Q A. A A D A B C B C C A Q A. A,C,D A,B,D A,B,C,D A,B,C A,C Q A SOLUTION. 3. Ans.

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1 PAPER CODE LEADER & ENTHUSIAST COURSE PART- : MATHEMATICS V. As. (A) TARGET : JEE 4 y dy y - e. - e + ta d + Þ y y æ - e.dy e d ta + ç + d è+ ø Þ d( e y ) d(.ta ) Þ e y ta + C at (, ), e p + C Þ 4 C e p - 4 e y ta p + e - 4 e y - 4ta + 4e-p 4 - æ4 ta + 4e -p y logç è 4 ø. As. (A) Covertig give epressio i terms of si & cos 4 4 æsi 4+ cos ç si 4.cos è 4 ø æ(cos 4 -si 4) 6ç è si 4.cos 4 ø C T si 4.cos si 4 + cos (si 4 + cos 4) +.si 4.cos 4 PAPER- PATTERN : JEE (Advaced) Date : SCORE-II : TEST # 9. As. (D) -( + ) + 8( + ) -5 ƒ() + Q A. A A D A B C B C C A Q. 4 5 A. A,C,D A,B,D A,B,C,D A,B,C A,C Q. 4 5 A. 5 7 æ ç ( + ) è + ø 4. As. (A) Writig the curves i terms of & y y a & ( 4) + y 4 for tagecy 5. As. (B) Let P be (t, t) \ PQ : ty + t \ Q : ( t, ) \ RQ : y t t Þ R (, t ) Let S be (h, k) \ a + a Þ h + (- t ) t + & Elimiatig t, we get (4 ) 8y 6. As. (C) a ± k+ t-t z- z z + z -Re(zz ) ( z z ) + ( z Re (z)) z -z ( z - z ) \ z Re(z) - ( z - z ) - \ z Re(z) < Corporate Office : ALLEN CAREER INSTITUTE, SANKALP, CP-6, INDRA VIHAR, KOTA-45 PHONE : , Fa : , ifo@alle.ac.i Website: KOTA / HS - /

2 PAPER 7. As. (B) Give epressio ca be writte as KOTA / HS - / æ æ ç + a å r ç è + ø r è+ ø \ a r C r r 8. As. (C) AB BA + A Þ B B + I & AB A BA Þ B I B \ B + I B I 9. As. (C) The give epressio ca be writte as æ æ 5 æ 9 ç + ç + ç èyz ø èz ø èy ø æ 5 æ 9 æ 9 æ æ æ 5 -ç - z ç ç ç - è øèy ø èy øèyz ç ø yz ç z è øè ø \ 5 9 \ 5y 9z \ H.P. yz z y. As. (A) ìa6 a7 a ü ò ƒ()d í aý< î þ Þ There eists Î (, ) with ƒ() < Also ƒ() a > \ ƒ() has a root i (, ). As. (A,C,D) ƒ'() ta æ - ç ta + R ³ " Î è + ø \ both ƒ & ƒ' are cotiuous & differetiable o R.. As. (A,B,D) (AB')' BA' Þ AB' BA' Þ BA' AB' (AB)' AB Þ B'A' AB & (AB')' AB' Þ BA' AB' Subtractig (B' B)A' A(B' B)A' A(B B'). As. (A,B,C,D) (A) ma(ƒ(),g()) is always cotiuous if ƒ() & g() are cotiuous (B) ƒ() & g() has atleast oe real root (C) lim ƒ().g() Q g() is cotiuous at (D) true Q ƒ() & g() are cotiuous at. r TARGET : JEE As. (A,B,C) a [ ] Þ a Þ a ( + ) \ a ca be, & 5. As. (A,C) Either two pockets each have two chocolates & other pocket has or two pockets each have oe chocolate & other pocket has \ Number of ways C 5 C C + C 5 C 4 C 5 \ m 8 SECTION IV. As. 5 A p + \ [A] 5. As. As, ƒ() log ƒ() log + ƒ() ƒ() Þ + log lim ƒ(). As. b+a ò cos d 9 Þ b + a 9 p b-a ò si d 8 Þ b - a 4p p \ a & b 4 b-5a \ p 4. As. A (b,mb) D B(a,a) 7p 4 uuur uuur Area AB AD ab(m ) ab(m ) \ Number of itegral solutios As. 7 First vector ca be chose i 6 C ways, secod i 4 C ways (leavig vector alog its lie of actio) third i C ways. 6 4 \ N 6 4 7! N 7 64 C CT94

