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ICSE Class X Prelims 2025 : Mathematics (Calcutta Girls High School (CGHS), Kolkata)

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Calcutta Girls' High School (CGHS), Kolkata
9 Science and Computer

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Dau~ J;".1)'"$ fn:t"ttS1 l11 tl!C' tnlC' ofti% f11t1 , At lhl.l: lime of mr.udt) 11,Uii-)' ,c~t!.h'{'d by Jcn11 i, . aJ R,.11150 b) Jls.120~1.1 <) lti ,7:SOd) No111o1oflhcsc In the gi\'cn 1iJ&1TC. BC-= 16 Q!l, BO .. 4 cm. Ute,, Alt IJ etiu::sl 10 ,. a)j l.".m -b)Scm c)6ii!m d)4 cm 0 C J'vJ lo thc.lldJoUling fiSUl'l'~~ SEC= 1154:1111JL_0 ACD-= 2511; lhCn lhc:mglQu'AC is: ) 1009 b) r1011 c) 90' d) 6S v) C ' \ L! t r ' I !.l I ,1 t ,. -. -:,..~ II 1 r A o J1, the g:t\'cri ligu,c, tf:c angle ordcprtssfon of paint D from poinl A is: a)S5 b) JS~ t) 4S d) 60" D I' , 1) '"" "" "'" (A \lul1111w- ,,t d~ 1.lttl' ,1 \l1l1tte I Ii.!11 cit! t,e lr,, ~t ou t (,r, in a ( Ub e o ( \ < r,J p- lm .,, t1()!u,111 1 t,ka ..-., (k ) Tht .~ '"" ' ,of dit ~ dr el on n 1..-m I i i ~~1bt10 11.,1 c.a:, be (ll n'c J O'JI fro 111 I (libO or .-) A ,~ ,m CA) "t.'"Uf'. Rc-n\Un (R) u f.ahc ~) A. .., .., .11 \l h Cah<. 11.,.. <i llmll l\.. ..,1 lon (A l & Rn .., (11 1" "" ' >oo \Il l ftW < d) llolh "'- "" "'" (A l & Ru ,.. , (R) 1110 f,l>C , ul l<' t the lo lP fl.A ,l1"11bu1lott [t..,,... I I i~;o o~ \ lh : wn , c,r1i.t 1n limits \ '0 ;21< 1u;.20 zo;2s \ ofdie ml J!: 1 c.la)t anJ u>Olhl c laa Is I U bl Z5 c) 30 \ nil F" ' J ~ UIC rr ~h 4) lS () - (Ir ,... .., a p.n ico la, t,w .t d 0.: . \ft ,c l'W hLN' U\I O) ~ . a did he )cd .\0 g.t;mu., ~ a) S b) 16 c) l2 d) 2& a) G"s4}cr, :11~ ~},rt1e, 1~1)fp,q rmul1 :ucTC1p.'\.lhc.ly ~ 1J p 1. q= J. r -.4 an d s 8 b) p 7, 9- -~ ,r -l ao d1 -- 1 ) Th e1 11 =- -- -'-1bd ,,. =! ,t t"Y l-" "''_ . a) xy x+ y s,-. <) x-y x,l A .iio pk cq ,cr bu)S goods "'Otlh of GS T is r,r, :! a1 r+)' 1d X -y .2 .. b) c) .!) p -4 .9 ,1 ., 1 11 !1 4J -l p - l.f -8 , ,- 7M J.s -.l is !; ? xy cl) RJ.50001n,hc1!1 lhem >t pn,fll of l0% lhcll bill >mocml i,; !,! ! ,:y . lfl llc .,. . a) RJ.6000 bJ Rs.5ZS c) Rs.S77S xii) Arun iovdlS Rs. 3600 d) W 2S O 0 on Rs.60 sN:<S ii pmniu m or211'/4. The Compony Jccl:lt div i.k td of t S %. td AU<rti>n (A): Anul'sonn uo Rca$on(R): The: dividend l inc:omc is Rs.