DATE : HINTS & SOLUTIONS PAPER-1 PART-I : PHYSICS JEE PREPARATORY TEST-2 (JPT-2) (JEE ADVANCED PATTERN) TARGET : JEE (MAIN+ADVANCED) 2018

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Clifton Walters
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1 DTE : -5-8 PPER- PRT-I : PHYSIS. I the cicuit... Sol: R +( Q q) ( Q q) Q q q ir c c Q q Rdq c dt q dq dt Q q Rc Q t /Rc q e dq Q t /Rc i e dt Rc Q Q q e Q H 4c t +q q t /Rc. The electic... V ( y + z ) Ple pllel to z ple + z costt Ple pllel to -y ple y costt. The figue... Q E Q E Q D U dielectic JEE PREPRTRY TEST- (JPT-) (JEE DVNED PTTERN) TRGET : JEE (MIN+DVNED) 8 URSE : INDI TEST SERIES (VIKP) SS: XII/XIII dq i dt Q E Q k k k E E t k t k k 4. euto... v H y costt its cicle z costt its hypebol HINTS & SUTINS E 4 E.75 ev k.75ev K > 5.5 ev 5. Which of the... () [ E] [Mº T ] () [] [M - T ] () [foce] [M T ] E (D) [Mº T ] 6. soleoid of... E/R R/ R R/ R E R, U E 4E E R R R Hsol, H R H U E R S 7. Foce o... y (, y) F ( ) ( )ˆ F is cosevtive y f mv k (k) m E E. ev (k) m >. ev k >.4 ev m k v i dw F.d ( )d op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58- Toll Fee : IN: U8RJ7P49

2 f w ( c )d f i f i () i, f 9 w 4 4 ( ) () i f w () i f 4 W 8. oside the... (f ) m () kg () kg (f ) m 4 5 () kg (f 4) m 6 fictio betwee () & () N fictio betwee () & () 4 N fictio betwee () & goud 5 N 9. shped... y V - V V V V V V V( )d 8V V ( + y) dy V V (V V ) (V V ) 9V 7 8V V 9V. Some mout... FD of pt (hoizotl foce blce) d g(d) g d d d g FD of + (Hoizotl foce blce) ( + si) t g t 9 ( + si) t g t g t ( si) g. The eds of... Hot ed dt d icesig cool ed dt K d ostt Sice dt d icesig decesig os tt dt K d op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58- Toll Fee : IN: U8RJ7P49

3 . peso idig... m/s 4 m/s bseve S m/s S m/s D Fequecy obseved by S (48) 49.6 Hz Fequecy eflected & tsmitted by S 49.6 Hz Fequecy of eflected soud eceived by obseve Hz et fequecy obseved by obseve (5. 48). Hz 4 Fequecy eceived by detecto hz 6 wvelegth obseved 5m 5.4. Thee is... +Q +Q + Q q Q q q d d q + Q q + q q q Q...() q q d d q + q...() fom () & () Q q Q q Q (q ) i +Q (q ) f q + q chge flow fom S 5Q Q (q D) i +Q (q D) f Q + q q 4. peso V m/s V m/s chge flow though S 7Q m/s m/s d m/s m dt m, 4, P woode cubicl... M D N S S D +q q +q + Q q + q ) -q ( Q q + q ) mg fo o topplig mg mg mg mg mg 4 mg 4 op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58- Toll Fee : IN: U8RJ7P49

4 6. I dioctive... N N e t N N ( e t ) N t N 5 e t 5 t 5 N 6 Ne N 9 N ( t e t ) e t e t 5 t t 6 sec t 8 log 5 t 6 log log 7. o-uifom... dm d d F F M T T F F F F 4F Td F y(,) h h h h + + t y time t. y Vt h Vt y Vt ; h y(, t) h Vt Vt ; h h Vt Vt + ; Vt + ; Istteous powe y y P f t Vt h P FV Vt Vt h FV Vt Vt + Vt + 9. hoose the coect... Vt + y t y h y hv t y h y hv t y y t 8. tigul... t y V h + E si t R E si t R E cos si t R 6 op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-4 Toll Fee : IN: U8RJ7P49

