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ICSE Class X Prelims 2024 : Mathematics (Bombay Scottish School, Mahim, Mumbai)

9 pages, 41 questions, 19 questions with responses, 19 total responses,

Shikhar Karmakar
Gokuldham High School & Junior College (GHS), Mumbai
1st to 10th science

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ombap 6cotti1t, 6tf,ool, abim PRBLIMl?fARY ASSESSMENT MATHEMATICS : 10 Grade : 05.01.2 024 Date Duratio n : 2 hour 30 mins ar s M ax. Mk . 80 No. of Questio ns : 10 No. of Printed sides : 09 Answer s to this Paper must be written on the paper provide d separately. You will not be allowed to write during first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing answer s. Attemp t all questio ns from Section A and any four questio ns from Section B. All workin g, includi ng rough work, must be clsarlg shown, and muat be done on the same sheet as the rest of the anawer . Omtsai on of essenti al workin g will result in lo" of marks. The intende d marks for questio ns or parts of questions are gi.ven in bracket s [] . Mathem atical tables are provide d. Section A ns from this Section.) questio (Attempt all Questio n 1 Choose the correct answer s to the questio ns from the given options . (Do not copy the questio n, write the correct answer s only.) i) ii) [15) The length of a tangent from an externa l point T on a circle with centre 0 is always greater than OT. (a) equal to OT. (b~ always less than OT. (c) insuffic ient data. (d) Which of the following is a diagona l matrix? 1. [~ ~] 2. [~ ~] 3. [~ ~] 1 Only 1. 1. and 3. (c) Only 2. (d) Only 3. r . . _2x For the given mequ ation , 1 (a) (b) ill) (a) 2! (b) 3 3 ' (c) (d) . 1v) the mini mum :value of x is 9 - Sx, x e W , 2 cte from a deale r for ,sooo and sold it to a A shop keep er purc hase d an arti t custo mer at a profit of 10 %. If the ra e Of GST is 18%' the amo unt of inpu t . , CGS T for the shop keep er 1s .. (a) (b) (c) (d) , , , , 0 900 450 495 v) -1 is the root of whic h of the following equa tion? (a) x 2 + 2x - 3 = 0 2 -2x -3= 0 , (c) x 2 (d) - ' =0 5 =0 4x + 3 x 2 + 4x - vi) The _points (-1,-2) and (7,6) are two oppo site verti ces of a recta ngle . The othe r two verti ces lie on the line y - 2x - k = 0, then the valu e of k is (a) (b) (c) (d) -4 2 -1 4 vii) The ratio of the sl~t heig ht of a cone to the heig ht of a cylin der with the same base radiu s and same curved surfa ce area is (a) (b) 1:2 3: 1 (c) (d) 1:3 2: 1 2 viii) P(2,3) is reflected in the line I to get the image P'(8,3).Equation of line 1 is y O (b) (c) (d) , = 5 y =3 X =0 X ix) Identical cards bearing numbers between 1 and 12 are placed in a bag. A card is selected from them at random. The probability that the card selected is an even number and a multiple of 3 is (a) -61 (b) -107 (c) -32 (d) 1 10 x) If sum of n terms of an AP is n2 + Sn, then the general term of the AP is (a) (b) (c) (d) Sn 2n+4 n+2 2n-4 xi) When x3 + 3x2 - kx + 4 is divided by x-2, the remainder is k. The value ofk is (a) (b) (c) (d) 12 16 -8 8 xii) If llABC - llPQR , AM and PN are the ~edians of llABC and llPQR respectively, then llABM - llPQN by which of the following test? B M , 3 ,;; s.s.S test s.A.S te st . d"vide the join of AB where A(4,-1) and 8(5,3)? xiii) In