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ICSE Class X Prelims 2025 : Mathematics (Gurukul Academy, Lucknow)

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Gurukul Acade my MATHEMATICS Ma-.:imum Marks: 80 Time allowed: Three hours Answt!rs 10 this Papa must be wrillen on the paper pro idtd Srtparaul; You will not be allowr!d to write during first 15 milmte.s n,is rimi! is lo be SJX!nl in reading the question p per 711.! tim.? given 01 the liiad of this Paper is the time allowed/o r writing the a11S\4 ,rs Allemp/ all q11eslionsfrom Section A and anyfour q11es1io11Sjrom Sec/ion B the rest of All working, i11c/11di11g rough work, must be clearly shown, a11d must bt done on tht same shee.t as lite answer. Omi.<s/011 ofcsselllia/ working will resufl in loss ofmarks. The illf,znded marks for questions or parts ofq11~1ion.s are gn fn :r. C....:ic<rts {] Ma1h,111alical fables are pro,-fdcd SECTION A (Attempt all question s from this Section.) Qucstio11 1 Choose the correct answers to the questions from the given options: (i) A ludy deposited" 1800 per month for 15 montJ1s in a recurring deposit account at 7% per annum simple interest. The interest earned by her at maturity is (b) '\' 1080 (d) '\' 1500 (a)~ 900 (c) " 1260 (ii) 3 \Vhut number should be subtracte d from 2x has (2x - 3) as a factor? (c)4 2 If [_ 1 - Sx 2 + Sx so that the resulting polynom ial M3 W2 (iii) [15] (d)s iJ [;] =[_?2), then the valurs of x and y are (:i)x=- 2,y=l (c)x = 2,y l In the adjoinin g figure, if AB II ED, Stateme nt 1: 6 ABC -6 DEC Stateme nt 2: 6 ABC =!!6 DEC = (b)x=2 ,y=-1 (d)x = -2,y -1 = A Which of the fol101,~ng is valid? (a) Bot11 tl1e statements are true. (b) Both the statements are folse. (c) Statement 1 is true and Statement 2 is false. (d) Statement J is fa.lse and Statement 2 is true. (v) D The solution set of the linear inequati on -8 :5 x - i < -4, x E I is (b) {0,1,2,3} (a) (x: x E R, -1 :5 x < 3} (d) {-1,0.1,2} (c) {-1,0,1,2,3) Mathematics (Pre -Board Examination 2024-25-Class X (!CSE)) Page 1 of 6 1,1 {xi) IXU) G II I' ,i) L~ thl' mit! 1)01nt of the line M1tmcnt joining lhc points Q(-6.S) ;ind R(-Z.3), then lhc, 11]11eof:1 is {nJ ,J (h)-6 (c) t:! In :m ,, I'.. ,1 :i"' I. a. 20 nm.IS~ (a) 19 (cl;1S (d) 1:! ::::,\ ISt'(IU:tl In 1 (n) :.!sin: 8 (r)sln: a = 399. then 11 is (b):11 (d)4:1 (b) 2cos: 0 (d)cos: 0 (xm) A shopkecp1. ~ m J11i1iur sold a !111)to1, to a con. mrncr in J:111mr forl'4:i,ooo. If the rntc ot GSl'is 18%,lht:n IGSTi~ (.i) ~ ;pSo 01} t 7!if,O (c.) nil (d) noucoftli.:sc (,1, l !(the prnh.