5 E E si t R 6 si t Z 6 R Z, Phse diffeece, Powe fcto cos 6 Rec tce, t Re sis tce R R Z R R R,. electo... h h mh m h m itege, so itege multiple of h PRT-II : HEMISTRY e llowed.. 8 m stuted. Mss of solutio 8 g Sice the slt is spigly soluble i wte, eglectig mss of ios dissolved i wte, Mole of wte i solutio 8 / 8 mol (Pº P s) / P º (mol of ios / mol of wte) Moles of ios dissolved i wte.54 mol Moles of Ml dissolved i wte.8 mol [M + ].8 mmol / 8 m. M [l ].6 mmol / 8 m. M K sp [M + ][l ] 4 6. Which step(s) is/e. od bekig d ioistio eegy e lwys edothemic. ttice mkig is lwys eothemic. Electo gi ethlpy of hloges is eothemic.. Which of the followig. Fo eothemic ectio, equilibium costt deceses with icesig tempetue. ut, te costt of y chemicl ectio iceses with icesig tempetue. 4. solutio of ukow. White ppt with dilute Hl implies pesece of goup ctios. gl dissolves i mmoi solutio. White ppt of Pbl dissolves i hot wte, PbI is yellow ppt. Possibility of Hg l is uled out becuse white ppt of Hg l does ot dissolve i mmoi solutio.. 5. Give fo H. [H + ] fo H 7 4 K 4. M [H + ] fo NH 7 9 KK M 6. Whe solid NH 4SN. Sice gs is poduced fom solids etopy hs icesed. g >. I closed cotie, P-V wok is zeo. w. Tempetue dop implies het is bsobed by the system duig the pocess. q >. Thus, s pe fist lw E q + w >. H E + RT g. Thus, H >. G <, becuse the pocess is spoteous. 7. mol ed led. Pb 4 + 8Hl Pbl + l + 4H Pb 4 + 4HN Pb(N ) + Pb + H 8. Followig is/e. Two oyge toms pe tethedo e shed fomig igs. Hybidistio of ech Si is sp. 9. The followig digm. ow ccucy becuse mesuemets e f off fom coectly vlue. ut, they e highly pecise, becuse they e vey close to ech othe.. Two mole of electos. I fist cell, t ode: l (I) l (g) + e t cthode, N + (l) + e N(s) I secod cell, t ode : l (l) l (g) + e t cthode, H (I) + e H (g) + H. Which sttemet(s). Sop d deteget both hve hydophillic s well s hydophobic goups, hece both c fom micellles. boyltes e moe bsic th lkyl sulphtes, becuse cboylic cids e weke cids. I cidic ph, stete gets pototed to fom coespodig ftty cid, which is ot much soluble i wte due to log hydophobic chi. Sop pecipittes i hd wte becuse its clcium slt is isoluble.. Which digm epesets. I optio, oppe cot educe feic io to io.. Which of the followig. ojugte bse of Q is omtic, hece it is the most cidic compoud mog give hydocbos. 4. X H coc. NH Y. H H coc. NH itmolecul cizo ectio H H H H H H op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-5 Toll Fee : IN: U8RJ7P49

5. The commoly used. Nittio of pheol with dilute HN, gives mitue of o- itopheol d p-itopheol; of which o-itopheol (X) is stem-voltile. Y o eductio gives p-mio pheol. 6. Two ketoes, P d Q.

