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rr<.Ht\tlll sT.G REGORTOS H tGH SCHOJIL PRELI M I NARY EXAM I NATIO N.DECEM BEt( STD X MATHEMATICS 2913 ryMB[s Note: The first fifteen minutes ar:e,for readinF onlv.No writine work to be dofie during this time. Atternpt all questions from section A and anv four ouestions from section B SECTION A Questionl- r r- ^1 (a) lf A =L? -'ll and B =F ;.| ;find matrixX,suchthatA+2X=38 (3) (b) A man invests{10,000 foitwo years at a certain rate of interest compounded annually. At the end of one year this sum amounts to {t1,200.Calculate .' (i)the rate of interest per annum (ii)the interest for the second year. (3) (iiilthe arnount at the end of the Second year. (c)Using remainder theorem, find the factors of the following polynornial: (4) x3 -61+jx+L0 II QUESTION 2 (a)lf a:b=c:d then show that ( a + c):(b + d)= (b)Solve the following quadratic equation ' Fr' fiao7 ' forxand giye your answer L ! {3) correct to two decimal places i (3) 5{x+2}=l (clln the given figure AB is the diameter of the circle with centre O .Tangents at C and B meet at D.lf lPBc=sO', find the value of a,b,c and d fi- V, (4) \ D I li ,. 33 q ,l QUESTION 3 (a)Find the mearymedian and mode for the following distribution; g, Lo,l -6,70,LLJ,!3,10 (3) (b)Find the area of the shaded region Given:OA=OC=7cm and OB =OD (3) (c)ln the given figure two straight lines OP and AB intersect at point C. Point C the midpoint of AB and it divides OP in the ratio 1:3.Find : (i)the coordinates of c. (iilthe slope of AB (iiilthe coordinatqof P. is . (ivlthe distance of AB , (4) QUESTION 4 - (a)Solve the following inequqtion and plot it on a number,line : -z+ - ft= ri, x I (b,tvaluate: -Z sitt6zo tonhoo Tszz. *;Ef (3) O + cos -d (3) (clusing a graph paper and taking a sca'le as 2cm=1 unit on both the axes (i) Plot the pbints A(-3,-2I and B(1,1) (ii)Form a quadrilateral A(BD such that y-axis is its line of symmetry. write down the coordinates of C and D. (iii) Assign a special name to the quadrilateral r^(. (( -J- ACBD (4) 3\ SECTION B (ATTEMPT ANY FOUR QUESTTONS FROM THI S SECTION) ' ' nuFsTtoN q (alFind the value of p if the following quadratic has equal roots i 4x'-(p- 2)x +1=0 (3) (b)Mr. Gupta paidt300 per month in a Recurring Deposit Account of a bank for two years. He receivedEJ500 as the maturity amount. Calculate the (i)rate of interest Per annum. (ii)total interest earned by him. (3) (c)The entries in a Saving Bank Passbook are as given below DATES PARTICULARS 01-01-12 01-a2-L2 B/F t2-a2-L2 CHEAUE WITHDRAWAL BALANCE DEPOSIT +6000 Rs'5 0 o + 3750 BY CASH @ + 14000 ? 20000 ? 20500 424250 BY CASH 05-04-12 20000 TO CASH +4250 15-04-12 + 21500 a 1500 BY CASH 09-0s-12 *23000 BY CASH 04-05-12 ? 1500 Calculate the interest for six months (January to June) at 4% per annum. (4) t II i ? : QUESTION 6 (a) ln what time will {8,009 yield fl261 as compound interebt atSYo per year ? compounded annually (blThe marked price of a refrigerator (31 is q568 and sales tax at the rate of " L2%is to be charged on it. Mr.Shah wants to buy it for t8r558 including sales tax. Find the reduction needed in the price of the refrigerator. (3) (c)The angle of eleyation of the top of a tower from a point A on the ground is 301 On moving a distance of ZO metres towards the foot of the tower to a point B, the angle of elevation increases to of the tower. r3 601 Find the height (4) 3S QUESTION 7 (a)The printed price of ah article is (10p00.A shopkeeper buys it at a discount of Z0% and sells it at the printed price. The rate of vat is L0% at every stage (ilthe price inclusive of tax at which the shopkeeper purchased the article from the wholesaler(iilVAT paid by the shoPkeePer, (3) (, lflUsiy properties of proportion, solve for:C; \/ i+t* 341 F; =u (c) ln thg.gi.ven figure PM is the tangent and. PA=AM, prove that ? (i)APMB is an isosceles triangle (4) (ii)PA.PB=PM2 are recast into a single sphere. lf there is no loss in metal find the radius of the sphere (3) (a) 45 solid cones of radius 5cm and slant height 13 cm (b)Write down the equation of the line passing through the intersection 'of 2x +y=5 and x-2y=$ and having y-intercept equalto -4, (3) Aa (i)Construct a A ABC such that AB=Scm,.BC=5cm and %=4cm (iilConstruct a circle circumscribing the triangle ABC. of, ie ,;"rlrgrld"h is entu.&'sbit tiiiif ina a point D .on the eir..rrnfr,cta Aaatd Ae' [** QUEsrloN (a) (b) -: (4) !r A=[' sinA-zsif,A (3) ffi=tonA. *1r., t=f f t'"0 the value or4 when A2=9 (3) 3L "t (t 4 t l. 9 Provethat I i t (c)Use ruler and compasses only: (iv)JoinABbcand measure length BD. j t -l (c)Calculate the mean of the following distribution using short cut method i (4) QUESTION 10 {a) ln the given diagram the two circle meet at point B. C is the centre of the bigger circle. [frl=trf E= 5cm and AP=9cm, find the length of fig;ari&PB (3) {b}A card is drawn at a randotx from a well shuffled deck of'52 playing cards. Find the probability that it is: j r. (i)arr ace {ii)a ten or a spade (iii}neither a iork nor a ? E (c)A trader buys'r'articles for a total cost ofT600 (i) Write down the cost of one article.' (ii) lf the cost per article'wasT5 riore, the number of articles that cciuld be bought for { 600 woutd (3) . (4) QUESTION 11 (a) Mrs. Mehta investedfl$2Oo in 15% T100 shares at20% discount. After T90 each and invested the proceeds (including her dividend) in 20%,a 50shares at r 42.Find: (i)the dividend for the first year. (ii)her annual incbme in the second year. a year she sold these shares at (iii)the percentage change in her return on her original investme'nt '?, r I ,, be 4less (iiilWrite down the equation in rand solve it I " (4) 3-r ::..'ii' rri?ry&-i{*::1:-r:,.!1:rT:{saii++trcEF-3.sijFiqar'.-- -.'F;-:iqr.qry . :.: r::'i.: (blUqe a graph paper fddffi$a'&ffi'$*drily:":;: t: iiji'*r : Thq marks obtqined by 200 students in a science test are given in the ..'i. .t. ''. :'.-.: t,j_,i;i;; i ..,.. .following table^Draw.an ogive fior the given distribution and use your n -i"1,. ii"}. (ilthe lower quartile rnarks," (iil the pass mai '.;.,iqI":;;1r:ii;?.;i; rj ,i:.i,,: l:a 1l'- ri' i a;tiii,i: $rf{"J' :.i '! ii::.r . ''-' :., 1-',:' 6 \: r:'. ;j't
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