~hility of nn 1 , enl is p, then tilt' proh11hili1y ofit:; ,:omplc:uent:iry c, cnt "'111 IK' lX\') (:1)p- 1 (h)p t, ) l - p (d) l -~ If a kite is 11~,n~ at :i he1,sl11 of I0\13 metres from the le\ el ground. an ached to a s~ri1i~ indincd ;u 60" to the hori1.011t:il. thi:n the length of1hc string is {:i)80m {b)60\13m (, ) 80/3 m (d) 120 rn Qur;-.hOll :! (1) G1,cn tlml (x- !)and (x - 2)arc foctor.-ofx3 + 3): 2 -hx -6, fin<ltl:c\Jluc-sof a nnd U, With the;<(" ,11]11c1- of 3 ancl h, foc.torisc the given c.xpr~sion corr:,"lclcly. Mathtmat1cs (Prt- Board Examlnition 2024 25-Class X (ICSE)) [4] t'.ig~ -1 of6 (~J y UU ul In 111,- 111ho1nm 11.:u~ \Ill' iii in n,tl< ' and Ill" i~ )Mlralltl 10 mr-h re,,pc c Q and P t u,~ r th" 1 t111f'l'M"1 Af Atl anJ ' I \\ nlr th(- cocw,:l1n111es, ,( A 1 \h 1':','::t i't::~~t ~u!:.~: ~d~~d e&AC. cJ ~ 1,i.l 1hrt"qu n:1on uftht UncAC (u ~~; ttbued or1 lr1th.-a d,01m nr:fi u rr.J'Qu iatang .tnltoth corck1 : A.AB1 od".'a f.a] 01 -CAQ and .d'AC 1ce-pccti cl}' rf .:.8.-\Q,. 30'.pn, o.t th.a: (II) Ill> I, :i dl.,m:t cro(th t drtlt (h) 11 \8( L~ an l~l~ tn.snd(' Ju 11 (, I' tlw !!uni It-rm 1-.. :i.111.nJ 6"' lrrm ,~ 1qJ I ind !ht' 10 trrm 11I !IA /UI l"-..mi: o1 j>lrllph JXlf~. r. 111111 tlw jhllllh A,c., 4 and B;o. ,. ,.il Rdl, ~1 A aml H III lhl' vr:~111 lo &:rt m~r~ .\ and 8 \\'nit 1l1t ,.,.,rJm .ek. ,( \ .111d 8 ,, ,1.1h th, ,.:,..,,11111n.:.al n .. m, :, r 1hc 1i,:ut1: .\SA 8 ,tll l;m,I 11, 1)('nnw h't sn~n o~n .\n, mr an., four .;.a ,1.11.1:-.:- ;r ::: ':.J, ~ ,tu :: \fr 1u lnn .,t, , :~: ., r., ~i ( lo.. s~.s t'I .a:~: i:e-..--: c: F -, w- , \h~ ts ~1.1:ir t,.._-c, fc, 11nJt. ':<rt- '. J!a1.h .,,,:vun tc::O~ F:r..!: :a'.i,;~:::cr 4: ~ ,mt! tr.m....i..:t: 1~ \ m .. i i ) ~ ~ : ,1 -., ,-~ :?:5- ~ \\nit t::l' ..ih;t:, n .. _.: .:.::J ~, rn.~y~::: .'. "" t!;(." >.!..:.:! i:l'.R ~!a1henu:1cs (Ptt' -Board [,.an1i11adon 20J4-:! S Cbu X (!CSE)) {J QunllonS (1) In 1Macijol.nm1 nJUIC, l'AB b MU.nl Dd PT a l ngcnt 1u1hcattklollh c,en!rcO. U.U.TP 40'.PA 9cmandA.8= cm. ~,. I""' J, Find (a) LA.rT(h) k~h of PT. {11) Mr [JI Gupt.;iopcncdar umngdeposuucountm banli llcdl"J111'1ted IJ~ t :tSOO per month for l"Yl)'Cllrll, Al thr timr ofmat\lril) he ot C6"S00, find: (1) tht totnl inttrl'i"t orncd hy )lr Gup1a. (b) 1hc- l'IIIC o{ inlerctl pcr annum. {-1i (id) ,\ tndcr bll)-.1 anlfflj (Of a total tlN oft 600. (a} \\"nlrdo..