JEE ADVANCED EXAMINATION 2014 QUESTIONS WITH SOLUTIONS PAPER - 2 [CODE - 4]

Transcription

1 JEE ADVANCED EXAMINATION 4 QUESTIONS WITH SOLUTIONS PAPER - [CODE - 4] 94,5 - Rajeev Gandhi Nagar Koa, Ph. No. : , IVRS No : , 5, 5, www. moioniijee.com, info@moioniijee.com

2 IIT-JEE 4 Soluions by Moion Edu. Pv. Ld. Koa PHYSICS. A meal surface is illuminaed by ligh of wo differen wavelenghs 48 nm and nm. The maimum speeds of he phooelecrons corresponding o hese wavelenghs are u and u, respecively. If he raio u : u : and and hc 4 ev nm, he work funcion of he meal is nearly (A).7 ev (B). ev (C).8 ev (D).5 ev A 4 E 5eV 48 A 9 R [T 4 () 4 ] 4 R 8 () T 4 T K 4. During an eperimen wih a mere bridge, he galvanomeer shows a null poin when he jockey is pressed a 4. cm using a sandard resisance of 9, as shown in he figure. The leas coun of he scale used in he mere bridge is mm. The unknown resisance is 4 E 4eV 5 + 4k...() 4 + k...() On solving.66.7 ev. If Cu is he wavelengh of K X-ray line of copper (aomic number 9) and M is he wavelengh iof he K X-ray line of molybdenum (aomic number 4), hen he raio Cu / Mo is close o (A).99 (B).4 (C).5 (D).48 B By Mosley s Law : f a (z ) As v f f c Inverse relaion and hence : (Z ) (A) 6.5 (B) 5.56 (C) 6.5 (D) 5. C R R 9 n R n 9 + n + n dr d R + d dr dr R (6 ±.5) Page Z Z (4 ) (4 ).4. Parallel rays of ligh of inensiy I9 Wm - are inciden on a spherical black body kep in surroundings of emperaure K. Take Sefan- Bolzmann consan Wm - K -4 and assume ha he energy echange wih he surroundings is only hrough radiaion. The final seady sae emepraure of he black body is close o (A) K (B) 66 K (C) 99 K (D) 55 K 5. A plane of radius R (radius of Earh) has he same mass densiy as Earh. Scieniss dig a well of deph R on i and lower a wire of he same 5 lengh and of linear mass densiy - kgm - ino i. If he wire is no ouching anywhere, he force applied a he op of he wire by a person holding i in place is (ake he radius oif Earh6 6 m and he acceleraion dur o graviy on Earh is ms - ) (A) 96 N (B) 8 N (C) N (D) 5 N Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

3 B D R Re df 9.d. Re / R e R e 5 5 R e A wire, which passes hrough he hole in a small bead, is ben in he form of quarer of a circle. The wire is fied verically on ground as shown in he figure. The bead is released from near he op of he wire and i slides along he wire wihou fricion. As he bead moves from A o B, he force i applies on he wire is h T cos ( + /) h s bg cos ( + /) 8. Charges Q, Q and 4Q are uniformly disribued in hree dielecric solid spheres, and of radii R/, R and R respecively, as shown in figure. If magniudes of he elecric fields a poin P a a disance R from he cenre of spheres, and are E, E and E respecively, he (A) always radially ouwards. (B) always radially inwards. (C) radially ouwards iniially and radially in wards laer. (D) radially inwards inially and radially ou wards laer. D By heory 7. A glass capillary ube is of he shape of a runcaed cone wih an ape angle so ha is wo ends have cross secions of differen radii. when dipped in waer verically, waer rises in i o a heigh h, where he radius of is cross secion is b. If he surface ension of waer is S, is densiy is, and is conac angle wih glass is, he value of h will be (g is he acceleraion due o graviy) (A) E >E >E (B) E >E >E (C) E >E >E (D) E >E >E C KQ KQ E E R R 4KQ.R KQ E (R) E R > E > E 9. A ennis ball is dropped on a horizonal smooh surface. I bounces back o is original posiion afer hiing he surface. The force on he ball during he collision is proporional o he lengh of compression of he ball. Which one of he following skeches describes he variaion of is kineic energy K wih ime mos appropriaely? The figures are only illusraive and no o he scale. (A) (B) s cos bg (A) s cos bg (B) s cos / bg (C) s cos / bg (D) (C) (D) : , Toll Free 8799 url : :info@moioniijee.com Page

