MODEL SOLUTIONS TO IIT JEE ADVANCED 2017

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Clifton French
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1 ODEL SOLUTIONS TO IIT JEE DVNCED 7 aper I Code RT I , B, B, D B, D, C, B, B, C, D B, C, D C C C B B Sectio I. () Capacitor blocks () correct (B) L & C ol ipedece requec depedet (C) ω LC ω 6 6 LC 6 6 (C) wrog (D) Behaves iductive (D) wrog si + δ. () µ si (B) i + i + δ i + i (r + r ) r + r i i r r (D) µ sir µ + D si si' cos si si () correct cos µ µ cos (C) i + i + δ 8 or grazig agle 8, 9 si, cos cos Substitutig si 4 cos cos 4 si 9 eerget ra tagetial ad icidet ra tagetial (C) correct 3. () e iduced i loops is proportioal to the diereces i area sice iduced es oppose () wrog (B) Rate o chage o lu is aiu whe φ cosωt dφ e ω siωt aiu whe ωt 9 (C) e siωt (C) wrog (D) Iduced e is sall coil ωt siωt (ω/ siωt) ω siωt (D) correct

2 4. u v u v ( air) ( air) + ( air) ( air) et p ( air) air t v u Velocit o approach u v Velocit o separatio u v v u v Displaceet o C o poit ass ( + R) ( + R) ( + R) ( + ) R R + (C) oit ass at + R R R + R (c) wrog + + () v + v gr v v v v..v v + v gr + gr gr v () correct + (D) Siilarl proceedig D is wrog (D) wrog v v i v t v air, p + v p. p ( ) (u v) ( î ) + vî u î + vî ( v u )î v i u î ( air) i [ v ] u v + u u ( air) ( ) [ v + u] et + [ 4u ] et is costat acceleratio is costat. (B) Displaceet o C o block 6. () () ulse () t a poit T g + kg v µ µ t a poit distat ro load v is give b above epressio. Setrical velocit w.r.t both eds () correct (B) Velocit becoes largest at Hece B correct v λ, λ icreases T (C) v, v idepedet o requec µ (C) correct (D) t id poit as per the epressio v is sae or both (D) correct 7. () Theoretical wrog (B) U σ(t B 4 T b 4 ) σ[t + T) 4 T 4 ]

3 4 4 σt T T + T σt + T T T σ T 4 4 T. σ 3 4T. T correct T (C) W σ ( ) 4σT 3 (T T ) 4(σT 4 ω ). T J correct 3 (D) D is correct obviousl wrog 8. V i V vi v 3.6 i 3.6 i ev ev 6.. i (Q i ) 9. R /3 r r R / 3 Sectio II E 4R T E 4r T 4R T /3 E 4R T( /3 ) 4. / 3 4 ( ) 3 4 /3 6 α 6 v + v. c v v c Hz t / T / / art o this..98 ractio 3. Velocit o blood. 3 l. litre. si i si r si r ( ) si r si r ( ) sir ( ) ( ) ( ) si r ( ( ) ) d r si C ( ( ) ) ( ) ( ) Theoretical 4. Theoretical. Theoretical 6. Theoretical I, iv, Q 7. udaetal II,iii, 8. Basics III, ii, S Sectio III

4 RT II B, C, B, C, B, D, B B, D, B, D D D D D C C Sectio I 9..O picture shows *p ad *p are doubl occupied i Haloge olecules (HOO). The σ*p z is ept (LUO). Colour is due to ecitatio ro * orbitals to σ*. s the distace o these orbitals icrease ro ucleus (or as value icreases) the gap becoes saller. Hece ecitatio eerg. X Co + cotais 3 upaired e Y [Co(NH 3) 6]Cl 3 o upaired e Z [CoCl 4] sp 3 d shell cotais 3 upaired e t low teperature, octahedral [Co(H O) 6] + is ore stable tha tetrahedral [CoCl 4] Z give the V. o pure L 3. ΙUC 4. dditio o to tras-but--ee gives eso-,3-dibroobutae whereas cis-but--ee gives raceic iture o,3-dibroobutae. () HClO 4 is the strogest acid ad hece its cojugate base ClO 4 is the weakest base, weaker tha H O (B) The total uber o σ bods ad loe pair is our i both HClO 4 ad HClO (D) ClO 4 has ore resoace structures tha ClO due to ore uber o oge. () ree epasio has zero work hece both isotheral ad adiabatic R(T (B) T ) W adia Q T > T γ V Wiso RT l V T > T T W iso > W adia (C) Work doe will be aiu whe the process is carried out reversibl (D) or a isotheral process U or a adiabatic process U W gai or a epasio process, W ve U is ve. give solutio shows positive deviatio ro Raoult s law L Z 6. κ C l 7 6 κ 3 Λ c [H ]. α 4 α Λ 6 Sectio II Λc 6 α S c 4 ol L L

