( r) 3. For constant speed, 8. Mutual inductance M = Þ f M
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1 LL ND PEN ES/JEE (Mai)/55 ENHUSS & LEDER CURSE RGE : JEE (MN) 5 LL ND PEN ES # DE : 5 5 st y : Majo st Patt : JEE (Mai) NSWER KEY u s. 4 u s u s u s. 4 4 u s. 4 4 HN SHEE. Fia coo tatu S + S S + S bcaus giv \ S S w w + S + S & S S w giv, + w w æ + ç + è ø w æ w ç + è ø & his is a to w Mthod :. z E E'(t) y E' E E E' E E' S S w giv, so, wat has o tha itia, hc i itu, it wi oos ss tatu & ia tatu wi b a to w. CE4 sid a uio hoow sh, E t So, E' E HS/7
2 . Fo costat sd, g g si g si 5. So o th chaactistics o a otica ib a as oows (i) his woks o th ici o tota ita ctio. (ii) t cosists o co ad u o gass/siica/ astic with activ id, which is suoudd by a gass o astic caddig with activ id ( > ). h activ id o caddig ca b ith chagig abuty o gaduay chagig (gadd id ib). (iii) h is a vy itt tasissio oss though otica ibs. (iv) h is o itc o stay ctic ad agtic id to th sigas though otica ibs. 6. df s (df)si (d) si æ (Rd) ç si èø Rsi d ( ) R si d ( Rsi ) df ( d) R Rsi df 8. Mutua iductac M Þ M LL ND PEN ES/JEE (Mai)/55 æ N ç N èm ø N M M N.8.7 Wb 9. Fo icit adiatio ad ctio th hight.. o th tasittig ad civig atas shoud b coaab to a uat wavgth o th siga usd. ho FM has shot ata ad M has og ata. a V R br R Pythagos tho a + R (b R) so, b + R br v æ b a R ç ç b è ø k k k k HS/7 F s dfs 7. itiay Fiay s d µ + + cos cos6 So, ais uchagd. s s Lt bock b disacd though i dowwad dictio ad ogatio i sig th cos...() Rstoig oc F k cos F k cos Hc sc kcos k CE4
3 LL ND PEN ES/JEE (Mai)/55. F Î ho it cuts SHM. ais aways withi th sh. d dt Î Þ gua ucy w Î i to ach o ct to suac t 4 Î t...(i) 4 4 w w W kow that 4R 4Î R so o (i) t. Nub dsity o atos i siico sci 5 8 atos 5 atos c. Sic, ato o idiu is dod i 5 7 siico atos, so tota ub o idiu atos dod c o siico wi b d sa giv dt ad P 4P æ 4ç è ø ad, d L dt L 4 L v F atosc 5. s Î oy bcaus o E E + E P 6. Stss g bcaus o & both ( u + ) stss u g/ stss g / d L d L / ( + ) ( d L ) / u u u u ædl u u u ç + è dl ø u Lt iitia itsity o ight is. So itsity o ight at tasissio o ist oaoid P P 9 P tsity o ight ittd o P cos u. tsity o ight tasittd o ast oaoid P cos (9 ) P cos si U L P (si cos ) 8 U U L L P si 8 CE4 HS/7
4 8. Fo atic to sca away, it has to coss th ak i ottia gy o ith sid. Now, w wi giv iitia vocity i ight sid dictio but it wi tu & ca sca away o t sid dictio at ow sd. HS4/7 v J v /s 9. ou o a ocs is i sa dictio so, t + t + t. v FR + FR ( + ) + FR.5 R Mg g a. /s t.s v. Fo aow sig sit diactio width o cta. aia is width. b v v æ ç è b ø. wh, h ad b is sit v væ væ+ 4ç ( + ) 4ç ( + ) è ø è ø v ; ( << ) 4. oo ovs towads ight outwad u icass, so accodig to Faaday's aw, cut ow wi oos this chag & dictio o cut wi b cockwis. oo ovs towads t th, iwad u icass, so to oos this chag, cut dictio wi b aticockwis. 4. h ath dic itoducd by a at o thickss t ad activ id is giv by D ( ) t. ath dic o itoducd a has shit o b wh b D/(d), d saatio btw sits LL ND PEN ES/JEE (Mai)/55 So, a ath dic o ( )t itoducs a shit o th sc giv by ( )tb Fo ist at : ( )tb ( Fo scod at : )tb ( ) ( ) Þ ( ) (.5).75 \ Þ 5. Fo at agt w a atia with high ttivity (so as to ak a stog agt) ad high cocivity (so that agtizatio ay ot b wid out asiy). o ctoagt w high satuatd agtis ow cocivity ad ast ossib aa o hystsis oo so that ctoagt dvos high agtizatio, is asiy dagtizd ad gy oss i a agtizatio cyc is ast. ho, P is suitab o akig at agt ad o akig ctoagt. 6. i ( ) i 5Å ; 4 D E E V 8.8V 5 Hc ioizatio ottia is 8.8V 7. idt aa o i v/s t gah t ( D ) Dt aso, i hat oss æ ç t+ èdt ø i Rdt i 4R Dt 8. Duig ti 't ' caacito is dischagig with th h o sisto 'R' \ t/rc V V t/rc [ CV] Dt CE4 t
