image is equal to the length of object.(D) If middle portion of the lens is painted then the length of image is smaller than length of object.

A B

10cm

30cm

f=20cm

AB ,d js[kh; fcEc gS tks fd fp=kuqlkj izdkf'kd v{k ds vuqfn'k fLFkr gSA xyr dFku@dFkuksa dks fpfUgr dhft;s&

(A) izfrfcEc dh yEckbZ fcEc dh yEckbZ ls de gSA(B) izfrfcEc dh yEckbZ fcEc dh yEckbZ ls vf/kd gSA(C) izfrfcEc dh yEckbZ fcEc dh yEckbZ ds cjkcj gSA(D) ;fn ysal ds e/; Hkkx dks iksr fn;k tk;s rks izfrfcEc dh yEckbZ] fcEc dh yEckbZ ls de gksxhA

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2. A rabbit is hidden in grass at a point A near a pond. A dog is drinking water at a point B in the pond. Therabbit can run on the ground with a velocity (3i 4j)+$ $ ms1. Dog can run with a speed 189ms- . Thecoordinate of points B and A are (0,0) and (5,10) respectively. If the rabbit starts to run immediately thedog starts then dog catches rabbit in minimum time t0.Tick the correct alternative (s)-(A) X-component of velocity of dog will be 5ms1(B) Y-component of velocity of dog will be 8ms1

(C) The value of to will be 5

2s.

(D) Data insufficient,d [kjxks'k rkykc ds fudV ,d fcUnq A ij ?kkl esa fNik gqvk gSA ,d dqkk rkykc esa fcUnq B ij ikuh ih jgk gSA [kjxks'k/kjkry ij (3i 4j)+$ $ ms1 ds osx ls nkSM + ldrk gSA dqkk 189ms- dh pky ls nkSM + ldrk gSA fcUnq B rFkk A ds funsZ'kkade'k% (0,0) rFkk (5,10) gSaA tSls gh dqkk nkSM+uk 'kq: djrk gS oSls gh ;fn [kjxks'k Hkh rqjUr nkSM+uk izkjEHk dj nsrk gS rksdqkk [kjxks'k dks U;wure le; t0 esa idM + ysrk gSA lgh dFku@dFkuksa dks pqfu;s&(A) dqks ds osx dk X-?kVd 5ms1 gSA (B) dqks ds osx dk Y-?kVd 8ms1 gSA(C) t0 dk eku

52 s gSA (D) vkadM+s vi;kZIr gSA

3. A solid sphere S1 is connected to a charge reservoir through a heater H as shown in figure. flux througha closed spherical surface around S1 is given by f = at2 where a is a constant and t is time in seconds.If resistance of heater is R then select correct alternative/s-(A) Power consumed by heater will be a202Rt4.(B) Electric flux through a closed spherical surface around S2 will be at2.(C) Rate of change of electric flux through a closed spherical surface around S2 will be 2at.(D) All of the above are correct.

Solidsphere

ChargeresevoirHeater

S1 S2H

fp=kuqlkj ,d Bksl xksyk S1 ghVj H }kjk ,d vkos'k ik= S2 ls tqM+k gqvk gSA S1 ds pkjksa vksj ,d can xksyh; i`"B ls fuxZryDl f = at2 }kjk fn;k tkrk gSA tgk a ,d fu;rkad gS rFkk t lsd.M esa le; gSA ;fn ghVj dk izfrjks/k R gks rks lghdFku@dFkuksa dks pqfu;s&(A) ghVj }kjk 'kfDr O;; a202Rt4 gSA(B) S2 ds pkjksa vksj ,d can xksyh; i`"B ls fuxZr fo|qr yDl at2 gSA(C) S2 ds pkjksa vksj ,d can xksyh; i"`B ls fuxZr fo|qr yDl esa ifjorZu dh nj 2at gSA(D) mijksDr lHkh dFku lR; gSA

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4. If the volume elasticity (i.e. bulk modulus) of fresh water and the sea water are assumed to be thesame. It is necessary that for the velocity of the sound to be the same :(A) Fresh water must be at a higher temperature(B) Sea water must be at a higher temperature(C) Both must be at the same temperature(D) Fresh water must have higher refractive index;fn rktk ty rFkk leqnzh ty dh vk;ru izR;kLFkrk (vk;ru izR;kLFkrk xq.kkad) leku ekuk tk;s rks /ofu ds osx lekugksus ds fy;s vko';d gS fd&(A) rktk ty mPp rki ij gksA (B) leqnzh ty mPp rki ij gksA(C) nksuksa dk rkieku leku gksA (D) rktk ty dk viorZukad mPp gksuk pkfg;sA

5. A galvanometer has a coil of resistance 100 W showing a fullscale deflection at 50 mA. Then selectappropriate alternative(s).(A) The resistance needed to use it as a voltmeter of range 50 volt is 106 W.(B) The resistance needed to use it as a voltmeter of range 50 volt is 105 W(C) The resistance needed to use it as an ammeter of range 10 mA is 0.5 W(D) The resistance needed to use it as an ammeter of range 10 mA is 1.0 W,d xsYosuksehVj dh dq.Myh dk izfrjks/k 100 W gS rFkk 50 mA /kkjk ij ;g iw.kZ fo{ksi n'kkZrk gS] rks mfpr fodYi@fodYiksadks pqfu;s%&(A) bls 50 oksYV ijkl okys oksYVehVj ds :i esa iz;qDr djus ds fy;s 106 W izfrjks/k dh vko';drk gksxhA(B) bls 50 oksYV ijkl okys oksYVehVj ds :i esa iz;qDr djus ds fy;s 105 W izfrjks/k dh vko';drk gksxhA(C) bls 10 mA ijkl okys vehVj ds :i esa iz;qDr djus ds fy;s 0.5 W izfrjks/k dh vko';drk gksxhA(D) bls 10 mA ijkl okys vehVj ds :i esa iz;qDr djus ds fy;s 1.0 W izfrjks/k dh vko';drk gksxhA

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6. An Xray tube is operating at 50 kV and 20mA. The target material of the tube has a mass of 1.0 kg andspecific heat 495 J kg1 C1. One percent of the supplied electric power is converted into Xrays andentire remaining energy goes into heating the target. Then :(A) the average rate of rise of temperature of the target would be 2C/sec(B) the minimum wavelength of the Xrays emitted is about 0.25 1010 m(C) a suitable target material must have a low melting temperature(D) a suitable target material must have low thermal conductivity,d Xfdj.k uyh 50 kV rFkk 20mA ij lapkfyr gks jgh gSA uyh ds y{; inkFkZ dk O;eku 1.0 kg rFkk fof'k"V"ek 495 J kg1 C1 gSA nh xbZ fo|qr 'kf dk ,d izfr'kr Hkkx Xfdj.kksa esa ifjofrZr gks tkrk gS rFkk 'ks"k lEiw.kZ tkZy{; dks xeZ djus esa iz;q gks tkrh gSA rc %&(A) y{; ds rkieku esa o`f dh vkSlr nj 2C/sec gksxhA(B) mRlftZr Xfdj.kksa dh U;wure rjaxnS/;Z yxHkx 0.25 1010 m gksxhA(C) ,d mi;q y{; inkFkZ dk xyukad vYi gksuk pkfg,A(D) ,d mi;q y{; inkFkZ dh rkih; pkydrk vYi gksuk pkfg,A

