. C. A. C. B 5. C 6. A 7. D 8. B 9. C 0. C. D. B. A. B 5. C 6. C 7. C 8. B 9. C 0. A. A. C. B. A 5. C 6. C 7. B 8. D 9. B 0. C. B. B. D. D 5. D 6. C 7. B 8. B 9. A 0. D. D. B. A. C 5. C Set Pper Set Pper I is true. Accordig to the grph, the solutio of the iequlity f(x) < is < x < b. II is ot true. The equtio of the xis of symmetry of y f(x): b + ( ) x b x III is ot true. The swer is A. Sectio A. C A ( + ) 6 ( + )( + ( )( + )( + ) ) 7. D x + > d 5 x < x + 8 x + > d x < x > 5 d x > The solutio of the compoud iequlities is The lest vlue of x is 0. x >.. C By substitutig x, we hve m[( ) ] + ( ) + 7 [( ) + ] + [( ) ]. B 9m 8 + 7 5 9m 6 m f 8 7 7 9 + The required remider is. 5. C The equtio hs equl roots. Δ 0 i.e. ( ) ( + 0)(5) 0 5 50 0 ( + 5)( 0) 0 5 or 0 + 6 + 6. A The grph of y f(x) itersects the x-xis t two distict poits. The discrimit of the equtio f(x) 0 is greter th zero. 8. B Let $x be the cost of c of Potto Ct Food. The sellig price of c of Potto Ct Food $ x( + 0%)( 0%) $.x The profit percetge $(.x x) 00% $ x % 9. C α + β 5 α β α + 6β 0α 5β 7α β α β 7 α : β : 7 0. C y is prtly costt d prtly vries directly s x. y + x, where, 0. The grph of y + x is stright lie with o-zero y-itercept. The swer is C. Perso Eductio Asi Limited 0
Solutio Guide d Mrig Scheme. D Averge usge before pm 50 vehicles per miute (50 60) vehicles per hour 000 vehicles per hour The verge usge from 8 m to 6 pm 6 000 + 760 vehicles per hour 0 90 vehicles per hour 5. C Joi BE.. B 7 5 6 5 7 6 5 7 8 7 6 5 9 7 8 9. A Mximum bsolute error of the mesured weight of solid metl g 0.5 g The miimum weight of the solid metl (5 0.5) g.5 g Mximum bsolute error of the mesured weight of smller solid metl g 0.5 g The mximum weight of ech smller solid metl (5 + 0.5) g. B 5.5 g 0.055 g The smllest possible vlue of.5 0.055 76.7 The smllest possible vlue of is 77. Obviously, BCDE is squre. BE cm BAE 90 d AB AE AB + AE BE (Pyth. theorem) AB BE AB BE 7 cm Are of ABCDE Are of ABE + re of BCDE ( AB)( AE) + ( BC)( CD) ( 7) + cm 80 cm 6. C With the ottios i the figure, ABC ~ ADE (AAA) AB cm AB + cm 8 cm AB cm AC + cm 5 cm (Pyth. theorem) d AE 6 + 8 cm 0 cm (Pyth. theorem) The totl surfce re [( π 8 0 π 5) + π + π 8 ]cm 0π cm Perso Eductio Asi Limited 0
Set Pper 7. C With the ottios i the figure, 0 cm x 5 cm x 5 cm y ( 5) cm 7 cm ABE ~ CDE (AAA) z 7 cm 0 cm 5 cm z cm Are of trpezium ABCD (0 + ) cm cm 8. B I BCD, CD t CBD BC cm t 60 BC BC cm BDC + CBD + BCD 80 BDC + 60 + 90 80 BDC 0 I CDE, DE cos CDE CD DE cos0 cm DE cm AD BC cm (property of rectgle) Are of ADE si 60 cm 8 cm cm 9 C Whe 0 θ 60, siθ. + ( siθ ) ttis its mximum whe siθ ttis its miimum. The required lrgest vlue + [ ( )] + 9 0. A DCE CDE 60 (bse s, isos. ) I CDE, CED + 60 + 60 80 CED 60 DCE CDE CED 60 CDE is equilterl trigle. I is true. BCE CED 60 (lt. s, AD // BC) II is true. The iformtio give is ot eough. AB my ot be prllel to CE. III my ot be true. The swer is A.. A Joi AB. ABC + ADC 80 (opp. s, cyclic qud.) ( ABO + 80 ) + 60 80 ABO 0 OA OB (rdii) BAO ABO 0 (bse s, isos. ) I OAB, AOB + 0 + 0 80 AOB 00 Altertive Solutio Joi OC. OB OC (rdii) OCB OBC 80 (bse s, isos. ) I OBC, BOC + 80 + 80 80 BOC 0 AOC ADC ( t cetre twice t ce ) AOB + 0 60 AOB 00. C CBD CAD ( s i the sme segmet) ACB CAD (lt. s, AD // BC) ACB ABD (rcs prop. to s t ce ) Perso Eductio Asi Limited 0