~oo. po.id by lhc coml)3:ly on ilS cachlhart is Rs.9 a) Assc:nioo (A) is lnle, Rt asoo (R) is false Assertion (A) is false, Ro aso c) Both Assertion (A) .t Re o (R) is bU t ason (R) arc lr\lC d} Both A.sscmon (A.) & Rc asoo (R) :ll' t ~h e > xiii) Which or1he following cqlUlions a) 2zl - 3./i x +! b) .r + x - s = O =0 hi s 1WO rw m l dislin<I DJ U? e) d) x' + 3.t + 2. J! " 0 7x '-3 x + I = 0 ,.. 1r-xU 1k'.llli\oC11llf.r.":U lh1m 11'1t ~1t11ti( n ' '-' n, , ... JiJtU lnc11 .-I "" ! -t t(x .,,, ) t , , >0 Urw: -'C"it'nc,u AO ~nh,111111hr r-, ln!, ,\ - (O. fN an.I 11 cltJ, !\J 1' Otv,ii-!:d 111 cma,I)' llltl) 11'-e cqua,I r,lnt b)' P,Ji111 ~ r, Q . K ..f'l,11$ l hlfCtM>fd jn,oln (11 f oOOrt <J l (8. 4) 0 b) t'' -3) .:J t a, - -') lll'T.: J ( 4 ~ al ~~ I L i) /. !!,lO:ICfflt!III 11 51MlillJl lh.a.t 1 ( z) = ~% - 27x1 -100x- -t- 300 ,~ c1u-r:tl)' dtvblbl, t,y (3,.c + 10) .. a) S hnw lhc .n:1.ll!nte:rd ill true by us.in& rcmjlimkr and fel!tOt cbcuttm ar.d ju,,,tify )'Q'Ur ru,swcr with propc:r- tuwn. b) Al50, f3G1llrlitc the.glYt:n e.ll.pn:!Uion ca'Tlpkldy. ii) In (he adjoinlng figure, OA8C ls p;11allcl.), titm, 1.nc.Ur\Alion Clf OC is Mr a.,d the poinl B has coordinalet (ii, 3). fllnd 1he oq~tkms of 1111 lhc i ffl-ohh.! Paralk:li.'tQT.IL"l OABC, y iii) rn 1he al.\fOiniPtl'.fiJtll"1. AO i5 a dl:imdtt e!a c i~I~ ~th \:COCre O. If AO is p11ral\d CO BCandLCBD Jr.Jmd a)LOllD b) L,AOB <) 48ED C 3. (4+4+5\ i) "11n'CC uuml,en, arc j" o.r. wh~ sum b /0. tr\M.~xttc-n,CS bc c&Gh m.uhlp \ kd. by "4 ud tbc-mcms by S~ they wUI be in AJ>. Find the numbcrS. ii) A wooiten toy is .in the f.orm or cone-1urmoun1ed an a hemisphere.. Thi! dilu11c.h:r or tl!e base or lhe e:.one is 6 cm and ill height i$ 4 c.m. fi.nd the c:M1 of pa.intin$ the toy 1u ~e ~ ofRJ.S per 1000cm2 3 ,, r I \ ~"~ n nn,-4 \tdnJ'- } (1\llrn,nt ~~o1cl 11t1y ;4 II fl'l..,I Mr. f'mc,\ h 111,r.t~J )h.rn OU on lb Hi:t ~lwntrnl 11 1fo,co11111 tifltiJ V~>\!\~ lit~ 11J l~!C '-'i11rcs 11\ II rr:1.;1\ltfl ~1f its.10 F1t1d " 1II\ 1--i:!l.1. 1\ I I he t 1'11 c( I'll!,': f,:llt; Ju: " ( 11) IU ILiU\1111 1!1' ~W,ld (b) Th,: pio(h ('lllfU:J l,ic?i).11, ' t.l~ J1\~ c1 .d. IT> SoJ\~ U>e f"-ll""'ing Jnr~u:tiOn nnd 1t,rrQC~ tbc sul11:io~sd c,11 nun,licrliuei 2 <,r-t- i $i+l>:z,c ' )"'" lt1 l'tl AAnc. AU- &.h,, AC~ ll,.