JEE-2017 : Advanced Paper 2 Answers and Explanations

Transcription

1 DE 9 JEE-07 : Advancd Papr Answrs and Explanatons Physcs hmstry Mathmatcs 0 A, B, 9 A 8 B, 7 B 6 B, D B 0 D 9, D 8 D 7 A, B, D A 0 A,, D 9 8 * A A, B A B, D 0 B 9 A, D 5 D A, B A,B,,D A 50 A, 6 5 A D B B 5 D 7 6 A 5 B A 5 B 8 A, B 7 6 B, D 5 B B, 5 9, D 8 7 A, 6 D 5 A, 5 L Educat Lmtd gstrd ffc / orporat ffc A -, Lowr Ground Floor, Espr Buldng, Mohan o-opratv Industral Ara Man Mathura oad, Nw Dlh 00, ontact No / 00 I

2 PAT - I : PHYSIS. Sun d Ms = 0 5 M. d =.5 0 v =. km/sc. Applyng E Earth Vs 0 a 0 A GMsm GMm mv s 0 d B(du to sngl sgmnt) = cos cos GMs GM v s = d v = v s = GM GMs v d Snc d =.5 0 d + d G 0 M v s =.5 0 = v + v = v v s = v 5 v km/sc. QP...() P b S...() S b Q...(). B From () S b Q b Q P Q b PbQ a A A = a = a sn0 = a,, 6 B o = cos cos a 6 a B = 6 a a. A For photo lctrc llct hc K h h D p mk h K m D D h hc m Dffrntatng w gt, h m D D D D hc......

3 5. D T L L g...() whr = vlocty of sound. dffrntatng ths quaton w gt 6. M V L L T T g L ; L g L puttng valus w gt M = Takng log L 00 % L logm = loglog log Dffrntatng 8. A, B Snc no forc acts horzontally, thrfor M n horzontal drcton dos not shfts, thus t falls vrtcally. pton B s corrct. A (0, 0) L/ B ntr of mass falls down from L/ to L/ cos Dsplacmnt of M s L/ L/ cos pton (A) s corrct. If w tak th bottom pont as orgn th coordnat of pont A wll b x = x y L L L sn, y = Lcos whch s an quaton of llps. Pont B on th rod s acclratng n x-drcton Snc s constant. t wll also b constant.; t t A ma x L/ L/ B 7. In a polgon of sd n h n cos = h h cos L L ax cos sn Whr a x s th acclraton of pont B w.r.t pont B, w also nd to consdr torqu du to psudo forc ma x. L L B mg sn max cos L L L L B mg sn m cos sn cos whch s not drctly proportonal to sn. h h h h cos cos n......

4 9., D x = n a cos = n P cos = 7 n n6 0 0 n a.8 0 S S d P = 600 nm d =.8 mm path dffrnc x(at P ) = S P S P = d =.8 0 m for mnma x = (n + ) 0 sn 0 n sn n = for angular dparaton btwn two succssv maxma. sn As, w mov from P to P, dcrass and ncrass. hoc (B) s ncorrct. x.8 0 n + = = = 6000 whch s vn. At P, w don t s a dark spot. hoc (A) s ncorrct. At P, hnc, w s a brght spot. hoc () s corrct as for maxma, x = n n 6 0 = 000 = n At P, x = 0 = n n = 0 hoc (D) s corrct P N S S M d P 0. A, B, v V LL L L L b t / V V a V b = V v a L L v t L L L L L L t / L L L Lt P = a = S = S = m N = M = a cos x = S P S P =( + acos) ( a cos) a cos for maxma. d L V V V dt L L t L L a b t L d dt v LL L L t......

5 . B L L t L L,L L v L L VL L L t L L LL Smlarly: L L t VL L L t LL vl vl t ; & L L L L Also; L (at all frms) = L P x S Q whn forc s appld at P-tangntally = (torqu du to F) + (torqu du to mg) = F mg(x) whr x = momnt arm of mg Snc th valu of x dcrass ncrass. whn forc s appld to crcumfrnc at P, thn th whl wll hav no tndncy to rotat, = 0 (pton B s corrct) whn forc s appld at x. Th torqu du to F rmans constant, But th torqu du to mg agan dcrass dos not rman constant. whn forc s appld at S, th torqu may rotat th whl.., D Drawng phasors. Y V sn( t + )V V sn( t + ) Potntal dffrnc b/w x & y = V Z X (Vsn t) V Vms Snc th phasons ar dntcal, potntal dffrnc b/w all ponts wll b dntcal.. A, B All ponts on th crcumfrnc of th flat surfac ar qudstant from th charg Q, hnc thy ar qupotntal. Th lctrc flx through th currd surfac of th hmsphr = (lctrc flux through th flat surfac) = (lctrc flux through th con drawn blow) 90 Lt us consdr a sphr of radus r around a pont charg (at ts cntr) and fnd flux through th con. A d xd Th surfac ara of th curvd part A

