2018-JEE Entrance Examination - Advanced Paper-1

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Damon Parker
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1 SLUTINS 8-JEE Etrac Eamiatio - Advacd Papr- PAT-I PHYSICS.(C) kr U ( r) du F kr dr L m v mk mv k k v m V V.(AC).(AC) F () t i () j a t i j m () t t v a dt i t t t j r vdt i j 6 t At t s r i j 6 F () i () j r F k k k 6. Hc A is corrct is alog k. Hc is icorrct v( t s) i j. Hc C is corrct s r 6 m. Hc D is icorrct. cos h rg h r A is corrct h is icorrct If lift is goig up gff g a cos h r( g a) h g a (C) is corrct h cos which is ot proportioal to D is icorrct VMC Papr- JEE Etrac Eam-8 Advacd

2 V.(D) i i V t L t L t V i i i L For i to b ma/mi t L di di V dt dt L L t t L L L t () D is corrct Also w ca s that at t, I ma V V I 5.(AD) du to I at origi ( k ) I du to I at origi k 6 origi I I I k 6 d i is v i is ma. dt ; du to I at origi So if I I A is corrct is corrct I ( k ) So if I I I will hav a valu for which ca b zro. is corrct. So if I, I origi has to b alog k C is icorrct. I If I I at th ctr of loop k As Z-compot of du to I & I cacl out V i L i i i i i L I V I D is Corrct. 6.(CD) I procss, V is chagig A is icorrct I procss, Tmp is costat ad volum is icrasig V Q T v V is corrct. T Similarly, I procss IV, Q v C is corrct II For Isobaric procss I III P IV T V V Straight li passig through origi D is corrct 7.( or. or.) A a cos ti si t j ; A a costi si t j VMC Papr- JEE Etrac Eam-8 Advacd

3 t A cos ; si t A ; A cot t A t t. 6 8.(5 or 5. or 5.) f c f c cos 9.(.75) f f c c cos f c cos 5 at frqucy f f 5 c h cosc t ; a t t rig Disc h h g si g si a k h h g si t trig tdisc h h h.75.(.9) v v () (Momtum cosrvatio) Also ( v v) () (Cofficit of rstitutio) v v v As kg is attachd to a sprig, T m Tim tak by kg to rtur to its iitial positio is t sc. k Distac mov by kg i this tim vt h.9 kg kg 5m A m/s ( ) f m obsrvr (at rst) f m f kg rst kg m/s ( ) f.(.5 or.5) Iitial circuit: Iitial charg o C CV 8 C Fial circuit: y cosrvatio of charg: q q 8 C o VMC Papr- JEE Etrac Eam-8 Advacd

4 q 8C Q 8C 5C C Also by KVL q q q C C C r 5 r.5 C r C.( or. or. or. or.) mv m, t q q mv m, t q q Cas-: Magitud of avrag vlocity alog -ais Cas-: t t mv q. m 5 q Distac alog -ais = mv q m m Tim = t t q q mv q Avrag spd = m q.( or. or.) v cm Powr icidt o th ls = Itsity at P = I( ) r I I r KW / m. cm I P r [ r from similar triagls] VMC Papr- JEE Etrac Eam-8 Advacd

5 .( or. or.) K K K H K K 5.(C) 6.(D) 7.() L L K ( r ) ( ) K ( r ) ( ) H L L E v [ E] [ L][ T ] [ ] c ( a) r a dr o ( c) o o o 8.(C) ( t N N ) dcayd ( a)( da) ( a) da ( a) N l t N Nd [ o] [ L] [ T ] da ( a) o Nd t N N d K r K r a r ( a). PAT-II CHEMISTY.(C) NHN N H 7 T C (NH ) Cr N Cr H a(n ) a N MgN dcompositio occurs..(c) 6 F [Ar]d s ; 8 Ni [Ar]d s : C is strog fild ligad F(C) 5 Ni(C) Valc lctros (Low spi compl) (Low spi compl) If oidatio stat of M is icrasd: M C bod strgth dcrass ad C bod strgth icrass du to lss tt of back bodig. If oidatio stat of M is dcrasd M C bod strgth icrass ad C bod strgth dcrass du to gratr tt of back bodig..(ac) A : Mtal oids ar mor basic i atur (Corrct) : NF is mor covalt tha if (Corrct) C : PH boils at lowr tmpratur tha NH (Corrct) D : N N P P (bod strgth) (Icorrct) VMC Papr- 5 JEE Etrac Eam-8 Advacd