4 B V g KE m (g) Relaion is parabolic C ia oi h / a h a cos. A poin source S is placed a he boom of a ransparen block of heigh mm and refracive inde.7. I is immersed in a lower refracive inde liquid as swhon in he figure. I is found ha he ligh emerging from he block o he liquid forms a circular brigh spo of diameer.54 mm on he op of he block. The refracive inde of he liquid is a i a h cos / a h a h a / a h (A). (B). (C).6 (D).4 C sin C Also sin C n n.7 M.7 Paragraph & The figure shows a circular loop of radius a wih wo long parallel wires (numbered and ) all in he plane of he paper. The disance of each wire from he cenre of he loop is d. The loop and he wires are carrying he same curren I. The curren in he loop is in he counerclockwise direcion if seen from above. a 4 a h a.4a +.4h.6a.4h h a h. a. consider d>>a, and he loop is roaed abou is diameer parallel o he wires by from he posiion shown inhe figure. If he currens in he wires are in he opposie direcions, he orque on he loop a is new posiion will be (assume ha he ne field due o he wires is consan over he loop) (A) (C) B l a d l a d (B) (D) l a d l a d. When d a bu wires are no ouching he loop, i is found ha he ne magneic field on he ais of he loop is zero a a heigh h above he loop. In ha case (A) curren in wire and wire is he direcion PQ MB sin and RS, respecively and h a (B) curren in wire and wire is he direcion PQ ia oi sin and SR, respecive and d h a (C) curren in wire and wire is he direcion PQ and SR, respecively and h.a oi a oi a (D) curren in wire and wire is he direcion PQ d d and RS, respecively and h.a Page 4 Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

5 Paragraph & 4 In he figure a conainner is shown o have a movalble (wihou fricion) pison on op. The conainer and he pison are all made of perfecly insulaing maerial allowing no hea ransfer beween ouside and inside he conainer. The conainer is divided ino wo comparmens by a rigid pariion made of a hermally conducing maerial ha allows slow ransfer of hea. The lower comparmen of he conainer is filled wih moles of an ideal monaomic gas a 7 K and he upper comparmen is filled wih moles of an ideal diaomic gas a 4 K. The hea capaciies per mole of an ideal monaomic gas 5 are CV R,CP R, and hose for an ideal diaomis 5 7 gas are CV R,CP R.. Consider he pariion o be rigidly fied so ha i does no move. When equilibrium is achieved, he final emperaure o he gases will be (A) 55 K (C) 5 K D R (7 T) (B) 55 K (D) 49 K Paragraph 5 & 6 A spray gun is shown in he figure where a pison pushes air ou of a nozzle. A hin ube of uniform cross secion is conneced o he nozzle. The oher end of he ube is in a small liquid conainer. As he pison pushes air hrough he nozzle, he liquid from he conainwer rises ino he nozzle and is sdprayed ou. For he spray gun shown, he radii of he pison and he nozzle are mm and mm respecively. The upper end of he conainer is open o he amosphere. 5. If he pison is pushed a a speed of 5 mms -, he air comes ou of he nozzle wih a speed of (A). ms - (B) ms - (C) ms - (D) 8 ms - C From equaion of coninuiy A V A V () 5 () v v 4 5 mm/s m/s 6. If he densiy of air is a and ha of he liquid l, hen for a given pison speed he rae (volume per uni ime) a which he liquid is sprayed will be proporional o (A) (C) A a l l a (B) a l (D) l R (T 4) + 5 R (T 4) T 49 K 4. Now consider he pariion o be free o move wihou fricion so ha he pressure of gases in boh comparmens is he same. Then oal work done by he gases ill he ime hey achieve equilibrium will be (A) 5 R (C) R D Q Q (B) R (D) - R 5 R (7 T) 7 R (T 4) T 55 K W.D. by lower gas R 75 5 R W.D. upper gas R 5 5 R ne W.D. R Pressure a poin in nozzle P P P a V...() P P l V l gh...() equaion () and () a V l V + l gh Neglecing he erm r e gh V a l V Rae of liquid flow AV AV a l Rae of liquid flow a l : , Toll Free 8799 url : :info@moioniijee.com Page 5