6 5. The commoly used. Nittio of pheol with dilute HN, gives mitue of o- itopheol d p-itopheol; of which o-itopheol (X) is stem-voltile. Y o eductio gives p-mio pheol. 6. Two ketoes, P d Q. Rcemiztio of opticlly ctive ketoe i bsic medium is possible due to tutomeistio oly if the lph-cidic H is ttched to chility cete. I optio, both P d Q will udego cemiztio. I optio, Q is opticlly ictive. I optio, Q will udego cemistio. 7. NH NH (i) H Mg (ii) H I + P. 5 P ezee ll Z(Hg) Hl Q Sl W V NEt/EtH, het NS(eq.) U l4,hv H Q + S Sl U EtN/EtH H S 4 ll l R NH 4 NS/l 4 W T H P NH 4 T V R ll S H ll Z(Hg) Hl PRT-III : MTHEMTIS H S 4 + HI 8. Which of the followig. -bomopope + Mg/ethe followed by ; followed by hydolysis would give isobutyic cid. 9. bseved the followig. yclobutecboitile is N H/ethe educes it to pimy mie cyclobutylmethylmie (). udegoes ehustive methyltio by eq. of H I to give qutey mmoium slt (). is fomed by substitutio. is iodide slt of N + futhe udegoes hoffm elimitio o hetig with gh. is H 4. et m be... Suppose tht both d + e solutios to the equtio 4 m The 4 m, d lso ( ) ( ) 4( ) m Subtctig the fist of these equtios fom the secod gives ( ) ( ) 4, o 9 o 5, d put i give equtio 4. If tigle... u u v u v. u u v u v u v u v. uˆ v ˆ. uˆ vˆ. u v u v 9 cos cos cos 4cos coscos op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-6 Toll Fee : IN: U8RJ7P49

7 4. et Z iy, Z iy i i Z e,z e,re(z Z) /, i i 4 5 Z e,z ie,z cos( i) Z si( i) 6 m m... The give seies c be witte s m S ( ) ( ) coefficiet of m i ( + ) coefficiet of m i ( )( ) coefficiet of m i [( + ) ] coefficiet of m i ( + ) coefficiet of m i ( + ) coefficiet of m i ( + ) m if m (m ) m m d if m <. 45. If is o... () ( ) ( ) ( ) ( ) ( ) et + X X X X X X (s ) (i) X o et M M M ( M M) M () M ( ) M plyes of P(), P( ), 5 P( ) 47. The e bouded P(), 6 The desied e is show s shded egio / 4 4( )d 4( )d( ) Suppose tht... f()f f() f()f(999) 999f(999) f(999) 999 The umbes 999 d 999 e i the ge of f. Hece, by itemedite vlue popety of cotiuous fuctio, fuctio tkes ll vlues betwee 999 d eists., The such tht f() 5 f()f f() f(5) 5 Similly, 99, , thus f 99, the thee ut thee is othig to show tht 999 lies i the ge of f. Thus (d) is ot coect d (c) is lso icoect. op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-7 Toll Fee : IN: U8RJ7P49

8 49. fuctio f : R R... f() lim b c e c.e b c e lim ; c. e b c e lim ; c. e b c e lim ; c e b c; ; ; c sice f() is cotiuous fuctio R lim f() lim f() f() lim lim( b c) c c c c,, b R 5. et f() be... f()f '() f '() f() 4 f() f() Itegtig o the itevl (, b), we get b b f()f '() b d d t f() 4 b f() b lim t f() lim t f() b 4 5. stight lie... et equtio of lie psses though (, ) is y cos si Poit o it (cos, si ) If this poit is lies o + y 9 cos si If this poit is lies o + y + 4 si cos s. si + cos + 4si cos 4 cos 4si cos+ si (cos si)(cossi) t, Equtio of lie y + + o y + ( + ) y d y + 5. If gph of... et imge of poit (,) bout y is (, b). Mid poit of b i.e. M, lie o y b b d slope of b b Subtctig (i) d (ii), 5 4b b 5 8b 6 b 4 b 5 5 (,) lies o y 4b b b 7b 5 7y y 5 5. cicle touches... Fmily of cicles touchig + y t (, ) is ( )(y )( y ) y( )( )y () Give cicle is: y 4 5y 6 () Equtio of commo chod PQ is S S. ( 6)( 7)y 8 () () PQ lie: + y 6 6 7; which is impossible 7 (b) PQ lie : y 6 ; which is impossible 7 ut whe, we c see tht the cicles () d () e ot itesectig ech othe d thei dicl is is pepedicul to the give lie y Eq. () c be witte s 6 7y 8( y ) which is i the fom Solvig d, we get the poit of itesectio (6, 4) (i) (ii) op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-8 Toll Fee : IN: U8RJ7P49