7. Which of the following statement(s) is/are correct?(A) Nuclei with small mass number and atomic number are more likely to undergo fusion than fission(B) Nuclei having a small binding energy per nucleon are more likely to undergo fusion than fission(C) Nuclei having large binding energy per nucleon are more likely to undergo fusion than fission(D) Nuclei with large atomic number are more likely to undergo fusion than fissionlgh dFku@dFkuksa dks pqfu, %&(A) vYi O;eku la[;k rFkk ijek.kq ekad okys ukfHkdksa dk fo[k.Mu dh rqyuk esa lay;u vf/kd gksrk gSA(B) izfr U;wfDy;ksu vYi ca/ku tkZ okys ukfHkd fo[k.Mu dh rqyuk esa lay;u dh izf;k ls vf/kd xqtjrs gSaA(C) izfr U;wfDy;ksu mPp ca/ku tkZ okys ukfHkd fo[k.Mu dh rqyuk esa lay;u dh izf;k ls vf/kd xqtjrs gSaA(D) vf/kd ijek.kq ekad okys ukfHkd fo[k.Mu dh rqyuk esa lay;u dh izf;k ls vf/kd xqtjrs gSaA

8. A cylindrical empty vessel is kept vertically, with its open end up, on a horizontal ground when it rainsuniformly and vertically. The rate of filling in the vessel with rain water will :-(A) remain unchanged, if its length is made inclined to the vertical(B) decrease, if its length is made inclined with the vertical(C) remain unchanged if a slow wind blows horizontally(D) decrease, if a slow wind blows horizontally.,d csyukdkj [kkyh ik= dks /okZ/kj :i ls {kSfrt /kjkry ij bl izdkj j[kk tkrk gS fd bldk [kqyk fljk ij dh vksjgksA ;gk o"kkZ ,dleku :i ls /okZ/kj fxj jgh gSA o"kkZ ds ty ls ik= ds Hkjus dh nj %&(A) vifjofrZr jgsxh ;fn bldh yEckbZ dks /okZ/kj ds lkis{k > qdk fn;k tk,A(B) ?kV tk,xh ;fn bldh yEckbZ dks /okZ/kj ds lkis{k > qdk fn;k tk,A(C) vifjofrZr jgsxh ;fn ;gk ,d /kheh ok;q {kSfrt :i ls cgus yxsA(D) ?kV tk,xh ;fn ;gk ,d /kheh ok;q {kSfrt :i ls cgus yxsA


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(ii) Paragraph Type (ii) vuqPNsn izdkj

This section contains 2 paragraphs each describing theory, experiment, data etc. Four questions relateto two paragraphs with two questions on each paragraph. Each question of a paragraph has only onecorrect 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 2 vuqPNsn gSA nksuksa vuqPNsnksa ls lacaf/kr pkj iz'ugSa] ftuesa ls gj vuqPNsn ij nks iz'u gSaA vuqPNsn esa gj iz'u ds pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesals dsoy ,d lgh gSA

Paragraph for Questions 9 and 10 iz'u 9 ,oa 10 ds fy;s vuqPNsn

A block resting over a horizontal floor has a symmetric track ABC as shown in Figure. The mass of theblock is M=3.12 kg and length AB = BC = 1m. A block of mass m=2 kg is put on the track at A and thesystem is released from rest. (Neglecting friction and impact at B.),d CykWd ,d {kSfrt Q'kZ ij fp=kuqlkj j[kk gqvk gS rFkk blesa ,d lefer iFk ABC cuk gqvk gSA CykWd dk nzO;ekuM = 3.12 kg rFkk yEckbZ AB = BC = 1m gSA ,d m=2 kg nzO;eku ds CykWd dks iFk ij A ij j[kk tkrk gS rFkk fudk;dks fojkekoLFkk ls NksM+k tkrk gSA (?k"kZ.k rFkk B ij VDdj dks ux.; ekfu;s)

37 37M

mA C

B

9. During motion, the centre of mass of the system moves-(A) Left ward (B) Right ward(C) Upward (D) As periodic motion in vertical direction.xfr ds nkSjku fudk; dk nzO;eku dsUnz xfr djrk gS&(A) cka;h vksj (B) nka;h vksj(C) ij dh vksj (D) /okZ/kj fn'kk esa vkorZ xfr ds vuqlkj

10. When the smaller block is at point C, bigger block is-(A) In rest (B) In motion in lefter ward(C) In motion in rightward (D) No sufficient informationtc NksVk CykWd C fcUnq ij gksrk gS rks cM+k CykWd &(A) fojkekoLFkk esa gksrk gSA (B) cka;h vksj xfr djrk gSA(C) nka;h vksj xfr djrk gSA (D) lwpuk i;kZIr ugha gSA


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

The collector of the photocell (in photoelectric experiment) is made of tungsten while the emitter is ofPlatinum having work function of 10 eV. Monochromatic radiation of wavelength 124 & power 100watt is incident on emitter which emits photo electrons with a quantum efficiency of 1%. The acceleratingvoltage across the photocell is of 10,000 volts (Use : hc = 12400 eV ),d izdk'k fo|qr iz;ksx esa QksVks lsy dk laxzkgd VaxLVu dk cuk gqvk gS tcfd mRltZd IysfVue dk gS ftldk dk;ZQyu

10 eV gSA 124 rjaxnS/;Z rFkk 100 okWV 'kfDr dh ,do.khZ; fofdj.k dks mRltZd ij vkifrr fd;k tkrk gS ftlls1% DokUVe n{krk ds lkFk QksVks bysDVkWu mRlftZr gksrs gSaA QksVks lsy ds fljksa ij Rojd oksYVrk 10,000 oksYV gSA(hc = 12400 eV iz;ksx djsa)-

Platinumemitter Tungsten

target

radiation124

V =10,000VA

11. The minimum wavelength of radiation coming from the tungsten target (collector) is-VaxLVu y{; (laxzkgd) ls vkus okyh fofdj.k dh U;wure rjaxnS/; Z gS&(A) 124 (B) 1.24 (C) 1.23 (D) 12.3

