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ST. XAVIER'S INSTITUTION. l'AN111m REARSHAL TEST 2024-25 SUBJECT. MATHEMATICS Cl. AS S 10 WR mN GT IME -JH HS F.\1-80 lns1ruc-tion.s f(lr unly 1<'.Klmg the- 11uet k.,n I. C.1nd1o.l,1M, JR' ,1lll' "l'l.f l1f"'I 15 minulC'~ p,aprr .ilJ0\\1,I (Of wrilm.g tht ,mw t'ri l TIit tun.. li'"'"" JI thi hr.kl ,-t tht J'-11"'' 1~ four qun tion ~ fn.,m Sttt ion 8 3. Att, rnpl .ill th..~ qun tinM for S ti on A ,ind .tn\ t or p,uts ol qunl!t:'fb Jr. S" ,.,1 m / J ,I Tht mf\'OJl.'J m.ar b for q!,K_...bOl'l. be- dir.uh ,IIO\\'fl ,md musl 1"' rm.- on dw S All \\'Ork1ng,. induJ1ng rough work mia t "'111 N!'Uh m I~ Of ,H\SWl"r ~ i o n o{ n.wntl.al trnrldn,i; S,lffl f' shtt t .a, tht ~ of tJw m.ut.s SECTION A f40 MARKSI (Att emp l .a.II question from this St.'C'lion) Qur stio n: J fISJ tlw gi\'t..'11 options Choose thecom--ct answer to theq u~t ion s from 3. i) A,sertion (A): If -Sy > -15 , then y < c is po,i th ~ .and bc < ac if Re,,ason fR): l( a > b, then ac >b e. if c is neg.it-Ive. .i) A is true, R is false. b) A is fals.:-, R is true. 'Ct reas on for ,\ c) Both A and Rar e lrue, nm! R is thecom. t re.tSOn for.- \ d) Both A and Rar e false, .md R ii. mcom--c , m:1n ~tis 4 ;. proftr on his ii) By pur chu ing t lS slaa rn for t .W rach invn tmtn l, th~n 1hr ralt of dh-idrnd b: d).i .S . c)6..m bJ4.6% 1)6. 8% ~n in .a lot of 600 is O.Ol.5. ~ iii) The prob .ibif ity o( grit lng .1 deft ctiv e num ber of ddt ttiv e ~n s in the lot is J 27 b) 270 c) .l6 iv) 1i the r.;atio of volu mes o( two sph eres 1w fatt .are.as is c) I :S b) 1 :4 a) I :2 d) .l60 is I: 8, then the r.alio of thei r d) I: 16 d on equ.11 b,1 ~ .1nd have. v) A cone, .a hcm i,ph ere and .a cyli nde r st.tn is the sam e height. The r.1lio of thei r volu mes d)J : 2: I c)2 3: I b)2 :l:3 a)l :2: 3 vi) In the give n figure, XQY is .a t.u1gmt .at Q lo .a. drd e. I( PM is .a cho rd p.ua..llel to XY .and LMQY 70 , then find: .tPQ M b) 35 a) 20 d) 70c) 40 ( o"1 1w o giv en 1 ; ~:: ," :; ,;~ poi11I I' i": Jic u~ vii} A point P mo vn io tlu l ii$ pt.-rf"'~ 1 1 -.J par:,lh I t(I 1twrn ) ~~1 Jil. , 4u ,m. CO .and AB , line l ;llr pu1 111 l'l.'1 1 AB mK dj a line t anywhcn~ in lx IW 6,'' II I IO tht IH C.IJ 11d CD ar1J p.ir ,i c'D c) a finr tin tilt' millw,1)' o( ;\U " 1 J'f, thA U,n kl b) a linr t perpendK'Ul,ir to' """ ,\U ,llk l d)a line fpt' ql\! mlk ul,1 rb1 S4' f'lo r o ,.ll rl to KC JI viii) In 1M ,1dJoining figu re, XY Is p.u ,11 p,1rls, XY div idn the tri,.nglc inl o two rqu thr n . cqu.11..: >* I,)~ <) ll)~ I.Kl The equ atio n of, . UM p.u ,1ll d toX ~!o ~~ ~I ~- b) x+ 8 0 - axi s ,1nd al a disl.1ncc of S unlt.9 c) y- 5 0 ~t) y+ S O rd 1 (J, - f) is bi.5 i " lhr Q ,1nd P nt poi 1hr ing join nt ,:) If a line ,eg me tt origin, the n 1hr co-oe'din.atr of Pac)( d)( -3, 4) -3, -4) ) 3,4 b)( )( 3,- 2) + I), the n the rrm ;aln drr is xO J( (z101 + JOI ) lsd ivl drd by (.r d)- 10 1 c)O b)IOO a)J0'2 .-li )lf rof ma tri xri sf! !JP f !J,then1Moc)rdrl"I d)t ic2 a)2>12 b)2 "1 ~ . ax . asx s, .... .... .. i xJil) The com mo n rall o o( 1hr G.P. 2 1 d) a x c) a x b) a 1 ~ 1 a) -;}-;r .a p t lo thr lin e y -2 .an d lirs ,.t xiv) A poi nt Pis lnn ri.a nl wil h rn sid e o( the Y - axi s. Th e co- ord ina te,s di sl ~ of 2 uni t, on the rig hl han d o( lhr poi nl P arr d) (-2 ,2) c)( 2,2 ) b) (-2 ,-2 ) a)( 2, -2 ) drl crm ine d gro 1ph kal ly? xv) Which of the fol low ing can not br d) Up per qua rtil e c) Mo de b) Medi.in a) Mt an Que stio n: 2 (i) Vinit factorized the give n polynomial : x3 - 7."