Transcription

1 Eedu : Pribh e/elerig This quesio pper ws prepred by seior fculy members of Sri Chiy Educiol siuios JEE-DVNCED MDEL GRND TEST PPER - Time : 3 hrs ] [Number of quesios : 6 PHYSCS SECTN Sigle Correc swer Type This secio cois muliple choice quesios. Ech quesio hs four choices (),, d ou of which NLY NE is correc.. pricle P srs from origi s show d moves log semicirculr ph. oher pricle Q crosses x xis he is pricle P leves he origi. Q moves wih cos speed V prllel o y xis d is ll he ime hvig y co-ordie sme s h of P. Whe P reches dimericlly opposie poi, is verge speed is : () π V Y P Q V πv X V V. f y 5ÉmmsiQ is he equio of oscillio of source S d y 5ÉmmsiÉQ Q/6be h of S d i kes s d / s for he rsverse wves o rech poi from sources S d S respecively he he resulig mpliude poi, is : - - S S () 5 + 3mm 5 3mm 5 mm 5 mm

2 3. The verge d effecive vlues for he wve shpe (posiive hlf cycles of sie curve) show i he figure re : v V m π π 3π (rdi) () Vm V m d Q Vm Q V d m Vm V m d Q Vm V d m Q 4. smooh uel is dug log he rdius of he erh h eds he cere of erh. bll is relesed from he surfce of erh log he uel. f he coefficie of resiuio is. bewee he ed of uel d bll he he ol disce rvelled by he bll before secod collisio he cere of erh is () 6 R 7 R 9 R 3 R Two pricles execue SHM log x-xis bou he origi wih sme mpliude d frequecy ω. ceri is, hey re foud disce /3 from he origi o opposie sides bu heir velociies re i he sme direcio. Wh is he phse differece bewee he wo? [ssume h he pricles do o collide] () cos 7 9 cos 5 9 cos 6. cubicl woode block of side L d relive desiy.5 is floig o he surfce of wer s show i he figure. srig is ched o i hrough idel pulley fixed o he boom of vessel s show i figure. The grph of esio T i he srig vs disce of he boom of he block from he free surfce of he wer whe he ed of he rope is slowly pulled up will be (block is movig very slowly d he vessel is very wider): T 4 T L T T 9 cos T 9 () Z Z Z Z 7. bicycle speedomeer, br mge is ched o he spokes of he wheel d coil is ched o he frme so h he orh pole of he mge moves ps i oce for every roio of he wheel. s he mge moves ps he coil, pulse of curre is iduced i he coil. compuer he mesures he ime bewee cosecuive pulses d compues he bicycle s speed. Figure shows he mge bou o move ps he coil. Which of he grphs bes represes he resulig curre pulse? (Tke couer clockwise curre i figure o be posiive): - -

3 frme Mge (orh pole fcig he viewer) ω Ple of coil is eres o you h h of mge () 8. Cosider hree closed loops drw usig solid lie i he mgeic field (mgeic field lies re drw usig doed lie) of ifiie curre-crryig wire orml o he ple of pper s show. 3 f,b d c represe he vlues of lie iegrls of he mgeic field log he phs, d 3 respecively, he : () > b> c = c> b = b= c c > b> 9. smple of gs is heed by hree differe mehods from sme iiil se s show. ech mehod, he supplied is sme. mehod piso moves up by some mou. mehod piso moves dow d i mehod piso does o move. Specific he of he gs clculed i ech of he mehods o be C,C dcrespecively. f he piso, wlls of vessel re mde of isulors d piso is fricio less, he B () Gs () Gs () Gs fixed Heer Heer Heer () C > C > C C > C > C C > C > C C > C > C - 3 -

4 . dielecric slb of re d hickess d is isered bewee he ples of cpcior of re d disce bewee he ples d, wih cos speed V s show i figure. The cpcior is coeced o bery of emf ε. The curre i he circui vries wih ime s: (Curre hrough he cell i he direcio of emf is posiive) V E () SECTN Muliple Correc swer(s) Type This secio cois 5 muliple choice quesios. Ech quesio hs four choices (),, d ou of which NE or MRE re correc.. deicl dielecric slbs re isered io wo ideicl cpciors d B. These cpcors d chrgeble bery re coeced s show i he figure. Now he slb of cpcior B is pulled ou wih bery remiig coeced: b ()Durig he process, posiive chrge flows from ob Filly, chrge o cpcior B will be less h h o Durig he process, posiive work is doe by he exerl force F, pr of which ppers s he i he circui. Durig he process, ierl eergy of he bery icreses.. The mmeers coeced i he followig circuis hve zero resisce. The volmeer i figure () hs ifiie resisce d shows redig 8V. The vlue of resisce R hs o bee specified. Which of he followig circui (s) hs sme curre i he mmeer? V B V () R V 4Ω V 4Ω 8Ω V Ω - 4 -

