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(xv) DJ\BCD is a rhombus with coordinates A(3, -1) and C(S,6). The slope of diagonal BO is: -2 (a) 7 [I '" 7 (b) 2 2 A/ (c) 5 (3,-1) (d) 7 M ' / C / (5.6) ,/ B Question 2 Prom a circular cylinder of diameter 10cm and height 12cm, a conical cavity of the (i) same radius and of the same height is hollowed out. f-'ind the volume and the whole ?;Sl 0 surface area of the remaining solid. (rr = 3.14) l4J (ii) ln the given figure DE II BC, AD: DB = 5: 4 l4) Find: (a) DE: BC (b) If AE;::;2.5cm, find AC. (c) A(t.ADE): A( oDBCE) "') (111 p h cos/I sin/I C . A +cos A rove t at:--+--=sm 1-cotA 1-tanA Question 3 (i) (ii) From the top of a tower of height 60m, the angle of depression of the top and bottom of a pole arc 30 and 45 . Find r4l (a) I low far the pole is from the bottom of the tower. (b) The length of the pole. Draw a regular hexagon of side 4cm. Construct its incircle. Measure the radius. (iii) Draw an ogive for the following distribution. 141 l5 I Take Scale on one axis, 2 cm = {l 00 and on the other axis, 2 cm = 50 employees Monthly 600income 700 No. of 40 employee Determine: (a) The median income. (b) The percentage of employees (c) The interquartile range. PPSK 23-24/ l O / MATH EMATICS 700800 68 800900 96 9001000 120 10001100 90 l l 001200 40 12001300 -26 whose income exceeds I 1 80 Pg 4 of 7 SECTION B (Attempt a11y four questions from this secrion) Question 4 (i) If A= [!1], B Find:AB = [ ]. c = [ 4] + 2C - 4D and D = [;] [3 J (ii) The model of a building is constructed with the scale factor I :30. (a) If the height of the model is 80cm, find the height of building in meters. (b)lf actual volume of the building is 27m 3 , find the volume of the model in cm3 [3] (iii) Solve the quadratic equation and give the answer correct to two significant figures. 4x 2 - 7x + 2 = 0 [4 J Question 5 (i) A mathematics aptitude test of 50 students was recorded as follows: Marks 50-60 60-70 70-80 80-90 90-100 o of 4 8 14 19 5 Students Draw a histogram for the above data using a graph paper and locate the mode. Take Scale: on x - axis 2cm = lOunits, on y - axis, 2cm = 2units (ii) Mr. Rahul goes to a shop to buy a leather coat which costs Z885(list price). The rate of GST is I 8%. I le tells the shopkeeper to reduce the price to such an extent that he has to pay 131 885 inclusive of GST. Find the reduction needed in the price of the coat. (iii) Shobha has a recurring deposit account in a bank for 3ycars at 7.5% p.a. simple interest. [4] if he gets 8325 as interest at the time of maturity, find (a) The monthly installment. (b) The amount of maturity. Question 6 l3 J (i) In a GP, if the third term is 72 and the sixth term is 1944, find the nth term. (ii) A hollow sphere of internal and external radii 6cm and 8cm respectively is melted and recast into small cones of base radius 2cm and height 8cm. Find the number of cones formed. PP K 23-24 /IO/ MATHEMATICS [31 Pg 5 of7
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