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r \IILLA TI{ERESI*a rlrttrfl 'l &145'&q*.,xd PRBI,IMS JANUARY 2014" MATHEMATICS x std. 'tIME:2trrs 3O cmims DATE;13. i.201"4 hflA.RK$:8O papenpmwrded separmfefy. Amswers to ffiis papr mast M witten on fhe f $ re?,ma#es You r,vilf nat, beallowed fo wnfe during ffie,Tf6f Tf',s,stinleto&espenfinreadingflregxesft.of?pffipen altowed fonwrtd'"'mgr The tirne givan at the head of this Paperis the time fdae a'lswers' quesfi'oms frorm $eefiese ffi" Attempt all questionsfrom Secffon A and any four and rnust be done on ffie s&tme Att worktng, lniltudlfig tf,,ailhgruflt mil,,t b: Atnrly *hoWn $treet as tfie reEt of the answen omissionofessenffatwt*lttgwllltuultJalossofmarks. given in bfacketsf paits of questions are The inten&d marks forquestions otr Mathematical taDles arc Provided' J' SECTIOfi A AtWmPt trltr Qt guartioncfonr this Seotion for t 1800s' Trader A selns it tm a A) A manuf,acturer sells a T.V. to a trader pnmtrt q ?50 and trader B sells it to ffi" cCIffisuxyler for a of profit a at B trader o{r90CI"[ftherateofsalestaxunderVATistrOY*ffi*d.,',. /;\ ehe arnount of ta:r received by the Governrnent ror the ffi;: ts) r'v' "o"*"*er "ffi;;;*;;; the ratio 3:5. If 8 is added t$ ee'ch milmher Two numbers are in the ratio becomes 2:3' Find the numbers' C) A rnan invests t 46,875 at (3) {4\ ["]] 4ahp-a.-compound interest for 3 years' Calculate(i}Theinterestforthefirstyear).].. of the second year ({i} The &mCIunt standini to fria credit *l th* end year {iii} The imterest for the third 3 (iv) The alnount that the man will receive after circle, calculate if IBCD (4) * 2x2 - /cx * 10" fractor" * Z)is a factor of' if Q2 A) Find the value of ' k' {x Hence determine wether (x * 5) is also a B) In the given figure yemrs" : x3 13!o,and AD is a diameter (il zDAB (ii) IADBR eifl (3) the (3) Im-ffisrvenq c) XBCD'ia a square of side 14 vur. cm. rA,B,C,D LrUr\rrLJ are centres of the equal circles which touch externally in pairs" F imd the area Sf the shaded region. t4) !".t {,:" ' rl I Q3 ,q) Aruna deposits r 1600 per month in a cumulative account fon 3 years at ttrre rate af go/o p.a. simple interest. Find the am?ount that stre will ger a.t the time of maturity. m) (S) im the givera figure, O ip the centre of the circurncircle of AXFZ Tangents at X a.nd Y iniersect at T. Given zxry = B0o and zXOZ * 14Oo. Calculate thc value of zZt{y. ?,; (3i question C) Use graph paper for ifris (i) Plot the poinrs A (3,I) and B (-2,-4).use 1 cm: (4) lunit on both a.xes. (iii "&dls the irnage of A when reflected in the x axis. write down the co:ordinates of ^( and plot it on the graph paper. (iii) Bl is the irnage of B when reflected in the y axis, folloqred by reflection in" the origin. write down the co-ordinates of . B/and plot it on th: graph paper {iv} ,}.+ A) write down Frove th.e gedmetrical name of the figure Rabe/. Xffid -* (cerr# - cos ec A)2 ts) solv* the imequm.tiCIn and graph the solution set on the numben line Zy -B < y + Z S By* S ;yeR {3} {3} I 'l ritd ihe mean bf distribution by the short cut method 40 -50 30 -40 Wages in Rs No of 20 10 so -60 40 ES -qs 7CI -E& 60 -70 6 & 16 workers SECTION B this Sect'iorl' Attempt an'y lout questiotx ftom of a solid metallic sphere is 616 QS A) The surface area cltrx2" It is mel.tedandrecastintosmallerspheresofdiameterS.Scrn. (3) be obtained? Ftrow many such spheres can tanA+ secA-1= t+ sinA (3) ts) Prove rff_*"rA+l -;;;- C}ivlrJohnhasasavingsbankaccount.Hispassbookentrieg Deeenrber 3ffi on are as fo110ws. Mr .lorrn elO8es his accotrnt him if the rate catrcurate the interest received by Date 1.4,13 Fartlculars trIlthdrawals B/F 11.4.1.2 To self 8.6.12 By cheque 1,A.7 .L2 Depoeit To cheque of, interest is 4S00 1000 860 4860 3360 1500 By eash 3000 6360 t "10"12 By cash 2000 s36CI 18.1 CI.12 To cash 1 1.12 25. X2. n"2 Q6 A) In 5360 3000 By cheque 1000 By cash 2000 the given {igure z ACE: 43" and values of a, b and c' ('$) Balamee 5000 L2"9:12 5. 