ALL INDIA TEST SERIES

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1 AITS-FT-I-PCM (Sol)-JEE(Man)/6 FIITJEE Students From Classroom / Integrated School Programs have secured to Zonal, 6 State & 8 Cty Topper Ranks. n Top 00, 78 n Top 00 and 05 n Top 500 All Inda Ranks bagged by FIITJEE Students from All Programs have qualfed n JEE (Advanced), 05. FIITJEE ALL INDIA TEST SERIES ANSWERS, HINTS & SOLUTIONS FULL TEST I (Man) JEE(Man)-06 S. No. PHYSICS CHEMISTRY MATHEMATICS. A B A. C B C. A B C. C C B 5. D A A 6. A B B 7. A C C 8. A A D 9. D B A 0. B A A. B C B. B B A. D C C. B A B 5. D C A 6. B C C 7. A C C 8. B A B 9. C C C 0. A A D. C B A. A D C. B B C. C A A 5. C C B 6. B C D 7. A A B 8. A A A 9. C B A 0. B A D FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

2 AITS-FT-I-PCM (Sol)-JEE(Man)/6 Physcs PART I. y For an adabatc process PV k Here y = / and k = constant PV k logp log v logk P v 0 P v V P V P V P V P 9 SECTION A volume decreases by about. contact pont 0 mg ma o R mg sn0 a g R ma cos0 % 9 o m a N mg f 0 o a. I 0 0 mr f mg 5 & f = ma = mαr 0 0 f mg mg N mg 5mg, 7 7 R 60 0 O P mg mg f a. for deal gas () and () are correct = for same pressure and no. of mole PV PV V V T T nt nt T T 5. Conservaton of lnear momentum. P L/6 C L/ J J J MVf Vf M FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

3 AITS-FT-I-PCM (Sol)-JEE(Man)/6 Conservaton of angular momentum about C L ML 6J J ML J KE Icm MVf M 6. Intally ncrease n temperature ncreases the densty and after T = o C ncrease n temperature decreases the densty 5V 7. Let s the length on potentometer A 5R.5 A m 8. p0 p p0 cos x p0 cos 6m 60HZ 9. r E V / m V V V f V V V f f sound 0 wnd sound source wnd f. Place another dentcal hemsphere on gven one, so that flat faces of two concde. The total flux Q lnked wth cross- secton of bottom half (lower hemsphere) s as charge enclosed by gven hemsphere s zero. So flux lnked wth flat face of hemsphere s. f T. () T 0 Q 0 N mg mg f N = mg + mg. () (T + f)r = mg R. () f mg N mg mn FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

4 AITS-FT-I-PCM (Sol)-JEE(Man)/6. N m r mg g r. 0 7 m H 8 m n M x R 0 6. Requred knetc energy = m N m n m H m C 9MeV =.99 MeV 7. 0 D D 0 d d Tme constant wll be RC 9. For refracton at bottom of slab 0 V 0cm V 5 For mrror V 0cm 0 V 60 For refracton at bottom of glass slab 5 0 V cm V 0 For refracton at upper surface of slab / 5 0 V cm V 5 5 I o B cos cos r I o cos0 cos5 d 0.. I o d d dt 5 0 d x P FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

5 5 AITS-FT-I-PCM (Sol)-JEE(Man)/6 d R B dt dr B R dt B R t antclock wre o. The current n wre AB, ncrease the flux through crcular loop. Hence current n crcular loop wll be antclockwse.. F0 ky 8 ky ky y y m y F 0 = Tenson n the strng F 0 = 8ky 9F0 y y y 8K F0 8K K eq y 9 9m T 8K. C A Vx Vx Vyj P.D VBl P.D = along y axs = VxBl P.D along x axs = V y B.l P.D along AC = V x Bl + V y Bl B 5. Assume the hemsphere to be made of thn hemsphercal layers. 6. Co-effcent of mutual nductance = n n r r o 0 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

6 AITS-FT-I-PCM (Sol)-JEE(Man)/ Hence M r R 00 g x g x 0cm V x 000cm 8. Electrc feld and magnette feld wll be parallel and velocty wll also parallel to electrc fled All three are parallel Hence only electrc force wll act on t 9. y R mv v o o qb B0 R r g 0. V d T 9 0 r r.77 0 m 6 D r.5 0 m FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

7 7 AITS-FT-I-PCM (Sol)-JEE(Man)/6 Chemstry PART II SECTION A. K CrO7 HCl KCl CrCl Cl 7HO n-factor of HCl = 6 7. CH Br CH Br CH CH CH () () () Br (v) (v) Br Br. PV nrt P nrt / V PV const P V dv V dp 0 dp dv P V G 0.059logk nfe k, G 0 o 0 cell Br 0.0, Br 0.0 Ag 0.05 CaBr KBr AgNO Both Br - & Ag + ons act as common ons, so larger the conc. of Br - or Ag + more s the suppresson of onzaton of gbr 7. Because sheldng effect and ncrease n effectve nuclear charge are cancelled 8. Not les n same plane 9. NOF has lone par whle NO F has no lone par 0. Zn NaOHA NaZnO H B NaOH P C NaHPO PH NaOH NH Cl NaCl NH D H O. Due to low electronegatvty of N n compound C basc character decreases. Due to umbrella effect, A s least reactve.. Non super mposable mrror Image. Due to cyclopropyl unque stablty.. In (II) negatve charge present on O atom whle postve on C. (I) s most stable due to neutral. 5. Each rng contrbutes DBE. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

