PART TEST-5 (PT-5) TARGET IIT-JEE 2011 CLASS-XII/XIII COURSE : ALL INDIA TEST SERIES (VIKALP)

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1 PAT TEST-5 (PT-5) TAGET IIT-JEE CLASS-XII/XIII CUSE : ALL INDIA TEST SEIES (VIKALP) Hits & Solutio PAPE- PAT-I (Chmisty) H C H I th actio squc, C Cl NaH Na C H S Na C 7 NaH Na C AgN Na C (A) NaCl H Na C 7 (B) Na S H Na C (C) H Ag C (D) NaN Wh ml of M NaCN solutio Iitially ph will dcas fast, th slowly du to buff fomatio ad th will dcas fast as buff actio dimiishs If at 98 K, th solubility of AgCl K SP fo AgCl 9 () E Cl / AgCl/ Ag 8 59 log V A aquous solutio cotais Mthod of spaatig Ba 5 A cll actio ; de 78 Sº F Joul/K 6 Aquous solutio of Na S mais coloulss sic solutio is acidic & HPh shows pik colou oly i basic mdium 7 Compoud (X) o tatmt with HI Hot KM 9 Which of th followig is/a coct (D) Givs pussia blu pcipitat of F [F(CN) 6 ] with F Which of th followig agts ca (B) S Ag [AgS ] additio of mo agt [AgS ] Ag Ag S (whit) H Ag S (C) 5S I H boil Ag S H I stach blu colou No colou chag obsvd with C (D) S C 7 H I 5S 8H ; C (g solutio) S H No colou chag obsvd with C I which of th followig solutios, I AgN ad NaCN solutios, th solubility of AgCN will icas as compad to pu wat bcaus of compl fomatio as [Ag(CN) ] I NH solutio ad buff of ph 5, th solubility of AgCN will icas du to compl fomatio i cas of NH solutio ad hydolysis of CN ios i cas of buff of ph 5 Which of th followig agt(s) is/a CH CHCH CH H B / CCl B 8 X Mg Y ( i) Dy C th (ii) H CH CH CH CH H B KM C H Mg Hot KM B CH CH CH CH B Z CH CHCH CH dust (D) CH CHCH CH H M CH CHCH CH Tolls agt CH CHCH CH Idtify th coct d of oidisig pow : I < F < < Cl < M d of ducig pow : I > F > H > Cl > M So, M ca oidis all th oth ios/molculs Cl ca oidis H / F / I ios/molculs SL6 -

2 5 Which of th followig lctochmical All hav Eº cll gativ 6 agt P 7 Th stuctu of th poduct Q is : 8 Th stutu of 6 to 8 PAT-II (Mathmatics) i 7 If ag, th which of i 6 i ag i 6 y y ta ta 6 y y y ag ( i) ag ( i) 6 y y ( ) y ct (, ), adius Th coductivity of a aquous solutio m ad m 5 5 So 8 As If 56 ml of H gas at STP is fd ito ml of H gas mols of H gas mols of 8 t t t is 9 A o-o vcto a is paalll to th li of Nomal vcto to pla P is Nomal vcto to pla P is kˆ î ĵ kˆ H gas mols of lctos (î ĵ) (î ĵ kˆ ) 5 9 / 965 C of lctical chag 85 C So, lctical cut i Q 85 8 A t 6 5 Th activ igdit i aspii is [Actyl saliclic acid] 6 6 g L 5 By stwald's dilutio law M 8 K a C M ph log [H ] 5 D Cl Cl / F ; D Cl ; D Cl ; D Cl If ()d g() put f ad f () is f () d f () (f ()) d f () t f () f(t) (f ()) d f () g(t) f () g(f ()) C If th plas cy b, y a c cy b y a c b ay pass though a li c b c a b a ( a ) c ( c ab) b (ac b) a c abc abc b a b c abc If is a imagiay fifth oot of uity, log log log [As ] SL6 -

3 / Th valu of / / / / / d si si d si / d / d Hc / / si si is d (o placig by ) Th poit of itsctio of ag Sic ths ays dos ot itsct hc th is o poit of itsctio 5 If th vtics of a quilatal tiagl a sc 8 If d si sc si (si) d d I I sc Applyig by pats o I, w gt ta (si ) (si) ta cos d (si ) ta d C (si ) (si ) ta I I (si ) P(/) ta P() (si ) d C, P() ta ag ag ( ) ag ( ) 6 Which of th followig itgals (A) / / (cot ) d / (ta ) d ( (cot ) (ta )) d (B) (C) (D) / si d d ( ) / cos d 7 If th valu of p ) q p si d ( ) ( ( ) / ) / / cos d cos d q q ( si icos q q q ( i) cos isi i p Ad : ( p )(i) 5i 8i i 98i 8( i) p a b p 9 Valu of A Valu of C Valu of (9,, ) Difftiatig both sids 6 6 (A B C) ( ) (A B) 6 6 (A B C) ( ) (A B) ( ) compaig cofficits of lik pows of : A A A / : 6 A B 8A B B 6 B : B C 6A B C Costat tms : 6 C B thoct of ABC Cicumct is (oigi) Sic othoct divids th sgmts joiig cicumct ad th ctoid i th atio : tally affi of othoct is Affi of th poit Lt affi of E b ag ± SL6 -