6 7. A person in a lif is holding a waer jar, which has a small hole a he lower end of is side. When he lif is a res, he waer je coming ou of he hole his he floor of he lif a a disance d of. m from he person. In he following, sae of he lif s moion is given in lis I and he disance where he waer je his he floor of he lif is given in Lis II. Mach he saemens from Lis I wih hose is Lis II and selec he correc answer using he code given belsow he liss. Lis I Lis II P. Lif is acceleraion verically up.. d. m Q. Lif is acceleraing verically. d>. m wih an acceleraion less han he graviaional acceleraion. R. Lif is moving verically up wih. d <. m consan speed. S. Lif is falling freely. 4. No waer leaks ou of he jar Code : (A) P-, Q-, R-, S-4 (B) P-, Q-, R-, S-4 (C) P-, Q-, R-, S-4 (D) P-, Q-, R-, S- C Lis I Lis II P. Q, Q, Q, Q 4 all posiive. + Q. Q, Q posiive; Q, Q 4 negaive. - R. Q, Q 4 posiive; Q, Q negaive. +y S. Q, Q posiive; Q, Q 4 negaive 4. -y Code : (A) P-, Q-, R-4, S- (B) P-4, Q-, R-, S- (C) P-, Q-, R-, S-4 (D) P-4, Q-, R-, S- A (P) All +ve (Q) Q, Q +ve Q, Q 4 ve d v gh h h which is independen g of g. Bu when he lif falls freely no waer leaks ou of he jar as g eff. 8. For charges Q, Q, Q and Q 4 of same magniude are fied along he ais a -a, -a, +a and +a, respecively. A posiive charge q is placed on he posiive y ais a a disance b >. Four poions of he signs of hese charges are given in Lis I. The direcion of he forces on he charge q is given in Lis II. Mach Lis I wih Lis II and selec he correc answer using he code given below he liss. (R) Q, Q ve Q, Q ve (S) Q, Q +ve Q, Q 4 ve Page 6 Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

7 9. Four combinaions of wo hin lenses are given in Lis I. The radius of curvaure of all curved surface is r and he refracive inde of all he lenses is.5. Mach lens combinaions in Lis I wih heir focal lengh in Lis II and selec he correc answer using he code given below he liss. Lis I Lis II P.. r f eq r r f eq -r f r r r Q.. r/ R.. -r S. 4. r Code : (A) P-, Q-, R-, S-4 (B) P-, Q-4, R-, S- (C) P-4, Q-, R-, S- (D) P-, Q-, R-, S-4 D f r r f r r f eq r eq P - Q - 4 R - S -. A block of mass m kg anoher mass m kg are placed ogeher (see figure) on an inclined plane wih angle of inclinaion. Various values of are given in lis I. The coefficien of saic and dinamic fricion beween he block m and he plane are equal o.. In Lis II epressions for he fricion on block m are given. Mach he correc epression of he fricion in Lis II wih he angles given in Lis I, and choose he correc opion. The acceleraion due o graviy is denoed by g. L f m R f r r R f r f r f r f eq f eq r f f f r f r r eq f r f r f r eq r f eq Lis I Lis II P. 5. m g sin Q.. (m +m ) g sin R. 5. m g cos S. 4. (m +m ) g cos q Code : (A) P-, Q-, R-, S- (B) P-, Q-, R-, S- (C) P-, Q-, R-, S-4 (D) P-, Q-, R-, S- D There will be no slipping if fricion balances he ne force acing downwards along he incline f s ma m g cos Force in he downward direcion is (m + m ) g sin h us an gl e a wh ich slipping sars (m + m ) g sin m g cos. an. given an.5. Thus.5 Thus for angles less han.5 here won be any slipping hence fricion is saic and equal o (M + M ) g sin for greaer han.5 he fricion is dynamic and is equal o m g cos. : , Toll Free 8799 url : :info@moioniijee.com Page 7