12. If the source of monochromatic radiation of wavelength 124 has an efficiency of 50%, and the powerof X ray emitted by the tungsten target is 3W, the overall efficiency of the apparatus of X-rayproduction is-;fn 124 rjaxnS/; Z ds ,do.khZ; fofdj.k L=ksr dh n{krk 50% rFkk VaxLVu y{; }kjk mRlftZr X fdj.kksa dh 'kfDr3W, gks rks X-fdj.k mRiknu ds fy;s midj.k dh laiw.kZ n{krk gksxh&(A) 1% (B) 0.1% (C) 1.5% (D) 6%

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(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

13. n versus Z graph for characteristic X-rays is as shown in figure.X-fdj.k vfHkyk{kf.kd ds fy;s n - Z vkjs[k fp= esa n'kkZ;k x;k gS&

1 2 34

Z

n

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

(P) Line -1 (1) Lajs[kk -1

(Q) Line -2 (2) Lbjs[kk -2

(R) Line -3 (3) Kajs[kk -3

(S) Line -4 (4) Kbjs[kk -4

Codes :P Q R S

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

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14. Information I : Six point charges each of magnitude q are placed at six corners of a regular hexagon of side a.Information II: One charge is now removed. Match the List-I with List-II for above given information.lwpuk I : izR;sd q ifjek.k ds N% fcUnq vkos'k] a Hkqtk okys le "kV~Hkqt ds N% dksuksa ij fLFkr gSAlwpuk II: vc ,d vkos'k dks gVk;k tkrk gSA mijksDr nh xbZ lwpuk ds fy;s lwpha I dk lwpha II ls feyku dhft,A

ListI/lwphI ListII/lwphII(P) Magnitude of Electric field at centre of hexagon in information I (1) Nonzero

lwpuk I esa "kV~Hkqt ds dsUnz ij fo|qr {ks= dk ifjek.k v'kwU;

(Q) Magnitude of Electric field at centre of hexagon in information II (2) zerolwpuk II esa "kV~Hkqt ds dsUnz ij fo|qr {ks= dk ifjek.k 'kwU;

(R) Electric potential at centre of hexagon in information I (3)0

6q4 ap

lwpuk I esa "kV~Hkqt ds dsUnz ij fo|qr foHko

(S) Electric potential at centre of hexagon in information II (4) 20

q4 ap

lwpuk II esa "kV~Hkqt ds dsUnz ij fo|qr foHkoCodes :

P Q R S

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

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15. Find correct match for the figure in ListI as shown with the items given in ListII :Match the following column :lwphI esa iznf'kZr fp=ksa dk lwphII esa fn;s x;s ifj.kkekas ds lkFk feyku dhft,A

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

(P)

B

I

I

(1) F 0

(Q)

I

I

B (2) F = 0, t 0

(R) I

I

R 2B

R

R (3) F = 0, t = 0

(S)

2B B

RI

(4) F 0, t = 0

Codes :P Q R S

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

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16. Connections made in a post office box are shown in figure. R = 10 W denotes that when R = 10W thepointer in the galvanometer is as .

iksLV vkWfQl ckWDl esa cuk;s x;s la;kstuksa dks fp= esa iznf'kZr fd;k x;k gSA R = 10 W ;g iznf'kZr djrk gS fd tcR = 10W gS rks xsYosuksehVj dk ikWbUVj izdkj ls gS&

S

R

P Q

G

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

(P) P = 100 W, Q = 10W, R = 400 W, R = 500 W (1) 46 W < S < 47 W(Q) P = 100 W, Q = 1 W, R = 460 W, R = 470 W (2) 0.46 W < S < 0.47 W(R) P = 100 W, Q = 10W, R = 460 W, R = 470 W (3) 40 W < S < 50 W(S) P = 1000 W, Q = 1W, R = 460 W, R = 470 W (4) 4.6 W < S < 4.7 W

Codes :

P Q R S

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

SECTION II / [k.M II & SECTION III / [k.M IIIMatrix-Match Type / eSfVDl&esy izdkj Integer Value Correct Type / iw.kkd eku lgh izdkj

No question will be asked in section II and III / [k.M II ,oa III esa dksb Z iz'u ugha gSA

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SECTION-IV : (Integer Value Correct Type)

[k.M-IV : (iw.kkd eku lgh izdkj)This section contains 4 questions. The answer to each question is a single digit Integer, ranging from0 to 9 (both inclusive)bl [k.M esa 4 iz'u gSaA izR;sd iz'u dk mkj 0 ls 9 rd (nksuksa 'kkfey) ds chp dk ,dy vadh; iw.kk d gSA

1. In the figure electric field lines of three charges are shown. If q1= +8mC and q3 = 12mC what ismagnitude of charge q2 in mC.fn;s x;s fp= esa rhu vkos'kksa dh fo|qr {ks= js[kkvksa dks iznf'kZr fd;k x;k gSA ;fn q1= +8mC rFkk q3 = 12mC gks rksvkos'k q2 dk ifjek.k mC esa Kkr dhft,A

+

+

q1

q3

q2

2. A wire of steel of length 0.5 m and density 4.4gm/cm3 is clamped tightly between two rigid supports.The initial temperature of the support are 100C. The temperature of one of the supports is suddenlydropped to 20C. If, after the steady state has been reached, the fundamental frequency is(f 100) Hz . Then find the value of f (Young's modulus of steel Y = 2 1011 N/m2, a = 11 106 K1),d 0.5 m yEckbZ o 4.4gm/cm3 ?kuRo okys LVhy ds rkj dks nks n`

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3. A resistance coil, wired to an external battery, is placed inside a thermally insulated cylinder fitted witha frictionless piston and containing an ideal gas. A current I = 240 mA flows through the coil, whichhas a resistance R = 500 W. At what speed v (in cm/s) must the piston of mass m = 48 kg move upwardin order that the temperature of the gas remains unchanged? [Assume that the cylinder is placed in vacuum]fdlh ckg~; cSVjh ls tqM+h gqbZ ,d izfrjks/kh dq.Myh dks "eh; dqpkyd csyu ds vUnj j[kk x;k gSA bl csyuesa ,d ?k"kZ.kjfgr fiLVu yxk gS rFkk blesa vkn'kZ xSl Hkjh gSA dq.Myh dk izfrjks/k R = 500 W gS rFkk bllsI = 240 mA /kkjk izokfgr gksrh gSA nzO;eku m = 48 kg ds fiLVu dks fdl pky v(cm/s esa) ls ij dh vksj xfrdjuh pkfg;s rkfd xSl dk rki vifjofrZr jgsA (ekuk fd csyu fuokZr~ esa j[kk gqvk gS)

v

Gas

R

I

4. The vernier of a circular scale is divided in to 30 divisions, which coincides with 29 main scale divisions.If each main scale division is (1/2)o, the least count of the instrument in minutes iso`kkdkj iSekus dk ofuZ;j 30 Hkkxksa esa foHkkftr gS tks fd eq[; iSekus ds 29 Hkkxksa ds lkFk lEikrh gSA ;fn eq[; iSekus dkizR;sd Hkkx (1/2)o gks rks bl midj.k dk vYirekad (fefuV esa) gksxkA

