ALL INDIA TEST SERIES

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1 FIITJEE Sudens Frm Classrm / Inegraed Schl Prgrams have secured Znal, 6 Sae & 18 Ciy Tpper Ranks. in Tp 100, 78 in Tp 00 and 05 in Tp 500 All India Ranks bagged by FIITJEE Sudens frm All Prgrams have qualified in JEE (Advanced), 015. ALL INIA TEST SERIES FIITJEE FULL TEST I Paper 1 Time Alled: Hurs Maximum Marks: 46 Pleas e r ead h e insrucins carefully. Yu are alled 5 minues specifically fr his purpse. Yu are n allwed leav e h e Exam inain Hall befre he end f he es. A. General Insrucins INSTRUCTIONS 1. Aemp ALL he quesins. Answers have be marked n he OMR shees.. This quesin paper cnains Three Pars.. Par-I is Physics, Par-II is Chemisry and Par-III is Mahemaics. 4. Each par is furher divided in hree secins: Secin-A, Secin-B & Secin-C 5. Rugh spaces are prvided fr rugh wrk inside he quesin paper. N addiinal shees will be prvided fr rugh wrk. 6. Blank Papers, clip bards, lg ables, slide rule, calcular, cellular phnes, pagers and elecrnic devices, in any frm, are n allwed. B. Filling f OMR Shee 1. Ensure maching f OMR shee wih he Quesin paper befre yu sar marking yur answers n OMR shee.. On he OMR shee, darken he apprpriae bubble wih black pen fr each characer f yur Enrlmen N. and wrie yur Name, Tes Cenre and her deails a he designaed places.. OMR shee cnains alphabes, numerals & special characers fr marking answers. C. Marking Scheme Fr All Three Pars. 1. Secin A (01 07) cnains 7 muliple chice quesins which have nly ne crrec answer. Each quesin carries + marks fr crrec answer and 1 mark fr wrng answer. Secin A (08 11) cnains 4 muliple chice quesins which have ne r mre han ne crrec answer. Each quesin carries + marks fr crrec answer. There is n negaive marking. Secin-A (1 16) cnains paragraphs. Based upn paragraph, and muliple chice quesins have be answered. Each quesin has nly ne crrec answer and carries + marks fr crrec answer and 1 mark fr wrng answer.. Secin B (01 0) cnains Marix Mach Type quesins cnaining saemens given in clumns. Saemens in he firs clumn have be mached wih saemens in he secnd clumn. Each quesin carries +8 marks fr all crrec answer. Fr each crrec rw + marks will be awarded. There may be ne r mre han ne crrec maching. N marks will be given fr any wrng maching in any quesin. There is n negaive marking.. Secin-C (01 06) cnains 6 Numerical based quesins wih answers as numerical value frm 0 9 and each quesin carries + marks fr crrec answer. There is n negaive marking. Name f he Candidae Enrlmen N. JEE (Advanced)-016

2 Useful aa PHYSICS Accelerain due graviy g = 10 m/s Planck cnsan Charge f elecrn Mass f elecrn h = J-s e = C m e = kg Permiiviy f free space 0 = C /N-m ensiy f waer waer = 10 kg/m Amspheric pressure P a = 10 5 N/m Gas cnsan R = 8.14 J K 1 ml 1 CHEMISTRY Gas Cnsan R = 8.14 J K 1 ml 1 = Li am K 1 ml 1 = Cal K 1 ml 1 Avgadr's Number N a = Planck s cnsan h = Js = ergs 1 Faraday = culmb 1 calrie = 4. jule 1 amu = kg 1 ev = J Amic N: H=1, He =, Li=, Be=4, B=5, C=6, N=7, O=8, N=9, Na=11, Mg=1, Si=14, Al=1, P=15, S=16, Cl=17, Ar=18, K =19, Ca=0, Cr=4, Mn=5, Fe=6, C=7, Ni=8, Cu = 9, Zn=0, As=, Br=5, Ag=47, Sn=50, I=5, Xe=54, Ba=56, Pb=8, U=9. Amic masses: H=1, He=4, Li=7, Be=9, B=11, C=1, N=14, O=16, F=19, Na=, Mg=4, Al = 7, Si=8, P=1, S=, Cl=5.5, K=9, Ca=40, Cr=5, Mn=55, Fe=56, C=59, Ni=58.7, Cu=6.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=17, Xe=11, Ba=17, Pb=07, U=8.