8 CHEMISTRY. For he idenificaion of -naphhol using dye es, i is necessary o use (A) dichloromehane soluion of -naphol (B) acidic soluion of -naphhol (C) neural soluion of -naphhol (D) alkaline soluion of -naphhol D The correc order of heir boiling poin is : (A) I > II > III (B) III > II > I (C) II > III > I (D) III > I > II B Boiling poin surface area branching 5. Assuming s-p miing is NOT operaive, he paramagneic species among he following is: (A) Be (B) B (C) C (D) N (C) if s-p miing is no allowed hen MOD will be like O. s * s s *s p p y p z * p y * p z *p.. For he elemenary reacion M N, he rae of disappearance of M increases by a facor of 8 upon doubling he concenraion of M. The order of he reacion wih respec o M is : (A) 4 (B) (C) (D) (B) r K [M] 8r K [M] 6. The produc formed in he reacion of SOCl wih whie phosphorous is : (A) PCl (B) SO Cl (D) SCl (D) POCl (A) P 4 + SOCl PCl + SO + S Cl whie 7. The major produc in he following reacion is. For he process H O (l) H O (g) a TºC and aomsphere pressure, he correc choice is : (A) S sysem > and S surroundings > (B) S sysem > and S surroundings < (C) S sysem < and S surroundings > (D) S sysem > and S surroundings < (B) H O (l) + Hea H O (g) S sysem > & S surroundings < (A) (B) (C) D (D) 4. Isomers of heane, based on heir branching, can be divided ino hree disinc classes as shown in he figure. (I) (II) (III) Page 8 Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

9 8. Hydrogen peroide in is reacion wih KlO 4 and NH OH respecively, is acing as a (A) reducing agen, oidising agen (B) reducing agen, reducing agen (C) oidising agen, oidising agen (D) oidising agen, reducing agen Ans. (A) 9. The acidic hydrolysis of eher (X), shown below is fases when Paragraph For Quesion and X and Y are wo volaile liquids wih molar weighs of g mol and 4g mol respecively. Two coon plugs, one soaked in X and he oher soaked in Y, are simulaneously placed a he ends of a ube of lengh L 4cm, as shown in he figure. The ube is filled wih an iner gas a amosphere pressure and a emperaure of k. Vapurs of X and Y reac o form a produc which is firs observed a a disance d cm from he plug soaked in X. Take X and Y o have equal molecular diameers and assume ideal behaviour for he iner gas and he wo vapous. (A) one phenyl group is replaced by a mehyl group. (B) one phenyl group is replaced by a paramehoyphenyl group (C) wo phenyl groups are replaced by wo para-mehoyphenyl groups (D) no srucural change is made o X Ans. C Rae of SN reacion sabiliy of carbocaion. If wo phenyl group is replaced by wo p- mehoy phenyl group hen i gives mos sable carbocaion so fases reacion.. Under ambien condiions, he oal number of gases released as producs in he final sep of he reacion scheme shown below is Ans. XeF 6 Complee Hydrolysis P Q Producs + oher produc - OH /HO (A) (B) (C) (D) (C) XeF 6 + H O - slow disproporionaion in OH /HO Complee XeO Hydrolysis + HF XeO + OH (basic medium) HXeO 4 HXeO 4 + OH Slow 4 XeO Disproporionaion 6 + Xe + O + H O. The value of d in cm (shown in he figure), as esimaed from Graham's law, is (A) 8 (B) (C) 6 (D) (C) Coon wool soaked in X rae rae y d d y d L 4 cm MM MM y / / Iniial formaion of he produc MM MM d 4 4 d d 48 d d 6 y Coon wool soaked in Y. The eperimenal value of d is found o be smaller han he esimae obained using Graham's law. This is due o (A) larger mean free pah for X as compared o ha of Y. (B) larger mean free pah for Y as compared o ha of X. (C) increased collision frequency of Y wih he iner gas as compared o ha of X wih he iner gas. (D) increased collision frequency of X wih he iner gas as compared o ha of Y wih he iner gas. (B, D) : , Toll Free 8799 url : :info@moioniijee.com Page 9

