QUESTION PAPER WITH SOLUTION OF JEE ADVANCED - 7 (HELD ON st MAY SUNDAY 7) FEEL THE POWER OF OUR KNOWLEDGE & EXPERIENCE Our Top class IITian facult tam promiss to giv ou an authntic answr k which will b fastst in th whol countr. MATHEMATICS CODE - [PAPER-] 37. If is a tangnt to th hprbola a 6, thn which of th following CANNOT b sids of a right angld triangl? (A) a,, (B) a,, (C) a,8, (D) a,, Sol. (ABC) tangnt to th hprbola a 6 is a 6 Now and a 6 ar sam lin thn a 6 a 7 a 7 i.. a,, ar sid of a right angl triangl. 38. If a chord which is not a tangnt of th parabola ( h, k ), thn which of th following is (ar) possibl valu(s) of p, h and k? (A) p, h, k (B) p, h, k 3 (C) p, h 3, k (D) p, h, k 3 Sol.(C) W solv 6 and quation p,w gt 6 has th quation p, and midpoint ( p) 6 p p 6 ( p 6) () p ( p ) p 8p 6 p.now a, m T S k 8( h) k 6h k 8 k 8h 8 8k k, k k k 8h h h 8 8h k k k thn k, p & h thn possibl valu(s) of p, h and k ar p, h 3, k. 39. Lt [ ] b th gratst intgr lss than or quals to. Thn, at which of th following point(s) th function f ( ) cos( ( [ ])) is discontinuous? (A) (B) (C) (D) Sol.(ACD) lim cos [ ] lim( a h)cos( ( a h [ a h])) cos a a lim cos [ ] lim( a h)cos ( a h) [ a h] acos( a ) a h ma b continuous at a onl ( cos(a ) cos a for a Z a a whr a Z ) H.O : JABALPUR :, Nar Stadium Wright Town, Ph. (76), 83999 Pag
. Lt f : (,) b a continuous functions. Thn which of th following function(s) has (hav) th valu zro at som point in th intrval (,)? (A) (C) 9 f ( ) (B) f ( t)cost dt (D) f ( t)sint dt f ( ) f ( t)sin t dt Sol.(AB) (a) 9 g( ) f ( ).Now g() f () f () g() f () f () (,) thn g( ) ma b qual to g( ) f ( t)cost dt (b) / g() f ( t)costdt g() f ( t)costdt f ( t) (,) & cos t (,) thn g( ) ma b qual to (c)lt g( ) f ( t)sin t dt g '( ) f ( )sin if (,) thn g '() f ()sin and g '() f ()sin ( f () (,)) thn g( ) / (d) Lt g( ) f ( ) f ( t)sin t dt.now (,) & f ( ) (,) and sin (,sin) i.. g( ) thn g( ). Which of th following is (ar) NOT th squar of a 3 3 matri with ral ntris? (A) (B) (C) (D) Sol.(BD) (A) I. I. (B) I A or A is not squar of a 3 3 matri with ral ntris (C) is squar of a 3 3 matri with ral ntris (D) A or A is not squar. H.O : JABALPUR :, Nar Stadium Wright Town, Ph. (76), 83999 Pag
. Lt a, b, and b ral numbrs such that a b and. If th compl numbr z i az b satisfis Im, thn which of th following is (ar) possibl valu(s) of? z (A) Sol.(AB). (B) a ai b i ( ) i i (C) ( a b) ai ( ) i ( ) i ( ) i (D) ( a b) ai ( ) i a a a b Im. ( ) i ( ) i ( ) ( ), 3. Lt X and Y b two vnts such that P( X ), P( X Y ) and 3 Sol.(AB) (A) P( Y ) (B) P( X ' Y ) (C) P( X Y ) (D) P ( X Y ) ( ), P X Y, P( X ) P( X Y). thn P( Y) P( X) 3 3 P( Y X ). Thn P( X Y ) P( Y) 7 P( X Y).Now P( X ' Y) P( Y) P( X Y) 3 P( X ' Y) P( X '/ Y) P( Y ) thn P( Y ) & P( X ' Y ). For how man valus of p, th circl thr common points? p and th coordinat as hav actl Sol.() p p passs through, for p and touchs ais if p p for p valu of p H.O : JABALPUR :, Nar Stadium Wright Town, Ph. (76), 83999 Pag 3