5 7. Te L. L. N S L. Xe L. 3 Total L.s 6 8. Cclopropel catio, cclopetadiel aio, ccloheptatriel catio, pheathree ad are aroatic 9. Vol. o uit cell a c 3 6 Vol. o 6 g 3 c No. o uit cell i 6 g No. o atos i 6 g N σs, σ *s, σs, σ * s, p, p σ O σs, σ *s, σs, σ * s, σp z, p σs, σ *s, σs, σ * s, σp z, p, p Diaagetic species are (i) H (ii) Li (iii) C (iv) N ad (v) 3. D 3. D 33. D Sectio III, p z, p, * p * p 34. Toluee udergoes side chai substitutio b ree radical echais whe treated with broie i presece o light COCH 3 CHO NaOH / ( 3 CH CO) O / CH COOK COONa 3 + CH 3 3. H σs + He σs, σ *s Li σs, σ *s, σs Be B C σs, σ * s, σs, σ * s σs, σ *s, σs, σ * s, p, p σs, σ * s, σs, σ * s, p, p CHCHCOOH + CH 3COOH Ciaic acid eists as cis ad tras isoers

6 RT IΙΙ , D B, C B, C, D B, C, C, D B, C, D D C D B C 37. Sectio I ( a + b) ( + ) az + b + ia Ι Ι z + + i ( + ) a b + ± ± 38. Let i (, ) + ( t) si t + si t e [The () t cos () t cos i (, ) si t e si t e si i (, )] 9 () 9 s [B, C] 9 cos t whe (, ) is a taget to i a 6 c a b i.e., 4a 6 7 a 4. (X) 3 ( X ) ( Y ) Y X ( X Y) Y ( X) X ( X Y) (a) alse 3 ( X Y) X Y Y 4 (Y) (c) true ( Y) (X Y) (X) + (Y) (X Y) (d) alse 3 ( X' Y) ( Y X) X' Y (Y) Y 4 ( X Y) ( Y) 4 4 Y 4. Let be a 3 3 atri (with real or cople etries) B B B is o egative & Clearl these are NOT squares o atrices. lso Ι Ι Ι is a square o a real atri 4. cos( + ( + [ ] )) li li cos[ ( + [ ] ) li cos( ( + ) ) cos3 + li + li cos + ( [ ]) ( ) cos ( ) cos

7 () is ot cotiuous at III l it is ot cotiuous at & But at ( + ) ( ) it is cotiuous at 48. [ ] 3 li () t ' () t 3 li si t cos t Equatio o the chord with id poit (, ) is T S 8( + ) 6 k 8 ( + h) k 6h k 8 k 6h + 8h 8 + k k 8h () But chord is + p () ro () & () 8 k k 8h p k 4 4p k 8h 4p 6 8h p 4 + h (3) Clearl optio p & h 3 satis (3) Sectio II 44. I a d, a, a + d are the sides (d >) (a + d) a +(a d) a 4d Now a ( a d) 4 4d 3d 4 d legth o sallest side 6 4. We should have [ + α α + α + α] [ ] α + α + α 46. No o legth which o digit repeated ()!! Nuber o words with! eactl oe letter repeated 9! 9 9 9! p p 4 (i it touches ais) But the the circle does ot eet ais p p there is ol oe value viz p No. o solutio 49,, Sectio III Colu Ι Colu ΙΙ colu ΙΙΙ Ι Circle (i) taget to () oit o parabola cotact o taget to parabola ΙΙ Ellipse (i) taget to (Q) oit o circle cotact o taget to circle ΙΙΙ arabola (iii) taget to (R) oit o hperbola cotact o taget to ellipse Ιv Hperbola (iv) taget to (S) oit o ellipse cotact o taget to hperbola 49. s (D) a,. s () (a 8, ). s (C) ( ) 3, 3, 4. Colu Ι ΙΙ ΙΙΙ Ι (i) ΙΙ (ii) Q ΙΙΙ (iii) R ΙV (iv) S () + log log () log as () as is icreasig i (, ) is decreasig i (e, e ) is decreasig i (e, e ). (D) 3. (B) 4. (C)

MODEL SOLUTIONS TO IIT JEE ADVANCED 2015

MODEL SOLUTIONS TO IIT JEE ADVANCED aper II Code ART I 6 7 8 6 7 9 B D B, C A, B 6 D A, C B, D A 7 8 9 A, C D A, D A, C. Sectio I ΙA 8kR 8 8 Ι B 8k.R 6 r dr. Ι ρ A ω C Sphere A d r dr ρ(r) kr kr dr r dr