<z t I x - u iinJ h.. , the result as (x + t)(x - 2. )(X - J) Usmg fac,or lh,-.. 1%,,, nnd im.lcr rt rn,, . V(>rif whet h lhe rorn_'\.l h ...u~: ll\.. er his resul t 1s corrl'\ t. If ,ncorn.-.ct, gh c Y st'('ts x _ a,is t I\ (ii) Equa t~n of lir'K' AB 1s 2x + Jy - 1Z = 0, whir h inl("r point S, then fi"il and Y - d~1s .11 8, If PQ pcrpendicuforly bisccls AO at the the equation of PQ ,tnd the c0-0rdinal<' of the point S. (iii) In the figuw give n below, i( LAC D 43 and LCA F 62 ', th .'n find the values of 21:,yand z. J4 4 +4J Que stion : .1 soliJ block an.- in GP (i) The lengths of tlm.-e unequal eJge s of a rec-1,mgular is 252cm~ and its volu me is 216cm>. Jf th<' total surface area of the block then find the length of sides of 1~ solid Mock. length 42 m milk booths supplil-s milk to the two boo1hs in the mtio 3: 2. One of the has a had cubo idal vtSSel having base area 3.96 sq.m and the other in e.tch of thl' cylindrical vessel havin g r.1dius I m. Find lhe le\'el of milk vessels. 2 m and (ii) A milk tanke r cylindric.al in shap e having dianll"tcr tion s: (iii) Stud y the grap h and answ er lhe follo wing ques a) Write lhc C();)rdinates o( the points A, 0, C and 0. write the b) Give n that, poin t C is the im.,ge of point A. Nam e an~t equa tion of lhe line o( reflection. r reflection c) Writ e lhc co-o rdina tes of the image of the point D unde in X - axis. point itself? d) Wha t is the nam e given to a point whoS\.' image is the e is formed. e) On joini ng the poin ts A, 8, C, D and A in order, a figur Nam e the closed figure. y' ,, 4+5J SECTION - H140 MARKS I IANSWER ANY fOURI Qu r,tj on: 4 .sharw, pay ing 15% div ide nd (I) Avi nav inv ests a sum ol mo ney in , 6lJ nd is t 1800, the n find : quo ted at 20" pre miu m. If ann ual div ide a) total num ber o{ shares ht- bou ght , b) his total Investment. fep ttSc nt th~~IYlion &rt on a (ii) Solve the foJJowing ine:guatlon .and -3 (x- 7) ~ 15 -? x> -;- . xe R ~ (Iii)~ 3 sln3 8 + co s 8. Hence, pro ve the following identity: 38 dnl s+c os sln 8+c os8 + sln 8c os 8 = 1 Ou est ion :5 [3+ 3+ 4J at P and tou chi ng AB and AC t: produced at Q and R respectively. Pro ve tha AQ i ( Perimeter or 6A BC ) years, the tota l amou.nt dep osi ted (ii) In a rec uni ng dep osi t acc oun t for 2 by him is one -tw elft h o( his total by a per son is t 9600. If the inte res t ear ned res t. . a) his mo nth ly dep osit , b) the rate of inte deposit, then find: (i) A circle is tou chi ng sid e BC or 6A BC (ur) Tht d.1ily "'fk:nditur e of 100 (.amili..... 1., ,ti""'" bo:'luw EAI:,C,!!.' !_i~ 40-60-+ 60-80 HO- IOU; !1)0_ ;.l(,11111 I '"' b .i 5 Numbero( 't f1miliN 11K' meJn daih l'lipcndilU"'-' l"'r (;11111h ,,; t AA I mJ th v hJ of 1~ b 25 11. J. 41 ?ueslio~: 6 I 11 n O ,.. 1h1 .. , 111n of nrdi . rh, 11111y,en1 vr n,,,..t, tht , (1)Jntlwp,1 11 1! ~ ~h.antt: terRQpro-lm't'llall ..1.)f'ron: 1hJ.t ~POT- ~PrR k b)lff""T 6 cm,QR 9 cm Find the length of PQ. 11 o ,. (ii)A(4,-6 ), 8(3,-2) and C(5,2)aN \'l.'rtia-so faA1\UC. Mlsapoin t on ABsurh th,11 Ai\l: MB l: I, Find the co-ordinate s of M. M~nC(> find the equation of lim through ~I and parallel lo AC. {iii) A duler in Kolk.tt.J suppli1e1 tome good to .t wholes.al in Sodepur ,u the details e!en below 5 ~ I ---.