3 Physics PART I SECTION A Sraigh Objecive Type This secin cnains 7 muliple chice quesins. Each quesin has fur chices (A), (B), and () u f which ONLY ONE pin is crrec. 1. A paricle srikes a hriznal fricinless flr wih a speed u a an angle wih he verical and rebunds wih a speed v a an angle wih he verical. The c-efficien f resiuin beween he paricle and flr is e. The angle is equal 1 (A) (B) an ean 1 1 an an e () 1 e. In he given siuain disc and ring (kg) are cnneced wih a sring. Bh are placed n he rugh surface. A frce F = 10N is applied n he cenre f disc hriznally. Assume iniially bh bdies were in res. Then fricinal frce acing n he ring will be Ring 0. R R isc F = 10N 0. (A) 0 N (B) 10 N Zer () Nne. In he circui shwn C 1 = C. Swich S is clsed a ime = 0. Le i 1 & i be he curren flwing hrugh C 1 and C a any ime, hen he rai I 1 /I (A) is cnsan (B) increases wih increase in ime decreases wih increase in ime () firs increases hen decreases C 1 C R R s V

4 4 4. The capacir f an scillary circui f frequency 10 4 Hz is enclsed in a cnainer. When he cnainer is evacuaed, he frequency changes by 50 Hz, he dielecric cnsan f he gas is (A) 1.1 (B) () A curren carrying wire is placed in he grves f an insulaing semicircular disc f radius R as shwn. The curren eners a pin A and leaves pin B. eermine he magneic field a pin. 0 (A) i (B) i 0 8R 4R i 0 4R () Nne C R i 0 i 0 B A 6. The rgan pipes, bh clsed a ne end, have lenghs and vibraes in fundamenal mde. Neglec end crrecin. If he velciy f sund in air is v, hen he number f beas/sec is assume (A) v 4 (B) v v 4 v () 7. Ligh is inciden nrmally n face AB f a prism as shwn. A liquid f refracive index is placed n face AC f he prism. The prism is made f glass f refracive index /. The limi f fr which al inernal reflecin akes place n face AC is (A) (B) 4 () 4 A Liquid 60 0 B C

5 5 (Muliple Crrec Chice Type) This secin cnains 4 muliple chice quesins. Each quesin has fur chices (A), (B), and () u f which ONE r MORE THAN ONE is/are crrec. 8. A phn cllides wih a sainary H am in grund sae inelasically. Energy f he clliding phn is 10. ev. Alms insananeusly, anher phn cllides wih same H am inelasically wih an energy f 15 ev. Wha will be bserved by he deecr? (A) w phns f energy 10. ev (B) w phns f energy 1.4 ev One elecrn having kineic energy nearly 11.6 ev () One phn f energy 10. ev and an elecrn f energy 1.4 ev 9. An elecrn in H am is excied frm grund sae level firs excied level. Selec he crrec saemens: (A) Kineic energy f elecrn is decreased (B) Penial energy is increased while kineic energy f elecrn is decreased Time perid f rain and angular mmenum bh are increased () Tal energy is increased while angular speed is decreased 10. In he given circui, curren in resisance R is 1A, hen (A) V 5vl s (B) impedance f newrk is5 Pwer facr f given circui is 0.6 lagging () Pwer facr f given circui is 0.6 leading R V L 8V C 4V V s 11. Figure shws variain f magnificain m(prduced by a hin cnvex lens) and disance v f image frm ple f he lens. Which f he fllwing saemens are crrec? (A) fcal lengh f he lens is equal inercep n v - axis (B) fcal lengh f he lens is equal inverse f slpe f he line Magniude f inercep n m axis is equal uniy () Nne m v

6 6 Cmprehensin Type This secin cnains paragraphs. Based upn ne f he paragraphs muliple chice quesins and based n he her paragraph muliple chice quesin have be answered. Each f hese quesins has fur chices (A), (B), and () u f which ONLY ONE is crrec. Paragraph fr Quesins 1 & 1 A disc having radius R is rlling wihu slipping n a hriznal plane as shwn. Cenre f he disc has a velciy v and accelerain a as shwn. Y 0 (0, 0) P (x, y) v a X 1. Speed f pin P having crdinaes (x, y) is (A) V x y R (B) V x y R R V x y R R () Nne 1. If V ar, he angle beween accelerain f he pms pin and he hriznal is (A) 0 (B) 1 45 an Paragraph fr Quesins 14 & 16 () 1 1 an A cerain subsance has a mass f 50g/ml. When 00J f hea is added 5 gm f sample f his maerial, is emperaure rises frm 5 45 C. 14. The hermal hea capaciy f he subsance is (A) 5J / C (B) 5J / C 15J / C () 0J / C 15. The specific hea capaciy f he subsance is (A) 00J / kg C (B) 400J / Kg C 16. The mlar hea capaciy f he subsance is (A) 0J / ml C (B) 40J / ml C 500J / Kg C 0J / ml C () () 600J / kg C 60J / ml C