5 3. ri movig log es wih cos speed v, boy revolves bob wih srig of legh o smooh surfce of he ri, wih sme cos speed v relive o ri. Mrk he correc opio (s). v v () Mximum speed of he bob is v i groud frme. 4mv Tesio i srig coecig he bob is is. mv Tesio i srig is ll he momes. Miimum speed of bob is zero i groud frme. JG 4. pricle is movig wih cos momeum P log lie MN s show i figure. Lie B is prllel o MN. Mrk he correc semes. B M y 45 () gulr momeum of pricle bou y poi o lie MN is zero. Wih respec o y referece poi o lie B, gulr momeum vecor of he pricle is cos. Wih respec o y referece poi i xy - ple i hird qudr, gulr momeum vecor of he pricle is i posiive z -direcio. Wih respec o y referece poi i xy - ple i hird qudr gulr momeum vecor of he pricle is i egive z -direcio. 5. phooelecric effec experime, if f is he frequecy of rdiio icide o he mel surfce d is he iesiy of he icide rdiios, he mrk he correc seme(s). () f f is icresed keepig d work fucio cos he soppig poeil d mximum kieic eergy of phooelecro icrese. f disce bewee chode d ode is oly chged he soppig poeil remis sme. f is icresed keepig f d work fucio cos he soppig poeil remis sme d surio curre icreses. Work fucio is decresed keepig f d cos he soppig poeil d mximum kieic eergy of phooelecros icrese JG P N x

6 SECTN Muliple Correc swer(s) Type This secio cois 5 muliple choice quesios. Ech quesio hs four choices (),, d ou of which NE or MRE re correc. 6. The pricipl secio of glss prism is isosceles %PQR wih PQ PR. The fce PR is silvered. ry is icide perpediculrly o fce PQ d fer wo reflecios, i emerges from bse QR, orml o i. The gle of he prism is give by π rd. Fid he vlue of. α α 7. blloo is filled wih helium he mospheric pressure P. The volume of he blloo is V. The blloo is mde of he meril of desiy ρ d is mss is m. fer beig relesed, P/. Jus before he blloo burss liude where he mospheric pressure is ( ) bursig, he blloo hs volume of.5v. f he mximum sress h he blloo meril 75 c wihsd is give by P, fid he vlue of k. ssume h he emperure of helium k remis cos, he blloo remis sphericl, hickess of blloo meril is very smll whe compred wih rdius d he desiy of he meril remis virully cos. [Tke 3 3 : V = 8m, ρ= 5kg / m,m = 8kg ] 8. Two uig forks d B ech of url frequecy 85 Hz move wih velociy m/s relive o siory observer. Fork moves wy from he observer while he fork B moves owrds him s show i he figure. wid is blowig wih speed m/s i he direcio of moio of fork. Fid he be frequecy mesured by he observer i Hz. [Tke speed of soud i ir s 34 m/s] B 9. The ierl eergy of mooomic idel gs is.5 RT. e mole of helium is kep i cylider of cross-secio 8.5cm. The cylider is closed by ligh fricioless piso. The gs is heed slowly i process durig which ol of 4 J he is give o he gs. The emperure rises hrough C. The disce moved by he piso is give s ( ) scieific oio. Fid he vlue of α+β. [Tke pressure=kp] β α mi 5 R = i S uis, mospheric 3