10 Paragraph For Quesions and 4 Schemes and describe sequenial ransformaion of alkynes M and N. Consider only he major producs formed in each sep for boh he schemes. C. The produc X is (A) (B) (C) I gives + Ve iodoform es and i is funcional isomer if X. Paragraph For Quesions 5 and 6 An aqueous soluion of meal ion M reacs separaely wih reagens Q and R in ecess o give erahedral and square planar complees, respecively. An aqueous soluion of anoher meal ion M always forms erahedral complees wih hese reagens. Aqueous soluion of M on reacion wih reagen S gives whie precipiae which dissolves in ecess of S. The reacions are summarized in he scheme given below: SCHEME: (D) Terahedral Q R M ecess ecess Square planar A HO CH CH CCH NaNH HO CH CH CH C Na + CH CH I HO CH CH CC CH CH CH I CH O CH CH CC CH CH H /Lindlar's caals 4. The correc saemen wih respec o produc Y is (A) I gives a posiive Tollens es and is a funcional isomer of X. (B) I gives a posiive Tollens es and is a geomerical isomer of X. (C) I gives a posiive iodoform es and is a funcional isomer of X. (D) I gives a posiive iodoform es and is a geomerical isomer of X. Terahedral Q R M ecess ecess Terahedral S, soichiomeric amoun S Whie precipiae Whie precipiae ecess 5. M, Q and R, respecively are (A) Zn +, kcn and HCl (B) Ni +, HCl and KCN (C) Cd +, KCN and HCl (D) Co +, HCl and KCN Ans. (B) M Ni + KCN [Ni(CN) 4 ] dsp sq. planar Ni + HCl [NiCl 4 ] sp (erahedral) Page Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

11 M + Zn + KCN + Zn + HCl [Zn(CN) 4 ] (Terahedral sp ) + [Zn(Cl 4] + H (Terahedral sp ) Zn + + KOH Zn(OH) OH (whie pp.) [Zn(OH) 4 ] (color less soluion) 6. Reagen S is (A) K 4 [Fe(CN) 6 ] (B) Na HPO 4 (C) K CrO 4 (D) KOH Ans. (D) 7. Mach each coordinaion compound in Lis-I wih an appropriae pair of characerisics from Lis-II and selec he correc answer using he code given below he liss. {en H NCH CH NH ; aomic numbers : Ti, Cr 4, Co 7; P 78} Lis-I (P) [Cr(NH ) 4 Cl ]Cl (Q)[Ti(H O) 5 Cl (NO ) ] (R) [P(en)(NH )Cl]NO ] (S) [Co(NH ) 4 (NO ) ]NO Ans. Lis-II () Paramagneic and ehibis ionisaion isomerism () Diamagneic and ehibis cis-rans isomerism () Paramagneic and ehibis cis-rans isomerism (4) Diamagneic and ehibis ionisaion isomerism P Q R S (A) 4 (B) 4 (C) 4 (D) 4 B 8. Mach he orbial overlap figure shown in Lis- I wih he descripion given in Lis-II and selec he correc answer using he code given below he liss. Lis-I (S) Lis-II () p d anibonding () d d bonding () p d bonding (4) d d anibonding P Q R S (A) 4 (B) 4 (C) 4 (D) 4 Ans. C 9. Differen possible hermal decomposiion pahways for perosysers are shown below. mach each opahway form Lis wih an appropriae srucure from Lis II and selec he correc answer using he code given below he liss. Lis-I (P) Pahway P (Q) Pahway Q (R) Pahway R (S) Pahway S Lis-II () () (P) () (Q) (R) (4) : , Toll Free 8799 url : :info@moioniijee.com Page

