Key. Section I 5. B 6. C. Section II 22. D 23. C 24. A 25. D 26. B 27. D 28. D 29. D 30. C 31. A 32. A 33. A 34. C 35. C PEARSON.

Transcription

1 K Scion I. D. D. D. 5. B D. Scion II. B. B. D. 5. D B 8.. D.. B. D.. 5. B B. B. B. B Scion Ι Gnrl piu Soluions for qusions n :. D.. 5. D 6. B 7. D 8. D. Probbili (h sum no bing qul o 8 Probbili (h sum bing qul o 8 h numbr of ws of slcing wo ingrs on from ch s is 5. h sum cn b 8 whn h ingrs slc r n, 6 n, 8 n, n 8. Probbili h h sum bing 8 quir probbili Wor: S P I N G Logic: 5 7 o: S W P W Similrl, Wor: L S I Logic: 5 7 o: F O F Z P Soluions for qusions n :. o rimburs is o p bck h mon spn. o inmnif is lso o p bck mon (for som loss or mg. Offs is n moun h iminishs or blncs h ffc of n opposi on. I os no mn gurn, s os inmni.. ucous is hrsh or hors. Ohr snonms r, gring, iscorn, jrring or srin. Soluions for qusion 5: 5. Whn w g ino b compn w g ino ho wr or g ino roubl. Ohr iioms o no work in h con. pic of ck is job/sk h is vr s whil bck o h rwing bor mns fil mp h hs o b sr gin. o b roun h bush is o voi spking opnl/ircl bou n issu. hoic (B Soluions. D B D.... D Soluions for qusions 6 o 8:. B. 5. B B. D B 5. D B 6. HI is prlll o h -is. n lin prlll o h -is mus hv is quion of h form consn. HI cn b n of h lins 8 or 7 or. or or or.. 8. (Q 8 8, 7 5. Suppos HI is h lin 8. hn H cn b n of (8, 7, (8, 8, (8, 5. H hs possibl posiions. For ch of hs possibl posiions I cn hv n of h rmining 8 possibl posiions. HI hs 8 7 possibiliis. s plin bov, i similrl follows h whn HI is h lin 7 or 6 or.. 8, HI hs 7 possibiliis in ch cs. ol numbr of possibiliis for HI (7 (7 h ringl is righ ngl H. h -coorin of G mus b h sm s h of H n is -coorin cn b n possibl vlu ohr hn h of H. h -coorin of G hs 7 6 possibiliis. G hs 6 possibl posiions. From ( n ( h ringl GHI hs 6 58 possibl rrngmns i.., 58 ringls cn b form sisfing h givn coniions. lrn Soluion: Givn 8 8 n 7 5 i.. hr r 7 vricl lins n horizonl lins. h numbr of rcngls form wih hs lins is 7. W know h on rcngl givs righ ngl ringls. ol numbr of righ ngl ringls form is In U n PQ, is common. U PQ h bov conclusions mn h hir pir of ngls of boh s mus b qul. h hir ngl of ch 8 (sum of h ohr wo of is ngls. U PQ. U U ( PQ Q

2 Similrl UQ SQ. U QU ( S Q ( S U ( PQ QU QU 8 U 5 QU U 5 U QU U 5 Q U 5 U Q 5 U From ( 8 U 5 m. 8. W hv o slc h bo h is lbl s miur. Now if w g pn, s h bo cnno hv miur, i hs pns. Now h bo which is lbl s pns cnno hv miur. [ If i hppns hn h bo wih lbl pncil mus conin pncils] h bo wih lbl pns hs pncils n h wih pncils hs miur of hm. Soluions for qusion :. Birh fcs r congnil (prsn from birh n no hrir, compulsiv, or congnil (ffbl; frinl.. Mr. Du hs ci o flo h firs grn pr in Ini fr visiing ngln. I is clr h hr is grn pr in ngln n Mr. Du is imprss wih h pr. ssum h cs whr Mr. Du lrn bou h grn pr whil in ngln bu hr is no grn pr in ngln; in such cs, hr woul no b n rlvnc o h visi o ngln. Hnc Ι follows. ccoring o h smn, Mr. Du wns o flo h firs grn pr. I implis h hr cn b svrl grn pris. hr cnno b mor hn on pr wih h sm nm. Hnc, ΙΙ follows. Mr. Du ss his grn woul rplc h rs in Bngl. From his, i cn b conclu h h grn pr in going o b flo in Bngl s wll. Hnc, ΙΙΙ oo follows. hrfor ll follow. Scion ΙΙ lcronics n ommunicion nginring Soluions for qusions o 55: hoic (B. Givn iffrnil quion is ( whr ( ompring ( wih f(, w hv f(,,, ( n sp siz h. h. B lor s sris scon orr mho, w hv, h h (! f(, f(, f f (f(, ( Hnc Subsiuing hs in (, w g. (. (.!.. hoic (B. Givn z i Now z i ( i i. i i (cos i sin i cos i sin i cos n sin ( Squring n ing, w hv ( cos ( sin (cos sin ln. From (, w hv ln ln cos n sin ln cos n ln sin. Givn curv is h lngh of h curv from (, o (8, cos n sin cos n sin π n π; n, ±, ±,. 8 π n π; n, ±, ±,. Givn im (V 7, S V n L(S V h numbr of vcors in S m. lso, hs m vcors r linrl pnn.