CHEM

ISTR

Y

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PART-2 : CHEMISTRY

Hkkx-2 : jlk;u foKkuSECTIONI : (i) One or more options correct Type

[k.M-I : (i) ,d ;k vf/kd lgh fodYi izdkjThis section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONE or MORE are correct.bl [k.M esa 8 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls ,d ;kvf/kd lgh gSA

1. Which of the following statements is/are correct regarding adsorption -

(A) Adsorption is always an exothermic process accomplised by decrease in residual forcess on the surfacei.e. decrease in surface energy

(B) 1 gm of activated charcoal adsorb more methane (critical temperature 190K) as compare to SO2(Critical temperature 630K)

(C) Freundlich adsorption isotherm is applicable for both adsorption of gas on solid and liquid on solid(D) Chemical adsorption increases with increase in temperature

vf/k'kks"k.k ds lUnHkZ esa fuEu dFkuksa esa ls dkSuls lgh gS@gSa -

(A) vf/k'kks"k.k lnSo ,d "ek{ksih ize gksrk gS] tks lrg ij vo'ks"kh cyksa esa deh }kjk iw.kZ gksrs gS vFkkZr lrgtkZ esa deh gksrh gS

(B) 1 gm lf; pkjdksy SO2 (kfUrd rki 630K) dh rqyuk esa esFk su (kfUrd rki 190K) dks vf/kdvf/k'kksf"kr djrk gS

(C) s.Myhp vf/k'kks"k.k lerki] Bksl ij xSl ds rFkk Bksl ij nzo ds vf/k'kks"k.k] nksuksa ds fy, ykxw gksrk gS(D) jlk;fud vf/k'kks"k.k] rki esas o`f ds lkFk c

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2. Using given information :

Temp='T' Temp='T'Temp='T'

1AX 2AX 3AX1BX 2BX 3BX2 2A BY Y 2TP

3TP3 3A BY Y

Where XA , XB = mol fraction of 'A' & 'B' in liquidYA , YB = mol fraction of 'A' & 'B' in vapour

A BP ,P = vapour pressure of pure liquid A and pure liquid B respectively

PT = vapour pressure of solutionGiven : XA1 = XB1

A BP P>

Select the correct set/ sets of relation(A) YA2 > YB2 , PT2 = PT3 (B) YA2 > XA2 , YB2 < XB2(C) YA2 > YA3 , PT2 > PT3 (D) XA2 < XB2 , PT2 < PT3fn xbZ tkudkjh dk mi;ksx djh;s

rki='T' rki='T'rki='T'

1AX 2AX 3AX1BX 2BX 3BX2 2A BY Y 2TP

3TP3 3A BY Y

tgk XA , XB = nzo esa 'A' rFkk 'B' dk eksy izHkktYA , YB = ok"i eas 'A' rFkk 'B' dk eksy izHkkt

A BP ,P = 'kq nzo A RkFkk 'kq nzo B ds ok"i nkc

PT = foy;u dk ok"i nkc

fn;k gS: XA1 = XB1 A BP P>

lEcU/k dk lgh leqPp@leqP;ks dks pqfu;saA

(A) YA2 > YB2 , PT2 = PT3 (B) YA2 > XA2 , YB2 < XB2(C) YA2 > YA3 , PT2 > PT3 (D) XA2 < XB2 , PT2 < PT3

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3. Phosgene (COCl2(g)) undergoes dissociation as : COCl2(g) CO(g) + Cl2(g) ; DH > 0. Whichof the following will increase the dissociation of phosgene(A) Adding Cl2(g) at constant volume(B) Adding Neon to system at constant pressure(C) Decreasing the total pressure(D) Heating the container in which reaction occurs.QkWLTkhu (COCl2(g)) dk fo;kstu fuEu izdkj gksrk gSA : COCl2(g) CO(g) + Cl2(g) ; DH > 0.

fuEu esa lsa dkSulk dkjd QkWLthu ds fo;kstu esa o`f/k djsxkA

(A) fu;r vk;ru ij Cl2(g) feykus ls(B) fu;r nkc ij ra= esa fuvkWu feykus ls(C) dqy nkc esa deh djus ls(D) ik= ftlesa vfHkf;k gksrh gS] dks xeZ djus ls

4. For the reaction : I2 + NaOH NaIO3 + NaI + H2O. Identify the correct statements(A) Reaction is an example of disproportionation(B) Oxidation number of iodine in I2, NaIO3 & NaI is 0, +5 and 1 respectively.(C) 1 mol of I2 reacts with 6 moles of NaOH(D) NaI and NaIO3 are formed in 5 : 1 molar ratiovfHkf;k ds fy, : I2 + NaOH NaIO3 + NaI + H2O. lgh dFku dk p;u dhft;sA(A) vfHkf;k fo"kekuqikru dk ,d mnkgj.k gS(B) I2, NaIO3 rFkk NaI esa vk;ksfMu dh vkDlhdj.k la[;k e'k% 0, +5 rFkk 1 gS(C) 1 eksy I2, 6 eksy NaOH ds lkFk f;k djrk gS(D) NaI rFkk NaIO3 , 5 : 1 ds eksy vuqikr esa fufeZr gksrk gS

5. Identify reactions in which, on heating diatomic gas is evolved leaving behind metallic residue :,slh vfHkf;k,sa igpkfu,sa ftuesa xeZ fd;s tkus ij f}ijekf.o ; xSl mRlftZr gksrh gS rFkk /kkfRod vo'ks"k 'ks"kjgrk gS :(A) NaN3(s) D (B) [Ni(CO)4](g) 250 CD(C) KClO3(s) D (D) HgO(s) D

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6. If a metal ion M+n forms paramegnetic octahedral complex, paramagnetic tetahedral complex andparamagnetic square planar complex with suitable ligands. What is the correct electronic configurationof metal ion M+n :;fn ,d /kkrq vk;u M+n mi;qDr fyxs.Mks a ds lkFk vuqpqEcdh; v"VQydh; ladqy] vuqpqEcdh; prq"Qydh;ladqy rFkk vuqpqEcdh; oxkZdkj leryh; ladqy cukrk gSA /kkrq vk;u M+n dk lgh bysDVkWuh; foU;kl D;k gS :(A) d7 (B) d8 (C) d9 (D) d10