7 . Three smll blls of equl mss m re coeced by ligh isulig iexesible hreds of legh ech d kep o level smooh o-coducig groud. The blls d B re give chrge Q ech. The srigs re ll u. The srig coecig d B suddely sps. Wh is he mximum speed (i m/s) of C durig he resulig moio? Q = µ C, =.5m, mss m=g. Q Q m B m C m CHEMSTRY SECTN Sigle Correc swer Type This secio cois muliple choice quesios. Ech quesio hs four choices (),, d ou of which NLY NE is correc.. Which of he isomeric compouds would you expec o hve he lowes boilig poi. () NH NH X dry. Z + Mg eher CH 3 CH. H + 3 deify X d Z i he bove sequece of recio () CH3CHBr d HCH CH3Br d CH CH CH3 CH3Br d CH3CHCH CH3Br d CH3CH FeCl 3. CH 3 CH3 + Cl Cl CH CH3 Which of he followig is key iermedie i he recio show bove.. () CH CH3 CH CH3 Cl CH CH3-7 - Cl N CH CH3 4. pyrose form is cyclic hemicel wih six-membered rig. Which of he followig compouds c o exiss i pyrose form CH CH H CH H H H CH H H H H H H H H H H H H () H H H H H H H H H H H H H H CH H CH H CH H CH H NH

8 5. The equio of se of gs is ( P+ T / V) V C = ( RT + b) where, b, c d R re coss. The isoherms c be represeed by P = V m BV where d B depeds oly o emperure d () m= cd = m= cd = m = cd m = c d = 6. smple of cois oe Fe() for every hree Fe(). The he vlue of x will be () 8/9 9/8 4/3 6/5 7. Liquid udergoes self ioizio o form B + d C wih he equilibrium + B + C for he equilibrium is 3. How my C ios re prese per cc of he liquid (ssumig behves like bse). () he followig sub quesios choose he correc swer from mog he followig possibiliies d selec correc code of your swers (swer of P,Q R d S respecively ): (P) The mos sble low vle hlide () GeX () SX (3) PbX (Q) o exisig hlide () SCl 4 () PbCl 4 (3) Pb4 (R) purely cidic oxide () Pb () S (3) Si (S) Thermlly mos sble hydride () NH 3 () PH 3 (3) sh3 () 3,,,3,3,3, 3,3,3,,,,3 9. ssume h ( ) Fe H + 6 io is high spi complex d he ehlpy of hydrio of Fe + io is -.4kcl/mole which is higher h h expeced i he bsece of crysl field sbilizio eergy he he esimed vlue of for his io is () 734cm 868cm 88.4cm 85cm 3. Give he d 5 C + g + e g ; E =+.8V g + e g + ; E =.5V he he vlue of log K sp for g is () SECTN Muliple Correc swer(s) Type This secio cois 5 muliple choice quesios. Ech quesio hs four choices (),, d ou of which NE or MRE re correc. 3. Which of he followig represes pir of cosiuiol isomers? () d CH3 CH CH CHd CH3 CH CH CH3 Br H Br d H Br Br H H H d

9 3. Some semes re give bou followig compoud ( ) CH3 C CH CH CH3 deify correc semes () gives yellow precipie wih i q NH Soluio does form silver mirror wih Tolles rege e of Hydrolysis producs of give compoud gives red precipie wih Beedics soluio Boh, he give compoud d is oe of hydrolysis producs gives posiive es wih, 4 DNP 33. Which is icorrecly mched for refiig of mels? () Si, Ge from impuriies zoe refiig mehod Copper refied from is meloxide cupellio mehod l from impuriies Hoop s mehod Z, Cd from impuriies wih high boilig poi liquio 34. he queous soluio of sops bove CMC : () he cios ssocie o form he ggreges d o direced owrds wer. he ios ssocie o form he clusers of colloidl dimesio he polr eds of he ios formig he clusers re direced owrds wer he o-polr (hydrocrbo) eds re direced owrds wer 35. Which of he followig recios give he sme iroge coiig gseous produc? () Heig of NH4N By pssig NH 3 over heed Cu Heig of B( N3 ) Cu cold d dilue HN3 SECTN eger swer Type This secio cois 5 quesios. The swer o ech quesio is sigle digi ieger, rgig from o 9 (boh iclusive). 36. The ehlpy of mooomic gs 7 C is 3yclorie he he vlue of y is 37. How my of he followig would be expeced o give posiive es wih Beedic s rege? D-Glcose D-Frucose Sucrose D-ribose Lcose Glucoic cid Mlose 38. Number of chlorie oms prese i molecule of orgic produc of followig recio Cl + CCl3 C H HS4 Chlorobezee Trichloroceldehyde - 9 -