4 If a compl umb t is dfid by t ( c) a b (t a) b tc b tc t a b tc t a c th locus is a cicl if c b / c t t a 5 If satisfis th quatio 8 i ( ) ( 9 i) o ( ) d c d put, 7 5 t t 7 7 c 7 si si d si si d si 8 If th compl umbs,, Sic th poits li o uit cicl with ct at oigi Sic th tiagl is quilatal, ctoid of th tiagl is th sam as th cicumct 9 If,,,, 5, 6 a th oots i is 7th imagiay oot of uity So as 6 5 Fid th distac of th poit P (, 8, ) Lt A b th poit (,, ) so that AP is paalll to th giv pla Th ( ) ( 8) ( ) 8 6 d Thfo, A is (5,, 8) PA ( 5 ) ( 8) (8 ) cos 5 If d A cos cot ta cos si d cos 5 If S S si d cos B 8 / / ( ) d S [ ] S PAT-III (Physics) 5 Th two ds of a A A P V A V B E i < E i B 5 A coductig ig Cosidig pu ollig of A about A: th iducd mf acoss A will b: B() Fom L law, will b th gativ d, whil A will b th positiv d Hc v v A B 55 Th quivalt sistac A C / D AB (By What sto balacd bidg cocpt) B SL6 -

5 56 As show i th Toqu of magtic foc about PQ () m ( L B) L cos L B cos () Toqu of gavitatioal foc about PQ g [(L) g L si ( L) g (/) L si] L g si () IB m g ta g 57 A coaial cabl is loop () B loop () loop () B B i i (i i i B B ( 5 ( ) (i i) loop () B As (C) 58 A paticl is Poit A shall cod o magtic fild (du to -paticl) wh th -paticl is at positio P ad Q as show i figu Th tim tak by -paticl to go fom P to Q is t o t 59 Cut i a coducto dv i ja EA A d Sic i is sam at vy sctio dv A is sam at all sctios d 6 A AC voltag souc At soac, LC ad at this agula fqucy, lctic bulb will giv maimum bightss 6 I a pottiomt i ma V ma i ma amp 75 6 V ag of pottiomt to 6 V, so voltag gat tha 6V ca ot b masud ) 6 Th istataous P i E t/c E E Fom gaph, Pma (i) > C > C (ii) Maimum chag C E C E (iii) Fom (i),(ii) & (iii), E E C C >, C > C & E > E 6 Two difft coils di L Sic P P o i v i v & v di L v i L & w I i w LI 6 A paticl of chag E B k qe (a) E m (v) mv mv qa o mv v v mv At P at of wok do by E qev a At Q at of wok do by E qe (v) cos9 At Q at of wok do by B 65 Th valu of 66 Th sistac 67 Th sistac As E is icasig it's cut also icass, So, icasig gaph is of i i wh E E E 6v Now ; i A, i A, E 8V 8 6 & 68 Maimum dowwad 69 Maimum cut 7 Maimum vlocity Ldi Bv Ldi d B Li i B L (i) 8 d mg Bi m ma (ii) SL6-5