7. Choose the incorrect option(s).

(A) Rate of SN2 I

> I

(B) Ph CHCH MeOH D

Optically pure

N

HIS 1

racemic mixture

(C) MeCl 2

MoistAg O MeOMe (major) (D) MeI (excess) + NH3 Me3N

xyr fodYi dk p;u dhft;s&

(A) SN2 dh nj I

>

I(B) Ph CHCH Me

OH D

izdkf'kd 'kq

N

HIS 1 jslsfed feJ.k

(C) MeCl 2

MoistAg O MeOMe (eq[;) (D) MeI (vkf/kD;) + NH3 Me3N

8. C

NOH

EtMeH O3

+

Major product (eq[; mRikn gS)

(A) Me C OHO

(B) Et C OHO

(C) MeNH2 (D) EtNH2

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(ii) Paragraph Type (ii) vuqPNsn izdkj

This section contains 2 paragraphs each describing theory, experiment, data etc. Four questions relateto two paragraphs with two questions on each paragraph. Each question of a paragraph has only onecorrect 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 2 vuqPNsn gSA nksuksa vuqPNsnksa ls lacaf/kr pkj iz'ugSa] ftuesa ls gj vuqPNsn ij nks iz'u gSaA vuqPNsn esa gj iz'u ds pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesals dsoy ,d lgh gSA

Paragraph for Questions 9 and 10

iz'u 9 ,oa 10 ds fy;s vuqPNsnThe iron(II) ion form many crystalline salts like Mohr's salt, green vitriol, sodium nitropruside andpotassium ferrocyanide etc. Some of the complex salts are paramagnetic but some others are diamagneticalso, which depends on type of ligand coordinated with iron(II) ion.vk;ju(II) vk;u cgqr ls fLVyh; yo.k cukrk gS tSls eksgj yo.k] gjk fofVvkWy] lksfM;e ukbVksizqlkbM rFkk ikSVsf'k;eQsjkslk;ukbM vkfnA dqN ladqy yo.k vuqpqEcdh; gSa rFkk dqN vU; izfrpqEcdh; Hkh gSa tks vk;ju (II) vk;u dslkFk milgla;ksftr fyxS.M ds izdkj ij fuHkZj djrk gSaA

9. Which of the following does not contain Hexaaquairon(II) ion :(A) Mohr's salt (B) Greenvitriol (C) Ferric alum (D) None of the abovefuEu esa ls fdlesa gSDlk,Dokvk;ju(II) vk;u mifLFkr ugha gS :(A) eksgj yo.k (B) gjk fofVvkWy (C) Qsfjd ,sye (D) mijksDr esa ls dksbZ ugha

10. Using the spin only magnetic moment, select which complex of iron (Fe+2 / Fe+3) is 1 : 1 type electrolyte(cation to anion ratio).(A) Sodium pentacynonitrosoniumferrate(......) ; = 0(B) Potassium tetrachloridoferrate(......) ; = 24 B. M.(C) Hexaaquairon(......) sulphate ; = 24 B. M.(D) Potassium hexacynidoferrate(......) ; = 3 B. M.dsoy p.k pqEcdh; vk?kw.kZ dk iz;ksx djrs gq;s crkbZ;sa fd vk;ju (Fe+2 / Fe+3) dk dkSulk ladqy 1 : 1 izdkjdk oS|qr vi?kV~; gS (/kuk;u dk .kk;u ls vuqikr)(A) lksfM;e isUVklk;uksukbVkslksfu;eQSjsV(......) ; = 0(B) ikSVsf'k;e VsVkDyksjkbMksaQSjsV(......) ; = 24 B. M.(C) gSDlk,Dokvk;ju(......) lYQsV ; = 24 B. M.(D) ikSVsf'k;e gSDlklk;ukbMksQSjsV(......) ; = 3 B. M.

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iz'u 11 ,oa 12 ds fy;s vuqPNsnAn organic compound (X) shows following reactions

O

O(X)

aq.K CO2 3 PNH NH22 QH O22

(i) MgHgR(ii) H O2

H+ S LAH T H+

U(Major

product)

,d dkcZfud ;kSfxd (X) fuEu vfHkf;k,sa nsrk gSAO

O(X)

aq.K CO2 3 PNH NH22 QH O22

(i) MgHg R(ii) H O2H+ S LAH T H

+

U(eq[; mRikn)

11. Compound which can show stereoisomerism.

;kSfxd tks f=foe~ leko;ork iznf'kZr dj ldrk gS&(A) P (B) Q (C) U (D) T

12. Incorrect statement for ' T '.(A) Evolve H2 with Na metal (B) Tertiary alcohol(C) Optically active (D) None' T ' ds fy, xyr dFku gS&

(A) Na /kkrq ds lkFk H2 xSl mRlftZr djrk gSA (B) r`rh;d ,YdksgkWy gSA

(C) izdkf'kd lf; gSA (D) buesa ls dksbZ ugha

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13. List-I List-II

(P) Critical pressure for Vander Waal's gas (1) 8a27Rb

(Q) Z for vander waal's gas at low pressure (2) Pb1 RT+

(R) Z for vander waal's gas at high pressure (3) 2a

27b

(S) Critical temperature for Vander Waal's gas (4)m

a1V RT

-

lwph-I lwph-II

(P) okW.Mjoky xSl dk kfUrd nkc (1) 8a27Rb

(Q) U;wu nkc ij okW.Mjoky xSl ds fy, Z (2) Pb1 RT+

(R) mPp nkc ij okW.Mjoky xSl ds fy, Z (3) 2a

27b

(S) okW.Mjoky xSl ds fy, kfUrd rki (4)m

a1V RT

-

Codes :P Q R S

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

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14. List-I List-II

(P) Rate vs time for zero order kinetics (1)

(Q) Concentration of reactant vs time for zero order (2)

(R) Half life vs initial concentration for zero order (3)

(S) Concentration of reactant vs time for 1st order kinetics (4)

lwph--I lwph-II

(P) 'kqU; dksfV xfrdh ds fy, nj v/s le; (1)

(Q) 'kqU; dksfV ds fy, vfHkdkjdks dh lkUnzrk v/s le; (2)

(R) 'kqU; dksfV ds fy, v/kZ vk;q v/s izkjfEHkd lkUnzrk (3)

(S) 1st dksfV xfrdh ds fy, f;kdkjdksa dh lkUnzrk vs le; (4)

Codes :P Q R S

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

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15. List - I List - II(Pair of species in Aqueous solution)

(P) Pb2+ , SO42 (1) Can exist together(Q) KOH, HCO3

(2) Does not exist together because bothform a insoluble salt

(R) Sn4+ + Hg2+ (3) Does not exist together because bothunder goes in acid base reaction

(S) I + Fe3+ (4) Does not exist together because theyundergoes in redox reaction.