12 Code : P Q R S (A) 4 (B) 4 (C) 4 (D) 4 A Compound (I) follow he pahway (P) and form formaldehyde as carbonyl. I remove CO in I sep Compound (II) follow he pahway (S) and form formaldehyde as carbonyl. I remove CO in II sep Compound (III) follow he pahway (Q) and does no form carbonyl. I remove CO in I sep Compound (IV) follow he pahway (R) and does no form carbonyl. I remove CO in II sep 4. Mach he four saring maerials (P, Q, R, S) given in Lis I wih he corresponding reacion schemes (I, II, III, IV) provided in Lis-II and selec he correc answer using he code given below he liss. Lis-I (P) (Q) \ Lis-II. Scheme I (i) KMnO 4, HO, hea (ii) H +, H O (iii) SoCl (iv) NH. Scheme II (i) Sn/HCl (ii) CH COCl (iii) Conc. H SO 4 (iv) HNO (v) dil. H SO 4, hea (vi) HO. Scheme III (i) red ho iron, 87 K (ii) fuming HNO, H SO 4 hea (iii) H S. NH (iv) NaNO, H SO 4 (v) hydrolysis 4. Scheme IV (i) conc. H SO 4, 6ºC (ii) conc. HNO, conc. H SO 4 (iii)dil. H SO 4, hea Code : P Q R S (A) 4 (B) 4 (C) 4 (D) 4 C (P) Aceylene Benzene Dinirobenzene m-niro aniline m-niro benzene diazonium ion (R) (Q) m-niro phenol (C 6 H 5 NO ) (S) Page Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

13 (R) (S) : , Toll Free 8799 url : :info@moioniijee.com Page

14 MATHEMATICS SECTION A Single Correc 4. In a riangle he sum of wo sides is and he produc of he same wo sides is y. If c y, where c is he hird side of he riangle, hen he raio of he in-radius o he circum-radius of he riangle is (A) (C) y ( c) y 4( c) B a + b, ab y (a + b) c ab cos C C also C Now y c (B) (D) r (s c) an6 R c sin y ( c) c y c( c) y 4c( c) (s c) c 4. The common angens o he circle + y and he parabola y 8 ouch he circle a he poins P, Q and he parabola a he poins R, S. Then he area of he quadrilaeral PQRS is (A) (B) 6 (C) 9 (D) 5 D a a a R, a, S, m m m m y m + m P R m 4 + m (m ) (m + ) m ± R(, 4) & S(, 4) P(, ) Q(, ) Area (PQ + RS) AB ( + 8) 4. The quadraic equaion p() wih real coefficiens has purely imaginary roos. Then he equaion p(p()) has (A) only purely imaginary roos (B) all real roos (C) wo real and wo purely imaginary roos (D) neiher real nor purely imaginary roos A p(p()) p() purely imaginary roos No real value of will saisfy For real, LHS is purely real 44. Si cards and si envelopes are numbered,,, 4, 5, 6 and cards are o be placed in envelopes so ha each envelope conains eacly one card and no card is placed in he envelope bearing he same number and moreover he card numbered is always placed in envelope numbered. Then he number of ways i can be done is (A) 64 (B) 65 (C) 5 (D) 67 C Required ways 6!!! 4! 5! 6! Three boys and wo girls sand in a queue. The probabiliy, ha he number of boys ahead of every girl is a leas one more han he number of girls ahead of her, is Page 4 m m 4 m (m ) A Q S B (A) (C) (B) (D) 4 A BGBGB BGBBG BBGGB BBGBG BBBGG Probabiliy 5(!!) 5! Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

