INDIA XI STD IIT_LJ Jee-Advaced Date: 08-0-08 Time: HS 0_P MODEL Max.Marks:80 KEY SHEET PHYSICS b a b 4 d 5 b 6 c 7 c 8 c 9 d 0 b a,b,c a,c b,c 4 a,c 5 b,c,d 6 5 7 8 4 9 0 6 CHEMISTY c c b 4 a 5 c 6 b 7 d 8 b 9 c 0 c a,b,c b,c,d c,d 4 a,b,c,d 5 b,c,d 6 7 7 4 8 5 9 40 MATHS 4 c 4 a 4 d 44 a 45 b 46 c 47 c 48 d 49 a 50 c 5 b,c, 5 a,c 5 a,b,c,d 54 a,b,c 55 a 56 0 57 6 58 6 59 60 7
SOLUTIONS PHYSICS. Coceptual. V w vr vx v siθ i vr vy cosθ ( j) vr v v v i vj v siθ i cosθ ( j) wr. vcm g siθ 5g 4. a K 4 5. Coceptual 6. From coservatio of mometum mv r mv r... v r v r i From coservatio of mechaical eergy GMm GMm GMm GMm mv mv, m v v r r r r ( ) 08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s GMm r r v r GMr r r r r r r m v, v GMr r L mvr m ( r r ) 7. (C) At the poit P, we have I I 0 (because the gravitatioal field iside a shell is zero). Hece, I I 8. As I dv dx, if I 0 the V costat. 9. Potetial icreases by 0 J / kg everywhere so it will be 0 5 5J / kg at P Gm Gm Gm 0. Net potetial at origi V... r r r Gm Gm Gm 4 8 O m m m m m m 4m 8m XI_ IIT_LJ Page
08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s. dl τ A L dt τ L dl τ L dt. Li Lf mvr I0ω0 mr mv0r ω0 ω0r v0. 0 mg si 60 > µ N mg > 0.4mg 4. m m m V G G G... r r 4r Gm m... G r 4 r m m m I G G G... r 4r 6r Gm m... 4G r 4 6 r 5. W ext -40-(-0)-0j/kg V 40 0 0 6. 7. V 0 Ex 0 N / kg r Itesity may be E y or E z G π ρ π ρ r V r r 9 V r r 6 V 4 r 4 r A A A B B B r r r A B B A A A V r r 5 V r r 9 V 5, N 5 V A XI_ IIT_LJ Page
K E x K K V Edx x x N 8. 9. 0. L i V lg siθ k lg siθ N 4 L mg Iω ml mgl ω ω g L V g L L Lg V 4 N L Iω I ' ω 0 f 4lg si ML ML L ω0 m Mω0 ω M 6m X 6 θ ω 08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s XI_ IIT_LJ Page 4
. C Maximum buffer capacity whe [salt] [acid] 08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s CHEMISTY. C P H Pk a. B A buffer of H CO ad HCO is formed. 4. A ph logk a log [Salt] [Acid] log0 log 4 [Sice K a K b 0 4 Give K b 0 0 K a 0 4 ] 4 5. C (00 V ) ph pk a log ; let V be volume of bezoic acid ad thus (00 V ) is volume of V bezoate. 00 V 4.5 4. log V 00 V V V 00 ml 6. B NH HCl i : will give NH NH 4 Cl i : ratio. 7. D Buffer solutio 8. B Fid solubility for each separately by S K SP for MS ad ZS. 08S 5 K SP for Bi S ad 4S K SP for Ag S. 9. C Let S is the solubility of BaF i a solutio of BaNO, the K SP [Ba ][F ] ; the [F ] S; the [F ] S 0. C Presece of commo io decreases the solubility of salt.. Coceptual. Solubility XI_ IIT_LJ Page 5
S K 0 mol / lit sp ( s ) ( s )( s) 0 0 5 AgCl s Ag Cl 0 0 s 5 0 M AgCl s Ag Cl Ag NH Ag NH Cl XI_ IIT_LJ Page 6 s AgCl s NH Ag NH Cl sp ( s) [ NH ] Ag NH Cl K K K s f 0 0 0 8 0 08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s s 0.8M. I HNO ad CH COONa combiatio if HNO is preset i limitig amout, it will be eutralized completely, leavig behid some excess of CH COONa, CH COONa HNO CH COOH NaNO Buffer Combiatio 4. Methyl orage (acidic idicator) 5. Cl, CN, SCN forms precipitate with Cu(I), remove Cu(I) io from equilibrium ad reactio shift i backward directio by Le-Chatelier s priciple. 6. Here solubility of CuCl is much greater tha that of AgCl. Cl K ( CuCl) 0 M Now for sp AgCl : Ksp.6 0 Ag Cl Ag 0 Ag.6 0 7 7. H CO NaOH NaHCO H O ph ( Pka Pka ) ( 4.6 8 ) 6. N V N V N 0 0. 0 N 0. 0 NaHCO NaOH NaCO H O milli mole C M 50 ml 5 ph ph 0. 6. 4