\;ri\ u:,, iLa,:w . i' w,J Qmt ro:nll ~ ll1c s,l.!es st AO ilAJAC rcsp rlvd )' sucb tliJ.1 PQ- ?.:.111:.-~I Ll'QA "'- 9~ ltl) A) Pn:i, c th111 /:,.AQI' ,t.6ABC a:.:1-imi1a: b) Olli:11111~ :..~c 1111.:1 r,t,6..>iQP <) At , liDJ (1\1U o( q""1ril.Jt,:gl f'UCQI i\1;Hrl,\ ,'UC) !>----', {Hl,4) sra.-:a cos1 8 l 1) Pro~ c- thll.l; ~ +~:: $(n1 B,c..JSl O 2 u) Pn) a bu I cu:ni.lmh'c dmc dtpot~ a.-COl,Ult ia tb~1k. SI~ dcp;,riu R11:GO0 pct moMh fur~ )'clU'I. Jf~t die end o(nu.'1.1rlry i'trioJ.i.fJI! gets Rl.51112. fiDd lhc tllEC of b1tnd:li lls'"'I>.,.p-<l lot' crJiod, C.:.i.,,._J.>ic,dIC IJIC::!lllP:Ui-$0 ' (~I~ !OIIOWUII ' d' ' 11trlbutl .... , " c i...lnltr\'al I lO-l 5 fr ;u<n,y I 5 Sl-60 ~s ZD 10 6J.i0 10 70:15 9 80-IS IS-00 75-IO 6 12 6. JJ 8 ()t]t-11 or~ "11111io11 oflln, 1., i1y"'I J b) c) , Wrlle O;e l<'l" c(line L:, lfl.: II ll1C b!JC<l<lr o( an.ll)cO. WriAO 11,c co-<>rdln>tcl ofpol111 I'. Fuwl dw: cqwition of L, 4 ~.--11-----,;-, :___ a & 1 J IV.... !i ' '' n ,. : , 1,t ilJ. I l ,1.-J.:il1 LIL u, 1~1 I lllfL,,,,J~ II I I r I11I\. r;1,, h I, 1,,, 1lf'i1HI O,' ,. u \ Ill~ l!1~1 '.~' i j'\ , 11 Tl~,t~~~ 1.1, ru r ~_!.n~J _1.~1i~,- L:;.,:,~ ~ -~----==-, i;,:'l.iaL1I 1 ,\ ~ H , 1 , , :.i 0 It I". ,}r~ii '11 I , I 'i f-..\ ,~--rf!:f!__' = _J_ :ii.~';':- [ 1 ,J 1. 1t r-1-~1\i",-, 1 I\~ ( lJ Lr1;1m 1l,e1 l~p .J <I I,) "'r.111 li.,:./,1111L1l,L-'.. lht> Xl1"kn r lkf'i-'1.',J;i ~ r rv,.... gf",d l,Ilf'IUl'l'! lht:: w ,~c 11"1o.:11;1f IJ!t ~,.,r;.1'1.:t.i,~ rn Lim 11111..tiLI ,, 11'1" 'I' r.lAi ,~ .. I-~ _,. C !Jr&., 111'-ii: tOUT llt1,latlill ill~'l'l'l~t ~tu.:b ' ,..111.J mh.1 \Ii~~ ~ , ....;.."II di!! L\"'L' 1 1\1 t llnd'\' ,.J, _, :n,~ Lt,.r, - ~,1i fo ibt! nmr~ f:ic~I i:.. ":,,I' Ki Ill II ~r c C! orH,D 1111at1m 11:1 l ll 11l,J[1t~ 1'h-'J,...d 1,1,~..:I L~I Ii di t..:i,..,r.t,, Wn:."t's.(g~ R ,); ~ 10 LQ-:(1 !O-_ll} }D- !U 111 - 1110 ~i,1 - ~ !Yo- hi i'O li!Ji ,I ~ l fj ~4 lJI } I.) ~ Na, a'l'!JtllMlo'fi! 3:! ~, , ett~'-ci irur ~ U\1-" ~1. ~rs-m ,,1.AJr,,~ Lh.c h\r U:tiq, .a cn pb r,:iric,, dmu ~ a~;,-c: lllil ~-,~-'o\.\1,;t ;)I l_,tq 1:iillllJ~ 1111:!'.! II) m!:d UR \II n~~ of !'Ii-: l\\ai,.,n. Ill ui,"C GUlfITT~ Wi!!,'E: nl tlke "lll'l1fLciJ.. 