-n lhe<Dl1 olone.utidcin temUI ol;,r lfthcl"('lf:l p('rlirtK:k"'t'fi' t5 mo , the numbtt of an,d" that o.n be boagh1fort00011,valJ bt fvur It<~ Cb) \\'n!C dO""-u tht' f'qU tioo h11 foc tht' abal c ,11. .uon Ml -'Ol -c i1 to find, ~ion6 (i) 'ind the cqu tion ol a l1M, which bas they U'\11.'rttpt ,, ind b pmilk-110 !ht (3] hnt' 2,: - )y- 1 O. Find thecoordin.a!l.'Sof1hr poinl whc~ 1tru\J 1hr ~ uis. (ii) In lhC' adjoinln1t f-,utt. CE it a tangent to the circle al 110mt C. ABCD it a eycl!cquaJri!1tcr11l. If 1.AIIC"' 93' rmJ -'DEC JS . Find: (u) -'AOC (b) -'CAD bl .,'---._-:,, (I.") ..:ACD. ~ I, :41 (iii) The pnnttd p:ia of an artick is , SO0OO. Tbr" holesvt: alJoll,~ 1 dLcroum of lttl:. to I sbopk -pc:r. 'nlc ahopkcepcr K!I!! t.lw.- :artidc to I cow:urxr 11 4 abO',.-c tM marbd pnN, lfthC'ultc .,... 1n1r.11-,ut~ and the r.attofGSTll 18~.. find (.a) ll:e am inl indus!\'t oft:ax (under CST) \<ilkb the ahopketpl'~ p;i~"I for the article (b) the 1moon1 ~id by the consumer for the an irk(c) th.: amount of tu (unJn GST) p.1id by lhe !hopktt)lt'r to the Central G,.1\ ~rm1:tnt. (d) the 1mo11n1 of tu (llndt"r GST) received b:, the State Go-,crnmcnt M111thtmatics (Prt -D~td Enmlnatlon Z024--2S Cl..u:s X(ICSE)) I'.~.. ,11->16 Q-.11,'.,.hon (11 \I a jll'~nl url J,..,-J ~.,.,Kl, thc-al\lt)r ofrll"'llk x1of, T1lk1I 11,wtf !tfound !U f I) be, 'IUCh 1h t 11~ lui,:rnt 1 .i Ot1 -.IW1 I'll m ro,wan l,.1br1 -.l~l.tll, ltnl uitbr nJI, "I lt.111nJ lob.-;, Fmd th.- hnpitof lhr IUWff (11] ll!dll$ RrmalnJ er lM(\l'rru l111 tvtiM' tl.e Jl(ll)11oml1I.I tOmpktc l)' " ~ ,. - lh /:ii t, !1111 rhr~1:m "'lhN'l'n 1.1111h rr,ln/\r ll!-301nddwn111oo(ftr 1numbr:1101hor [41 tM1J n1.1m!Jc,1 l 3 7, t'1111l 111,, nmnher;,, (.~tKID S 11 :tS d"""-" numbr:rtJ I lo 25, Th'") Ire pul 1n I ckN!d box Ind .tuiffft Thl'ff - thrw,!lhl A diK i! dr1., n ~1111111.lom fro1111he (3) bo~. t'lnd the, vrob,lb.lily 1h11 the numhn on tht d1u ii ,111nod dQ!ffllbn tb) dwis1hl.. b) :t .ind 3 both (r)1n1.1mbc,rlt':i#than16 1U l'r\"Ttha t ,::."'.- C Q$ A-C OIA (.u) Gl\'l'n\ = ~l ~ ::r::e~::;z ~~ ~DDmp ontndoa nddJ\'id endo1op n;,,'ttha t [3J f J t ' }.:~:\ \ Qat,t10,; 1Q fl) /fr:, t1rnc- lht' l'!l ch tc:-r.io!ar1A.P. ttequal ton hmNlll nth term, then find tU (31 1"": il, ..tem 10..-cr (111,1 Thr an,t,1 ofc:C'\ arion ofthr 1opof1 to...er from pom1 A (lucllOUth oftht ["] 10and ffflfllBc! IH'N.r1o ilbt-t"""C 'ri1fl UAI dwiit.1,d iowthal MW.1o frM :,,_.CTL'i~J find the t(rJ..1h Jn ,ltt-~ m,nur 1i) I mJ th<"11wn oftt!t'!J.. r:n~ 7.77.177 ,17i7... ton lrmis. JbtlMm atla (Pn Bcarcl Wldutl on 2024,?S -O. .ll (/CSE)} 131 (iii) 7/2 times the squar e root of the total numb er of swan s are playing in pond and rema ining two are swim ming in the water. Find tDl4I numb er of swans. (4]

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