3 PART- : PHYSICS V. As. (B) 4u v + vm æ mv 4 v ç è ø & v u. As. (B) S W > S A so T eq will be closer to T W.. As. (A) (i) Some eergy is lost through sides of beakers (ii) Water splasshes, so mass of water become less 4. As. (A) ( T) dt KA T - Cv dt d sice oyge is diatomic so C V is 5R. 5. As. (A) 6. As. (B) T p 7. As. (C) l g eff PAPER LEADER & ENTHUSIAST COURSE -5-4 Q A. B B A A A B C C D B Q. 4 5 A. A,B,C A,C A,B B,D B,C,D Q. 4 5 A As. (B) + v v As. (A,B,C) If 'S' ope, V same w/i outer sphere If 'S' closed, V er spl. Þ kq + kq Þ q R R. As. (A,C) Iduced emf or e pa a e I PQRS ( pa) r db A dt Q - I PR. As. (A,B) Wave-legth missig, so coditio of destructive iterferece yd d - l D D d A d T/ pt Y L a L /L ( + - ) 8. As. (C) E Dmc Dm amu 9.5 MeV 9. As. (D) 6 9 U 4 94 Xe + Sr d l D ( - ) 4. As. (B,D) + V (- ) V, m D CT94 KOTA / HS - /

4 PAPER 5. As. (B,C,D) Takig torque about R.H. side of loop l mg T ibb. As. 6 m les PART- : CHEMISTRY V. As. (A). As. (C). As. (B) 4. As. (D) 5. As. (A) 6. As. (D) 7. As. (C) 8. As. (C) 9. As. (D) - l -. As. (A). As. (B, D). As. (C, D). As. (B, D) V t, distace of other source from - f f 4- -f solvig about equatio we get 6 cm f f 4 4 SECTION I TARGET : JEE 4. As Q A. A C B D A D C C D A Q. 4 5 A. B,D C,D B,D A,B B Q. 4 5 A. 4 7 u m +Q m +Q v r mv + mv mu Q ( m+ m) u - 4 pî r ( m ) m Q u m Q v Q + m v - 4 pî / æ Q Give u ç pî mr è ø Þ r. As. 4. As. e (A + d) i ( + ) 6 5. As. 8 BE 7 + (9) As. (A,B) 5. As. (B) SECTION IV. As.. As.. As. 4. As As. 7 KOTA / HS - 4/ CT94

5 PAPER CODE LEADER & ENTHUSIAST COURSE PART- : MATHEMATICS KOTA / HS - 5/ TARGET : JEE 4. As. (A,B,C) cos y - si cos y d si - cos y si dy Q,y Î I st quadrat \ cos y cos d si siy dy dy d cotcoty Þ ò dy coty ò cot d Þ l secy l si +c æp p Q it passes through ç, è4 4ø Þ c l Þ secy si Þ si cosy (Q,y Î I st quadrat) (A) si( + y) + si( y) cosec - æcosec (B) cos y Þ y cos ç è ø (C) put Þ Þ curve does ot corss y-ais. As. (B,C) cot(a 7b) ta(5b a) Þ cos(a 7b) si(5b a) si(a 7b) cos(5b a) Þ si[(5b - a) (a 7b)] Þ si(4a b) Þ 4(a b) p Þ Q a b Î ( p,p) Þ p p p - < < C T 9 5 a-b p PAPER- PATTERN : JEE (Advaced) Date : SCORE-II : TEST # 9 Corporate Office : ALLEN CAREER INSTITUTE, SANKALP, CP-6, INDRA VIHAR, KOTA-45 PHONE : , Fa : , ifo@alle.ac.i Website: Q A. A,B,C B,C A,B,D A,C A,C B,C B,D A,D A C Q A. C B C B A B C C A B Þ 4 < < 4 Þ,,,,,, æp Now, si ç is iteger for,, è ø æp si ç is irratioal for,,, è ø. As. (A,B,D) -( a) ( + ) cos ƒ, ³,a > - sec a ì a é ù Domai í Þ Î, a+ ³ ê a ú î ë û ƒ() is decreasig (Q N r is ad D r is ) ad cotiuous (Q sec ((a + ) ¹ ) é æ ù Þ Rage is êƒ ç,ƒ a ú ë è ø û i.e. é ù ê, ú ë û 4. As. (A,C) (t,t) (4,4) Let ay poit o the parabola y 4 be (t,t ) t Î [,] {} it also lies o Þ b a, y a +,e - a b b t a 4t + a 4