Solutio Guide d Mrig Scheme BAD + ABC 80 BAC + CAD + ABD + CBD 80 8 + ACB 80 ACB I BCE, CED EBC + ECB (ext. of ) ACB 66. B As show i the figure below: The swer is B. (it. s, AD // BC). A The polr coordites of the imge of A re ( 0, 5 ). The rectgulr coordites of the imge of A (0cos5,0si 5 ) (5, 5 ) 5. C As show i the figure below: 6. C The equtios of the locus of P re x h or x h +. Slope of x-itercept of L, slope of d y-itercep of L L d, y-itercept of d c. Slope of L < 0 < 0 I is true. Slope of L < slope of L L, x-itercept of L b c b L, < c c < II is ot true. x-itercept of L > x-itercept of L b > d III is true. For IV: y-itercept of L > y-itercept of L b d > c bc > d d > bc IV is true. The swer is C. 7. B The coordites of the cetre of the circle re,. The cetre of circle lies o the y-xis. x-coordite of the cetre is 0, i.e.. The rdius of the circle 0 + ( ) ( 5) The circumferece of the circle π 6π 8. D Refer to the tble below: + + + + + + + + + + + + + + + + + + Totl umber of possible outcomes d totl umber of fvourble outcomes 8 The required probbility 8 7 9. B Accordig to the stem-d-lef digrm, we hve 0 h d 7. If 7, IQR (0 + 7) (0 + h) Perso Eductio Asi Limited 0
Set Pper 7 h IQR 7 h h i.e. 0 h I is ot true. IQR (0 + ) (0 + h) 0 + ( h) 0 + ( h) h + h h 0 i.e. 7 II is true. If h 0 d, IQR (0 + ) (0) h > III is ot true. The swer is B. 0. C Me of A ( 8) + ( ) + + ( + ) + ( + ) 5 Me of B ( b ) + ( b ) + ( b + ) + ( b + ) b my ot be greter th b. I my ot be true. Mode of A + Mode of B b + + > b + II is true. Medi of A ( b ) + ( b + ) Medi of B b > b III is true. The swer is C. Sectio B. B The H.C.F. of the expressio x y d P is x y. is oe of the fctor of P. The L.C.M of the expressio 8 xy d P is 8x y. d y x re the fctors of P. x P y. B logx + logx log(x) log00 + logx log(x) log 00x. D x 00x x( x 00) 0 log log 5 5 y x y log y log x 0 (rejected) or 00 5 5 ( x ) + log log5 y log5 x + log5 log is the y-itercept of the grph. 5 log5 5 65. D 000000000 7 + + 7 + + + + 7 + + 7 5 x 0 + + 5. D Let L cut the x-xis t (, 0), where >. The, we hve AC d BC log. AC > BC > log log log > log > log log > > h I is ot true. Accordig to the shpe of the grph, we hve h > d >. h > II is true. 5 Perso Eductio Asi Limited 0
Solutio Guide d Mrig Scheme AC BC log log log log log log h III is true. Aswer is D. 6. C Obviously, α d β re the roots of equtio x 6x + 0. ( 6) α + β d αβ α + β ( β ) β 6β + 9 + β β β + 9 + 9 9 + β 7. B ( xi)( + i) + i xi xi ( + x) + ( x) i ( xi )( + i) is purely imgiry. + x 0 x 8. B si x si x 0 (si x + )(si x ) 0 si x si x ± 0 x 60 x 90 or x 70 9. A By usig Hero s formul, we hve: Are of DEF (6.5)(.5)(.5)(0.5) cm 5.685 cm or ( β 6β + 0 β β ) si x (rejected) + + 6 + + 6 + + 6 + + 6 6 cm Are of ABC is equl to re of DEF. 7 5 si ABC 5.685 si ABC 0.077 ABC 7.7 0. D ABC 90 ( i semi-circle) ACD 90 (tget rdius) ABC ACD I is true. OBE 90 (tget rdius) ABC ABE + ABO ABO + OBC ABE OBC II is true. (cor. to sig. fig.) Altertive method ABE ACB ( i lt. segmet) OB OC (rdii) OCB OBC (bse s, isos. ) ABE OBC II is true. Let DCB x. The DBC x. (tget properties) BDC 80 x BAC DCB x ( i lt. segmet) OA OB (rdii) OAB OBA x (bse s, isos. ) AOB 80 x AOB BDC III is true. The swer is D.. D ( x + 5) + y 9 By solvig, we hve y mx ( x + 5) + ( mx) 9 ( + m ) x + 0x + 6 0...(*) y mx is tget to the circle. Δ of (*) is equl to 0, i.e. 0 ( + m )(6) 0 9 6m 0 ( + m)( m) 0 m or 6 Perso Eductio Asi Limited 0
Set Pper. B 8 6 Mid-poit of OA, (, ) d 8 6 Mid-poit of OB, (, ) The equtio of the perpediculr bisector of OA y ( x ) 6 0 8 0 x + y 5 0 d the equtio of the perpediculr bisector of OB y 6 0 [ x ( )] 8 0 x y + 5 0 x + y 5 0 5 By solvig, we hve x 0 d y. x y + 5 0 5 The coordites of the circumcetre of OAB re 0,. 5. C The required vrice 6 ( ) Altertive Solutio 8 + ( 8) The x-coordite of the circumecetre 0 Let (0, y) be the coordites of the circumcetre of OAB. The (0, y) is the cetre of the circle pssig through O, A d B, with rdius equl to y. Rdius is equl to the distce betwee cetre d A. y y 6 + y y + 6 y 00 y (0 8) + ( y 6) 5 5 The coordites of the circumcetre of OAB re 0,.. A The umber of differet groups c be formed 6 C C 7 990. C P(cosists of both sex) P(ll mle) P(ll femle) 9 6 C C 5 5 C C 08 55 7 Perso Eductio Asi Limited 0