Formatting page ...
\ THE BISHOP'S SCHOOL. CAMP . PUNE EXAMINATION (2017.2018) - SECOND PRELIMINARY MAT}IEMATICS CLASS: 10 'READING TIirE: TOTAL MARKS - AO WRITING TIME! 2 r/2 HOURS l5 MINs Dlfet 4.L2.2o17 Anst^rer to this paper must be wfitten on the paper Provided seParatalY. You witt not be attowed to wfite during the first tS minutes. This time is to be spent in reading the question paper. The time given at the head of the paper is the time a otted for wrlting the answers. SECTION A (Sotve all questions in this section) ouefition (3+3+4) 1 A) Find the value of a. if the division of ax3 + gx'z + 4x 10 by (x+3) leaves - a remainder 5. B) lYanoj opened a recurring deposit account in a bank and deposited Rs 500 per month for 3 years. The bank paid him Rs 20220 on maturity. Find the rate of Interest pa'd by the bank. C) The price of a T,V set Inclusive of sales tax of 9olo is Rs 13407. Flnd its marked price' If the sales tax is increased to 13olo, how much more does the customer pay for the (3+3+4) a!e t&!_z ,A) Solve the following inequation and represent the solution set on the number line' ---a < 333 1+:5: xeR lf the sum of first 7 terms of an A P ls 49 and that of flrst B) 17 terms is 289, find the sum of first n terms, c) ln the given figure PQ is a tangent to the circle at A. AB and AD are bisectors oZCAQ and IPAC. If tBAQ = 30e, Prove that BD is diameter of the circle i) Find the measure ofr-ii) ZDCA iii) ZABC a (3+3+4) Ouest.ion 3 cotA cotA-a lr)Provethat_-.--=---..--..' z.sec"A 1+tanA B) Solve th.r following quadratic equation for x and give your answer correct to three slgnincail c) 2x2-4x-3=O -14x - 3 = l) fiqlres:- -.31 and - l? bJa.d t! ;J E Let o=. r-"r a.. -2x2 )-sl p-l-8^ uY ouestion 4 rjr . rina tn" matrix P if pQ=R. (3+3+4) A) All the three face cards of spades are removed frcm a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack Find the probability of gettlng : i) A black face card ii) A queen iii) A black card Calculate the median and mode for the fottowing distribution Weiqht(in Kq) 10 11 12 14 No. of Children 4 7 5 8) 3 5 C) A hemispherical bowel of Internal radius gcm is full of tiquid. This tiquid is to be filled into conical shaped small containers each of diameter 3cm and height 4cm, How many containers.rre necessary to empty the bowel? SECTION B (Attempt any four questions in this section) (3+3+4) A.ucstlsr-E A) Find the sum cf first 51 terms of an A.P whose 2nd and 3.d terms are 14 and 18 respecflvety. B) Let A = uno. = _'rl, r - 16 C) [0, 'rl l:i ;l Find A, + ACi - 58 With the help of a graph paper, taking 1cm 1 unit along both x and y axls: i) Plor, points A(0,3), B(2,3), C(3,0), D(2,-3) and E(0,-3), ii) Rellect points B, C and D on the y axis and name them as B', C'and D'. iia) Wfite the co-ordinates of B', C'and D,. iv) U/rite the equation of the line B'D', v) 1{ame the figure BCDD'C'B'B, Ouestion A) 4 (3+3+4) ArJCD is a trapezium in which OA = 2OC and AB and AB= 10.8cm, i) Prove that AAOB - ACOD ii) Find DC iii) ll DC. If AC and BD intersect at O Find B) Find the ratio in which the line jojning (-3,-1) and (5,7) ls dlvided by the line x=2. Also, find the co ordinates of the ooint of intersection C) A solid figure is a cylinder surmounted by a cone. The diameter of the base of the cylinder is 6cm. The helght of the cone is 4cm and the total height of the solid is 25 cm, taKe n = 22t / Find the: i) Volume of the solid ii) Curved surface area of the solid Give your answer correct to the nearest whole number. (3+ 3+4) Ouestion 7 A) ln .ZAC,O given figure O is the centre of the circle. Tangents at A and B meet at C. = 30s, Find r) zBCO r) ii B) i) th,e lf IAOB Z APB The 1't and Bth term of a G.P are 5 and 640 respectively. Find i) The common ratio ii) Sum of its first 6 terms C) The mean of the following distribution is 52 and the frequency of class interval 30 40 is f. Find f. 1.)-20 5 ue 20'30 40-50 30'40 50-60 60-70 2 6 7 3 (3+3+4) g'.restion 8 A) 70-80 Prove that tan3 e cot3e ;J;;A + i,*rr= sec e cosec 0 - 2sinBcosg joining the points B) Find the equation of perpendicular bisector of the line segment (4,-3) and (3,1)! . C) Using the Propertles of proportlon, solve tor x t' / t-px\ \7; ) (4+6) Ouestion 9 and each meter of cloth A piece of cloth costs Rs 2O0 If the piece was 5m longer' unchanged How long is costed RS 2 less, the cost of the piece would have remained the piece and what is the original rate of cloth per metre? B) -fhe weight of 50 workers is given below a)- Weight in No. of 50-60 60 70 70- 80 80-90 90- 100 100-110 110- 120 7 11 T4 6 5 3 graph paper' Take 2cm = 10Kg on Draw an ogive of the given distribution using a the oglve drawn to estamate one axis aid 2cm = 5 workers along the other axis. use the following: i) ii) ili) Median The uPPer and lower quaftiles lf weighing 95kg ancl above workers who are overweight is considered overweight find the number of (3+3+4) Qlr9Eligllo A) ui -' are supplementary Prove that the opposite angles of a cyclic quadrilateral of A Determine ,n"t,nu4x - 3y + 12 = O meets x axis at A Write the coordinates 3y + 12 = 0 of ihe line through Aand perpendicular to 4x the pays sales-tax at the rate "q,ration of 3oo/o and C) A shopkeeper buys an article at a discount 8o/o'Theshopkeeper,inturn,se|lstheafticletoacustomerattheprintedpriceand price of the article is Rs 2500 FInd charges sales-tax at the same rate lf the printed i) ii) iii) The price paid by the shopkeeper' The Price Paid bY the customer' The VAT paid by the shopkeeper' (3+3+4) Ouestion 11 dividend and quoted paying 1oo/o invests a sum of money in RS 1o0 shares' A) A man 'p|.#iu.. these shares is Rs 560 calculate fi nit unnual dividend from at 2oo/o His total investment. rate of return on his lnvestment' The ii) the angles of depression- of two boats S1 nn airptane at an altitude of 250m, observes respectively Find the width of the on the opposite banks of a river to be 450 and 600 nLlmber' river, Write the answel correct to the nearest whoie IPBC=454 and 4cm C) (i) Construct a ABCP given BC = 5cm, BP = r) (ii)Comp!ete the rectangle ABcD such that a) P is equidistant from AB and BC' b) P is equidistant from C and D (iii) Measure and record the length of AB
|
