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Bombay Scottish School (Mahim) DATE : 09/01/2020 ; TIME : 2 HRS ; MARKS : 80 SECTION A (40 MARKS) Attempt all questions from this section Question 1 : [ 3 + 3 + 4 = 10 ] 1) Solve the following inequation and represent the solution set on the number line. 2 + 10 x 13 x + 10 < 24 + 10 x , x W 2) A wholesaler in Kanpur (U.P) marks an air conditioner for 50,000. He sells it to a shopkeeper in Banaras (U.P) at a discount of 10%. The shopkeeper sells it to a customer in Banaras at marked price. If the rate of GST is 18% , calculate the following : i) The shares of GST for both the state and the central government paid by the shopkeeper. ii) The amount paid by the customer for the air conditioner. 3) Rohit invested 10,800 on 100 shares at 20 premium paying 8% dividend. Rohit sold the shares when the price rose to 150. He invested the proceeds (excluding dividend) in 10% , 40 shares at 30. Find : a) Original number of shares b) Sale proceeds c) Change in his annual income from dividend. Question 2 : [ 3 + 3 + 4 = 10 ] 1) Solve for x the quadratic equation 2 x 2 + 5 x 4 = 0. Give your answer correct to 3 significant figures. 2) Find two numbers such that the mean proportional between them is 16 and the third proportional to them is 128. TEL : 9819019521 Page | 1 1 3) If M = [ 2 2 ] and I is a unit matrix of the same order as that of M. 1 Show that M2 2 M = 3 I. Question 3 : [ 3 + 3 + 4 = 10 ] 1) The maturity value of a recurring deposit account is 4491. If the monthly deposit is 240 and the rate of interest is 5% ; find the time (period) of this R.D account. 2) In what ratio is line joining ( 4, 3) and (1, 2) divided by the y axis? Also find the coordinates of point of intersection. 3) Given that x 2 and x + 1 are factors of f (x) = 2 x 3 x 2 + a x + b ; Calculate the values of a and b. Hence , factorise the expression completely. Question 4 : [ 3 + 3 + 4 = 10 ] 1) The first and the last terms of an A.P are 34 and 700 respectively. If the common difference is 18 , how many terms are there and what is their sum? 2) Prove that : sin A tan 1 cos = 1 + sec A 3) Using a graph paper plot the points A (3,2) and B ( 4, 0) (Take 2 cm = 1 unit on both the axes) i) Reflect A in the y - axis to get the image A . Write down its coordinates. ii) Reflect B in the origin to get the image B . Write down its coordinates. iii) Write the geometrical name for the figure AA BB and find its area. SECTION B (40 MARKS) Attempt any four questions from this section Question 5 : 1) If A = [ 4 sin 30 tan 45 [ 3 + 3 + 4 = 10 ] cos 0 3 ] and B = [ ]. Find the matrix X such that AX = B. 4 cos 60 9 2) Find the sum of 9 terms of the geometric progression. 96 48 + 24 .. 3 ) A trader bought a number of articles for 900. Five were damaged and he sold each of the remaining articles at 2 more than what he paid for it , thus getting a TEL : 9819019521 Page | 2 profit of 80 on the whole transaction. Taking the number of articles he bought as x , frame an equation in x and solve it. Question 6 : [ 3 + 3 + 4 = 10 ] 1) From a deck of 52 cards , all the face cards are removed and then remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is : a) A black card b) A card less than 8 iii) An even numbered red card 2) Find the equation of the line passing through (2, 6) and perpendicular to 4 x + 5 y = 6. 3) Construct a ABC, in which base BC = 5.5 cm, AB = 6 cm and ABC = 1050. Construct a circle circumscribing the ABC. Draw a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Question 7 : [ 3 + 3 + 4 = 10 ] 1) A model of a ship is made to a scale of 1 : 300. i) The length of the model of the ship is 5 cm. Calculate the length of the ship in metre. ii) The area of the deck of the ship is 2,70,000 m . Find the area of deck of the model. iii) The volume of the model is 250 litres. Calculate the volume of the ship in m . 2) A solid sphere of diameter 6 cm is melted and drawn into a wire of diameter 0.3 cm. find the length of the wire. 3) An aeroplane at a altitude of 1.5 km, finds that two ships that are sailing towards it in the same direction. The angles of depression as observed from the plane are 300 and 600 respectively. Find the distance between the ships. Question 8 : [ 3 + 3 + 4 = 10 ] 1) In the figure chords AB and CD of the circle produced to meet at P. i) Prove that PAC and PBD are similar. ii) If AB = 10 cm , PB = 6 cm and PD = 4 cm then find CD. TEL : 9819019521 Page | 3 2) The marks obtained by 160 students in an examination are given below : Draw an ogive for the given distribution taking 2 cm as 10 marks on one axis and 2 cm = 20 students on other axis. Marks 0 -10 10-20 20 -30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 No. of students 7 15 20 26 30 22 15 10 8 7 Using graph determine : i) the median marks ii) the lower quartile ii) the percentage of students who obtained more than 75% marks. iii) the number of students who did not pass , if the pass percentage was 35%. Question 9 : [ 3 + 3 + 4 = 10 ] 1) A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of conical portion is 16 cm and its height 6 cm. Determine the surface area of the toy. (Take = 3.14). 2) The distribution given below , shows the marks obtained by 25 students in an aptitude test. Find mean , median and mode of the distribution. Marks 5 6 7 8 9 10 Number of students 3 9 6 4 2 1 3) In the given figure , AB is the diameter of the circle with centre O and AT is the tangent. If ACD = 300. Calculate : i) ABD ii) TAD Question 10 : iii) BAD iv) BOD [ 3 + 3 + 4 = 10 ] 1) Find the equation of the line passing through (2, 1) and parallel to 2 x y = 4. TEL : 9819019521 Page | 4 2) In the given triangle PQR, LM is parallel to QR and PM : MR = 3 : 5. Calculate the value of ratio : i) iii) ii) 3) Using a step deviation method , find the mean marks of the following frequency distribution. Marks 11 20 21 30 31 40 41 50 51 60 61 70 71 80 No. of students 2 7 9 13 8 6 5 Question 11 : [ 4 + 6 = 10 ] 1) Draw a circle of diameter 9 cm. Mark a point P at a distance 7.5 cm from the centre O of the circle. Draw tangents to the given circle from the point P. Measure the length of the tangents AP and BP. 2) David opened a recurring deposit account in a bank and deposited 300 per month for two years. If he received 7,725 at the time of maturity , find (i) interest (ii) rate of interest per annum. 3) Given x = 2 + 1 + 2 1 2 + 1 2 1 . Use componendo and dividend to prove : x 4ax + 1 = 0 Please note this question paper of Bombay Scottish school is retyped without any changes done in it. Solutions to 12 prelim papers (Mumbai schools) available after 1st Feb 2020. For details Whatsapp on 9819019521 after 1st Feb TEL : 9819019521 Page | 5
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