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Grade Subject :X Date : Mathematics : 24/09/2018 Duration : 2 hrs 30 min Maximum Marks J( BILLABONG1:>CllHIGH ........TUUI Thane (W) : 80 First Terminal Examination Answers to this paptr must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the Question p&per. The time given at the head of this paper is the time ~llowed for writing the answers. Section I is compulsory. Attempt any four questions from section II. The intended marks for questions ur parts of question are in brackets l ].Mathematical tables will be provided. SECTION A (40 Marks) Attempt all questions from this section. Quest;on 1 a. Two coins are tossed simultaneously. Describe the sample space S. Find the probability cf getting (i)at least one head (ii) at most one head (iii) exactly one head [3] b. Is 56 a term of the A.P. 7, 10, 13, 16, 19 ............ ? Prove it [3] c. Draw a circle of radius 3.2 cm . Draw two tangents to it inclined at 2n angle Clf 60 with each other. [4] Q\ies\i~n2 a. Let M be a matrix such that M x [~ ~] = [4 -7] (i) State the order of M (ii) find M [3] b. In what ratio is the segment joining the points A(6,5) and B(-3, 2) divided by the y-axis? Find the point at which the y-c1xis cuts Ab. [3] c. A model of a ship is made to a scale of 1: 200. [4) (i) If the length of the model is 4m, calculate the length of the ship. (ii) If the area of the deck of the ship is 160000m2, find the area of the deck of the model (iii) If the volume of the model is 200 litres, calculate the volume of the ship in cubic metres Question3 a. Solve : 2x + 7 = x + 2 [3] b. In the given figure, PB and QA are perpendiculars to the line segment AB. If PO = 6cm, QO = 9cm and the aiea of!). POB = 120cm 2, find the area of !). QOA [3] . lution '.>Ct on a n umber lin e: ",olvl' 1hr hH! t1u ;1 tlu11 given IJl' luw and repr P<,c n l 11 > '.> O ,. lh 'i , 141 I ~))( , 11 <- 7-,., 12 , Kl H Ou ~,t lon4 " 111 1hr RIVC'll fl l{ur l", L DAD Gs , (. AB O -. 10 and LB DC = ,i 5 11) Provr th al AC Is a diam eter o f th<' tl rcl e . [31 I In d t.. /\CO (II) 1d_L - -- B [3J .JI +slttA cosA ~== =.J 1-s lnA 1 -sLnA b. Provc th al: l< avlt a ha~ a cumulat.lvP time deposit account in a barV She deposits Rs 800 per month c. and ge l !. Rs 16700 as maturity valu e. If the rate of in t erc'.it be 5% per annum, find t he total tlm ~ for which th e account wa c; held SECTION [4J n (40 Mark.'!) Atkmpt uny 4 quc, tion, out of7 questions from thiJ section. Questlt>n 5 tan 2 A a. Prove that (secA-1) 2 = l+cosA 13] 1-cosA 13) b . Olscuss th e nature of the roots of the following without actually solving it : (I) 2sxz + 30x + 7 = 0 (ii) 2x 2 + 2x +3 = 0 (iii) 9x 2 - 6x + 1 =0 c. Dr aw a regular hexagon of side 4cm. Circumscribe a circle to it. Qu@j tlon 6 [41 [3] a. E: valuat~ without using tables : Zcu. .- 60 l-tan 45 t., _ Dra w - 2s tn30 ] x rcott. 5 cosec307 cos0 lsec60 sln90 l3i a histogram to re present the followi ng data : j Cla~ -M ark I ~~e q~ency 150 15 160 170 28 12 180 36 190 8 200 18 tcm A cotA + - - - = secA cosecA + 1 l4l a. Solve th e followin g inequation and repr esent on a number line : (3J c. Prove th .it 1- co tA 1 - tan A y uestlon 7 4 - 3x ~ 3x - 14, XE N l b. The hearts of 60 patients were examined through X-ray and the observations obtained are given below [ l 3 Diameter 123 124 of heart (in mm) Number of patients 12 7 122 120 121 125 16 7 8 10 Find the med1.:n diameter in mm. c. In the given figure, medians AD and BE of 6ABC meet at G and DF Prove that (i) EF FC (ii) AG:GD 2:1 = ~ = II BE. [4] A Question 8 a. Find the value of k for which 3kx2 = 4 (k x - 1 ) has equal roots [3] b. 200 logs are stacked in such a w?y that there are 20 logs in the bottom row, 19 logs in the next row, 18 logs in the next row and so en. How many rows are formed and how many logs are there in the top row? [3] c. Aliya opened a recurring deposit account in a bank and deposited Rs 300 per month for two years. If she received Rs 7725 at the time of maturity, find the rate of interest per annum. [4] Question 9 a. In the given figure, DE is a chord parallel to the diameter AC of a circle with centre 0 . if LCBO = 70 , calcuiate L COE ---- -- [3) b. Two dice are thrown simultaneously. Write the sample space Sand find the probability of getting: (3J (i) A doublet of even numbers (ii) A total of at least 10. (iii) A multiple of 3 as the sum of two numbers that turn up c. Solve the equation 2x - ~ =7. Write your answer correct to two decimal places. (4) Question10 / a. A 6ABC with sides AB= 16cm, BC= 12cm and CA = 18cm is reduced to 6A'B'c such that the smallest side of the image triangle is 4.8 cm. Find the scale factor and use it to find the length of the other sides of 6 A'B'C'. (3) b . c. Given A= { 2 -1 )7 and I =l10 011and l41 Find the sum of a\l 2-digit numbers which are divisible by 3 yuestion 11 a. l31 2 A = 9A + ml. Find m . Find the lengths of the medians of a ~ABC whose verti,:es are;. A~\ 13 ), B ( 1, -1 )and C (5,1) . 4 Also ,find the co-ordinates of the centroid of ~ABC. l ) b. The table below shows the distribution of the scores obtained by 120 shooters in shooting competition. Using a graph sheet, draw an ogive for the distribution. (6) 80-90 70-80 60-70 50-60 0-10 10-20 20-30 40-50 Score 30-40 obtairied 4 Number of 5 16 11 9 22 26 18 \6 shooters . Use your ogive to estimate (i) The median; (ii) The inter-quartile range; (iii) The number of shooters who obtained more than 75% score. 90-100 3 I
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