9 54. et, d... et (t,4t),(t,4t) d (t,4t) Slope of t + t d t + t + t So, t (t t t) 4 lso, t t t, t (,4),(,) d(, 4) Hece P(6,) 55. The volume... Volume b c c 4 b 8 4 b c 8 b c Now, ( si) cos si 4 b c si cos si 4 si cos si pplyig R R R R d epdig b c cos cos,, Idetify the coect... (D) No of solutios e Which of the... If f() is ot costt o [, ] f '() t some poit i < < f is icesig t tht poit d we c t hve f( ) f() (b) Not tue If f is bouded cuve chges its cocvity If f is ubouded the cuve cosses -is (c) Not tue e.g. f() 4 (d) f '() + ( + )( ) < fo (, ) whee f() deceses. lso f "() 4 fo 58. If ( + y)... ( + y) ()(y) ( + ) ()() () Put y, we get () ()( ) ( ) ( ) (( )) () (())..(i) () (()) () Thus, () is eve. () No of solutios e 5 () d () d () d () d () d () () 8 8 No of solutios e 5 No of solutios e () d () d 59. dy et y f() d... dy y f() is lie diffeetil equtio. d I.F. e Solutio is ye ow if the ye + y(), ye + e f()d ye e e d op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-9 Toll Fee : IN: U8RJ7P49

10 y ; e y() e e( ) e lso y' e e e e y'() e e e If > ye e d ye e + y e + e s y is cotiuous lim lim(e e) e e e e fo > y e + e y() e + e e (e + ) y ' e y '() e 6. If k... k k k k k ( k )(k ) + k+ ( )( )( k ) ( )( )( ) k ( k 5k 6 (k 6) ) + k+ ( )( )( ) k k (k 5k 6) k (k ) k ( )( )( ) k ( )( ) k ( ) k k k k ( )( )( ) ( )( )( o solvig we get ) ( )[ ( ) ( )( )( ) p b q c d ( )] ( 4) ( k k )( ) op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i Toll Fee : IN: U8RJ7P49 PPER- PRT-I : PHYSIS. I the figue... () k / / mssless od / et the block is displced. Elogtio i spig () m k( ) / k k() 4 k/ 5 4 Restoig foce k ( ) 4 k k m 5 5 k 5m 5m, T k. pticle... y m k k( ) SJRJPTDV58-

11 V i ˆ ˆj kˆ i ˆ j ˆ kˆ 4i ˆ j ˆ 4 7º d mi 5 si 7 m 4. o-coductig... 5º 7º 5º E 45º 45º. Two smll... v 7º m m v v Electic field will be log gle bisecto. 5. Two uifom... V cm I M fme v v zeo v m m v v m 45º V m v ME mv M mv + k K + v k m mv m V 45º V V mv mv ( + ) v ( ) mv mv 4( ) k fte substitutig the vlues we get v. m/s mg m m cos mg cos() costt m mg ( 4) costt 5 m 6 4 mg costt m 5 g costt 5 g costt 5 d g d g 9g (gulfequecy) T 9g op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58- Toll Fee : IN: U8RJ7P49

12 6. Thee e... Suppose we hve coected bttey coss poits d. ll poits othe th d will be t sme potetil so equivlet cicuit will look like s give below 8 Poits cos mg f s N mg f s N mg mg f s cossi So equivlet esistce will be 6 7. Momet of... M b M ( + bb) + m 74. b 8. glss sphee... ( cos)r (si ) R 9 6R 4R uifom... g cos. Fou ideticl... q R ˆk R q 4 R R q qr. Rsi 4 kˆ 4 R q ˆk 8 R q. R.Rsi ˆ k 4 R q ˆk 6R q. R. Rsi 4 ˆ 4 k 4 R q ˆk 8 R q ˆ k 8R F q v q F 8 R q f s cos N mg cossi op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i Toll Fee : IN: U8RJ7P49. Fid the miimum... y, y( T ) y ( T ) ( T)( T) y, y ( T )( T) y ( T + )( T) SJRJPTDV58-

