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St. Mary's School (IC.S.E), Mazgaon (M.rrmMATrcs : Pnnr,rna Exnrr) Dnte z O6lAU20l4 Class -10 TotflI IVI*rks : 80 Totaltime:ZIn n Section (A) : 40 Marks (Alt questions Compulsory) .e Question I. l. The sirnple interost on a surn of money fior 2 years at 4Yo per annuno is Rs.340. Find : (i) The sum of money and (ii) The compound interest on this surn for one year payable half-yearty at the same rate. t3] t( , ) \-/ A shopkeeper buys a camera at a discoun t of 2}Yofrom the wholesaler, the printed price of the camcra being Rs.1600 and the rate of sales tax is 6a/o. The shopkeeper srells it to the bnyer at the printed price and charges tax at the same rate. Find : The price at which the camera can be bought. - (ii) The Yr{T (value Added frir) pa{d by the tsl lr) rhopkeepor. A page from the passbook ofa Savings BookAccount in a particular year is given below: Date Jan 3 Feb. 13 I\{arch 24 March 31 a{ay 20 JulyT hly 18 Sept 15 Sa{rt 26 Ifthe interest Particuler By Castt To Solf By Cheque By Interest By Cash To Cheque By Cash To Cheque Bv Cath Withdrawals Deposib (Rs.) trRs.) 5,000.00 5,000.CIo 2,000.00 t(Y[:rD 6tnPP 800.00 6o66 6eb6 l,00o"oo aifias 1,400.00 1,600.00 3,200.00 a Balance 2,350.00 lot"5 rczGB 136\5 is calculatedat6o/op.a. and is compounded atthe end ofMarchand september every year, find the interest earned up to 3l.r March and then aser completing all the entries, find the amount that the accornrt holder would have received had he closed the account on 20e Oct. the same year. I4I Question IL l. Mphan dapo*itod Rr.8Q prr rnonth in e eum*lntive depoeit accowrt for eix yaars. Find the amount payable to him on maturity, if the rate of interest is 6% per annum. t3l 2. A man a wants to btry 62 shares available at Rs.132 (par value being) Rs" 100. (,) How much he will have to invest? (ii) If the dividend is 7.SYo,what will be his annual income? (iii) If he wants to increase his annual income by Rs.150, how many extra shares shoutrd he buy? [3t 3" Solve andgraphthe solutionsetof-2 Question 1. ) <2x-6or-2s, + 5: 13; rrr. wherexeR. I4l Solve the following for x and give your answer correct to 2 decimal places. 3x2+5x-9:0 lsl Two dice are tluown simultaneously. Find the probability that (i) Eoth the dice show the same nurnber. (ii) The tntal (suru) of tlrs nurirboro on tlre dice is 9. (iii) The product of the numbers on the dice is : 8. 4-$e t3l Five years ago, a woman's age was the square of her son's age. Ten years hence her age will be twice that of her son'$ age. Find : (r) The age of the son five years ago. (ii) The present age of the woman. t4l Question IV. 1. (sinA* cosecA)' + (cosA* secAI: 2. 7 +tar*A+ cof'A. is the adjoining figure; PS is a diameter of a circle and of length 6 cm. Q and R are points on the diameter such that FQ. QR and RS are equal. Semicircles are drawn with PQ and QS as dianreters. Find the perimeter of the ahaded portion, .A.lno, frnd tha eru* sf rhndod partion, trn t3l t oQ,. ''' ' , *f"o tsl 3. Use graph paper for this question. The point A(2,3), B(4, 5), C(?,2) are the vertices of aABC. (r) Write down the coordinates ofAl, B', C' if AAtBtCt is the image of aABC, when reflected in the origin. (ii) Write downthe comdinates ofNl,Bil, Clt if AArtBilCu isthe image of aABC, when reflected in thex-axis. (iii) Mention the special name of the quadrilateral BCCllBll and find its area. t4l Section (B) : a0 Marks (Attempt any 4 questions out of 6) Question V l. The angle of elevation of a stationary cloud from a point 25 m above a lake is 300 and the angle of depression of its reflection in the lake 600. \Mhat is tkie taeiglat ofl the cloud above that lake-level? tr3I 2. Draw a circle of radius 5 orn. Drrw ftlim tangcnts to this cirolp p*r thnt the angle between the tangent is 450. 