Solutions to FINAL JEE MAINS/IITJEE

Transcription

1 Soluions o FINAL JEE MAINS/IIJEE - [CHEMISRY].(C By consrvaion of mols PV P V P V + R R R P + P am..(a.(d.(b KMnO will rac wih FSO only. mols 5 mols χ FSO / N (g + H (g NH (g a a a a q a a P PNH P. a AgNO 5.(C CH CH CH Cl AgCl + CH CH C H Allylic carbocaion. 6.(D 7.(B 8.(B 9.(A R.D.S. of Cannizzaro involvs ransfr of H ion o h carbonyl group. O CH C CH CH C CH HgSO / HSO H O π icr mols Mols..(C Magnic quanum numbr (m can ak valus from l o + l including O. Hnc C is incorrc..(d.(d Fac..(D Aluminium sols ar posiiv sols so ngaiv ions ar imporan for coagulaing hm and h bs ngaiv ion among h givn opions is PO (bcaus i has h highs ngaiv charg, so bs coagulaing agn is K PO..(C B.P. F < Cl < Br < I London Disprsion forcs. VMC/JEE- FINAL JEE MAINS/Soluions

2 5.(C P P V V P P V V 6.(D P V P V Whn air akn in, P, V rmain sam n n n 5 6 n 5 X coinss 8 8 Y fac cnrs 6. XY 7.(B Ecll ( Egah EAnod 8.(B Rd Po ( n + + Ca+ Ag Cu + Ag + + E.56 Zn + Ag Zn + Ag E Zn + Cu Zn + Cu E. + + E.76 Rd cll cll cll ( n cll Zn + H Zn + H E.76 Z h inrnal nrgy of gas pr mol Z R R Now, dv d Z CV R n d Z d R ( Z / + CP γ + CV Z / R Z. Rd Cu Zn E. E 8 Rd ag α C 9.(C For aquous soluion of NH i.., NH OH soluion, Kb α C Α Now, 5 Kb.6 α.6 C. Λ α ΛαΛ Λ E.5 Rd Ni ZR Z and CP CV + R + R R + Λ 9.99 ohm cm mol. a P+ V b R V.(B A poin A, P is high so ha a/v can b nglcd. Hnc, P( V b R PV Pb R PV Pb+ R PV Pb Pb + Z + ( R R R R Puing, P w g, V b Z + V VMC/JEE- FINAL JEE MAINS/Soluions

3 .(D.(B.(B π En z m k Z n h n Now, for + IE of H E E k k [for H, Z ] Li +, Z and for firs saionary sa n ( Z 8 E k.9 n 7. J aom. 8 k.9 J aom Qusion has bn canclld. If corrc daa is usd hn w g h following valus. As h racions ar paralll. k.6 % of B k+ k % of B.9 % of C 75..(A La(OH is mor basic han Lu(OH. As h siz of h lanhanoid ions dcrass from La + o Lu + h covaln characr of h hydroids incrass (Fajan s rul. Hnc, h basic srngh dcrass for La (OH o Lu(OH. + 5.(D Bcaus in NO, N aom is sp hybridizd (bond angl 8. In no ohr cas, N aom is sp hybridizd. 6.(B 7.(C Du o poor shilding ffc of d-lcrons of Ga h our lcrons princ mor aracion by h nuclus. 8.(A h principal group should gs h lows numbr i.., sars from COOH. 9.(A Buffrs ar wak acid/bas wih hir sals wih srong bas/acid..(a NaBO7 + 7HO Na B OH + HBO Sal wih srong bas Wak acid VMC/JEE- FINAL JEE MAINS/Soluions