6 Fom (i) & (ii), mg B L d m d B mgl ml B B ml & ma positio is at SHM mgl Amplitud A of SHM B Ma dowwad displacmt, mgl B B mgl i ma L B mgl B B ml mg B & v ma A 7 A pdulum mad of a Th magtic foc o bob dos ot poduc ay stoig toqu o bob about th hig Hc this foc has o ffct o tim piod of oscillatio 7 Two coaial coductig It is obvious that flu likag i o ig du to cut i oth coaial ig is maimum wh (as show) o th igs a also coplaa Hc ud this coditio thi mutual iductac is maimum 7 A dilctic is istd Th lctostatic foc o mtal of capacito is pssu aa of plat A chag p uit aa o plat Sic chag o mtal plat of a "isolatd" capacito dos ot chag, foc o mtal plat mais sam Elctic fild dcass du to iducd chags i dilctic, but this dos ot ffct th chag distibutio o isolatd mtal plat 7 A wi of uifom coss As th lgth of wi is doubld, th coss-sctio aa of wi bcoms half Thfo sistac of wi bcoms fou tims ad cut bcoms th of th iitial valu also v d A Sic cut bcoms o fouth ad coss-sctio aa of wi bcoms half, thfo fom abov quatio th dift vlocity of lcto bcoms half Hc statmt is fals 75 A fiit ladd cicuit If capacitac of C is qual to 6F Th quivalt capacitac of th ladd btw poits A ad B is bcoms i dpdt of th umb of sctio i btw poits 76 A stl ball fallig vtically V si V cos (i) V cos V si (ii) Dividig (i) & (ii) ta ta 77 Cosid th lctic Th cicld pat of cicuit ca b placd by a cll of mf E ad ital sistac by 6 8V E 8 / 6 / 6 6 V ad / 6V 6 6 This is show i th scod diagam Th pow dissipatd will b maimum fo vaiabl sisto I that cas th cut i is 6 I 6 A A Pow dissipatd i W W 78 Figu shows a squa Fo < t < s, i Bv/ A (aticlockwis ) Fo s < t < s, costat so i, Fo s < t < s, i Bv/ A (clockwis ), Fo t > s, i H i i J PAPE- PAT-I (Chmisty) Th ph of a M solutio of a wak C K b [H ] C 5 ph ph lit of a aquous coctatd Wh NaCl is lctolysd, 9 6 Q it 965 At aod : Cl Cl At cathod : H H (g) H F Mol So, [H ] ph Cosid th half cll () 6H B B H 6 E 6, G 6 F ( 6) () H B B H C C C C 6 µf E 76, G F ( 76) Fo actio B H B H E? G F ( E ) SL6-6

7 Tagt actio, E G G G F [ 6 F6 ] [ F( 76)] 66 5 E 55 V G F( E ) 65 kj I a cll that utilis th E cll Eº cll 59 log [H ] PH [Z ] Additio of H S will icas [H ] ad thus E cll will b mo ad Equilibium will shift to th ight 5 Which of th followig statmts (A) NaN 7NaH Z Na Z NH H NaN Z 5NaH Na Z H NH (B) Ni DMG NH H [Ni(DMG) ] (d) (C) Pb C PbC (yllow) Ag C Ag C (d) (D) Bi I BiI (black) Bi H Bi(H) Bi(H) [S(H) ] Bi (black) [S(H) 6 ] 6 Th coctatio of K i itio ad E Eº 59 log [ K ] t [K ]I 59 5 log 77 Volt (oksyv) 5 7 Black (A) H S (B) FS(A) H S H S FS FS will giv blu ppt with K [F(CN) 6 ] of pussia blu 8 A ukow wak acid is Milols of CH CH iitially milols of NaH Wh ph pk a (good buff) th CH CH mols 5 bcoms half 5 milols milols of HCl addd 5 Volum of HCl addd ml 9 Which of th followig is possibl Cl H H / H CuS NaH [X] X Cu(H) blu ; Y [Cu(NH ) ] dp blu Which of th followig statmts is/a Fo a salt solutio of (WA ad WB), h h K w K K a h 6 5 (>) b h h Th fomula ph (pkw pk a pk b ) dos ot ivolvs ay appoimatio Sic, th acid is lativly mo wak tha th bas, so fial solutio will b basic i atu (ph > 7) 5 Alkys ca udgo i which Cocptual 6 Tolu, wh tatd with B /F CH is a lcto lasig goup It icass lcto dsity at otho ad paa positio though hypcojugatio 7 Statmt- : N salt o ductio with K HgI KH is ssl agt 9 Statmt- : Additio of bomi to Additio of bomi to a alk is a ati additio a symmtical tas alk o ati additio foms a mso compoud Also i additio of alk fist of all B attacks thfo it is a lctophilic additio (A) Cu KCN (css) (A) Cu KCN K [Cu(CN) ] (CN) css ttahdal, do, diamagtic (B) Hg I Hg [HgI ] ttahdal, do, diamagtic (C) Ni KCN Ni(CN) css II K [ Ni (CN) ] (g) squa pla, diamagtic (D) Z NH H Z(NH ) ttahdal, diamagtic PAT-II (Mathmatics) Lt C dot th st of all compl A B is th st of compl umbs pstd by th shadd gio i th figu wh QC X ad CP maks a agl y P Q C i of with th positiv -ais Idtify th coct statmt (A) LHS [( ) c] c (B) Fom (A) w ca say (B) is also ot coct (C) LHS ( c) c d (D) W kow a 5 ( a ) c 5 If (, ) ad (, ) a two pais of ag ag ag ag SL6-7