10 39. The o of he possible orbils (upo = 3) which fulfill ll he followig codiios Cse hvig oly oe rdil ode Cse hvig XY ple s gulr ode Cse hvig oly wo mxim if curve is ploed bewee rdil disribuio fucio vs rdil disce 4. ceri recio B + is geig covered o ( 4 B + ) + i soluio. The re cos of his recio is mesured by irig kow volume of he soluio wih reducig ge which recs oly wih B + d B ( + 4)+. his process i covers + ( - ) + ( + 4) + ( B o B d B o B ) +., =, he volume of rege cosumed is 5 ml d = miue, he volume used is 3 ml. f he re cos for he coversio of ( 4 B + of B + ) + is x mi, he he vlue of x is (Ner by eger) MTHEMTCS SECTN Sigle Correc swer Type This secio cois muliple choice quesios. Ech quesio hs four choices (),, d ou of which NLY NE is correc. 4. f r = ( + )( + )( + 3) 8 he = r= r= r 4. () ( + ) ( + )( + 3) ( + ) ( + )( + 3) 3 p rπ rπ (3p+ ) si icos p= r= = ( + ) ( + )( + ) ( + 3) ( + )( + ) () 48i 6( i) 48( i) 6( i ) + x = C + Cx+ Cx C x he i< j 43. f ( ) c () ( ) ( ) + ( ) + c c c ( ) ( Ci Cj) + = 44. f wo smll squres of seleced rdom from chess bord he he probbiliy h hey hve excly oe commo verex is ()

11 45. r 3 8 lim = 3 r = 3 r + 8 () The lrges erm of he sequece = 3 is + () The rge of vlues of α for which he lie y = gx+ α is orml o he circle x + y + gx+ gy = for rel vlues of g is () [, ) [, ) (,) (,] 48. ( x )( y ) = 5 d ( x ) + ( y+ ) = r iersec i he pois,b,c,d d he ceroid of he rigle BC lies o he lie y = 3x 4. The he locus of D is () y = 3x x + y + 3x+ = 3y = x+ y = 3x+ 49. The posiio vecors of he poi,b,c re respecively iˆ ˆj 3, kˆ iˆ+ ˆj kˆ d 5iˆ+ ˆj 6kˆ. f he ierl gulr bisecor of i BC mee BC D he he legh of D is () The umber of roos of he equio cos 7 x+ si 4 x= ππ, is () 4 3 SECTN Muliple Correc swer(s) Type i he iervl ( ) This secio cois 5 muliple choice quesios. Ech quesio hs four choices (),, d ou of which NE or MRE re correc. 5. dx = ( + x ) + x x () cos + x x 5( x + ) + C + x x + + C 3 si x + C 5( x + ) + 3 si x + + C 5( x + ) - -

12 5. The ge poi P o curve mees X-xis i. f he re of he rigle P ( is origi) is () ( cos), he he equio of he curve is x= cy+ y y = cx+ x x= cy y = cx y 53. f he roos of he equio x x b= (, b R) hve bsolue vlue less h, he () b < + b< b < + b= x 54. Le,B,C be squre mrices of sme order d is he ui mrix of sme order such h + B + C = B + BC + C. Cosider he followig semes (i) BC = C C (ii) BC = B B (iii) CB = CB BC () (i) d (ii) re equivle (ii) d (iii) re equivle (i) d (iii) re equivle (i), (ii) d (iii) re equivle 55. Which of he followig seme is / re correc x 3 ()The umber of soluios of equiot T π x + = x 3 belogig o 4 he iervl (,) is T T T T π π f x d θ = si x+ cos x x, he θ 4 The vlue of 4 7 Si π π si Cos + cos 3 6 is π o erms is π T 4 + SECTN Muliple Correc swer(s) Type This secio cois 5 muliple choice quesios. Ech quesio hs four choices (),, d ou of which NE or MRE re correc. 56. The leer of he word MTHER re rrged i ll possible wys d he resulig words re rrged s i DCTNRY. f he rk of he word is K, he he umber of posiive iegrl divisors of K is 57. he rigle BC, pois K d L re ke o he segmes B d BC such h K : KB = : d BL : LC = :. Le P be he poi of iersecio of he lies Ld CK. f he re of BCP is squre uis he wice he re of rigle BC is - -

13 58. π x(+ si x) f = dx, cos he he iegrl pr of is π + x 59. x y f he ge o he ellipse + = b he poi ( cos θ, bsiθ ) mees he uxiliry circle i wo pois,b such h he chord B subeds righ gle he cere, he he eccericiy of he ellipse is α βsi where + θ ( α + β) = B c b 6. rigle BC, = he + B c = *** - 3 -