lwphI lwphII(tyh; foy;u es a Lih'kht dk ; qXe)

(P) Pb2+ , SO42 (1) lkFk&lkFk jg ldrs gSa(Q) KOH, HCO3

(2) lkFk&lkFk ugha jg ldrs gS D;ksafd nksuksa ,dvfoys;'khy yo.k cukrs gS

(R) Sn4+ + Hg2+ (3) lkFk&lkFk ugha jg ldrs gS D;ksafd nksuksavEy&{kkj vfHkf;k djrs gSa

(S) I + Fe3+ (4) lkFk&lkFk ugha jg ldrs gS D;ksafd osa jsMkWDlvfHkf;k djrs gSa

Codes :P Q R S

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

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16. Consider the following compounds.fuEu ;kSfxdksa ij fopkj dhft,A(i) IF5 (ii) ClFfl4 (iii) XeO2F2 (iv) NHfl2 (v) BCl3(vi) BeCl2 (vii) AsCl5 (viii) BO3

3 (ix) NOfl2ListI ListII

(Species in which central atom uses (Number of species out

valency shell orbital) of given above)

(P) All three p-orbitals are involved in hybridisation of central atom (1) One(Q) Only two p-orbitals are involved in hybridisation of central atom (2) Five(R) Only one p-orbital is involved in hybridisation of central atom (3) Three(S) Atleast one d-orbital is involved in hybridisation of central atom (4) FourSelect correct code :

lwphI lwphII

(nh xbZ Lih'kht es a ls og ftles a dsUh ; ijek.kq] la;k sth (mijk sDr es a ls Lih'kht dh

dks'k d{kd dk iz;k sx djrs gS) la[;k)

(P) dsUh; ijek.kq ds ladj.k esa lHkh rhuksa p-d{kd lfEefyr gSa (1) ,d(Q) dsUh; ijek.kq ds ladj.k esa dsoy nks p-d{kd lfEefyr gSa (2) ikp(R) dsUh; ijek.kq ds ladj.k esa dsoy ,d p-d{kd lfEefyr gS (3) rhu(S) dsUh; ijek.kq ds ladj.k esa de ls de ,d d-d{kd lfEefyr gS (4) pkjlgh dwV pqfu,sa :

Codes :

P Q R S

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



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[k.M-IV : (iw.kkd eku lgh izdkj)This section contains 4 questions. The answer to each question is a single digit Integer, ranging from0 to 9 (both inclusive)bl [k.M esa 4 iz'u gSaA izR;sd iz'u dk mkj 0 ls 9 rd (nksuksa 'kkfey) ds chp dk ,dy vadh ; iw.kk d gSA

1. If energy of 2p atomic orbital and 2s atomic orbitals in oxygen atom are 15.85 eV and 32.38 eVrespectively.Find number of bonding electrons in O2 molecules which have higher energy than 32.38 eV.

;fn vkWDlhtu ijek.kq esa 2p ijekf.o; d{kd rFkk 2s ijekf.o; d{kdksa dh tkZ e'k % 15.85 eV rFkk32.38 eV gS rks vkWDlhtu v.kqvksa esa , sls ca/kh bysDVkWuks a dh la [;k crkbZ;sa tks ] 32.38 eV ls vf/kd tkZj[krs gSaA

2. In hydroboration oxidation reaction which is a syn addition phenomena

gkbMkscksjhdj.k vkWDlhdj.k vfHkf;k tks ,d flu ;ksx ize gS] esa

(i) BH THF3(ii) H O /OH2 2

Total number of trans isomeric product is/are.

VkUl leko;oh mRiknks a dh dqy la[;k D;k gS

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3.

O O

2

KOHI Number of iodoform molecules produced per molecule.

O O

2

KOHI

izfr v.kq mRikfnr vk;MksQkWeZ v.kqvksa dh dqy la[;k crkb;sA

4. Number of moles of CrO3 required to oxidise completely of 9 moles of 2-heptanol to the correspondingketone ?

dhVksu ds lkFk lEcfU/kr 2-gSIVsukWy ds 9 eksyksa dks iw.kZ vkWDlhd`r djus ds fy, vko';d CrO3 ds eksyksa dh la[;kcrkb;s&


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PART-3 : MATHEMATICS Hkkx-3 : xf.kr

SECTIONI : (i) One or more options correct Type [k.M-I : (i) ,d ;k vf/kd lgh fodYi izdkj

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and(D) out of which ONE or MORE are correct.bl [k.M esa 8 cgqfodYi iz'u gSaA izR;sd iz'u esa pkj fodYi (A), (B), (C) vkSj (D) gSa] ftuesa ls ,d ;kvf/kd lgh gSA

1. Every solution of cos2x = 1 will be a solution of which of the following equation(s)-cos2x = 1 dk izR;sd gy] fuEu esa ls fdl lehdj.k dk gy gksxk -

(A) cosx + 3cos3x + 5cos5x + 7cos7x = 0 (B) sin2x + 2sin4x + 3sin6x = 0(C) tan2x + 2tan4x + 3tan6x = 0 (D) sin2x + cos4x + tan6x = 0

2. Let ( )10

10

x dx-

a = - a where a [9,11] and maximum and minimum values of (a) are M & m

respectively, then-

ekuk ( )10

10

x dx-

a = - a , tgk a [9,11] rFkk (a) ds vf/kdre rFkk U;wure eku e'k% M rFkk m gks] rks -

(A) m = 50 (B) m = 100 (C) M = 250 (D) M = 220

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3. 5 5 5 5P 1234 1235 1236 .... 4321= + + + +5 5 5 5Q 1235 1236 1237 .... 4322= + + + +4322

5

1234

R x dx= . Then(A) P < R (B) P + Q > 2R (C) Q > R (D) P + Q < 2R

5 5 5 5P 1234 1235 1236 .... 4321= + + + +5 5 5 5Q 1235 1236 1237 .... 4322= + + + +4322

5

1234

R x dx= gSA rc(A) P < R (B) P + Q > 2R (C) Q > R (D) P + Q < 2R

4. Let ( )1 3 2x xx 2-=+ ,

n(x ) =

n1(1(x)) for n > 2, n N and fn(x) = 2(x) + 4(x) +........+2n(x), n N then(A) ( ) ( )n 1 nx x x R+f > f " (B) ( ) ( )n 1 nx x x R++f > f " (C) ( ) ( )n 1 nx x x R++f < f " (D) Equation f4(x) = 5 sinx will have exactly 3 distinct real solutions.

ekuk ( )1 3 2x xx 2-=+ ,

tgk n > 2, n N ds fy, n(x ) =

n1(1(x)) rFkk fn(x) = 2(x) + 4(x) +........+2n(x), n N gks] rks(A) ( ) ( )n 1 nx x x R+f > f " (B) ( ) ( )n 1 nx x x R++f > f " (C) ( ) ( )n 1 nx x x R++f < f " (D) lehdj.k f4(x) = 5 sinx ds Bhd 3 fHkUu okLrfod gy gksaxsA