8 6 I a AB, E is th mid poit B ad D Lt A(a), B(b) b a PV of D b PV of E P AP Lt t, PD PE b a t(b a) Pv of P (t ) t (t ) t (t ) ( ( ) t (t ) 5 ) t () () 7 If i, is a imagiay cub ( i) [( i) ] (i) ( i) ( i) ( ) ( ) ( ) ( ) ( ) ( ) Lt ( ( i) ( i) )( [(i) ( i) ] [(i) ( i) ] (i) if is odd i (ii) if is v th 8,,, a distict compl Sic AD BC ad AD BC ABCD is a paalllogam Futh ag ABCD is a ctagl ) BAD 9 9 Lt f : b a difftiabl fuctio f() 6 f() t 6 5 t 5 ( ) 5 {f()} f() { f ()} 5 f () (6) 5 6 si cos If < < th si si cos si si cos d si cos si cos si cos d si cos d si c If 5i 5, th ma Ag Fom AC cos 5 ma ag () mi ag () cos 5 BA cos 5 If a î kˆ, b î ĵ kˆ ad c b a 5 î ĵ kˆ If a, b, c a o coplaa o-o b c a [a b c] a a a Similaly [a b c] b c a b c [a b c] Now [b c c a a b] [a b c] [a b c] [a b c] But [ a b c] So [ a b c] Hc a b c If is a o al 7 th oots of uity f() f() f( 6 ) 6 6 k f ( ) A Ak ( ) k 6 k k ( ) 7A A k SL6-8

9 5 7k k 7A A k k 7A k ( 7 ) si si cos si d si cos ta sc d ta (ta ) c () cot (ta ) c () cot cosc d cot (cos si si ) cot (cot ) c d si cos si si d si si d si cos si 6 If A si A ta (cos ) c d d sia cosb th th valu d si(a b) si(a b) d ta si(a b) si (a b) (a b) d (a b) (a b) d (a b) cas- A A A if a > b > if < a < b 7 Th dictio cosis of a li bisctig m m dictio atios of o of th bisctos a <, m m, > ) (m m ) ( ) ( dictio cosis of th biscto a m m, Similaly dictio cosis of th oth biscto a,, m m, 8 STATEMENT- : Th valu of th dfiit bt bt Statmt- at f ()d at f ()d f() d at bt f ()d f ()d Statmt- is tu T (b a) f() 7 Statmt- ( []) (si ) 9 d d 8 ( si ) d 6 Statmt- is tu ad is plaid by statmt- 9 STATEMENT- : ta ( ) Statmt- ta d ( ) ta d ( ) ta c Statmt- is tu Statmt- (f() f ()) d (f() f()) d f() f() Statmt- is fals d c (f() f()) d c STATEMENT- : a, b, c a th distict Statmt- is tu Statmt- (A ) a b c a b c a b c a b c b c a b c a Statmt- is tu ad is plaid by statmt- (A ) d d d d d d (B) { } d d d d (C) (sg( )) d d d 5 7 SL6-9

10 (D) I (f( ) f( ))d f( ) f( ( ))d I I (A) If compl umbs,, (A) Sic ( ) ( ) ( ) ( ) ( ) (B) ( ) ( ) oots of th quatio a,, Amog ths th oots ad satisfy th scod quatio 985 ad dos ot satisfy th scod quatio umb of commo oots is (C) (D) y i y y y y i m i m y y y i i m y y i y y PAT-III (Physics) I th giv LC C q C Q q Q Q E C q q Q C 6 y y 6 m A coductig wi I th loop cotaiig wi AB th flow of cut will b fom B to A bcaus mf gatd i that loop is lss tha th mf gatd i th loop cotaiig CD 5 A iducto coil U LI P I o 6 I th cicuit show ( ) V ( ) is lss tha So that, is gat tha 5 U L P 7 A ad B a two Th fild at A ad B a out of th pap ad isid th pap spctivly As th cut i th staight wi dcass th fild also dcass Fo B : 8 Two log cylids Lt th cut dsity i complt lft cylid is J, th cut dsity i complt ight cylid is J Th magtic fild at ay poit P i th gio of ovlap is B J AP ( J BP) J (AP PB) ( J AB) Thfo magitudof fild at ay poit i gio of ovlap is Jd ad its dictio is alog positiv y-dictio at ay poit P i ovlap gio 9 I th figu iitial (C) V Q Q C C Fial pottial diffc o Fial chag Zo Chag flow c fom A to D 5 A poit chag is movig Th poit chag movs i cicl as show i figu Th magtic fild vctos at a poit P o ais of cicl a B A ad B C at th istats th poit chag is at A ad C spctivly as show i th figu Hc as th paticls otats i cicl, oly magitud of magtic fild mais costat at th poit o ais P but its dictio chags Altat solutio Th magtic fild at poit o th ais du to chagd paticl movig alog a cicula path is giv by o qv It ca b s that h magitud of th magtic fild at a poit o th ais mais costat But th dictio of th of th fild kps o chagig B 5 A dipol is kpt at Kp cos Kp si cos si Th chag i th magtic fild which causs iducd cut ( B) is alog () dictio Hc, iducd mf ad hc cut should b such as to oppos this chag B Hc, iducd mf should b alog dictio which sults i a clockwis cut i 'B' Similaly, th will b aticlockwis cut i 'A' Hc (B) ta ta SL6 -