- _ _ 12 '"'c='=-----_Find - ~ T_6~ ~10~-_J__ ~I 12_:-] _ I ~ __ a) total CST paid by lhe whok-saler, b) total nmount o( bill {inclusive of GSl) 13 + 3 + 4) Question :7 (i) The horizontal distance behn'ffl lwo lowers is 120 m. The angle of elevation of the top and angle o( depression of the bottom o( the first tower as observed from the lop of lh<' second lower are 30 and 24 respectively. Find the height of thc.> two towers. (Giut yo11r answer com~ct upto; signiftc,nt figwm). (ii) The muks obt.ained by 120 students in a ttst ,ue given below: - .....!!!_rb ~ Wr IJ IO IG-20 lO JO J0-<40 1)-,0 ~6 21 16 ' S0-60 60~70 ijTu.90 T]ii".1007 J 7 4 6 II U "' U1ing graph sMet dr.1w iU1 ogive for the given-d.1t,1 a n ~ t lo find a) Median b) The number of students who obtained more than 75% marks in the test c) The numlx-r of students who did not pass the test. if minimum JS+ .5) marks requircJ to pass is 40. .. .. .. ~ ing bla " ' (i )A bo,co~radra\v n u m b e r; If w hl 1, 1,,11 .. if ,o 1, fm ,1 N ll s. t ~ , 1 wlul 1,,,1 f .ir-.n, ,11,~ ,. ,: f, o iflh 11 c k ball is h\ o-( 1 1115 SOmt>hlac l m bfJck N Ii s in Uw ean (ii) If b is the m t>.-tl '" -" ' .a ,1 p ru p o rh o n al a + a 2 b 1 b ;z ' 4 + b lc -l c ' : 11 tl of tltt rn l ,; ,h ih ly c, pru\' ' th ,1 t h \..,ater. A aJI filJed w itrg , d in 11 r ..u b m c l!l- p,.-.r_ uf er "f lt ,m Ji m . .. crn drical v1.'Ssd 6 0 ro p p e d in lo ii a ~ 15 ( , ~ I (111) A, cylin fJ + 3 + 4 J d ,s t 1 che \c r 36 m 11 te e m ia d f -r o 1L ,1 n sp h e "'-..-1 o f w cn._-a.!W in th e l'in .. t th d n fi . er wa1 fo ll o w s: . b Q u e s ti o n : 9 th e d .i i! y p O C (i ) Jn .a K h !O I 5 0 -6 0 4 0 -5 0 D ,i ly I ~:;i, pock I 12 Is . s~ u d e n ts k l. 'l ~ !. !Y o f SO 6 0 -7 0 2-1 l7 0 -8 0 - , 28 19 .as 80- 1s 90 - l 9 0----:TOO ,, 6 -1 . d <m 1s ox e n of _ _ -- -- '-ti-o n . Ta~t" 2 c m ( 10 in o q u es u u d ~ .n ts e r to so h c th is U se g ra p h p a p mds. lo n g th e o th e r n g th e ,,bovt d is tr ib u ti o n . a ts n e d u st IO n ti 2 cm to g rn m re p re se y. a ) D ra w a h is y pocket m o n e il a d l a d o m e b) E st im at e th s n te m 1 a n d al to n times it o l a n A .P is eq u s o f th e m " ' te rm n )1h te rm is z-: m. (i i) lf m tim1.:o + v e th a t it 's (m e m ~ n , th e n p ro 2 + p x - 1 5 = 0 a n d th x 2 n o e ti c e q u a ti en find the v a lu o f th e q u a d ra th t , o ts o ro a ro l is ua ) S :1 ec 0 has (i ii ) l( ((x2 + x ) + k = p n o ti a u q e c quadrati (3 + 3 + 4] o l' k '. e b a se lo n g e r th a n th 0 m 1 c : 2 n o is ti se s u e n u Q es of h y p o te d triangle, th e o f th e th re e s id s le g th n g a n t h le g e ri th a J F in (i) ln e sh o rt e st si d e . th n a th r e g n lo a n d 4 cm +71). the triangle. in d ( A '- S A (i i) I/ A = /: 2 ~I andl= r~ ~ /. th e n f th a t e to w e rs s u c h re th f o n o ke ti si o m to I c m , m a re p re se n t p 0 1 C f d o n a le 8 a . sc A a ts a k in g (iii) Poin t d C A 52 m. T n a m 3 7 c a ti o n o{ a p o in lo C e B , th m . 0 g 6 in w B A f b y d ra n c e fr o m a n y o f li.ABC. fi n d o ta g is d l in a w tu a c r a d s it a n ~ le , Band C, and 15 e q u id is ta n t fr o m A which (3 + 3 + 4 ) the towers.
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