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5. Let : [2p,2p] [a,b], (x) = tan1x + sinx + x5 3x3x be an onto function, then-ekuk : [2p,2p] [a,b], (x) = tan1x + sinx + x5 3x3x vkPNknd Qyu gks] rks -(A) 2a + b > 0 (B) 3a + b < 0 (C) a + 2b > 0 (D) 3a + 4b > 0

6. Let nth term of sequence 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,...... is given by tn, then

ekuk Js.kh 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,...... dk n ok in tn }kjk fn;k x;k gS] rks

(A) t100 = 14 (B) t200 = 20 (C) t300 = 24 (D) t400 = 287. Let : R R is polynomial satisfying (x 4)(x 1) = (x 7)(x), " x R. If (7) = 6, then-

(A) '(x) will have three distinct positive real roots(B) '(x) will have two distinct positive real roots(C) is surjective(D) is injectiveekuk cgqinh; Qyu : R R, (x 4)(x 1) = (x 7)(x), " x R dks lUrq"V djrk gSA ;fn (7) = 6 gks] rks -(A) '(x) ds rhu fHkUu /kukRed okLrfod ewy gksaxs(B) '(x) ds nks fHkUu /kukRed okLrfod ewy gksaxs(C) vkPNknd gksxkA(D) ,dSdh gksxkA

8. Let : R0 R, ( )2

x 4 x n 2

3 x = + -

l , then which of the following statement is true about function (x)

(A) (x) an increasing function(B) Range of (x) is R(C) (x) = 2 posses exactly three distinct real solution(D) (x) = 0 posses exactly one real solution

ekuk : R0 R, ( )2

x 4 x n 2

3 x = + -

l gks] rks fuEu esa ls dkSulk dFku Qyu (x) ds fy, lR; gksxk

(A) (x) ,d o/kZeku Qyu gSA(B) (x) dk ifjlj R gksxkA(C) (x) = 2 ds Bhd rhu fHkUu okLrfod gy gksaxsA(D) (x) = 0 dk Bhd ,d okLrfod gy gksxkA

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(ii) Paragraph Type

(ii) vuqPNsn izdkj

This section contains 2 paragraphs each describing theory, experiment, data etc. Four questions relateto two paragraphs with two questions on each paragraph. Each question of a paragraph has only onecorrect 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 2 vuqPNsn gSA nksuksa vuqPNsnksa ls lacaf/kr pkj iz'ugSa] ftuesa ls gj vuqPNsn ij nks iz'u gSaA vuqPNsn esa gj iz'u ds pkj fodYi (A), (B), (C) vkSj (D) gSa ftuesals dsoy ,d lgh gSA


iz'u 9 ,oa 10 ds fy;s vuqPNsnLet P : x + y + z = 3 is a plane and A(1,1,1) is a point on it. Q is a variable point on plane P such thatQA 2 2= . B(2,3,4) is another point then answer the following questions.

ekuk lery P : x + y + z = 3 rFkk A(1,1,1) bl ij ,d fcUnq gSA Q, lery P ij ,d pj fcUnq bl izdkjgS fd QA 2 2= gSA B(2,3,4) vU; fcUnq gks] rks fuEu iz'uksa ds mkj nhft,A

9. Maximum value of QB is -QB dk vf/kdre eku gksxk

(A) 3 2 (B) 6 (C) 2 6 (D) 3010. The coordinates of the point on the locus of Q such that QB is minimum is-

Q ds fcUnqiFk ij ml fcUnq ds funsZ'kkad tc QB U;wure gS] gksxk -(A) (1,1,3) (B) (0,1,2) (C) (3,1,1) (D) (1,1,3)


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

Let ( )1

n 1

0

n x sin x dx2

- p =

( )1

n 1

0

g n x cos x dx2

- p = , where n = 1,2,3,.......

ekuk ( )1

n 1

0

n x sin x dx2

- p =

( )1

n 1

0

g n x cos x dx2

- p = , tgk n = 1,2,3,.......

11. ( ) ( )nlim n 1 n

+

is equal to-

( ) ( )nlim n 1 n

+

cjkcj gksxk -

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

12.( ) ( )( ) ( )2n

3n 1 nlim

2n 1 g n++ is equal to-

( ) ( )( ) ( )2n

3n 1 nlim

2n 1 g n++ cjkcj gksxk -

(A) 32p (B) 32p (C) 34 (D)

32


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13. Let A(t) = [aij], is a matrix of order 3 3 given by ij2cos t if i j

a 1 if i j 10 otherwise

== - =

where |A(t)| is determinant value of matrix A(t).Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) ( ) ( )t 0lim A t A 4t

(1) 0(Q) maximum value of |A(t)| |A(3t)| (2) 1(R) 4A A

17 17p p

(3) 4

(S) ( ) ( )0

A t A 4t dtp

(4) 16

ekuk A(t) = [aij], dksfV 3 3 ds vkO;wg =

= - =

ij

2cos t i ja 1 i j 1

0

;fn

;fn

vU;Fkk

}kjk fn;k x;k gSA

tgk |A(t)|, vkO;wg A(t) dk lkjf.kd eku 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) ( ) ( )t 0lim A t A 4t

(1) 0(Q) |A(t)| |A(3t)| dk vf/kdre eku gksxk (2) 1(R) 4A A

17 17p p

(3) 4

(S) ( ) ( )0

A t A 4t dtp

(4) 16Codes :

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

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14. Let (1 + x)62 = C0 + x C1 + x2 C2+..........+ x62 C62 where Cr = 62Cr.Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II(P) C0 + C4 + C8 +.....+ C60 is divisible by 2n, (1) 61

then maximum value of n is(Q) C1 + C5 + C9 +.....+ C61 is divisible by 2n, (2) 60

then maximum value of n is(R) C3 + C7 + C11 +.....+ C59 is divisible by 2n, (3) 31

then maximum value of n is(S) C2 + C6 + C10 +.....+ C62 is divisible by 2n, (4) 30

then value of n can not be

ekuk (1 + x)62 = C0 + x C1 + x2 C2+..........+ x62 C62 tgk Cr = 62Cr 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) C0 + C4 + C8 +.....+ C60, 2n ls foHkkftr gks] rks n dk (1) 61

vf/kdre eku gksxk

(Q) C1 + C5 + C9 +.....+ C61, 2n ls foHkkftr gks] rks n dk (2) 60vf/kdre eku gksxk

(R) C3 + C7 + C11 +.....+ C59, 2n ls foHkkftr gks] rks n dk (3) 31vf/kdre eku gksxk