what ratio does x-axis t (d) (a) (b) (c) (d) 4:5 1:3 3: 1 5:4 . . the centre of a circle and AB 1s a chord. If the tangen t xiv) In the figure, O is of 400 with AB, then LAOS is AC at A makes an ang1e A -:::::==~:::---------(C 8. (a) 20 (b) 40 (c) 80 \ (d) gqo xv) Assertion (A) : If 3, x, 12 are in GP, then the value of x = 6 Reason (R): If a, G, bare in GP then o is the mean of a and b. (a) A is true, R is false (b) A is false, R is true (c) both A and R are true (d) both A and R are false Question 2 a) ,, ~ 3 -s],/ If A= [-4, 2 , find A 2 - SA- 141 , where I is an unit matrix of order 2x2 , (4] ' J 4 II I b) Calculate the median and the mode of the following distribution: 18 13 14 17 12 15 16 Age in years No of student s 2 3 5 6 3 4 (4] 2 . Mira investe d ,24000 in 7% hundre d rupee shares at 20 % discoun t. After one year she sold these shares at, 75 each and investe d the proceed s (including dividend of the first yeaij) in 18 % twenty-five rupee shares at 64% premiu m. Find: ' the original numbe r of shares. i) ,,, the sale proceeds. ii) (4) the change in her annual income from dividend. iii) c) "i: Questi on 3 a) I In the figure given below, AB is the diamete r of the circle with centre 0. The tangent at B and chord AC produc ed meet at.P. / 1 I i) ii) Prove that fl ABC - llAPB ..... If AB = 20cm and AC = 16cm, find AP and BP. . . -, , b) . Prove the following identity: A cos sin A cosec A+ cotA-1 sec A+ tanA-1 + (4] (4] = 1 ' c) Use graph paper for this questio n. Take scale as 1cm = 1 unit on both axes. Plot P(3, 1) and Q(0,5) . i) Reflect P in the y-axis to get R. ii) Reflect P, Q, R in the x-axis to get P', Q' and ~ . iii) Write the geometrical name of the figure PQRR'Q'P'. iv) Find the area of the figure formed. v) 5 ' l. .. Qu est ion 4 . a) Solve the following ine qua tio n, the num ber line . x+1 EI -3( x - 7) 15 - 7x > 3 'x b) cJ . f . wn te the s olu tio n set an d rep res en t it on , (3) 1 e wh ich ha s the y-i nte rce pt 4 an d is par all Fin d the equation7-oO aF.~~ the coord ina tes of po int wh ere it cu ts theel to the line 2x -3y - - 1 . [3] x-a xis . . ta !!.PQR in wh ich QR = 6.5 cm , P QR = 60 , PQ = 5cm . . tru ct the loc us of po int s at a dis tan ce o f 3 5 cm from p ;;i) c:1 :i:t ruc t the loc us of po int s eq uid is~ t fro m QR an d PR . iv) Ma rk 2 poi nts Ma nd N wh ich are at a dis tan ce of 3.5 cm fro m P ~d als o equ idi sta nt from QR an d PR. Me asu re MN. i) Co nst rue , c [4] Qu est ion 5 a) b) Fin d the nu mb er of ter ms of all two -digit na tur al nu mb ers wh ich are div isib le by 4. Hence, fin d its sum . (3) A ret ail er bu ys an art icl e fro m a wh ole sal er for f 30 00 0. He ma rks the pri ce of the art icl e 15% abo ve his co st pri ce an d sel ls it to a co ns um er at 5% dis cou nt on the ma rke d pri ce. If the sal es are int ra- sta te an d the rat e of GST is 12 %, fin d // i} the ma rke d pri ce of the art icl e. . / ,1 ii) the am ou nt pa id by the co nsu me r for the art icl e. ill} the GS T paid by the ret ail er to the Sta te Go ve rnm en t. [3] In the figure giv en bel ow , AC is a dia me ter of the cir cle an d BC II AE . If LBAC = soo E Fin d i) LA CB ii) L EDC iii) L BEC Hence, prove BE is als o a diameter. [4] 6 The weigh t of 50 work ers is