7 7 SECTION - B Marix Mach Type This secin cnains quesins. Each quesin cnains saemens given in w clumns, which have be mached. The saemens in Clumn I are labelled A, B, C and, while he saemens in Clumn II are labelled p, q, r, s and. Any given saemen in Clumn I can have crrec maching wih ONE OR MORE saemen(s) in Clumn II. The apprpriae bubbles crrespnding he answers hese quesins have be darkened as illusraed in he fllwing example: If he crrec maches are A p, s and ; B q and r; C p and q; and s and ; hen he crrec darkening f bubbles will lk like he fllwing: A B C 1. Mach he fllwing Clumn I (A) Zer graviy (p) SHM (B) k f a spring m (q) Y A Clumn II 1 KE = PE (r) rd he ime perid f y sin y sin (s) wris wach can give crrec ime (). Mach he fllwing () Per secnd Clumn I Clumn II (A) Nuclear fusin (p) Sraifies E = mc (B) Nuclear fissin Generally pssible fr nuclei wih (q) lw amic number decay Generally pssible fr nuclei wih (r) higher amic number and insabiliy () Exhermic nuclear reacin Essenially prceeds by weak (s) nuclear frce () Significan mmenum cnservain

8 8 SECTION C (Ineger Answer Type) This secin cnains 6 quesins. Each quesin, when wrked u will resul in ne ineger frm 0 9 (bh inclusive). 1. A prjecile is prjeced wih a speed 0 m/s frm he flr f a 5 m high rm as shwn. The maximum hriznal range f he prjecile is fund be 0 n m. Find n [Take g = 10 ms - ]. 0 m/s 5 m. A slid cylinder is made f radius R and heigh R having mass densiy. Nw w half spheres f radius R are remved frm bh ends. The mmen f ineria f remaining prin abu axis 9 5 ZZ can be calculaed as R. Find K. 6K Z R Z' R

9 9. Tw paricles each f mass m are cnneced by a sring f lengh 1m. The paricles are kep n a smh hriznal plane. The iniial separain beween he paricles is 0.5 m. One f he paricles is given a velciy 18 m/s as shwn. Find he magniude f angular velciy f ne paricle wih respec he her paricle jus afer he sring becmes au (in m/s). 18 ms -1 m 0.5 m m 4. Tw hin symmerical lenses f differen naure have equal radii f curvaure f all faces R = 0 cm. The lenses are pu clse geher and immersed in waer. The fcal lengh f he sysem is 5 4 cm. The difference beween refracive indices f he lenses is. Find n. The refracive n index f waer is A 10 m lng nichrme wire having 80 resisance has curren carrying capaciy f 5 A. This wire can be cu in equal pars and equal pars can be cnneced in series r parallel. Wha is he maximum pwer which can be bained as hea by he wire frm a 00 V mains supply (in KW). 6. In he given figure, a penial f +1 vl is given pin A, and pin B is earhed. Wha is he penial a pin P in vl? 4F A F P B F

10 10 Chemisry PART II SECTION A Sraigh Objecive Type This secin cnains 7 muliple chice quesins. Each quesin has 4 chices (A), (B), and () fr is answer, u which ONLY ONE pin is crrec. 1. Which ne f he fllwing is n rue abu dibrane? (A) I has w bridging hydrgens and fur erminal hydrgens. (B) When mehylaed, he prduc is Me 4 B H. The bridging hydrgen are in a plane perpendicular he res f he B H bnds. () All he six B H bnd disances are equal.. Fr he reacin, OH HO H (excess) A OH Wha is he prduc A? (A) (B) ()