1.'l J'llUD'ticru f "'\.11Lm \W"h,11:-Uil mc-ri;: ,hlU! 111. .:,5111 daJ, ,3 J r4l ll I) lo. b.1}!; i:,,mliltr,?i ~,o h,j}l_5 CJ11.ll l1f ,"t.1Lle~ m, ..,1b..nfi:; I ~J! rrtl. iic) 1t..,11~ "QLI I:& at.11,,"D 11.111.rntn,a tl\1m the b.ia. Rii.t Wd. pr~i~ } i.l.W.1 lt. b unm h.iiLI, .J.n: ~ 1,,1oJ1 l!1k ,IJ,...~ ct~c ~[~ ~ .airii1I l'tw.n,~ .. ,~ I.in.~ wm t1'l.:I b) l f' ~ more . !i ~ t lnr~ r.1~ pniN1:ill ')1OJl!rO.\\,,itt~ I ~ ~all L' ,Lf fi~t c;Ji J:.. lli!-11mnln~ (b= 'lo .;,\llC- =-~ of1t- ---1~------- A ; 1 ,.. e "Cl~I' "iu S<'n> ,nz hi, ".,.. ,.,,en u~~ .i. 1~11.~...,.. 1 h e 1tt1)C"t ,ha:i1U1-""r ,,1 tho '-'")' 1UtJ1k ,-I E,111'1,\ \\' "5 ' C.IU ....., lhC 1,olll'"' (lfthe J.!.la."" h.i1d ti<ml' l' hir::rlc.il 1ul:;('1I p.-n-1tr111 wh kh R!d\11,Je-d 1h c t;:;;il "II.IIJ 111 1111.' 1:1 ~ .., If 1he. kd.;ht the i:lo~ wa, 10 c:1u. flml w11111 the llil'J'WV l1 e;ip1trh)' <"rl!1c g l:l1il wna ,1..t wl~ n,c 11ehu l ctw:.clty """11.'i ur t._Uii~ .. J 3-H ), 1he mnnthly pr-oOt ln nr~-s c;if HIO ,.l'lc:pS, 1c dlitrl\114'td f11U;; ~~: ~'~ ..,-~,_.,=-,-:,::, Pn,fr1( 1111b.) (l 1()0 100-200 100 -J 00 } 300----4uu' 41)() . 500 $00--600 Ne,, or~h.:ip.1J 13 13 :1 20 n s U:S.e J m11h shcc1 fo., lhi~.:;um1,cu1. Tub 2C'.m - ih 100 alon,u ~ cu,.IJ ,u,d ~can 10 ShilNI ~ lo ng Ihe ,.,,her .ul.\, . , Ii) C l)naw a h i1'1~Y;lwiffl r"ell ld t'IUing the iabcwe di.'ltri~111iC1f1 b) I Jud tbe mod~I val ue oflhc datn... F llk.1 2 X 2 fflltlrl,, X " hlch satul1~ 1bc cqwuiun C !H~ !I+ 2X ~ [~. If the- mull-ohhi!- ~tmt i{l11 ,xA 2cx + ab 0 IUC' R";1I un:q1J..11,I. 1uovc l~l lhc c:qu;itfon It-,, -Z{ll +b)X .+ a> +b-: + Zcl :::: Oba:;, non.11.l mut:tt, = (1+3+4] 111c: sum of 5~ and 91:1. tecrns of M A--1'. ts 72 wt.d 1bc 11um uf ~--and 12 ti:nns. ii 91. Fhut lhc A.I'. Cn a IU.s,bt of 600 km, a aircn1fi ;n,s st,.m'Cd down doe to bad WCb.tlter, 115 uvc:r4e s-peed for the trip was reduced by ZOO ~lru'hr Md the ti.me o f t1lght l ucrc11Scd by 30 minul('~. Find 1ho dt!rati-On of flight. Iii) Usi11g onJ_v a rulier and comp:I.S).CS constru<.'t ~BC -=-1'20-. where AB= BC -= Scm. ,.) Mark two points O and E Whkh s.ittd.fy lhe condition U,tit they are equidi1tan1 ti) lhlm both llA ~ DC. b) Jn 1h obove figvN.joln AE ond EC. Describo the fii:,we AECD. 6

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