3 W know h, n subs of n vcors of n n-imnsionl vcor spc V r linrl pnn. Hnc h ls possibl vlu of m is W know h h r of h ringl wih n B s is jcn sis is B. Givn i j k n B i j k r of h ringl OB B ( i B i j k B From (, j k ( 6 r of h ringl OB 6 sq.unis. ωo 6. ( ω Qos ω ωo N I ; N os I Q os 6 ω ; Qos o L Qos 5 ω o L.mH 67µF O Im σ 7. VD ( 7(7 ( ( (7 5V hoic (B 8. F(s L{f(} - s s - h givn funcion is bilrl O in bwn - o. - < σ < K -. N N. F ϑ ϑ From h givn F -ϑ.5v N N hn F -ϑ? -[ F -ϑ ] K -( - K N N N - (I N F ϑ ( F - K ϑ ( -ϑ K - - F. ( V F ϑ.v. ppling KVL o h our loop. VDD D ID VDS S.ID VDS vols IP η.q. sponsivi W Po h.f Whr Ip phoo currn gnr Po incin opicl powr f frqunc of incin phoon h plnk s consn h J/s. from h givn η.7 Po.5 - J q /W hoic (B B o/p Y. b B n b B B b ( B B b ( B.B ( B. B B B Y B.B B B b Y. From h givn p 8ns N N n n o consruc MOD - rippl counr, w rquir flipflops. W know fclk n p 6 Hz 8 fclk.5mhz Bu w rquir h frqunc of h counr MSB (Q I oprs m MOD -. So o/p frqunc f ck.6mhz

4 . ol siz of mmor n.. K in bis Whr n ol no. of mmor chips K no. of rss lins X no. of lins ol siz of mmor KB 5. W know zro inpu rspons X( φ( ( φ( L {(si } Givn h n X( s s j(si si [ si ] [ si ] si (s (s s j(si φ(s s (s (s X(s s (s (s s s s X(s s X( n X( ILF s u( hoic (B 6. Givn G( s s.s zro S n pol S 5 Zro nrb origin, so i rprsns h L compnsor. Im 7. From h givn VPP 5V 8. From h givn 6 n D 6%.6 Fbck fcor β %. D.6 Df β 6..7% hoic (B. h givn circui is invring mplifir V 8 vols. I {IL If} m m 6 6 kω I IL If V kω I 6.5m.66 m 8.66 m hoic (B. W know in Dl moulor slop ovr lo fr coniion, is m s 56 6k { } 8-7 vols hoic (B 6. From h givn N 8 fm.5 khz fs.5 fm.5 khz fs.5 khz L n 56 n 8 rb N. n. fs khz 86 kbps. hoic (B. W know µ ω. µ m µ ωm. µ ( 6 π.5 µ µ (.86 µ µ.5 5 VP Vm 7.5V V Po ( m V m L L L V 56.5 m L 56.5 mw. W know skin ph δ π f µ σ δ wih f. ( ( * [h( * h(] ( * h( Impuls rspons h( h( * h( h - h ( τ.h ( - τ. τ