6 .() M (X) H 5.AD (A) CH C CH M Vidyamadir Classs r Pr, Et NaI (Acto) S N S N M I NaN, DMF S N M N Coc.H S + H : Acid catalyzd aldol codsatio atiomrically pur () Hatd iro tub M C CH ; Gas phas trimrizatio C CH (C) ) r NaH CHr C C + H HC sodalim CH + C CH CH (D) Z/Hg, HCl ; Clmms s rductio HC CH H C CH A(P VT ) C (PVT ) 6.(C) Volum (V) (P V T ) Tmpratur (T) Path A C CA Procss Isothrmal Isobaric Isochoric U U C V(T T ) U C V(T T ) H H C p(t T ) H C p(t T ) V W P W T l (V V ) W V V q C q TE l V (T T ) P (V V ) q C V(T T ) V qac UAC C V[T T ] UC W V T l V A WC P [V V ] P [V V ] qc C C P[T T ] HAC HCA C P[T T ] UCA C V[T T ] HCA UCA bcaus both ar gativ ad T T VMC Papr- 6 JEE Etrac Eam-8 Advacd

7 7.(.) H atom, N moomr (Suproid), dd lctro spcis Paramagtic Dimric sulphur i vapour phas. M,(NH ) [FCl ],(NH ) [NiCl ], KM Accordig to MT Upaird lctro i d orbital of ctral atom 8.(99.) Diamagtic KCr No upaird lctro i d orbital of ctral atom % (NH ) S Ca(H) CaS.H NH 58 mol mol % NiCl 6H 6NH [Ni(NH ) 6] Cl 6H 95 mol 8 mol. Mass of CaS H 7 6 gm (M 7) Mass of [Ni(NH ) 6] Cl 98 gm (M = ) As. = 99 gm Combid wight (i gm) = = 99 9.(.) M X CCP HV.(.).(.) X (Aio) M (Catio) Aod : Mg Mg Cathod: Cu Cu Mg Cu Mg Cu T Mg ] () E E,.7 Eº l, E E.7V F [Cu ] 5 () M X = M = Z X = M = VMC Papr- 7 JEE Etrac Eam-8 Advacd

8 Fid ad hat isulator (A) () m 5 bar K m bar K Aftr w chagd th partitio to movabl ad coductig, prssur ad tmpratur o both sids will b qual. A Hc.() V V A Lt aftr slidig volum of chambr A = V Th volum of chambr V From iitial coditios w ca stimat A ad P V P V A A A TA T P V T P V T A A A A A 5 Usig quatio: V V A.(9.) Coditio I: A V 5 V. m V 9.5,.5 A PA Usig aoult s Law Torr ad P M M A A P P P 5 ()(.5) P (.5) P Coditio II: 7 Torr A?? PM.5 Usig aoult s Law M A A A P P P ( ) A (5) () () 5 () () () 5 Torr.5 () 7( ) 5A 7.5 A A VMC Papr- 8 JEE Etrac Eam-8 Advacd

9 9 A, 9 A 9.(.7) A(S) A (aq) (aq) () (aq) H (aq) H(aq) () addig quatio () ad () A(s) H (aq) A (aq) H(aq) a a s s s K sp [A ][H] K [H ] a S 8 S S 5 S.7 y y.7.(.5) Cas : For solvt X Solut: NaCl Molality: m i T b (6 6) (from graph) T i(m)(k ) b b ()(m)(k b )..() ; Kb m From solvt Y Solut : NaCl Molality : m i T b (68 67) (from graph) Tb im(k b) y ()(m )(K b) y..() ; Kby Dividig () by () m VMC Papr- 9 JEE Etrac Eam-8 Advacd

10 m (K ) m (K ) (K ) (K ) b b y b b y Cas : For solvt X: Solut : No volatil Molality : m i i T a b () Tb im(k b) a im (K b) () For solvt Y: Solut : No volatil Molality : m i i y T a b Tb iym(k b ) y a iym (K b ) y (5) Dividig () by (5) Now a i m (K ) a i m (K ) y b y b y i (K b ) y i (K ) I solvt Y: S y b i i S.7.7. (.7).7 / ; iy I solvt X: S S ; i i (.5 ) i. y (.5 ). VMC Papr- JEE Etrac Eam-8 Advacd

11 . (.5 ) (C) 6.(A) C/HCl AlCl, CuCl Ph C CH (Y) PhCH arragmt (Z) Ac /NaAc Prki's codsatio Ph CH C HP Itramolcular F.C. acylatio : Ph CH CH CH (X) C Kbr CH CH 5 C H /Pd C r /Na C H CK CH C r H CH CH CH r 7K KH (A) 8.() VMC Papr- JEE Etrac Eam-8 Advacd