13 (y y) T y( T) y( T) Tesio yt ( T) y T ( T) y T ( 9 )( 5 ) (6 4 ) () Newto Fudmetl fequecy of st wie loe Hz (). Fudmetl fequecy of d wie loe 4 Hz ().75 Fequecy fo which both the wies will vibte (joit o ode) M of idividul fequecy Hz 4. Which of the... KQq KqQ E m m KQq KQq KQq If legth of semi mjo is is E KQq u +Q KQq 6 m egth of semi mio is KQq GMm M KQq Gm 4 6 T m Qq Qq G 4 Gm T 6 m Qq 6. Which of the... T 5T T P 5P T T costt costt T KV V PV RT P costt V T costt V costt costt P V P V T T P costt, U RT W RT R ( T ) RT U V costt W 5 5RT i W R(5T ) f U 5 Pocess Q U W 5U U U +U +U U 5 5 Net het U U v U 5 (.5) op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58- Toll Fee : IN: U8RJ7P49

14 8. Rdius of the... +e m P e ke( e) mv ke mv. The velocity... V M M (m) v mv ke mv mv ke mv mv J J 6V M V M J 6 M () + ( ) + () 9 ke v ke m ke( e) E mv ke mv mv k e m E 4 Fo hydoge tom V Ke 4 K e m E Fo this tom V Ke m V, fo V V 4 fo E E 7 7 P E E E E 9 E + 7E 4E P 4E MIT w..t com J Velocity of P J/6 4 9 J J J Ĵ î 6 J J î Ĵ 6 PRT-II : HEMISTRY. If P totl umbe of. 6 GI with followig ts pis e possible: ()(bb)(cd), (b)(b)(cd), (c)(bd)(b), (d)(bc)(b), ()(bc)(bd), (bb)(c)(d). ut of which d d 4th e chil. So thee e pis of etiomes d totl 4 chil steeoisomes.. The followig wve. The wve fuctio is idepedt of gle which implies it belogs to spheiclly symmetic s obitl. Futhe, it hs oly oe dil ode t Z/ which idictes s obitl. s obitl is fist ecited stte. op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-4 Toll Fee : IN: U8RJ7P49

15 . fist ode ectio. K. K. t ½.69 K. 5 log 8 K log 4 mi. mi 6 mi of ukow. Mol of gs 5.6 /.4 4 E vt v cl.mol.k p 5 cl.mol.k 5 idel gs is mootomic. 5. cystl is mde up. Effective o. of toms of X 4 4 (/8).5 Effective o. of toms of Y 4 Effective o. of toms of Z Hece, fomul is X 7Y 6Z 8 6. Whe the followig. omie dispopotiotes i bsic solutio of cbote. + N 5N + N + 7 oside the. 6, y. Fil poduct is bezee. 8. How my of the followig. Rectivity ode towds Gigd eget is s follows R H > R R > R R > R NR ly (i), (iv), (vi) d (vii) udegoes ucleophilic dditio ectio. 9. How my hypecojugble. + H H(H ) H H H Totl hypecojugble H-toms 6. How my of the followig. (S, S, S 5 & S 7 e coectly mtched). Metl M. K 7 is vey commo lb eget whose queous solutio is oge coloued but tus yellow i lklie medium due to fomtio of chomte. K 7 is obtied fom homite oe Fe. which c be witte s Fe( ). Thus, M is.. The gs. NH 4l + K 7 N + + 4H + Kl. Suppose two hypotheticl. *P *P y *P *P y e stte hs both electos i diffeet π* obitls but with opposite spis (violtig Hud's ule). the stte hs outemost electos pied i sigle * obitl (gi violtig Hud's ule).totl spi cses is zeo, hece both e siglet sttes. S i both the H + /vkf/kd; leku iqujko`f 4. Which of the followig. cid ctlysed dehydtio of lcohol (E elimitio) poceeds though cboctio itemedite, which e siglet species s they coti o upied electo. Thus, totl spi is zeo. Reime-Tiem fomyltio d bylmie fomtio ivolve fomtio of siglet dichloocbee by lph elimitio of chloofom by lkli. op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-5 Toll Fee : IN: U8RJ7P49