11 11. The wave funcin f amic rbial f H-like ams is given as under: 1 s Z Zr e 4 Zr / Given ha he radius is in Å, hen which f he fllwing is radius fr ndal surface fr He + in (A) 1Å (B) Å.5Å () 4Å 4. Cyclpenadiene + Na C + H C + FeCl + NaCl Which ne f he fllwing in n rue abu. (A) is an rganmealic cmpund (B) is an pically inacive cmpund EAN f Fe + in is 4 () All C C bnds in are f idenical lengh 5. Which ne f fllwing saemen is rue (A) G is an pically inacive cmpund (B) H is an pically inacive cmpund and have all C C bnd f equal lengh F and bh have equal n f -bnd () H is -mehylnaphhalene H O Tluene + O AlCl O A Zn(Hg) HCl B SOCl C NaOE/EOH, hea AlCl G NBS CCl 4, hv F H SO 4 E NaBH 4

12 1 6. Which ne f he fllwing reacin is n pssible:- (A) O O NaOH, H O (B) O O NaO, O O O NaO, O () O O NaOH, H O 7. (I) C(CO) 6 (II) C(CO) 5 NH (III) C(CO) 4 (NH ) (IV) C(CO) (NH ) (V) C(CO) (NH ) 4 (VI) C(CO)(NH ) 5 Which saemen is crrec fr hese cmpunds? (A) rder f C C bnd lengh in cmplexes is I > II > III > IV > V > VI (B) rder f C C bnd lengh in cmplexes is VI > V > IV > III > II > I rder f C C bnd srengh in cmplexes is I = II = III = IV = V = VI () rder f C O bnd lengh in cmplexes is I = II = III = IV = V = VI Muliple Crrec Chice Type This secin cnains 4 muliple chice quesins. Each quesin has 4 chices (A), (B), and () fr is answer, u which ONE OR MORE is/are crrec. 8. Which f he fllwing is/are crrec fr he reacin wih equilibrium cnsan K? Kf A g B g C g g ; H 0J Kb (A) K eq will increase n increasing emperaure (B) K f will increase n increasing emperaure K b will increase n increasing emperaure () K b will decrease n increasing emperaure

13 1 9. Which f he fllwing reacin is incrrec regarding he frmain f majr prduc (alkene)? H C Me (A) N + OH CH CH Me CH H C Me (B) H N + OH C CH CH HC Me CH Me N + OH Ph CH CH Ph Me CH Me N + () OH CH CH Cl C Me Cl H 10. Which amng he fllwing saemens is/are crrec? (A) ph f 10-8 M HCl is equal 8 (B) Cnjugae base f H PO is HPO 4 4 ph f 0.1 M NaCl (aqueus sluin) = 1 pk w () Inizain f waer increases wih decrease in emperaure g f Al (amic mass = 7) is depsied a cahde frm Al + sluin by cerain quaniy f charge. The crrec saemen/s is/are: (A) The vlume f H prduced a 0 C and 1 am pressure frm H + ins in sluin by he same quaniy f charge will be 5.6. (B) The vlume f H prduced a 0 C and 1 am pressure frm H + ins in sluin by he same quaniy f charge will be.4. The number f mles f Al depsied will be mles () The number f faraday used fr reducin f 1 mle f Al + is F. 18