15 46. Le f : [, ] R be a funcion which is coninuous on [, ] and is differeniable on (, ) wih f(). Le F() f( ) d for [, ]. If F'() f'() for all (, ), hen F() equals (A) e (B) e 4 (C) e (D) e 4 B F() f( differeniaing f'() f(). f'() f() ) d n f() + k f() k f() e F() e d d I.F. e I.F. e ln ( ) y 4 5 y y y 5 y d / 5 / d + 5 d / 5 / 5 / 5 5 d F() [ e ] F() Lim (e ) e 4 / d 47. The funcion y f() is he soluion of he differenial equaion dy d + y in (, ) saisfying f(). Then is 4 f() d / ( ) d / / ( ) d / sin d (A) (C) 6 4 B (B) 4 (D) dy d 4 y 4 : , Toll Free 8799 url : :info@moioniijee.com Page 5

16 48. For (, ), he equaion sin + sin sin has (A) infiniely many soluions (B) hree soluions (C) one soluion (D) no soluion D sin + 4 sin cos sin + 4 sin 4 sin (cos + cos ) sin cos + (cosec ) 4 Hence No soluion 49. The following inegral 7 ( cos ec ) d is equal o (A) log( ) u u 6 4 (e e ) du (B) log( ) u u 7 (e e ) du (C) log( ) u u 7 (e e ) du (D) log( ) u u 6 A co e u co e u e d e u u (e e ) du du an cosec an I e u ln ( ) log ( ) e u e u e u 7 u u 6. (e e ) du e e u u u e du u e 5. Coefficien of in he epansion of ( + ) 4 ( + ) 7 ( + 4 ) is (A) 5 (B) 6 (C) (D) C Given epression is ( ). ( + 7 C + 7 C C ). ( + C 4 + C ) Coefficien of. 7 C. C C C. C +. 7 C Paragraph Paragraph for Quesion Nos. 5 o 5 Bo conains hree cards bearing numbers,, ; bo conains five cards bearing number,,, 4, 5; and bo conains seven cards bearing numbers,,, 4, 5, 6, 7. A card is drawn from each of he boes. Le i be he number on he card drawn from he i h bo, i,,. 5. The probabiliy ha + + are in an arihmeic progression, is (A) 9 5 (C) 57 5 B,, Bo (),,, 4, 5, 6, 7 Bo () (B) 5 5 (D),,, 4, 5, Bo () A card is drawn from each Bo OOO + OEE + EOE + EEO The probabiliy ha,, are in an arihmeic progression, is (A) 9 5 (C) 5 (B) 5 (D) 7 5 C The only cases are,, 5, 47,, 4, 46,,, 45, 57 Required Probabiliy Page 6 Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

17 Paragraph for Quesion Nos. 5 o 54 Le a, r, s, be nonzero real number. Le P(a, a), Q(ar, ar) and S(as, as) be disinc poins on he parabola y 4a. Suppose ha PQ is he focal chord and lines QR and PK are parallel, where K is he poin (a, ). 5. The value of r is (A) (B) 54. If s, hen he angen a P and he normal a S o he parabola mee a a poin whose ordinae is (A) (C) C ( ) a( ) (B) (D) a( ) a( ) (C) (D) Tangen a P is y + a...() Normal a S is y s + as + as D Now s so s R(ar,ar) P(a,a) k(a,) F(a,) we ge a a y + + Adding () & () a a y a () a, Q a S(as, as) a 4 a a a( 4 ) m QR, m PK r a a a a( ) Paragraph for Quesion Nos. 55 o 56 Given ha for each a (, ), r r r r Lim h h h a ( ) a d eiss. Le his limi be g(a). In addiion, i is given ha he funcion g(a) is differeniable on (, ). 55. The value of g is (A) (C) A (B) (D) 4 r g(a) Lim h h a h ( ) a d g(/) Lim h h / h ( ) / d : , Toll Free 8799 url : :info@moioniijee.com Page 7