16 5. Which of the followig. Y is omtic cyclopetdieyl io. Z is feocee, i which feous io is cetl tom d two cyclopetdieyl io (Y) ct s ligd ech dotig 6 pi electos to feous io. EN 6 + (6) hoose the coect. (7) & (8) H H H H (X) H H 4. ompoud P d R. Hl KH (T) H / Ni (Q) (R) H H H H H H + H H H H H (Z) H / H H 4 S H (P) c / c, (S) HH H H PRT-III : MTHEMTIS 4. If, b, c... c b, b c, b c e ll positive Usig.M. G.M. (Y) H ( H) H / b c bc (i) c b b c b c (c b)( b c)(b c ) lso, (b c) ( b c)( b c) Similly b(b c )(b c ) H H c(c b)(c b) b c( b c)(b c )(c b) Thus bc ( b c)(b c )(c b) hece fom (i) bc (c b)( b c)(b c ) 4. If, b, c, d >... We hve bc (c b)( b c)(b c ) ( b c) (b b cd) b c d ( b)(b c)(c d) ( b)(b c)(c d) b c d b c b c o log b log log c, 4 log 65 7 log b [pply R R R R ] Now 97 4 log c 65 7 log b 97 4 log c 4. Suppose tht... h'() f() h''() f'() h(),f() f'() h'() h''() g( f g() 'g' is ivese of 'f' f ' g().g'() f ' g().g'() f '().g'() g'() 44. be sque... m q et, dj() p q p m et d mq p op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-6 Toll Fee : IN: U8RJ7P49

17 m qd ( d) d dj p( d) q md mq m d q d mqd p pd pd (mq p)(mq p)d m d q d mqd d (d d d) d(m q mq) d[(d )(m q) ] d,m q d dj (m q) 4(mq p) 4d Two pesos p( p) p( p) 6( p) 4p p If the dius... Thee e two wys fo lie ( k) to hve distict solutios with 5 + s show i figue se-i so y ( k), lie touches y 5 + t some > d cuts t two poits fo < 5 + ( k) + (k 8) + D (k 8) k 8 ±, k 6 is oly possible vlue fo which > k 6 o Similly fo < ( k) + (k + ) + (k + ) 4 o k 4 > so ejected k + ± k 4 o k < is possible vlue so totl possible vlues of k e d If the eccetic... If P is the poit (cos, b si), the coodites of Q e t t h b 4 b 7 (8) si 6 Hece, equtio of cicle is 47. Possible vlue ( k) ( 6)(y 6) 8 dw the gph of 5 + d ( k) y 5 + y ( k) cos, bsi i.e., ( si, b cos) whee 8, b 7 The e of PQ b cos b si e( y y) b ( 8)( 7) 7 sq. uits 49. The stight lie... op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-7 Toll Fee : IN: U8RJ7P49

18 et the pepedicul distce of P fom the lie be h, h 5 6( ) h( ) 5 lso tget pllel to the give lie is 4y Its distce fom the lie 4y IS H( ) 5 Hece thee e thee poits s show i the figue. 5. Numbe of the... si cos si cos si si o si( ) si si 7 cos 4 si 7 o cos 4 7 o 4, Z 7 o, Z [ b b c c ]... [ b b c c ] [ b c ] 5. If yb zc md... ( b)( c d)(b c)( d)(c )(b d) [ b d] c [b c d] [c d]b 6d Now d b c, whee,, e scls Tke dot poduct with b ( b) d [ b c] ( b) d Similly fid d So d [ b d]c [b c d] [c d]b 5. The vlue of The miimum... y f( y) f(y) 4 f()...(i) Itechgig d y, we get y f( y) f() 4 f(y)...(ii) y y f(y) 4 f() f() 4 f(y) f() f(y) k y y 4 4 f() k(4 ) f() k(4 ) k f() f(4) 4 4 f()() ( / ) / 4 Thus, f() hs lest vlue s / The vlue of The vlue... f() lim ( ) ( b), b, b, b 5, lim f() eists if lim f() lim f() lim( b) lim( ) b b...(i) lim f() eists if lim f() lim f() lim( ) lim( b) b b...(ii) Solvig Eqs. (i) d (ii), we get d b. m op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-8 Toll Fee : IN: U8RJ7P49