4 Soluions o FINAL JEE MAINS/IIJEE - [PHYSICS] KK 6.(D K K + K N / m K + K 9 m. π π π Hz. K 5.(A C E B & CB E in magniud. As 8 6 ˆ and 7 ˆ ˆ C i E j B. k.(b Only lcric forc acs on h paricl..(a Lows frquncy HCF of Hz & 5 Hz 5 Hz. 5.(B D is no conducing bu D is conducing i A + 6.(B Enrgy of proon MV 7.(C 8.(A v v R ( R R n n / n n + + π R R R V 9.(B P E / C ( E / C E / C.(C 6 i A ( (A If h magn is cu along is lngh (i.. paralll o lin joining S-N in hr pars and hs pars ar again suck oghr wih lik pols oghr, momn of inria dos no chang. Also, pol srngh of ach par is M/. Afr sicking oghr, pol srngh again bcoms.m/ M. So, nohing changs by h givn opraion. Hnc rmains sam..(d As P.d across L and C ar ou of phas. chang influ no of urns WW.(B inducd currn n oal rsisanc im ( R + R.(A N mg cosθ + F sinθ Nµ + F cosθ mg sinθ mg sinθ F cosθ µ and sinθ cos θ / mg cosθ + F sinθ N ( W n W 5R Nµ F mg VMC/JEE- FINAL JEE MAINS/Soluions

5 5.(C Avrag vlociy 6.(A 7.(B 5 5 / V ( R / Ic α α I. E V sinθ cosθ V sin θ + + H g / V sin θ g sin θ V cos θ + α β α / α. cos θ + cos θ V + cos θ 8.(B a b c + + a b c + + ( ( ( % 9.(C H ( KA l ( ( K A H ' l H ' H 5.(C L MR ω + MVR & U Rω L MR ω 5.(C C p C v + R ha rquird a consan volum nc nc nr 7 5(8. ( 66J 5.(A 5.(C C + C C + 6 C C 6µ F 5.(C L u and u y ar h and r componns of vlociy of m afr h plosion mu + and u + u y m.5 kg oal mass.5 kg 55.Qusion has bn canclld. 56.(A 57.(C I. A 6 + V. 6. V AB Po. grad.. V / m..5 m r ur r 5 cm v mgµ sr and ar gµ gµ as M m a + m sr (. 6 9m v p VMC/JEE- 5 FINAL JEE MAINS/Soluions

6 58.(A r+ c 6 sini 7 sin r r 6 sin 7 sin6 cos sin cos i µ i π π / n 59.(C B n. cos π R cos π / n nµ i π an π R n 6.(D 7 Soluions o FINAL JEE MAINS/IIJEE - [MAHEMAICS] 6.(A 6.(C 6.(C 6.(D 65.(A S S ( + + ( ( + ( + + ( ( + / 5 5 S f f... n f n l lim n n f f... n f n n( n + f + f ( n f f l lim n n l lim lim n f + f ( n f n n ( n + ( n + n n + f 6 ' i n ' n i n n i + i + i + α i i α α i i n n ' i i i i n X X nw + + n α n n α f f ( 5 ( 5 f '( 5 l lim form 5 g ( g ( 5 ( 5 g' ( 5 Apply LH Rul o g : Apply LH Rul again o g : f ' f '( 5 ( 5 l lim 5 g' g' f " f " 5 8 lim 5 g" g" 5 X nw X + α. α Diff. w.r.. dy sin cos y cos cos y sin sin y (i d form VMC/JEE- 6 FINAL JEE MAINS/Soluions

7 66.(B Vidyamandir Classs dy cos cos y d π π (, y, sin sin y π π (, y, Diffrnia (i w.r.. o g: dy dy dy d y sin cos y cos sin y cos sin y sin cos y sin sin y d d d d π π For (, y, d y d y ( ( ( d d π π (, y, + L + or ( + Now ( (D S (a, b R (7, 5 Mid-poin of PR Mid-poin of QS a + b,, a, b, ( P, 68.(C f { } { } + ; < ; + ; < f ( ; < ; lim f is is ru. (A Q (8, Y (B f ( ; f (. Hnc, f ( f is ru. O (C f ( is disconinuous a. Hnc, f ( is coninuous in [, ] is Fals. (D f ( aks all valus bwn f ( o f (. Hnc, i is ru. X 69.(C A A A I Pr-muliply A I A A by A VMC/JEE- 7 FINAL JEE MAINS/Soluions