5 -τ.u - - -τ...u - - -τ...u - - ( - τ τ...u( - τ τ ( τ..u( - τ ( τ.u( - τ τ.u( τ.τ - -τ...τ.u -τ [ -] - -. [ - - ].u( n mho: H(s H(s.H(s h( IL {H(s}.τ τ.τ 5. From h givn H π /m η H µ π η Ω ε εr W εo εr εo εr ( ηh - 6 W mj/m 6. Givn h chrcrisic quion of mri is λ λ λ B l Hmilon horm, w hv I O ( onsir B I ( I ( I. (From ( B Now D(B D( ( ( k k n, whr n orr of 8 ( m m for n posiiv ingr m B 8 ( W know h Prouc of h ign vlus of ( n consn rm in h chrcrisic quion of (whr n orr of ( ( Hnc from (, B 8 7. hoic (B 7. Givn iffrnil quion is ( ( ( pu z (O z ln( ( θ z n ( θ(θ, whr θ z subsiuing hs in (, w g θ(θ θ ( θ - θ - 6 θ ( θ - 5 θ ( lrl ( is homognous linr quion wih consn cofficins. h uilir quion of ( is θ - 5 θ ( θ (θ θ, θ h gnrl soluion of ( is c z/ c z c( z / c( z c( / c( ( z h gnrl soluion of ( is c c(. 8. W hv Y (, O (, B Grn s horm, w know h N M M N ( Hr M n N M n In h rgion, N vris from o M N N M ( ( ] X n vris from o [From (] 8-6.

6 ( ;. Givn fxy(, ; Y, < Ohrwis [ ] P( X< Y P( X< Y ( P X< Y X< Y P(X < Y/X < Y P X< Y P(X < Y/X < Y XY P(X < Y f (, ( ( P(X < Y ( X < Y X > Y O (. ( ( Y P(X < Y ( XY n P(X < Y f (, X Y X Subsiuing ( n ( in (, w hv P(X < Y/X < Y 8.. W hv f( 5 6 W know h h lor s sris pnsion of f( bou is f( f( ( f ( f ( f (!! ( Hr f( 5 6 f(- f ( 6 f (- f ( 6 f (- 6 f ( 6 f (- 6 n f (IV ( f (V (. From (, h lor s sris pnsion of f( bou is f( f(- ( (- f (- ( (! f (-. ( (!.. f(( 8( ( lrniv soluions: ( (! ( 6! f (- 6 W know h h lor s sris pnsion of f( bou is sm s h of h lor s sris pnsion of f( in powrs of. f( 5 6 [( ] 5[( ] 6[( ] [( ( ( ] 5[( ( ] 6( 6 ( 8( (. X < Y X Y. From h givn signl ( -(- I is o signl So o n n bn.sinnωo.sinnωo X > Y ( B(π, O (. X -π (-π,- - π

7 ; π ; - π < < π ls whr π ωo o Bu funmnl prio π ωo bn.sinn..sinn. π π π.sinn π π π.sinn W know u. ϑ. u. ϑ. u. ϑ. π cosn π cos n... π n n π π cosn sinn b n π n n.( π bn π n n n bn (- ; for ll vlus of n. nπ ω h n. -j n H(ω n - H(ω h( h(. -jω h(. -jω h(. -jω. -jω -. -jω -jω ( -jω ( -jω -jω ω ω - j ω j ω - j ω - j ω j - j -. - jθ -jθ Bu sinθ ( - H H j -j.5ω -j.5ω ( ω j..sin.5ω j..sin.5ω -j.5ω ( ω j. { sin.5ω sin.5ω} z n.u n > z. ; z n.u n z z z z ( z. ; < z < X z n.( n - z. Z L (n n-.u[n ] n.u[ n ] (n n.(n z z ( z.z z. X z - z. z z z z { z z z} X z ( z - z{ z } ( z z X( z - z { z - } z -. Unr D. coniions cpcior cs lik opn circui. 5. k 5 I 5 mmp 6k W V Jouls V vols V 5 V - W ( 5.77mJ W 5.5 mj Vh ± 5 m h V V Ω I Ω IN 8 I Vh I 8 I V Ω N Ω i Ω ppling nol nlsis no V n Vh V Vh 8I (i V Bu I V Vh 6 V Vh V Vh ( V Vh 6 (ii From (i n (ii V 6V n Vh 8V Vh N Isc Isc: V V 8I V V V 6 V V V V 8 (i kω kω V I kω kω V Vh Ω IS kω