19 57. et f be diffeetible... f is diffeetible t d g() is cotiuous t. 58. i.e. b d b lso + c + b b d c k() hs el d distict oots fo R 49 4(49k)() R 4k 4k R 6k 6k k(k ) k(, ) f() lim g() eists... f( h) b(4 h) H lim lim h g( h) h c( h) d 4b c d If we itechge y d z, the both equtios () d () emi uchged is isosceles with y z So fom () d (), we get 5y () d y + y (4) 4 Solvig we get,, y z R, P, Q 4 7 Now peimete s. R +. P +. Q Give peimete is smllest itege 7 s 7 s 7 sq. uit f( h) b(4 h) RH lim lim h g( h) h ( h) c 4b c f is diffeetible t i.e., b So, H RH (it is give tht limit eists) The idius... et t, t y, t z Q R I, y, z R P Q P put the vlues of R, P d Q i give eltio, we get 5y 5z 6 5y 5z 6() lso i the tigle, y + yz + z () op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58-9 Toll Fee : IN: U8RJ7P49

20 DTE : -5-8 DE- JEE PREPRTRY TEST- (JPT-) (JEE DVNED PTTERN) TRGET : JEE (MIN+DVNED) 8 URSE : INDI TEST SERIES (VIKP) SS: XII/XIII NSWER KEY PPER- PRT-I : PHYSIS. (D). (D). () 4. () 5. (D) 6. () 7. (D) 8. () 9. (D). (). (D). (D). () 4. (D) 5. (D) 6. (D) 7. (D) 8. () 9. (D). () PRT-II : HEMISTRY. (D). (D). () 4. () 5. (D) 6. (D) 7. (D) 8. (D) 9. (). (D). (D). (D). () 4. (D) 5. (D) 6. (D) 7. (D) 8. (D) 9. () 4. (D) PRT-III : MTHEMTIS 4. () 4. () 4. (D) 44. () 45. () 46. (D) 47. (D) 48. () 49. (D) 5. () 5. () 5. (D) 5. () 54. () 55. () 56. (D) 57. (D) 58. (D) 59. (D) 6. () PPER- PRT-I : PHYSIS. (5). (). () 4. (9) 5. (9) 6. (6) 7. () 8. () 9. (4). (). (). (). () 4. () 5. () 6. (D) 7. (D) 8. () 9. (). (D) PRT-II : HEMISTRY. (6, 4). (). (,,, 4) 4. () 5. (7, 6, 8) 6. (5,, ) 7 (9) 8. (4) 9. (6). (4). (D). (). () 4. () 5. () 6. () 7. () 8. (D) 9. () 4. () PRT-III : MTHEMTIS 4.,,, 4.,7 4., 44.,,4 45.,,5 46.,,4,8 47., 6 48.,,,,4,5, ,5,8 5. () 5. () 5. () 54. () 55. () 56. () 57. () 58. () 59. () 6. () op. Reg. / ffice : G Towe, -46 & 5, IPI, Ne ity Mll, Jhlw Rod, Kot (Rj.) - 45 Website : E-mil : cotct@esoce.c.i SJRJPTDV58- Toll Fee : IN: U8RJ7P49

ANSWER KEY PHYSICS. Workdone X

ANSWER KEY PHYSICS. Workdone X ANSWER KEY PHYSICS 6 6 6 7 7 7 9 9 9 0 0 0 CHEMISTRY 6 6 6 7 7 7 9 9 9 0 0 60 MATHEMATICS 6 66 7 76 6 6 67 7 77 7 6 6 7 7 6 69 7 79 9 6 70 7 0 90 PHYSICS F L l. l A Y l A ;( A R L L A. W = (/ lod etesio