3. Using the properties of proportion, solve the following equation for , Oy/ertion r. x : x2+3x-341 Ix,+T I t"T{ Vr. M Find the matrix M, such [4] el x *kl: _fl = n, 16I [3] DMde Rs.36,465 between '^N and oB'so that whentheir shares are lent out at 10 percent conrpound interest per yeax, the amount that 'A'receives in 7 years is the same as lvhat'B' receives in 5 years. tsI bc + 7 is a fuotor of 2# + 5.f * llr expression completely, using the factor theorem. thow thrul * 14, Hance factoriee the given [41 Question VII. l. Find the coordinates of the points of trisection of the line segment joining the points 2, A(6,-2) andB(-8, 10). [3] Find the eguations of, the lincs which pass through the point (-2, 3) and are equally inclined to the coordinate axes. 3. In the given figure, ABC is a triangle. DE is parallel to BC p! (i) Determinetheratios4P a"a (ir) Prove that aDEF is sirnilar to aCBF. AB .FB Hence, find EE : tsD2l ""d$p BC . (iii) What is the ratio ofthe and aBFC. t3I areas of aDEF t4t tion VIII. l- trn a circle, with centre O, a diameterAB and a chordAD are drawn. Another circle is drawr withAo as diameter to cutAD at c. prove that : BD:2 x oc. 2. t3l In the given figure, AB is the diameter and AC is the chord of a circle such that 300. The tangent at c intersects AB produced at D. prove that : BC : dAC : t3l 3' Ruler and compasses may be used in this question. All construction lines and arcs rnustte olearly shown and be sf euflioiefit length and alarity to pemrit ars6sment, construct a aABC, in which BC craln 9 cm and angle A.nC oor. (ii) Construct the locus of all points inside triangte ABC, rryhich lre equidistant from B and C. (iii) Construct the locus of the vertices ofthe hiangles with BC as base and which are equal in areato triangleABC. Mark the point Q, inyor.r constuctiorl which would make AeBC equal in area to aABC, and isposceles. (v) Meusure and rocord thc lcngth of Ce. (i) :6 : : tg t4l ry Qr/stion IX" '/ 1. 2. use graph paper for this question. plot the points A(g, 2) and B(6, 4). These two points are the_vertices of a figyre__which is symmetrical about ; : ; and, y : 2. Complete the figure on the graph. Writc downthe geometrical name ofthe iigur*. jil- A vessel is in thc fbrrn sf an invcrted corre, Irs height is t l.em and the *or*. top which is operl is 2.5crn It is filled with waterirp to the rim. When lead shots, each ofwhich is a sphere of radius 0.25 cm are dropped into the vessel, 2/5 of the watsr flows out. Findthe ntrmber of lead shots dropped into the vessel. t3I Thg weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gran\ by the step deviation method. *.*8 Weiofut itt *r.amc *J-ulnber ofsuole* 80-85 85-90 90-9s 95 100 105 - 100 5 8 t0 t2 105 8 - n0 4 t10-115 a J t4l l t proportfn between two numbers x and y and 48 is the tfuird proportiomal y. and Find the [3] 61s the illean ofx nunrbers In what period oftime will Rs. 12,000 yield Rs.3,972 as compound interest at l0g4 per annunr, if compounded on an yearly [3] basis? 3 The table below shows the distribution of the scores obtained by 120 shooters in a shooting competition. Using a graph sheet, draw an ogive for ihe distribution. Scores obtained 0-10 Number of shooters 5 10-20 9 20-30 30 -40 40-50 50-60 60 -70 16 70*i0 80*90 90 - 100 22 26 t8 1t 6 4 3 Use your ogive to estirnate : The median (ii) The inter quartile range, (rii) The numbor of rhooton wtro obt:ined mnrrp t}rrn 7so/o acotrBs. (r) t4l
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