(S) C2 + C6 + C10 +.....+ C62, 2n ls foHkkftr gks] rks n dk (4) 30eku ugha gks ldrk gS

Codes :P Q R S

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


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15. The set A = {z : z18 = 1}, B = {w : w48 = 1}, C = {zw : z A and w B} are three sets of complex

roots of unity and D z : 0 arg(z)3p =

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

(P) n(A B) (1) 4(Q) n(C) (2) 6(R) n(A D) (3) 9(S) n(B D) (4) 12

leqPp; A = {z : z18 = 1}, B = {w : w48 = 1}, C = {zw : z A rFkk w B} bdkbZ ds lfEeJ ewy

ds rhu leqPp; gS rFkk D z : 0 arg(z)3p =

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) n(A B) (1) 4(Q) n(C) (2) 6(R) n(A D) (3) 9(S) n(B D) (4) 12

Codes :P Q R S

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


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16. Let ( ) ( )( )x12 x x 3x 2 -= + + and two equations in n aren

10k 1

log (k) 1=

= .........(1)n

10k 1

log (k) 2=

= ..........(2)

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

(P) If n is odd in equation (1), then n is equal to (1) 0(Q) If n is even in equation (1), then n is equal to (2) 1(R) Number of even values of n satisfying equation (2) is (3) 3(S) Number of odd values satisfying equation (2) is (4) 18

ekuk ( ) ( )( )x12 x x 3x 2 -= + + rFkk n esa nks lehdj.kasn

10k 1

log (k) 1=

= .........(1)n

10k 1

log (k) 2=

= ..........(2)

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 lehdj.k (1) esa] n fo"ke gks] rks n cjkcj gksxk (1) 0(Q) ;fn lehdj.k (1) esa] n le gks] rks n cjkcj gksxk (2) 1(R) lehdj.k (2) dks lUrq"V djus okys n ds le ekuksa dh la[;k gksxh (3) 3(S) lehdj.k (2) dks lUrq"V djus okys n ds fo"ke ekuksa dh la[;k gksxh (4) 18

Codes :P Q R S

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




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[k.M-IV : (iw.kkd eku lgh izdkj)This section contains 4 questions. The answer to each question is a single digit Integer, ranging from0 to 9 (both inclusive)bl [k.M esa 4 iz'u gSaA izR;sd iz'u dk mkj 0 ls 9 rd (nksuksa 'kkfey) ds chp dk ,dy vadh ; iw.kk dgSA

1. Suppose is a function on the interval [1,3] such that 1 < (x) < 1 for all x and ( )3

1

x dx 0= .

If maximum value of ( )3

1

xdx

x is a

nb

l (where a,b are coprime numbers), then a + b is equal to

ekuk , vUrjky [1,3] esa ,d Qyu bl izdkj gS fd lHkh x ds fy, 1 < (x) < 1 rFkk ( )3

1

x dx 0= gSA ;fn( )3

1

xdx

x dk vf/kdre eku an b

l (tgk a,b lg&vHkkT; la[;k;sa gSa), rks a + b cjkcj gksxk

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2. In the given figure, two circles with radii 6 and 8 are drawn with centers (C1 and C2), 12 units apart. AtP, one of the points of intersection, a line QR is drawn in such a way that the chords QP and PR have

equal length (P is the mid point of QR). Then 21 QP26

is equal to

fn;s x;s vkjs[k esa] nks o`k ftudh f=T;k;sa 6 rFkk 8 gS] rFkk ftuds dsU (C1 rFkk C2) ,d&nwljs ls 12 bdkbZ dh nwjh ijfLFkr gSA izfrPNsnh fcUnqvksa esa ls fdlh ,d fcUnq P ij ,d js[kk QR dks bl izdkj [khapha tkrh gS fd thokvksa QP rFkk

PR dh yEckbZ leku jgs (P, QR dk e/; fcUnq gS)A rc 21 QP26

cjkcj gksxk

QP

RC1 C2

3. y = (x) is a solution of differential equation x

x

dy 2xeydx 1 ye

-+ =

+ such that (0) = 1, then ( ) 1

e

-

is equal

to {where [.] greatest integer function}

y = (x) vody lehdj.k x

x

dy 2xeydx 1 ye

-+ =

+ dk gy bl izdkj gS fd (0) = 1 gks] rks ( ) 1

e

-

gksxk

{tgk [.] egke iw.kkd Qyu dks n'kkZrk gS}

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4. In a DABC, AB = 85, BC = 90 and AC = 102. P is an interior point and line segments are drawn throughP parallel to the sides of the triangle. If these three line segments (as shown in the diagram by RQ, R'Q',

R''Q'') are of equal length d, then 5d34

is equal to

f=Hkqt ABC esa] AB = 85, BC = 90 rFkk AC = 102 gSA ,d vkUrfjd fcUnq P ls Hkqtkvksa ds lekukUrj js[kk[k.M [khaps

tkrs gSaA ;fn ;g rhu js[kk[k.M] (vkjs[k esa RQ, R'Q', R''Q'' }kjk n'kkZ;k x;k gS) leku yEckbZ d ds gks] rks 5d34

cjkcj gksxk

R'' R'

R Q

C

B Q' Q'' A

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D. vadu ;kstuk / Marking scheme :14. [kaM-I (i) ds gj iz'u esa dsoy lgh mkjksa (mkj) okys lHkh cqycqyksa (cqycqys) dks dkyk djus ij 4 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;sxkAFor each question in Section-I (i), you will be awarded 4 marks if you darken all the bubble(s) corresponding to only thecorrect answer(s) and zero mark if no bubbles are darkened. In all other cases minus one (1) mark will be awarded

15. [kaM-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 ughadjus ij 'kwU; (0) vad iznku fd;k tk;sxkA vU; lHkh fLFkfr;ksa esa .kkRed ,d (1) vad iznku fd;k tk;sxkAFor each question in Section-I (ii & iii), you will be awarded 3 marks if you darken all the bubble(s) corresponding toonly the correct answer(s) and zero mark if no bubbles are darkened. In all other cases minus one (1) mark will beawarded.

16. [kaM-IV esa gj iz'u esa dsoy lgh mkj okys cqycqys (BUBBLE) dks dkyk djus ij 3 vad vkSj dksbZ Hkh cqycqyk dkyk ugha djusij 'kwU; (0) vad iznku fd;k tk;sxk bl [ akM ds iz'uksa esa xyr mkj nsus ij dksbZ .kkRed vad ugha fn;s tk;saxsaAFor each question in Section-IV, you will be awarded 3 marks if you darken the bubble corresponding to the correctanswer and zero mark if no bubbles are darkened No negative marks will be awarded for incorrect answers inthis section.

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

allen paper 2

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