6 PAPER Þ a t 4 + t, t Î [,] {} Þ a Î (,4] Þ b Î (,48] Þ maimum area of ellipse pab p p Now rectagle of maimum area is square whose area 64 sq. uits 5. As. (A,C) TARGET : JEE ì - ± + 8 ïa Þ a < a í ï îa - Þ a > rejected false. 8. As. (A,D) r/ 4 r/ åe åe. r r L lim lim m m m m m ( + ) r + æ r å ( + ) åç. r r è ø for L to be o zero fiite m z ( ) w Ö/ w e d r/ åe. ò r e- L lim e- æ r / åç. ò d r èø 6. As. (B,C) Let P() ƒ() four degree polyomial. Q P() P() P() Þ P() ( ) ( ) ( ) ( a) Þ ƒ() + ( a) ( ) ( ) ( ) ƒ'() + ( a) ( ) ( ) ( ) Þ ƒ'() + ( a) ( ) ( ) +++ Þ + a a Þ ƒ() + ( ) ( ) ( ) Now Þ Î ì ïp P Þ P' c forsamec Î, Q í ïîp P P' c for same c, Þ P"(c ) for same c Î (c,c ) Ì (,) Þ ƒ"() for same Î (,) Ì (,4) 7. As. (B,D) Statemet- : r æ æ r ç ç r å C. + è ø è ø 5 True. Statemet- : Q sides are i A.P Þ sia, sib ad sic are i A.P Þ A,B,C Need ot be i A.P. Þ B eed ot be 6º false a Statemet-: a a -a Þ - Þ a + a- Q z is circumcetre of triagle joiig (,), æ æ wº -, ç è ø ad w º -, - ç è ø Þ z º (,) {Q w w } Q z lies i z + < Þ miimum value of z is amp(w z ) agle made by lie joiig z to w with real ais p Paragraph for Questio 9 & X (4 ) () + (6 4) B (8 9) ( ) + (9 8) 9. As. (A) Now Q. As. (C) B X Þ A A th å bkc k åbk ( adja) k k k elemet of B.adjA \ X BA Þ X B( adja) A Þ B. adja A X Þ () th elemet of B.adjA () th elemet of A X. A KOTA / HS - 6/ CT95

7 Paragraph for Questio & C (,,) L ^ ^ ^ i+j+k A(,,4) B P (,,). As. (C) Let foot of perpedicular from A to L is (l +, l +, l + ) Þ AC is perpedicular ˆi+ ˆj+ kˆ Þ (l ) + (l + ) + (l ) l Þ C(,,) Let foot of perpedicular B(a,b,g) a- b- g-4 æ-4 Þ - ç - è ø Þ a, b, g Þ B(,,) Þ D of triagle ABC is.. As. (B) P is plae passig through (,,) ad (,,) cotaiig the verte ˆi+ ˆj+ kˆ Þ ormal verte to P is ˆi ˆj kˆ A - i ˆ+ kˆ i.e. ˆi- kˆ Þ Equatio of plae P is z. Paragraph for Questio & 4 (t',t') Q B(,y) P(t,t) LEADER & ENTHUSIAST COURSE PAPER -5-4 y slope of AB - Þ AB is ormal to 4y at P(t,t ) equatio of ormal at P(t,t ) is y t - ( - t ) t it passes through B(,) Þ t Þ t, slopes of AB. As. (C) Product of slopes of AB 4. As. (B) Q t' -t- Þ t' -, t Paragraph for Questio 5 & 6 for < < h() for < < h() sg + b + Þ h() + b for < < h() sg + b + [ + ] + a Þ h() b + a + 4 for h() b + a + 5 Þ é if < ê - + b- if < h() ê ê b + a + 4 if < ê ë b+ a As. (A) Clearly h() is discotiuous at. if at, h() is cotiuous the b Þ b if at, h() is cotiuous the b + b + a + 4 Þ a for h() to be discotiuous at,,, a ¹, b ¹. 6. As. (B) dy Q d Þ dy d CT95 p at P(t,t ) t y A(,) slope of taget to 4y h ì ï - - < < ï ï í - < ï ï+ b- < ï î b + a + 4 < i Î (,) which is ot differetiable at,,. KOTA / HS - 7/