11 5 A ammt ad a A V V V Equaivalt sistac dcas so cut will icass V A V V Du to chag, V A icass so voltmt adig will dcas 5 Th switch S show (C) Switch is kpt closd fo a log tim, Cut though sisto i V Chag o th capacito at stady stat, q 5 5 µc at t, switch is opd, i i t/ C 5 5 µs Cut i 5 q 6 5 A V i 5 / 89 A 5 55 Th idtical discs Nt impuls o A is chag i momtum mv Sic collisio is lastic, kitic gy cosvs 5 F 56 A batty of mf E V E i fom gaph V 5i 5, E V E i ma amp 5 57 Th figu shows a 59 STATEMENT : A paalll bam of Th paalll bam of gativly chagd paticls passs udflctd though cossd lctic ad magtic filds Hc qvb qe Thfo vlocity of all paticls will b sam Hc Statmt- is Fals 6 STATEMENT- : A chagd pla (Modat) Lt th lctic fild i gio ad b E ad E Th pottial diffc acoss lft half capacito ad ight half capacito is sam Thfo E d E d wh d it plaa gap E E Hc statmt is fals, statmt is coct by dfiitio 6 STATEMENT- : I a sis,l,c Statmt is fals bcaus th giv latio is tu if all voltags a istataous 6 I ach situatio of (A) Fo pottial diffc acoss ach cll to b sam E E E i E i o i E E Hc pottial diffc acoss both clls caot b sam Cll of low mf chags up Fo pottial diffc acoss cll of low mf to b o E i which is ot possibl Cut i th cicuit caot b o E E (B) Fo pottial diffc acoss ach cll to b sam E i E i which is ot possibl No cll chags up Fo pottial diffc acoss cll of low mf to b o E i ad E i ( ) o E E which is possibl E > E Cut i th cicuit caot b o (C) Situatio is sam as i (A) cpt cut dcass fom E E to o Hc th oly optio that shall chags is 'cut shall fially b o' (D) Situatio is sam as i (B) cpt cut dcass fom E E to o Hc th oly optio that shall chags is 'cut shall fially b o' 6 A bam cosistig mv qb giv V C i AEFC V A V C V A V A s by KCL, at poit D (V A ) (V B ) (V C ) (V A ) (V B ) V D (i) A s by KCL, at poit B (V A V B ) (V D V B ) (V C V B ) (V A V B ) (V B ) V B (ii) A s addig q (i) ad (ii) (V A V D )(V B V D ) (V A V B ) (V B ) V D V B 6V A 6 V D 6V B V A V D V B 58 A L cicuit with a di EMF iducd L, st quatitis a o A C mv B mv B B mv B mv D B SL6 -

12 CDE - ANSWE KEY PAPE- QNo As A C D B D A D C ABC BCD Q No As BCD CD D C D B B B F T Q No As T F A A B B Q No As B A D D ABD ABC AC BD A D Q No As B A B D T F T T 7 Q No As B C D B C B A C Q No As CD AC ACD ABD B D B C B A Q No As T T F F 6 CDE - PAPE- QNo As B A A C C C B D C C Q No As A ACD ABCD ABD ABC AC C A C (A) p,q,s ; (B) p,q,s (C),s ; (D) p,s Q No As (A),s ; (B) q ; (C) p,q ; (D) s,t A C C A A C A D A Q No As B C ABC BC ABCD AD AC A C A Q No As (A) s ; (B) q ; (C) p ; (D) (A) q ; (B) p ; (C) p ; (D) C A C C B A C A Q No As C D C ABD BCD ABC ABCD ABC D D Q No As D (A) p,q,s,t; (B) p,,s,t ; (C) p,q,t ; (D) p,,t (A) s ; (B) p ; (C) q (D) SL6 -