14 14 Cmprehensin Type This secin cnains paragraphs. Based upn he firs paragraph muliple chice quesins and based upn he secnd paragraph muliple chice quesins have be answered. Each f hese quesins has fur chices A), B), C) and ) u f WHICH ONLY ONE IS CORRECT. Paragraph fr Quesin Ns. 1 1 On he basis f armaiciy, here are hree ypes f cmpunds i.e. armaic, nn-armaic and aniarmaic. The increasing rder f sabiliy f hese cmpunds are is under: Ani-armaic cmpund nn-armaic cmpund armaic cmpunds. Cmpunds be armaic fllw he fllwing cndiins (accrding valence bnd hery) (i) The cmpunds mus be be cyclic in srucure having (4n + ) e, where n = Hückel s number = 0, 1,, e.c (ii) The each ams f he cyclic srucure mus have unhybridised p-rbial i.e. he ams f he cmpunds have unhybridised p-rbial i.e. usually have sp hybrid r planar. (iii) There mus be a ring curren f elecrns in he ring r cyclic srucure i.e. cyclic srucure mus underg resnance. Cmpunds be ani-armaic, i mus have 4ne where n = 1, and i mus be planar and underg resnance. Nn-armaic cmpunds he name iself spells ha cmpunds mus be nn-planar irrespecive f number f elecrns. Eiher i has 4ne r (4n + ) elecrns i des n maer. The rae f reacin f any armaic cmpunds depends upn he fllwing facrs: (i) Elecrn densiy (ii) sabiliy f carbcain prduced Higher he amun f elecrn densiy f he ring, higher will be is rae wards armaic elecrphilic subsiuin and vice-versa. Similarly, higher will be he sabiliy f he prduced carbcain afer he aack f elecrphile, higher will be is rae wards armaic elecrphilic subsiuin. There is a grea effec f kineic labelling n he rae f armaic elecrphilic subsiuin. As we knwn ha higher he amic weigh r, mlecualr weigh, higher will be he van der Waal s frce f aracin r, bnd energy. Since here will be effec f kieneic labelling if he nd sep f he reacin will be he slw sep, (r.d.s.) herwise here will be n effec f kineic labelling. 1. Which f he fllwing is crrec rder f he rae f reacin f C 6 H 6, C 6 6 and C 6 T 6 wards sulphnain? (A) Same rae f reacins f C 6 H 6, C 6 6 and C 6 T 6 (B) C 6 T 6 C 6 6 C 6 H 6 C 6 H 6 C 6 6 C 6 T 6 () C 6 H 6 C 6 6 = C 6 T 6

15 15 1. Which f he fllwing is he crrec rder f rae f reacin f C 6 H 6, C 6 6 and C 6 T 6 wards nirains? (A) C 6 H 6 C 6 6 C 6 T 6 (B) C 6 H 6 = C 6 6 = C 6 T 6 C 6 H 6 C 6 6 = C 6 T 6 () C 6 T 6 C 6 6 C 6 H 6 Paragraph fr Quesin Ns The Berhle s equain f sae fr 1 mle real gas is given as under: a P (V b) RT TV Where a and b are van der Waal s cnsans. van der Waal s cnsan a signifies, he frce f aracin amng he gas mlecules. van der Waal s cnsan b signifies incmpressible vlume i.e. vlume having n effec f cmpressin and expansin. I is als knwn as c-vlume. Thereby he vlume having effec f cmpressin and expansin i.e. cmpressible vlume = V b (fr 1 mle real gas). One f he frm f van der Waal s equain f sae is virial equain. The virial equain fr 1 mle real gas is as under: A B C PV RT 1 higher pwer f n V V V where A, B, C are knwn as nd, rd and 4 h virial cefficiens respecively. The emperaure a which real gases bey ideal gas equain (PV = RT), is knwn as Byles emperaure i.e. T B. a 14. If T i =, Rb where T i is he inversin emperaure, hen which f he fllwing is he crrec relain f he Byle s emperaure T B bained by he Berhle s equain (A) T i = T B (B) T i = T B T i = T B () T i = T B

16 If he value f a and b increases by 8 imes and imes respecively, hen new Byle s emperaure will increases by hw many imes and wha will be effec n he ease f liquificain? (A) imes, ease f liquificain will increase (B) 4 imes, he ease f liquificain will increase 1 4 () 1 imes, he ease f liquificain will decrease imes, he ease f liquificain will decrease 16. If he hird virial cefficien f 4 mles f mn-amic as is 0.04 (li/ml) a NTP, hen wha will be he real gas a NTP? (A) 88.8 liers (B) 80 liers 89 liers () 90.4 liers SECTION-B (Marix-Mach Type) This secin cnains quesins. Each quesin cnains saemens given in w clumns, which have be mached. The saemens in Clumn I are labelled A, B, C and, while he saemens in Clumn II are labelled p, q, r, s and. Any given saemen in Clumn I can have crrec maching wih ONE OR MORE saemen(s) in Clumn II. The apprpriae bubbles crrespnding he answers hese quesins have be darkened as illusraed in he fllwing example: If he crrec maches are A p, s and ; B q and r; C p and q; and s and ; hen he crrec darkening f bubbles will lk like he fllwing: A B C 1. Mach he fllwing. Clumn I (Carbides) Clumn II (Hydrlysis f cmpund in Clumn I) (A) SiC (p) Resuling gas des n prduce red pp wih ammnical Cu Cl (B) Al4C (q) Unsauraed hydrcarbn is prduced CaC (r) N hydrcarbn prduced () MgC (s) Resuling gas prduce whie pp. wih Tllen s reagen () Sauraed hydrcarbn is prduced