18 Lim h h h d ( ) d ( ) sin d sin cos d / / sin cos d d sin cos / Mari Mach Type Maching Lis Type (Only One Opion Correc) 57. Lis I Lis II (P) The number of polynomials. 8 f() wih non-negaive ineger coefficiens of degree, saisfying f() and f() d, is (Q) The number of poins in. he inerval [, ] a which f() sin( ) + cos( ) aains is maimum value is 56. The value of g' is (R) ( e ) d equals. 4 (A) (C) D g(a) g'(a) g'(/) Lim h h h a (B) (D) ( ) a ( ) d a a d a (.ln ( ) a + a ( ) a n ( )) d / (.ln ( ) / + / ( ) / n ( )) d (S) (P) + cos log d equal 4. cos log d P Q R S (A) 4 (B) 4 (C) 4 (D) 4 D f() a + b a b a b / ( ) / ( ln + ln ( ))d...() / g'(/) ( ) / ( ln ( )+ln ) d Adding () and () g'(/)...() a b a b b a N b a a b Page 8 Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

19 a b a b (Q) [, ] : f() sin + cos 4, 4 9 ± (R) I 9, ± 4 4 e e e I d I P Q R S (A) 4 (B) 4 (C) 4 (D) 4 A (P) y sin(cos ) y' sin( cos ) y" cos( cos y ' 9 ) (S) I 8 numeraor is odd funcion 58. Lis I Lis II (P) Le y() cos(cos ),. [,], ±. d y() dy() Then ( ) y() d d equal (Q) Le A, A,..., A n (n > ). be he verices of a regular polygon of n sides wih is cenre a he origin. Le a be he posiion vecor k of he poin A k, k,,...,n. n If k a k a k n k a k a k, hen he minimum value of n is (R) If he normal from he. 8 poin P(h, ) on he ellipse 6 + y is perpendicular o he line + y 8, hen he value of h is (S) Number of posiive 4. 9 soluions saisfying he equaion an + an 4 an is (Q) ( )y " y ' 9y ( ) y" + y' 9y a n a O a 5 A n a a A 5 A 4 A A n n (a a ) (a a ) k k k k k k (n ) a k a k sin n (n ) a k a k cos n an n n 4 n 8 : , Toll Free 8799 url : :info@moioniijee.com Page 9

20 (R) y + 8 slope of Normal + dy d 6y an an 4 8 an an 5 5 Normal (h, ) slope a (h, ) is h 6 h 4 (S) an (4 ) ( ) + ( ), an an an an an Le f : R R, f : [, ) R, f : R R and f 4 : R [, ) be defined by if < f () e if f () ; f (f ()) if < f () f (f ()) if (P) f 4 is. ono bu no one-one (Q) f is. neiher coninuous nor one-one (R) f of is. differeniable bu no one-one (S) f is 4. coninuous and one-one P Q R S (A) 4 (B) 4 (C) 4 (D) 4 D f : R R, f : [, ) R, f : R R f 4 : R [, ) f () (P) f 4 () e f (f ()) f (f ()) e ono bu no one-one R.H.S. an 9 Page Corporae Head Office : Moion Educaion Pv. Ld., 94 - Rajeev Gandhi Nagar, Koa-5 (Raj.)

21 y k i (P) Z k e (Q) f () Z k h roos of uniy P is rue f differeniable bu no one-one. (Q) k {,,,... 9} (R) f f () e Z Z Z k e k i e i e i (k ) Z obuiously has a soluion in he se of comple numbers. False neiher coninuous nor one-one (S) f () coninuous and one-one y y (R) ( ) ( )( z )( z )... ( z 9 ) ( z )( z )( z )...( z 9 ) Now pu ( z ) ( z )... ( z 9 ) z z... z 9 6. Le z k cos k k + i sin ; k,,...,9. z z... z9 Lis I Lis II (P) For each z k here. True eiss a z j such ha z k z j (Q) There eiss a. False (R) k {,,...,9} such ha z z z k has no soluion z in he se of comple numbers. z z... z 9 equal. (S) 9 k k cos cos cos cos... cos 9 sin cos sin + (S) 9 k k cos equal 4. P Q R S (A) 4 (B) 4 (C) 4 (D) 4 C : , Toll Free 8799 url : :info@moioniijee.com Page