4%' 6360 8360 .zCAF = 62"" F'ind tlte {3} *--:**BfEe!teiiiii'ne the ratio in whicfi point (-5- 6 of A (-3, -1) and B (-8, 9). Also find the value of a. 3 tl L*1 2 ) cr rflA=[ -'--"- show that nz {3} - 5A + 7l = 0 {4} 87 A) In the given {igure, O is the centre of the circle. Deterrnine (n) ;AEC (ii) reflex "zAOC ,' (3) ;- :' it .t ffi) ?tre surre of th,e squares of trvo positive integers langer muffi?ber is 1E tirnes the srnaller number, ,i is 208. If the square of"the find the numbers. (3) C) The angne of eXevation of the top Q of the vertical tower pe from a gloint x orr the ground is 60o. At a point y, 40 m verticallSr above x, tlee amgne of elevat{on is 45". Find the height of the tower pe and ttre distamee XF" (4) Q8 A) F-ind the equatiom of the perpendicular bisector of t]:e line segffieI}tjoinfng-.tt*epointsA(2,3}and{6,-5}.y. ffi) usimg m*ler amd e&mipasses only construct IIC = & cm, AB = 5 crn {{} iiii and ^a ABC aa ABC {3} in whictr - 60" #omstruct the locus of points inside the A which are equidistamf f,nom BA and BC, Const-ruct the }ocus of points, inside the A which are equidistant Sronn ts and C. Mark the point P, which is equidistant from Ats, BC and aXso eqe"lidistant from B and C. Measure and record" length pts. t3) C) Ravi sotrd a eentaim mumtber of shares of r 20 paying 8% dividend atr tg amd" tr*e fmvested tlte prmeeeds in { L0 shares, paying L2a/adividend at S6yer premaiurn- if the eharage in his annual income is T L2O, find the numher of shares s trd by harir" (4) r ; -5- ,lo (3) QqA}Solvetheequationandgiveyouransvfercorrectt'o2d.p. i1 ':""1 ;:':i'l'' Br?*t?x*15=0 B) (-2, 2), (x,8), !' r- ^- *1 (6, y) are three points on the lce m{'n circtre whCIse ;rrcurn{erer r between between ^ arud' z ' Prove tkaat onal proportional filean the is -' lf v \ C} *l'n'!"=i x-2-Y-2+z f3} (4) = y4 arcplaced in a box and 29 7 5' 3' '9"" Qt0 A) Tickets numbered mixedthoroughly.oneticketisdrawnatrandornfrornthebox" Findtheprobabilitythatthgnumbgtrontheticketis less than t6 number (u) a otl*Uu' (i) a priml (3) (iiii a number divisible bY 3' (3) ts)Constructaregularhexagonofside4cm.Construetacirctre circumscribing the hexagon C)InALMN,PQisparalleltoMN.LP-2cm,PM=6cmandMN:20crn. Find (o PQ (rr) (4) e$rap:1:wraYrt) .."6 &auw, srd" x $ Q I I -6- Mathematics A) L-lsing a graph paper, draw an ogive for the following distribution which shows the marks obtained in a paper by stardents" 1O0 No of student the ogive to estirnate (i} the median (ii} the inter quartile range (iii) the number of students who score marks above 6s. {''Ise {5} ts) A toy is in tJre shape of a right circular cylinder with a t4) taermisphere on ome end and a cone on the other. The height and nadius of the cylindrical part are 18 cm and s cm respectively. T'}ae radii ofl the kremispherical and conical parts are the sarne &$ that of the cylindricat "part. calculate the surface area of the toy if the laeight of the comicatr part is 12 cm. t tLaq J t iSwrt + *****************
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