12 CH [] P (CH ) thyl glycol Dacro CH aliphatic kto + othr product CH CH CCl (P) H /Pd-C SCl MMgr NaH HC H + ClMg C C ClMg Mg Et Cl HCl H () (Q) CH CH CNH NH NC NHCH H NH r CHCl Pd C NaH NaH, H /Pd C.(AD) (i) arg i PAT-III (ii) Th fuctio is discotiuous at f arg Howvr lim f t lim arg t t t (iii) C is obviously tru MATHEMATICS ( S) (iv) I gral z lis o a cyclic quadrilatral..(cd) r PQ ; Q p VMC Papr- JEE Etrac Eam-8 Advacd

13 p r q cos pr q q PQ or QP ar PQ si 5 q si = Ara of circumcircl r 5 s 5.(CD) P : y z ; P : y z.(ad) i j k i j k i j k Dirctio ratios of th li,, Equatio of li y z i j k i j k Th agl btw plas is th agl btw thir ormals. i j k. i j k cos Equatio of P y z y z : Distac from (,, ) Sig prsrvig proprty of a cotiuous fuctio, Say a fuctio f is cotiuous at = a, th thr ists as op itrval aroud a i which f prsrvs it sig. W.L..G lt f(a) > Sic f is cotiuous at = a lim f ( ) f ( a) a f ( a) Choos f ( a) f ( a) f ( ) f ( a) f ( a) f ( a) f ( ) VMC Papr- JEE Etrac Eam-8 Advacd

14 5.(C) Vidyamadir Classs Thrfor thr ists som itrval i which f prsrvs its sig. Now cosidr th itrval (, ) whr. Th fuctio ca t b costat i th itrval as f '( ). f '() as f () 85 (Not possibl) Which would ma f ca t b costat aroud. Now ithr th fuctio will b o-o i, or it wo t b. pat this procss tims, th itrval is,. Lt go to ifiity. W arriv upo a cotradictio that f is costat aroud. f ', Assum that f ' or f ' f ' d d or f f or f f Which is absurd. I fact i ay itrval of lgth t. Cosidr f ' ca t cd. For all. t lim f f 85 si dos NT ist Cosidr g() f () f () Say Th fuctio is cotiuous is that g'( ). (Th fuctio will attai a trma). As g( ) g() 85 g '( ) f '() f "( ) f ( ) Now f '( ) as f () 85. Which is icorrct. Thrfor f "( ) f ( ). f () ' g() ' f () g () f () g() f '()d g '()d f () g() f () l() f () l f () g() g() f () g() g() f () g() g() ad f () g(), o accout of its is big diffrtiabl (, ) such g() VMC Papr- JEE Etrac Eam-8 Advacd

15 6.(C) f :[, ) f () f () g() g() g() f () f () g() f () g() l t f () f (t)dt t f () f (t)dt o ' f () f () ( f ()) f () ' f () f () ' f () f () ' f () f () ( ) d f () ( ) d f () d f (). 7.(8.) Ara = ().. sq uits log log 9 log 7 log 9 7 log log7 log log log 9 7 log 9 log 9 7 log (65.) Th last coupl of digits ca b (,,,, 5) Corrspodig to vry such combiatio, thr ar such umbrs 9.(78.) X 8 or Y 8 Tr r th trm of first A.P. P S = s th trm of scod P To fid Tr Ps r, s 8 r r r 7s 6 r ad s is a solutio r 7t r 8 5 t 7 X Y 88 X Y X Y X Y = 78 i i i i i i cos.(.) si VMC Papr- 5 JEE Etrac Eam-8 Advacd

16 bviously = is a solutio si si 8 5 Thr ist oly o solutio i, y ( )...( ) y l( )( )...( ) l( ) r l( r) l( ) l r r r lim l y lim l r.(.) I l( ) d l( ) l( ) l y l l l y [ y]. [ L].(.) c a yb (a b) a.c cos b.c cos y c y a b cos cos 8cos.(/) (.5) a cos bsi c,, a cos bsi c..(i) a cos b si c..(ii) (i) - (ii) a si si. b si G b b ta t whr t a a VMC Papr- 6 JEE Etrac Eam-8 Advacd

17 ta b (.5) a.(.) Ara of triagl PQ.. sq.uits Ara tak away by farmr =. sq. uits d (A) Clarly G (, ) E (, ) F (, ) E, E, F, F, 6.(D) Equatio of MN cos ysi h ; k cos si h k y y h k! D!!!! 7.(A) 5! 8.(C) Usig pricipl of iclusio ad clusio, th favourabl umbr of cass 5!.!.!.!!.!!!.!!!.!! 7 PT T T T VMC Papr- 7 JEE Etrac Eam-8 Advacd

1985 AP Calculus BC: Section I

1985 AP Calculus BC: Section I 985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b