17 17. Mach he sluin given in clumn I wih he prperies given in clumn II. Clumn I Clumn - II (A) 0.1 M Al (SO 4 ) (p) Sluin wih highes being pin (B) 0.1 M AlPO 4 (q) Van Hff facr in greaer han M Urea (r) Sluin wih lwes smic pressure () 0.1 M MgCl (s) Sluin wih lwes freezing pin () Sluin wih lwes biling pin SECTION C Ineger Answer Type This secin cnains 6 quesins. Each quesin, when wrked u will resul in ne ineger frm 0 9 (bh inclusive). 1. The number f bicarbnaes ha d n exis in slid frm amng he fllwing is... LiHCO, NaHCO, Ca HCO,KHCO,NH HCO,Ba HCO,Mg HCO. 4. In Brax (i) Number f B O B bnd is x (ii) Number f B B bnd is y (iii) Number f sp hybridized B am is z Calculae he value f x + y + z. Examine he srucural frmulas f fllwing cmpunds and find u number f cmpunds which shw higher rae f nuclephilic addiin han O C H C H O C CH O C H CHO CHO CHO CHO OCH Cl NO N(CH ) OH C N

18 18 4. Examine he srucural frmuals shwn belw and idenify hw many cmpunds will shw cupling reacin wih diaznium sal faser han anisle CH O OCH OCH OCH NH CHO Cl OCH NO H CO OCH OCH OCH 5. Fr he firs rder reacin 99% x 90% The value f x will be 6. Tal n f mlecules/ins which have nn zer diple mmen is CN HS OH Cl P CN 4 H Cl C C,,, H,, Cl H Cl C C C Cl H,, - I, XeF 4 CN SH OH Cl

19 19 Mahemaics PART III SECTION A Sraigh Objecive Type This secin cnains 7 muliple chice quesins numbered 1 7. Each quesin has 4 chices (A), (B), and (), u f which ONLY ONE is crrec 1. If P be a pin n uni circle wih cenre a pin O. If Q is anher pin inclined a angle OP and OT OQ r, hen he inerval in which r lies, s ha AT PQ, and OA a, ˆ is, (A) 7 1, 6 7 1, 6 (B) , 6 6 () Nne f hese. If a bag cnains five balls. Tw balls are drawn and are fund be whie. Wha is he prbabiliy ha all he balls are whie? (A) 1 4 (B) 1 1 (). If f(x) and g(x) are defined and differeniable fr x x0 and f x g x, f ' x g' x x x, hen (A) f x gx, fr sme x x0 (B) f x gx, fr n x x0 f x gx, fr sme x x0 () f x gx, fr all x x0 4. If z 1 and z are w variable cmplex numbers such ha, z1 169 & z 4i 5. Then he maximum value f z1 z,is (A) (B) 1 5 () 18

20 n 5 5. If S... up n erms & S K,Then, n 1 n (A) 1 K (B) 4 1 K K () 4 5 K 4 6. The perpendicular frm rigin he angen a any pin n a curve is equal he bscissa f he pin f cnac. If he curve passes hrugh pin (1, ), hen i als passes hrugh pin, (A) 1, (B) 1,, (),1 x y 7. Fr an ellipse 1, wih verices A & A, angen drawn a he pin P in he firs quadran 9 4 mees he y axis in Q and he chrd A P mees he y axis in M. If O is he cenre f ellipse, hen OQ MQ is equal, (A) 9 (B) 1 4 () 5 Muliple Crrec Chice Type This secin cnains 4 muliple chice quesins. Each quesin has 4 chices (A), (B), and () fr is answer, u f which ONE OR MORE is/are crrec If f x x x x x x. Then f(x) = 0 has, (A) dd number f real rs (B) Aleas ne r lies beween, 1 Greaes ineger value f a leas ne r = () All rs are negaive 9. Which f he fllwing is/are n rue, f x g x is cninuus a x = a, hen f(x) and g(x) are bh separaely cninuus a (A) if x = a. (B) If f(x).g(x) is cninuus a x = a, hen f(x) and g(x) are separaely cninuus a x = a If f(x). g(x) & f(x) are discninuus a x = a hen g(x) is cninuus a x = a () if bh f(x) and g(x) are discninuus a x = a hen f(x) + g(x) may n be discninuus a x = a