8. I ph Pka log 0 [ HI] XI_ IIT_LJ Page 7 08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s 9. Salt of weak acid ad strog base gives basic solutio o hydrolysis ad will term red litmus to blue KCN, K CO & LiCN. 40. PbI is 90% dissociated. Pb 0.9s ad I 0.9 s.8s Ksp Pb I ( 0.9s)(.8s) s.68 0 4. For A.P., 4. 4. x x x x ( ) ( ) log log 5. log 4 log log 5. Put x t 0t t 0 t, t 5 x log 5 x x s 5, r r 5 < r < 0 < x < 0 MATHS si d si d si d S... si a,si a si a si a si a si a S cot a, cot a 44. Give a,b,c are i G.P, the Let these are a, ar, ar Now, give ab, a b ad bc 6, b c ab 6... a b bc 8...( ) b c a ar ar From () 6 6. (4) a ar r ar ar ar From () 8 8 (5) ar ar r From () ad () r ad a 8 The a b c 04 45...4 5... as is odd
46. {..4... ( ) } H PQ P Q XI_ IIT_LJ Page 8 08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s ( ) ( ) 47. If x, y, z are i G.P, the log x,log y,log z are i A.P. 48. Give log ( c a) log ( a c) log ( a b c) log ( a c) ( a b c) ( c a) ( a c) ( a b c) ( c a ) ( a c )( a b c ) log log After solvig, ac b a c Hece, a, b, c are i H.P i j i ( i ) 49. j i i i j k i j i i i 6 6 50. H ab H, a b a b a b, H a b a H a b a Similarly, H b a b H b a b (i) (ii) H a H b H a H b 5. (B), (C) x cosec φ cos φ (sum of ifiite term of GP) Similarly xy y sec φ ad z cos φ si φ xy xy xyz z xy xyz xy z Also, si φ cos φ xy si φ cos φ si φ cos φ sec φ cosec φ x y xyz x y z 5. As a, b, c are i G.P., b ac. Now, the equatio ax bx c 0 ca be writte as ax acx c 0 ( ax c ) c c 0 x, a a If the two give equatios have a commo root, the this root must be ( c /a). c c d f e c e e Thus d e f 0 a a a c c a ac b d, e, f are i A.P. a b c 5. We have b > 4b b b r > 4b r b
08-0-8_XI_STD_IIT_LJ_JEE-ADV(0_P)_Key & Sol s r > 4r [ b > 0] r 4r > 0 r r > 0 r > or r < Sice r.5 ad r 5. are both greater tha, (c) ad (d) are also true. 54. b a c a c 8a c ( b) a c 8a c ( a c) a c ( a c ) ac( a c ) 8a c 0 a c ac a c 4ac 0 a c ac 0 or ( a c) ac 0 (a c) 0 or 4b ac a a c or, b, c are i G.P.Or a,b, c are i G.P. If a c the b c / S... 4 ( ) / 55. 56. a 4b 66 4d e a b b c c d d e b a c b d c e d D commo diff D D D D 0 57. Give a a 0 a 9d, 9d d /9 the a 4 a d / 7/ 9 d ', d ' (give h 0 ad h ) h0 h 54 7 8 7 8 Now, 6 d ', The h 7 therefore a4h 7 6 h h 8 7 7 7 58. a 4 4 / 4... 4 4 7 4 4 Now use b > a 59. Use A.M. > G.M for (a, b, c) The a b c > (abc) /..() Now ab c, a b c 4, a b 4 c 5 are i A.P. (a, b, c, > 0) The, abc, a b c are also i A.P. abc a b c, (abc ) 0, abc, put abc i equatio () 60. 5 ( ) ( )( ), ( ) 5 6 5 5 4 7 XI_ IIT_LJ Page 9