8 V V - V 8 V V (ii V vols V vols V Isc 8 N 6Ω 7. From h givn ρ.8ω m J 5 /m µn.6 m /V -sc µm ν ν V µ. µ. J. ρ m/sc µsc 7.5V - 5 Ω IN Ω N 6 Ω V H L 6. For < : - swich is clos L S. n O. h givn circui bcoms V -7.5 V V 5 6 V 7 V V 7V 7 V vols Vc( - vols IL( - mp IL( For > : 6 Ω Ω V F F Ω Swich opn, rprsn h givn circui quivln mol { 6 }Ω h chrcrisic quion of h sris L circui is s s L L s s. h roos of h bov quion is s -.5 n s V.. ; V( V n ic( mp (i Vc ic c { ] -(ii From (i n (i V( [ ]u( hoic (B 8. For boh rnsisors VD VG VDS(s VGS V VDS - V VDS > VDS(s So M n M r opring in surion rgion. I I,V V D D GS VGS VGS 5 VGS.5V GS W I µ n o L w [ V - V ] GS H - [.5 - ].75 m n. Jn q.d n. Dn µn V cm /sc.75 Bu givn Jn.5 /cm.65 [ 7 N] N N ( Jn N.6 65 N.76 6 cm. From h givn f(w,, Σm(,,, 5, 7 πm(,, 6. F ( w ( w B D F I I I I I I I I

9 Givn B slcion lin So B Io I I I From h ruh bl Io D D I D D D I D D I D D. From h givn circui LK -v g Q consir s clk o h n F/F I cs s n up counr Whn vr h NND g o/p X, i clr h circui. X onl whn Q Q Q i.., I is MOD-6 up counr V V b Ι mv k kω k kω kω V V V Vb 8 kω 6 kω 6 k Ι Q f o/p frqunc X clk 6 Q khz. rwing h givn circui mv V 8mV 5 6 mv V b 7.5 mv 8 Q V o 6 V 8 V V I K V b 5.65 mv Vo V Ι 8k Vo.8 mv..8µ. For full wv rcifir wih cpcior filr V VD Vm V VPP.5V.5 VD 8 7.5vols. M. S vlu of rippl volg V vols.5. Vols ippl fcor γ γ.57 Bu γ ( rms V VDc f.. L. 7.5 hoic (B F. µf 5. ppling currn mirror concp Ic Ic Vcc - VB I c c -.7 m.6 m 5 ppling kvl oupu loop. V.7.6 V V V 5. vols hoic (B 6. (s - - s /s (s (s ( s s s /s (s Simplif h givn block igrm ( s G s H s s s

10 Vi s. s ss l S G s.h s ( s s l G( s.h ( s k ϑ s ss.5 k ϑ ( s 7. W know rnsfr funcion G(s ( s 8. from h givn ( ( s - s s s s s ( s ( s s ( s.5s s 8 k B -.5s ( s s ( s.5s s 8 s( s s s s D J I V D ε ε I J. ε. ε W know ε. I I.5 6 π V. V. 5 k - V (s L{(} s sin n. V(m V; V(min.5V 5 I (min m m 5-.5 I( m m.5m IB(min m 5µ IB(m 87.5μ VB - 5 V k V - {- sin } hoic (B IB I IB Vi IB.B VB.7 I m.7m I (.7.5m.5m B min Vi(min V Vi(m IB(m.B VB IB(m (.7.875m Vi..7.V.78V Vi.V 5. W know B.w of SSB signl is fm onl G G G (.5575m B.W of mulipl signl n.fm Gur bn frqunc f 5 f 5 khz 5kHz G G fg f.5khz6khz G B.W ( 5 5 6kHz 6kHz 5. s zs z i.. is no prpniculr o h ircion of wv propgion (z ircion. Hnc i is M mo wih mo numbrs mπ π m nπ 5 π n b M mo 5. In h fr fil of nnn, α r i.. r -6 8k r k.8 µ V/m hoic (B 5. Vb V Vb 8 sin( z V 8 sin( z ρ.m ρb.85m Ponil in clinricl co - orins vris wih V P ln ρ q 8sin( z P ln(. q P ln (.85 q P 8sin( z -.5 sin( - z ln.85 v V â ρ p P â ρ p

11 5...5 ρ Displcmn nsi sin z âp V/m D ε ε r ε.5 sin zâρ ρ X( sin z âp n/m h puls of ( cn b rprsn - ;for < - ; for < h nrg of signl ( cn b clcul s -. - B simplificion w g. 6 - W know h probbili rror of mch filr is givn s P rfc. N..N N o - o o P.rfc rfc( From h givn roo locus, pols iss s - n s -5 Pols ming poin -.5 Zros α ± jβ -.5 ± j k s s.5 G s s s 5 S -.5 lis on h roo locus ( s s.5 k k ( s ( s 5 ( K hoic (B