6 . A, B rsn.rd r Q o con r r o Total flux through curvd and flat surfacs s sam as found arlr n opton (B) Th componnt of lctrc fld normal to th flat surfac s varabl as th dstanc of th pt. from th chang vars. r = mv QB From (): sn 8 or sn = from () : + rcos = + 5 r 8 8 Hnc, partcl xts from P P For B = ; r.., pt. n th abov fgur Q concds wth orgn and th partcl s movng wth p vlocty along +y-axs. for B >,r, So th Q partcl turns back and pass through rgonal agan. Th dstanc btwn P and pt. of r-ntry nto rgon s r or mv, whch s proportonal to QB mass(m). Th rqurd chang n momntum btwn P, and th forthst pont from y-axs s p p p. y r P 5. A E V E D V 6. A Stord Hat V V Q P V V 8 V 8 V W battry PE p Q 8p /Q 8 Th xt from p, rsn = /...() and + y = r...() V 8 Total Hat gnratd V V 8 6 V V V 8 V

7 PAT - II : HEMISTY 9. A Zn NaH(aq.) NaZn H. D 5. B.0T [Zn ] Ecll. log F [u ] 0. D T = 7K.5g of thanol ( H 5 H) P = bar 500 g of watr K f =. A.5 Tf Kf m = ( 5) ( ) ( ) ( ) HP HP 6 HP HP 6. B, D 7. A,.0T. log0 F.0T. F G nfe cll.0t F. F =.F +.0T. A. H () NaN / Hl 0 (A) (Q) / Hl Zn /H H + HH NH H H / Hl Zn /H N = N + H () (S) + HH / Hl Zn /H N = N + (Q) H + H H H N = N H / Hl Zn /H + H H N = N (S)

8 8. B, 9., D 6. D (S) s (H ) 0. A,, D H. B, D H B H H B H H ( cntr bonds) Bl s mor acdc than All.. A, B,, D All ar corrct.. B Mn / Kl Kl P P0 (wht P) (Excss). P 0 + HN N 5 + HP PAT - III : MATHEMATIS 7. B x, y, z 0 z = k x + y = 0 k total s n = 0 k + 5 k0 k = = Probablty c 5. B ( ) Et () HMgBr (Excss) () H /H ( ) H (H ) (Q) H S l 8. D 5 5 k k 6 5k 9. Lt g(x) = f(x) x g (x) = f (x) g (x) = f (x) > 0, hnc f (x), g (x) ar strctly ncrasng x Applyng oll s thorm for, on g(x) g() = g (/) = 0, thrfor g (x) = 0 for som x, () All f ' x 0 for som x, (H ) (S) 0. B f ' x for som x, Now f (x) n strctly thn f () > f (x),,f ' 9 x t dx tdt x

9 dx x t dt 8 x t dy x t dt t dy dt t dy dt t y t c y 9 x c y 0 7, c = 0 y A a p q M r b s t u c dagonal of M T M = a + b + c + p + q + r + s + t + u = 5 If on of th numbr s, thn on numbr s and rst 7 numbrs 0, total such numbrs 9! 7 7! If s not usd thn 5 tms on s usd, tms 9! 0 usd, total such numbr 6 5!! = 98. B P. Q. S. P Q. S P. Q S Q. 0. A P S Q. 0 SP Q SP s Alttud S s orthocntr 5. A, 6. B, D 7. A, f ' x f x log (f(x)) > x + c f(x) > k x f(x) x k > 0 g(x) = f(x) x k g(x) > 0 g (x) = (f(x) f(x)) x g (x) > 0 g s ncrasng x > 0 g(x) > g(0) f(x) x k > f(0) 0 k f(x) x > f(x) > x cos x cosx sn x f x cos x cos x sn x sn x sn x cos x cos cos x snx cosx f ' x 0 snx 0,or cosx. + f(x) s max at x = 0. cos cos cos cos 0 Usng half angl formula w gt tan tan tan tan 0 or tan tan 0 Hnc, (A, ) 8.* ptons ar wrong. B,

10 9. A, D y = x y = x x = 5. D X Y X Y sn = sn (P + Q) 5. B cos (P + Q) + cos (Q + ) + cos ( + P) [cos P cosq cos] 5. x x = 0,,, P Q cos 50. A, x x dx x x dx 0 0 x x x x x x f x cos,x, x x (a) x lm f x lm cos x x x x whch dos not xst (b) x x x lm f x lm cos 0 x x n n n p q n n n p q Lt & & p q 8 7p q 5 p q 56 7p q 8 5 p q 0 p q 8 0 & p q 0 p q p q 5. n n n n n n n n n p q p q a a a n n n a a a