. Lt f : b a diffrntiabl function such that f (), f 3 and f '(). If g( ) f '( t)cosct cot tcosc t f ( t) dt for,, thn lim g( ) Sol.() / lim ( f '( t)cosct cosct cot f ( t)) dt / / lim f '( t )cos c dt cos ct cot t f ( t ) dt / / / lim cos ct f ( t) cosct cot t f ( t) dt cosct cot t f ( t) dt f ( ) f '() lim f cos cf ( ) 3 lim 3 lim 3 sin cos 6. For a ral numbr, if th sstm solutions, thn z of linar quations, has infinitl man Sol.() ( ) 3 3 ( ) ( ) ( ) ( ), But for, thr is no solution for, 7. Words of lngth ar formd using th lttrs A,B,C,D,E,F,G,H,I,J. Lt b th numbr of such words whr no lttr is rpatd; and lt b th numbr of such words whr actl on lttr is rpatd twic and no othr lttr is rpatd. Thn 9 Sol. ()!.Now actl on lttr is rpatd that lttr can b slctd b C was, rmaining 8 lttr can b slctd b 9 C 8 was thn C C 9 8!!.9.!.So 9 9.! H.O : JABALPUR :, Nar Stadium Wright Town, Ph. (76), 83999 Pag
8. Th sids of a right angld triangl ar in arithmtic progrssion. If th triangl has ara, thn what is th lngth of its smallst sid? Sol.(6) Lt sids ar a d, a, a d whr d thn ara ( )( ) ( ) 8 a d a a d a...(i) and a ( a d) a ( a d) ad a d B (i) a 3a a a a a 8 8 6 8 thn d Columns, and 3 contain conics, quations of tangnts to th conics and points of contact, rspctivl. (I) (II) Column Column Column 3 a (i) a a (P), m m m m a ma a a a (ii) m (Q), m m (III) a (iii) m (R), (IV) a a (iv) m (S), 9. For a, if a tangnt is drawn to a suitabl conic (Column ) at th point of contact (,), thn which of th following options is th onl CORRECT combination for obtaining its quations? (A) (I) (i) (P) (B) (I) (ii) (Q) (C) (II) (ii) (Q) (D) (III) (i) (P) Sol.(B) For a,(,) satisfis onl a or. If a tangnt to a suitabl conic (Column ) is found to b 8 and its points of contact is (8,6) thn which of th following options is th onl CORRECT combination? (A) (I) (ii) (Q) (B) (II) (iv) (R) (C) (III) (i) (P) (D) (III) (ii) (Q) Sol.(C) 8 comparing with a m w gt m, a 8 m mting at a a, (8,6) m m H.O : JABALPUR :, Nar Stadium Wright Town, Ph. (76), 83999 Pag
. Th tangnt to a suitabl conic (Column ) at 3, is found to b 3, thn which of th following options is th onl CORRECT combination? (A) (IV) (iii) (S) (B) (IV) (iv) (S) (C) (II) (iii) (R) (D) (II) (iv) (R) Sol.(d) 3, ( acos, bsin ) ( acos,sin ) 3 a cos sin.now 3 a 3 Ans. (II) (iv) (R) Answr Q., Q. 3 and Q. b appropriatl matching th information givn in th thr columns of th following tabl Lt f ( ) log log, (, ) Column contains information about zros of f ( ), f '( ) and f ''( ) Column contains information about th limiting bhavior of f ( ), f '( ) and f ''( ) at infinit. Column 3 contains information about incrasing/dcrasing natur of f ( ) and f '( ) Column Column Column 3 (I) f ( ) for som (, ) (i) lim f ( ) (P) f is incrasing in (,) (II) f '( ) for som (, ) (ii) lim f ( ) (Q) f is dcrasing (, ) (III) f '( ) for som (,) (iii) lim f '( ) (R) f ' is incrasing in (,) (IV) f ''( ) for som (, ) (iv) lim f ''( ) (S) f ' is dcrasing in (, ). Which of th following options is th onl CORRECT combination? (A) (I) (i) (P) (B) (II) (ii) (Q) (C) (III) (iii) (R) (D) (IV) (iv) (S) 3. Which of th following options is th onl CORRECT combination? (A) (I) (ii) (R) (B) (II) (iii) (S) (C) (III) (iv) (P) (D) (IV) (i) (S). Which of th following options is th onl INCORRECT combination? (A) (I) (iii) (P) (B) (II) (iv) (Q) (C) (III) (i) (R) (D) (II) (iii) (P) to (BBC) f ( ) n n, f ( ), f '( ) n n H.O : JABALPUR :, Nar Stadium Wright Town, Ph. (76), 83999 Pag 6
f '() log, f '( ), = log f '( ) f '( ) is positiv in (,), f '( ) for in i. (Q) f is dcrasing in (, ) (, ) i.. og has on solution (Sinc og ) (II) f '( ) for som (, ) ( ) f ''( ) thn f ''( ) if n (ii) lim f ( ) lim n (iii) lim f '( ) (, ) i.. (S) ' f is dcrasing in = (, ) H.O : JABALPUR :, Nar Stadium Wright Town, Ph. (76), 83999 Pag 7