21 1 10. If 1 cs x an dx g x c,hen 1 sinx (A) g(x) represen an equain f parabla, whse cncave side is upward (B) g(x) have pin f exrema a x 4 g(x) represen an equain f parabla, whse cncave side is dwnward () Minimum value f g(x) = 11. If, are he rs f equain, such ha x a 1 x a a (A) a, (B) a, 8 x x a 1 0 and, are he rs f he equain,,,, hen he inerval in which a lies, Cmprehensin Type a,1 () a, This secin cnains paragraphs. Based upn ne f paragraphs muliple chice quesins and based n he her paragraph muliple chice quesins have be answered. Each f hese quesins has fur chices (A), (B), and () u f which ONLY ONE is crrec Cnsider he curves, 1 1 C1 y 4K1x, K 1, C x 4K y, K 1, 4 C x 0 Paragraph fr Quesin Ns Maximum area bunded by all f hese hree curve is, (A) 7 (B) 7 () 1 1. Minimum area bunded by all f hese hree curve is, (A) 7 (B) 7 () 1

22 Paragraph fr Quesin Ns Triangle ABC has circumcenre O and rhcenre H. Pins E and F are chsen n sides AC and AB respecively such ha AE = AO and AF = AH. If R be radius f circle circumscribing he riangle ABC. Then, 14. The area f quadrilaeral BFEC is equal, R (A) sinb sinc 4 R sina R sin A cs B C (B) 8 R sinb sinc () 15. The lengh f segmen EF is equal, (A) Rcs A (B) R RsinA () Rcs A 16. Le AFE, hen sum f squares f hree aliudes f riangle AFE is equal, (A) 9R 4 (B) R R () 8R

23 SECTION-B (Marix-Mach Type) This secin cnains quesins. Each quesin cnains saemens given in w clumns, which have be mached. The saemens in Clumn I are labelled A, B, C and, while he saemens in Clumn II are labelled p, q, r, s and. Any given saemen in Clumn I can have crrec maching wih ONE OR MORE saemen(s) in Clumn II. The apprpriae bubbles crrespnding he answers hese quesins have be darkened as illusraed in he fllwing example: If he crrec maches are A p, s and ; B q and r; C p and q; and s and ; hen he crrec darkening f bubbles will lk like he fllwing: A B C 1. Mach he fllwing: (A) (B) () Clumn I Le 1,,, 4 be eccenric angles f fur cncylic pins f ellipse x y 1, and 1 4 K, hen K can be, a b Nrmals parabla y 4x a P and Q mees a Rx,0, if x 4 and area f circle Circumscribing PQR is K hen K is equal, Le S x y 6x 8y 1 0. Then, max 1x 5y ;x,y s 7 7 In riangle ABC le 0,,E1,0,F 1,0 be he fee f r drpped frm A, B, C ppsie sides, Then square f he sum f rdinaes f pin A, B, and C is Clumn II (p) (q) 9 (r) 4 (s) () 6

24 4. Mach he fllwing: (A) (B) Clumn I The sluin f 1 + secx = c x Is given by x K, hen K is/are If, are rs f equain A x m Amx Cm x 0 hen Clumn II (p) A A C is/are equal (q) () The sum f binmial c efficien in expansin f x nx where m is psiive ineger lies beween 00 and 400 & he erm 5 independen f x equal 448, hen n divisible by If las digi f he number is and las digi f is, hen m (r) 4 (s) 8 () 9 SECTION C (Ineger Answer Type) This secin cnains 6 quesins. Each quesin, when wrked u will resul in ne ineger frm 0 9 (bh inclusive). 1. A line makes an angle f,,, wih he fur diagnals f a cube hen he value f cs cs cs cs is, where. denes he GIF.... Tangens drawn frm any pin P n he curve xy x y 0 inersec he asympes a A & B. Then he area f riangle QAB, is 4K (where Q is cenre f he curve). Then value f K is

25 5. Cnsider a riangle ABC whse sides lengh are AB = 4, BC = & CA =. If he bisecr f he angle C cus AB in and he circumcircle in E, hen he value f CE is (where, [.] E denes he GIF) If f xdx 5 & f K 1 xdx R. Then value f R is.. 0 K If he number f ways in which fur disinc balls can be pu in w idenical bxes s ha n bx remains empy is equal K, hen K =. 6. The value f K fr which he fllwing sysem f equains is cnsisen, K 1 x K y K K 1 x K y K x y 1