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CDE 5 JEE-5 : dvaced Paper swers ad Explaatios Physics Chemistry Mathematics 6 C 8 5 D B,D 6 5,D,C 6 B 5 B,C,D D 9 5,B 5 5,B 5 9 5 B,C 5 7 55,B,D 6 6 B,C 6 8 6 C,D 6 9 56,C 7 7 7,D 7 7 C 7 57,B 8 8,C 8 8 D 8 9 58 C,D 9 D 9,C 9 B 9 9 B,C 59,B,C,B,C D B,C,D B 5 B 6 C,D PT - I : PHYSICS. The phase diagram for amplitudes will be. 6 di dm r dm πr ρdr for sphere I 8πk r 5 dr 6 5 8πk πk 6 9 6 I 8πk 9 r dr B 5 IB 6 I 5 6 8πk 5 πk 5 5 res J I res I. e t/τ d e dt τ t/ τ Both sources have same at (t τ τ/ τ ρ τq e τ/τ Q τ ; ρ e ρ Q e......

. sii sir, 6. h λ p sir sii mv r h π dr sii cosr d t secod surface sir si θ sir siθ dθ dr cosθ sir cosr d dθ dθ dr sir cosr θ d cos d r - r dθ dr sir cosr θ d cos d cosr sii sir cosθ cosr cosr sii sir cosθ cosr P mv h πr πr π r h p z r λ π z here z 6πr λ, P z 7. 7 For tesio to be zero, GMm Gm l 9 T6 l 7M m, k 7 88.h mvr π 5. 6 C 8 B There is a wheatstoe bridge betwee & B whose equivalet is Ω. There is agai a wheat stoe bridge betwee & C whose equivalet is.5 6.5 D.5 8. E(t e αt log E(t log αt 9. D E α t E t.5% T t.5 5 Solvig we get E % E C ε/ d/ C C ε/ d/ ε/ C d......

C C, C B C, C C C equivalet capacitace C C C C C 7 C., B, C T,P,V T,P,V P Ideal mooatomic P P kx P V µt P V µt T T P P 7C a equilibrium P P kx P, P kx P kx further V x V V x V V Eergy stored (kx x P Chage i ited eergy c r (T T c r T But, P V T (T c r optio (B is correct.. ptio C: T T P V T T P P. i.e. work doe by gas is stored i potetial eergy of sprig ½kx. Plus the work doe v agaist atmospheric pressure P x work doe by gas P x ½kx V V x V {x V } P P kx P P kx P kx work doe by gas kx P x (kxx P x P x Px 7 Px 7 7 6 6 Chage i ited eergy c r (T T c r T P V T T 9 9 v Q W 9 7 Q ( 6 5 (P V 6 6 9 9 5 8 U Xe Sr x y Q k xe k sr k x k y k sr k xe 8 : 5 ( 6(7.5 989 77 9 k xe k sr 9 5 mev Mass umber 6 ( 9 (X Y tomic umber 9 (5 8 (x Y ly optio is (.......

. B, D dp πr r (π r dr ρ ρ at depth r will be directly proportioal to r. dp krdr. Itegratio L L P P σ σ P dp krdr ] r P k ( r Where k is some cost. solvig we get, optio (B & (C are correct Sice the rope is i tesio force o P will be upward, force o Q will be dowward. they will more i opposite directio if revosed. V.V P Q < {D} Sice the spheres are i equilibrium, T Net force due to wt & liquid 6πrV V p V q 7., D ev evdb w I IB vd e wd v ed if B, & I remai same v d v ; d v d V p {B} V q for d d v v for d d v v., C By dimesioal aalysis. ly optio & C are correct.. D Electric field iside cority ly optio is (D. Pa ε 5., B ( (B (from stress strai graph Teside stregth is the stress at which metal breaks. 6. B, C The situatio is similar to that of earth where pressure keeps o icreasig as we go dow. p 8., C if I & w remai same 9., C B v v B v B if B & v v if B B & v.5 v i c ( (C pdp for S Let us there a shell at r distace, the pressure o sides is (p dp & P. the differece i pressure dp ca be foud by dp et attractive force o shell dp drx ( ρ si c 5 for S i water & S i cos c 5 6 5,......