8 AITS-FT-I-PCM (Sol)-JEE(Man)/ Rng expanson wll take place 7. Anlne s NH COOH C H C H 8. Facts. 9. NaCl H SO NaHSO HCl NaCl NaHSO Na SO HCl Craft process 0. Bond strength thermal stablty. Fact.. XCr 0OH H O CrO green yellow Y CrO H O H CrO 5 H O Cr O 7 / O H SO Cr SO H O blue. Fact. Fact 5. (cs/trans).e. Geometrcal 6. Due to strong lgand t 6 e o 7. Self reducton Cu S Cu O 6Cu SO g 8. P = K H x logp logk logx H g 9. Electraode potental s ntensve property whle gbb s free energy s extensve 0. A B C P 0 0 Pr essure at t 0 P P P P Pr essure at any t P P P t Pt P or P K.0 P log t P P.0 P.0 P log log t Pt P t P Pt P FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

9 9 AITS-FT-I-PCM (Sol)-JEE(Man)/6 Mathematcs PART III SECTION A x x 0 m 0 x x snx. snx n nt egral value of snx m n. at the pont sn x P,. a a a,. P PP...P P P P f e e e n n n n lm f lm e. z x y real, real x y real x 0, x z Re z x, lm z sn sn y y 5. S 6 r 8r r 6 6 8r r r r r r r r r r r FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

10 AITS-FT-I-PCM (Sol)-JEE(Man)/6 0 6., a, a. A 0, 67 are n AP 67 a a... a AM GM a a a... a Maxmum value s (0) 0. cos cos x.cos sn cos x sec 7. cos cos x cos cos x A x sn, cos y cos y x 9. n cos sn n n n cos n n cos n n 6, cos 6 0. sn x 0 & snx 0 log sn x snx 0 sn x.snx x 0,, x 0,, for sn x snx sn x sn x 8 sn x 6 sn x 0 sn x sn x 0 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

11 AITS-FT-I-PCM (Sol)-JEE(Man)/6 sn x sn x sn x sn x 0 sn x x,, fnally x,. Requred no = 5!!!! 5! x x x n x x n. n n x x n n n n n n 6 n n Cx Cx... Cx Cx Cx... Cnx Coeffcent of x 5 n C n n n n n n n n n n n 5 C0 C C C C 6... C C9 C C C6 C5 n C n 5r Cr 5 r 0 B P B A B P A B P A B P A B P A B Now PA B PA PA B PA B PA PA B Also PA B PA PB PA B 7 B, P A B. Puttng x = 0, a 0 = Dfferentate both sde and puttng x = 0 we get a = a Dfferentate agan and puttng x = 0 a 6a b a a a a a a a a a a 6a b 5 a, b FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

12 AITS-FT-I-PCM (Sol)-JEE(Man)/6 5. a = 0, a =, a =, a = 0 0 A A 9 0 A CD 9 5 AD = CA Equaton of crcle s x y 8 7 shortest dstance wll take place along the common normal Equaton of normal for y = ax at (at, at) y tx t t If t passes through (6, 0) then t 5t = 0 t 0, t 5 A 5, 5, C 5, 5 PA PC 0 ; OP 6 Mnmum dstance = 5 unts 8. Let the md pont of chord be P(h, K); ts equaton wll be xh yk = h K h K h y x K K a It should be same as y mx m h a K h m and K m K K h h a K a K h.h K K h K h a Locus s x = y (x a) 9. equaton of tangents s SS = T x y 9 x y Rght angle a + b = 0 Solve t get = FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

13 AITS-FT-I-PCM (Sol)-JEE(Man)/6 0.. b a snx snx x x a b c x lm lm x x0 c x 0 c x c snx sn.x c c x x The value of lmt s non-zero only a + b c = 0 f x lm tdt x x f x f x lm f.f x 8f b y = f(x) x f y f x x tan x y f y tan f y y g y tan g y x g x tan g x Dfferentate g x sec g x.g x g x. f x cos x ax b sec g x g x x cos x ax b f x sn x a f x 0 sn x a 0 a. Let x x = t x logx logt logx dx dt t t logx dx dt I dt sec x x c t t 5. K K K K K...n lm K n n FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659

14 AITS-FT-I-PCM (Sol)-JEE(Man)/6 K r lm n n n K K K K x dx 0 0 K x K K K 6. x e I x dx x z ze dz z z z z ze e e e 0 e 7. Area = sn y dy cos y dy 8. 0 cos y sny 0 sq unt dy x xcosy sn y x.e dx x x cos ydy sn ydx x e dx d x.sn y x x e dx x x x sny x e x.e dx x x x x e xe e c x x sny e x x c 9. a b. a c d a b. a.d c c.d a a.d abc c.d abc a.d abc 0. let the plane ax + by + cz = & here x y z 6 When 6a + b + c = 0 a b = a b + 5c = 9 7 a, b, c x 7y z 85 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sara, Sarvaprya Vhar, New Delh -006, Ph , 65699, Fax 659