5 LL ND PEN ES/JEE (Mai)/55.. CE4 s V V ; V V t RC Duig ti 't ' caacito is chagig with th h o batty. \ ( t/rc ) o V V ( t/rc ) as V V ; V V t RC t + t RC v v (i) Egy cosvatio Þ h > h (ii) t doig bag h vocity dos t chags so h h > < h < 6 5 < 6 4. Z X ¾ 6 C +, Z 7 6. H + ¾ ¾ H + H + g. o H aaday usd F 75 F NH + 7 ¾ ¾ N + 6H NH D N C 5 M o igu M DN 5si6 5 Now i DND Þ (D) (DN) + (N) So ocus o C & D is + y Nub o aths assig though M a Nub o aths though N a s Lt yz 7 th ub o soutios a + C + C 5 C 4 C Lt y is a tagt to th cic + y 8 6y + 9 th gth o dicua Radius Þ (4 ) 6( + ) Þ Þ 4 7 s. 7 4 é 7 ê, 4 ë ø é ( + ) ùé ( + ) ù ê úê ú ë ûë û é ( + ) ù é... + ù ê ú ê ú [ ( +)] ë û ë û Coicit o 6 is C 6 ( + ) 6 HS5/7
6 66. HS6/7 Lt å + + å + ƒ() ƒ( ) é æ ( + ) ù ê(..... ) ç. ú ë è øû éæ4 + + ù êç... ( ( + ) ) ú ëè 4 + ø û åé ë ( + + ) ù û å ( + ) (+ ) + é + ù ( + ) ê + ú ë û 67. (z) R(z) < 5 Þ (z + i) ( + i) < 5 Þ z' ( + i) < 5 [Lt z + i z'] agad a z' sts th shadd aa, o igu < z' < si si é Î(, ] È, si ê ë5 ø P F N F s i ad P a th ag biscto o ÐF & F (ctio oty) FP FN F th FP FN F Usig coodo ad dividdo æ FN + FN æ F F ç ç FN FN F + F è øè ø LL ND PEN ES/JEE (Mai)/55 7. Ma sua dviatio is iiu about a i.. a 5 ad dia o th gou is a 5 Þ Mod wi aso b a 5 7. i + i ( + {}) {} {} + cos{} {} {} {} + {} {} i + {} 7. ƒ() si{ } ( [ ] & [ ] a itgs) \ ƒ() is discotiuous " wh is a itg ct at ad o Î [, 4] Þ Î [, 6] sicos d 74. d cos (4 cos ) 75. d {Lt cos } (4 ) 4 (4 ) d (4 ) ì d d ü í ý î / þ ìï üï í + ý+ C ï î + ï þ æ cos cos ç + 6 ç ç cos cos è 6 ø ta y y y + + ta 6 + d dy ta y y+ ta C ( ) y ta ta y + C 76. Ruid a /4 / cos d + /4 + si d sc( ) /4 / CE4
7 77. ƒ'() ƒ().( + ) ƒ''() ƒ()( )( + ) + ƒ ()( + ) ƒ''() ( )ƒ() + ƒ() CE4. ( +. ) 67. (. ) Þ ƒ( + ) ƒ( ) Þ ƒ( + ) ƒ( ) sytic about th i \ ƒ() ƒ(); ƒ(5) ƒ( ) ad ƒ() ƒ( 8) Þ ƒ( ) ƒ() ƒ() ƒ(5) ƒ() \ accodig to RMV ƒ'() hav at ast 4 oots i Î ( 5, ) ì {} ; ¹ ƒ() í î ; Gah o ƒ() wi b / / 4 \ Loca iia at,,,..., 9 Þ 4 oits. dy d Þ cos & Þ cos si cos ta Þ tagts a y ; y ± (aa to ais) Siiay ; ± oy y ± 6 7 ta d ta ta 8(ta ) 8(sc ta) 8(sc ) LL ND PEN ES/JEE (Mai)/55 8. a,b,c a i H.P. th b H.M. o a & c si atus ctu b 8 8. ag bisctos a ith tagts o oas to 84. th is y ± a + b ( ) a b o y ± a + b Now ut 5 y ± + y y (5,) (5Ö,) y th oits ust i i th shadd igu wh y > ad uaity hods i > such that + y < 85. Ratio o th aas o DC : DC : D is si : si : sic 86. si si 4 4cos is satisid by si 87. Cicuadius o DC ad DC ais sa (wh Þ othoct) Þ so s. 88. u aiˆ+ bj ˆ+ ckˆ v biˆ+ cj ˆ+ akˆ w ci ˆ+ aj ˆ+ bkˆ a b c b c a c a b Þ (a + b + c)((a b) + (b c) + (c a) ) Þ a + b + c ¹ Þ a b c Þ u v w So vctos,y,u,v,w a coaa C + C 7 5 C Þ Þ Þ P P P P P P P P HS7/7
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