given below : a} Weig ht (kg) 50-60 60-70 70-80 80-90 90-10 0 100-1 10 110-1 20 No.of work ers 4 7 11 14 6 5 3 Draw an ogive of the given distri butio n. Take 2cm = 10kg on one axis and 2cm= 5 work ers along the other axis. Use the graph to estim ate: the medi an. i) the uppe r quart ile. ii) If weigh ing 95kg and above is consi dered overw eight , find the iii) (5) numb er of work ers who are overweight. A conic al vesse l of radiu s 12cm and heigh t 16 cm is comp letely ftlled with water . A sphe re is lower ed into the wate r and its size is such that when it touch es the sides it is just imme rsed. b) 16cm ~d: i) ii) the radiu s of the sphe re. the fraction of the wate r that overflows. [5] taest ion 7 J A man depo sits , 900 per mont h in a recur ring depo sit acco unt for 2 years . If he gets , 1800 as inter est at the time of matu rity, find: the rate of inter est. i) (3) the matu rity value. ii) ) Show that (2x+7) is a factor of 2x3 given expre ssion completely. Sx2 - 11 x :_ 14 Henc e, facto rise the \ I (3] ' A mode l of a ship is made to scale 1 : 200 If the lengt h of the model is 4m, find the lengt h of the ship. i) ii) If the area of the deck of the ship is 1600 00m2 , fin9. the area of , the deck of the model. iii) H the volume of the model is 200 1 , find the volu me of the ship 3 mm . ,5- (4] Q ue st io n 8 a) , Solve th e gi ve n eq ua tio n and ex pres s yo ur answer c or re ct to 2 si gn if ic an t __,,fig ures. x - .!. = 3 % b) Fi nd th e m od e of th e following da ta , us in g a hi st og ra m . . M ar ks 0- 10 10 -2 0 20 -3 0 30 -4 0 No. of 5 12 20 9 St ud en ts (3) 40 -5 0 4 . . c) (3] Th e pr od uc t of th e fir st th re e te rm s of a G .P is 10 00 . If 6 is ad se co nd te rm an d 7 is ded_ to it s ad de d to its th ir d te rm Fi nd th e G.P. , th en th e te rm s ar e tn A .P (4) Q ue st io n 9 a) C al cu la te th e m ea n of th e following di st ri bu tio n by st ep -d ev ia m et ho d. G iv e yo ur an tio n sw er co rr ec t to th e ne ar es t w ho le nu m be r. C la ss es 0- 20 5 b) 20 -4 0 40 -6 0 8 10 60 -8 0 80 -1 00 J: 10 0- 12 0 12 7 A ba g co nt ai ns 18 ba lls ou t of w hi ch x ba lls ar e w hi te . i) If on e ba ll is dr aw n at ra nd om fr om th e ba g, w ha t is th e pr ob ab ili ty th at it is a w hi te ba ll. ii) If tw o ni or e w hi te ba lls ar e pu t in th e ba g, th e pr ob ab ili ty of dr aw in g a w hi te ba ll will be tim es th at of th e pr ob ab ili ty of w hi te ba ll in pa rt (i). Fi nd x. 8 i c) The angle of elevation of a pl an e fr om a po in t P on th e gr ou nd is After 12 se co nd s, th e 60 . an gl e of elevation ch an ge s to 30 . If th e pl an flying ho ri zo nt al ly at e is a sp ee d of 60 0{ 3 km /h , fi nd th e he ig ht is flying. at w hi ch ( 8 [3] it [4) I Q u e s t io n 1 0 a) b) c) \f x = +- b ays, he u A yp e5rd o f d a s o n w a s gm iv t , prove th a t 3 a x2 - 2bX + 3a '"" 0 l31 y s o f h is to e n ' 3 ooo fo r a to u r . I f h e e x te n s cut dow ds n h is d a il y ur program e ,t p e n s e b b i s t o u r p r o g t' a ll lm me. y 20. Fi e nd the nu m b er F r o m t h e fi g u r e g iv e n \ 3 \ b e lo w , F in d : i) ii) i t h e e q u a ti on t h e e q u a ti o f A B . on of CD. l41 l x X

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