8 PAPER 7. As. (C) Let poit of tagecy is P(a, a 4a + a) Taget is (y a + 4a a) (a 8a + )( a) passes through (, ) Þ a + 4a a a + 8a a Þ a (a ) Þ a & poit (, 4) is poit of cotact a & poit (,) is poit of cotact TARGET : JEE 4 Rage of ƒ() is (,] Local etremum are -5-4,, 4 4 oly itegral value of ƒ() is at ƒ() is ever equal to.. As. (B), 4 4 y y (4,8) I BC FC II BC FC O (, 4) y BC : Biased coi FC : Fair coi ìy Þ Equatio of taget are í îy - 8. As. (C) l ( PA) ( PB) l +l l4 whe l l l(let), l, l 4 the (PA) l (PB) l Þ PA PB (Q PA >, PB > ) Þ locus of P is lie which perpedicular bisector of segmet AB. whe l l l(let), l 4, l < l ¹ (let l a) the (PA) l a(pb) l Þ PA costat (¹) PB Þ locus of P is circle. whe l l l, l 4 > AB the PA + PB l 4 Þ locus of P is ellipse. 9. As. (A) Ö Probability of gettig head o biased coi is 4 Probability of gettig tail o biased coi is 4 p P{I(H) ad II(H)} æ ç. +.. æ ç. +. è+ 4 + ø è+ 4 + ø Þ Þp 75 96,p P{I(T) ad II(T)} Now, p {I(H) ad II(T)} p 4 {I(T) ad II(H)} /4 ½ /4 Graph of ƒ() is adjacet KOTA / HS - 8/ CT95

9 PART- : PHYSICS. As. (B,C, D) By Lez' law iduced curret will oppose chage i flu.. As. (A,D) L æml Mg ç w è ø w g L -w( - ) ( L-r) w v L r e COAM, w w+ mv( L-r) ML ML. As. (B,C,D) 4. As. (A,C,D) Strech i sprig y y l ( cosq) élcosq lù ê ú ë û U ky mg y du du 6 & dq Þq dq > 5. As. (A,C, D) Moti will be periodic but ot SHM 6. As. (B,D) Let velocity of wire at time t is v, the e Bvl q Ce, i dq dt F m ilb F F m ma CBla LEADER & ENTHUSIAST COURSE PAPER -5-4 Q A. B,C,D A,D B,C,D A,C,D A,C,D B,D B,D A,C, D A B Q A. A B C A A A B C B A 7. As. (B, D) O high temperature vibratio of atoms is icreased so vibratioal coordiate will be couted 8. As. (A, C, D) Equlibrium positio will be midway betwee & 6 m i.e. m ad amplitude 6 4 m 9. As. (A). As. (B) (9 ad ) æ p ( a ) ç èab ø y at E æ p vy at ( ae) ç èab ø æ - v q ta ç v y where v v. As. (A) è D A q C v B v a cos q d dt v dq asiq v dt A a si q da dt ø a cosq dq dt CT95 KOTA / HS - 9/

10 PAPER a æ v cos q ç èa si q ø df da e B dt dt. As. (B) e I, F Bia R. As. (C) 4. As. (A) 5. As. (A) r r r t M B TARGET : JEE 4 i p r ˆ j Bi ˆ ˆ -p i r Bk 6. As. (A) dw 5 ib w p cos q dq 7 m w 5 pib Þ si q 7 m 7. As. (B) 8. As. (C) 9. As. (B). As. (A) -5-4 PART- : CHEMISTRY Q A. A, B A,B,C,D B B, D A, C A, B, D C D B C Q A. B D C C D C C B A C. As. (A, B). As. (A, B, C, D). As. (B) 4. As. (B, D) 5. As. (A, C) 6. As. (A, B, D) 7. As. (C) 8. As. (D) 9. As. (B). As. (C). As. (B) As. (D). As. (C) 4. As. (C) 5. As. (D) 6. As. (C) 7. As. (C) 8. As. (B) 9. As. (A). As. (C) KOTA / HS - / CT95

JEE(Advanced) 2018 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 20 th MAY, 2018)

JEE(Advanced) 2018 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 20 th MAY, 2018) JEE(Advaced) 08 TEST PAPER WITH SOLUTION (HELD ON SUNDAY 0 th MAY, 08) PART- : JEE(Advaced) 08/Paper- SECTION. For ay positive iteger, defie ƒ : (0, ) as ƒ () j ta j j for all (0, ). (Here, the iverse