si i 5 m 5 si i m 9 6 & 6 5 si i 8 5 m 5 8 si i m 9 6 for S i air ad S i si i m (for S & 5 si i 8 5 m 5 8 si i m ( 5 (C. D if N < N we will take smaller umerical questio. KHX K HY K HX K HY i K HX log K HY ( log K HX ( log K HY pk HX pk HY 5. 9 8 6 ( ( o 9U 8Pb x He y e 9 8 x y x y 8 6 x x x 8 y 6 Pf V 9T P V T P i f P i 9 6. 8 [ ] 5Fe(H(C M H 5Fe H C M ate H ate M H M 8. PT - II : EMISTY 7. H heat. 6 H. 6 BH6 6H 6( B 6H. HX x C. M α HX HX α α X x HY x C. M α HY HY α. α K HX Cα.α K HY. α K HX.(. α K HX α K HY α 8. 9. B, methyl shift aq.dil. km (excess H H H H. B, C, D s oxyge chemically participates with metal ad metal doates electros to atibodig π-orbitrals of oxyge.... 5...

. C 5. B, C. C H (i (ii Z,H H C H NH 6. C, D H Cl HCl (ii Cl HCl (iii H H Cl HCl (iv For questios o. 7 ad 8. C H NH (i C Pd BaS H H H H N H N (i BH 6, (ii H,H C C, H. B High Pr essure, (ii Hg,H HC C C H (i C H 5 MgBr,H (ii H, heat radical iitiator 7. C (Major. NH NaN / HCl C N NCl 8. D 9.. B NaH CNa H Iitial.. Fial.. N N H 5. ph log( log. [. 5].699... 6...

PT - III : MTHEMTICS. 8 Coeff of 9 i ( x ( x L ( x Coeff of x 9 i ( x ( x L( x 9... 9 x y, 9 5 e F (,, F (, F (, F (, P : y 8x P : y 6x Taget to P (t, t : ty x t, it passes through (, t t m t t m Taget to P at ( t, 8t ty x, it passes through (, t m a cos a e e lim m a cos a ( ( e. sia. a e lim a m ma m ( ax ta x α 9.e dx x π 9 9x ta x e e π loge ( α 9 x 5. 7 F x f t dt F f x dt x ( ( ( ( G x t f f t df G x. f f t dt x x x ( F x F' x f x lim lim lim G x G' x x. f f x ( ( f f 7 f f x 6. 9 S i $ j $ 5k$ x 5 y 5 6 z 5 7. αk α k cost( r 8. 9 αk αk k αk αk k 7 [ a 6d ] 6 [ a d] r r 7 (a 6d 6 (a d a d a 6d a 8d 9 8d a 9d T 7 a 6d 5d < 5d < d 9 9. B, C h(x f(x g (x h( f( g ( h ( 6 h( h( h( h( h (x has oe root i (, & oe root i (, { h '' ( x }... 7...

5. B 5. D f(x (7ta 6 x ta x sec x π π ( 6 f x dx 7ta x ta x sec xdx 6 Let ta x t ( π 7t t dt 7 t t 7 ( xf x dx x f x dx t t dt 8 t t 8 8 8 5., D x x < x x x x < α α < < 5 5 <α α < or α > 5 5 < α < or < α < 5 5 α > α < < α < π 5. B, C, D 5., B 55., B, D 56., C 57., B B I B II P II P m 58. C, D.. 59., B, C f(x x.f(x f(. F( F (x < for x, therefore F( < F( f( < f (x F(x xf (x < for x (, f ( F( F ( < 6. C, D... 8...