8 7.(C a π π aan a an lim a a a a l lim a πh a a a lim π h πh a ( a + h an a π π l a (A ( ( + + ; (, ] [, ( ( + + ; (, ( ( + ; (, ] [, ( + ( ; (, Hnc,,, ar h roos of h quaion. 7.(A Uni digi can b,, 6, 9. ( ways (,, 6 (,, 6, 9 (,, 7 (,, 8 a π( a + h ah πh a an co lim a h a lim + a+ h a h h VMC/JEE- 8 FINAL JEE MAINS/Soluions Numbr of lphon numbrs. Hnc k. 7.(C a + yb + zc α ( i ˆ + yj ˆ + zkˆ ( ˆi + ˆj + kˆ + y ( ˆi + kˆ + z( ˆi + ˆj + kˆ α ( i ˆ + yj ˆ + zkˆ Comparing cofficins of ˆi, ˆj, k ˆ on boh sids, w g : α + y + z α y + z (i (ii + y+ α z (iii For non-rivial soluions, D α α α + α α [ C C C ] α α ( α + [ C C C ] α α α α + α Hnc, sum of valus of α 7. ( α + [ ] 6 α α, 8 7.(A For a n n mari, numbr of non-diagonal lmns n n. Uppr and lowr lmns ar corrspondingly n n qual. Hnc, numbr of disinc non-diagonal lmn ar. n n n + n oal numbr of disinc lmns (maimum + n 5 n 9 Y (D OA ; OB + 5 A + 5 X O B + y 9 + y OA : OB : 5 5

9 76.(D For S o b rfliv, (a, a, should b prsn. arb b a+ a a+ no possibl. 77.(D F Hnc, S is no an quivalnc rlaion on R. is rfliv as Ingr is symmric as if y I hn y also blongs o ingr. is ransiiv as if y I and y z I Hnc, is an quivalnc rlaion on R. an ; ; y + y z I + I i. z I+ I I hn f ( has rmovabl disconinuiy a. Also, f ( is coninuous ( (,,. y z 78.(C Poin A lis on lin L : λ and poin B lis on lin y z 6 L : µ 7 6 A( + λ, + λ, + λ and B ( + µ, + 7µ, 6+ 6µ ( µ λ ( 7µ λ ( 6 6µ λ AB + i+ + j + + k ( µ λ ( 7µ λ ( 6µ λ AB + i + + j + + k If µ λ + and 7µ λ+ hn λ ; µ µ λ Hnc, possibl vcor AB can b i+ j + k. Also, no ha if w ak µ λ + and 7µ λ+ hn λ and µ and + 6µ λ Hnc, AB can also b i j k or i+ j+ k. 79.(A f cos + an ( [, ] ( R f ( is dfind only for [ ] [ ], {common o boh domains π,, cos dcrass form π o and an incrass from π π,, cos + an, Hnc, [ ] π [, ], cos dcrass from o π and an incrass from o π π,, cos + an, Hnc, [ ] π π,,, Combining boh cass, w g : [ ] f π o. VMC/JEE- 9 FINAL JEE MAINS/Soluions

10 8.(D I ln ( ln + d L ln + ( Vidyamandir Classs d d I d d I + C I + C akcross 8.(D b c a b a c wih a ( a. b ( a. b a c 8.(D P( X 8.(B 8.(B, d ( + ( + P( X A is skw - symmric mari A A I + C ( ln + mb + a c ( a.b ( ( n ( [ is odd] B A B A A. A A A A A A C A C A A. A.A A A A A A A A n n n n D A D A A A n c c f f L Apply Apply lim f lim lim lim LH Rul LH Rul ( ( lim f lim lim f ~. 6 ; > > 85.(B ( lim f lim ; f c has hr roos if c n A is skw - symmric mari ( ( >,, + + Inrval [ 5, 5] has lngh of unis. Givn inrval has lngh of. (, (, 5 Hnc, prcnag of inrval is : 65% 8 8 j j ( (D ( j 8 9 j j j ( j 8 j + 5 j j VMC/JEE- FINAL JEE MAINS/Soluions 7 X j j j

11 j 8 j 5 + j j 8 j j (A Hnc, sandard dviaion ln( + d l lim from Apply LH Rul o g : j 9 5 j 8 8 ( ln( + ( ln( l lim l lim f sin. L + θ an anθ ( f sin sin sin an + an θ π an ; < f an ; π an ; > 88.(C f ( is non-diffrniabl a ± d 89.(A f ( ( an d + I f d an d an d + 9.(B ( I an ln + ( + ( ( ln ln l lim π π I ln I ln VMC/JEE- FINAL JEE MAINS/Soluions