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(PRE - FINAL EXAMINATION 2019 2020 ) SUB: MATHS CLASS: X (ICSE) TIME: 2hrs30min MATHEMATICS (Two hours and a half) Answers to this Paper 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 paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables are provided. SECTION A (40 Marks) Attempt all questions from this Section QUESTION 1 a) Mr. Nihal has a two years recurring deposit account in State Bank of India and deposits month. If he receives 37,875 at the time of maturity . Find the rate of interest. 1500 per b) Solve the following inequation and write down the solution set: Represent the solution on a real number line. c) A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that it will point at (i) 8 ? (ii) an odd number? (iii) a number greater than 2? (iv) a composite number? QUESTION 2 a) Mr. Shiva invests 8500 in 10%, 100 shares at 170. He sells the shares when the price of each share rises by 30. He invests the proceeds in 12% 100 shares at 125. Find: (i) the sale proceeds. (ii) the number of 125 shares he buys (iii) the change in his annual income. b) Points of A and B the coordinates (7, -3) and (1, 9). Find: i) The slope of AB P age |1 ii) iii) The equation of perpendicular bisector of the line segment AB. The value of p , if (-2, p) lies on it. 2 c) Solve the following equation and give your answer correct to 3 significant figures: 5x 3x 4=0 QUESTION 3 a) Find the value of k if b) If A = and B = leaves remainder -10 when divided by 2x+1 find the matrix D, such that 3A 2B +2D = 0 c) A sum of 12,480 is paid off in 30 installments, such that each installment is installment. Calculate the value of the first installment. 20 more than preceding QUESTION 4 a) Two numbers are in the ratio of 3:5; if 8 is added to each number, the ratio becomes 2:3. Find the Numbers. b) The 1st and the 8th term of a G.P are 4 and 512 respectively. Find (i) the common ratio (ii) the sum of its first 8 terms. c) A wholesaler buys a machine from the manufacturer for 50,000. He marks the price of the machine 30% above his cost price and sells it to retailer at 20% discount on the marked price. If the rate the GST is 18% and assuming that all transactions occur within the same state, calculate i) The marked price of the machine ii) Retailer cost price inclusive GST iii) The CGST and SGST payable by the wholesaler to the Govt . SECTION B (40 Marks) Attempt any four questions from this Section QUESTION 5 a) A shopkeeper purchases a certain number of books for 960. If the cost per book was 8 less, the number of books that could be purchased for 960 would be 4 more. Write an equation, taking the original cost of each book to be x, and solve it to find the original cost of the book. b) A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream c) Solve the following inequation and represent the solution set on the number line: P age |2 QUESTION 6 a) In the given fig. O is the centre of the circle. The tangents B and D intersecting at P. If AB is parallel to CD and ABC = 550, find BOD and BPD. b) A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 and from the same point the angle of elevation of the top of the pedestal is 45 . Find the height of the pedestal. c) If ( x 2) is a factor of (i). find the value of p (ii). with this value of p factorise the above expression completely? QUESTION 7 a) If x : y = (a + 3) : (a 3); prove that b) PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP. c) Marks obtained by 200 students in an examination are given below: Marks No.of std 0 -10 5 10 -20 11 20 -30 10 30 -40 20 40 -50 28 50 -60 37 60 -70 40 70 -80 29 80 -90 14 90-100 6 Draw an ogive for the given distribution taking 2 cm = 10marks on one axis and 2 cm = 20students on the other axis. Using the graph determines: (i) The median marks (ii) The number of students who failed if minimum marks required to pass is 45. (iii) If scoring 91 and more marks is considered as grade one, find the number of students, who secured grade one in the examination. QUESTION 8 a) If , find matrix B such that , where is a 2 X 2 identity matrix. b) A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x. c) Calculate the mode for the following frequency distribution of marks obtained in a Geometry test: Marks No.of students 0 10 10 20 20 30 7 13 15 30 40 12 40 50 3 QUESTION 9 a) The model of a building is constructed with the scale factor 1 : 30. (i) If the height of the model is 80 cm, find the actual height of the building in meters. (ii) If the actual volume of a tank at the top of the building is 27 m3 find the volume of the tank on the top of the model. P age |3 b) Use a graph paper for this question taking 1 cm = 1 unit along both the x and y axes: (i) Plot the points A(0,5), B(2,5), C(5,2), D(5, -2), E(2, -5) and F(0,-5) (ii) Reflect the points B, C, D and E on the y - axis and name them respectively as B , C , D and E (iii) Write the coordinates of B , C , D and E . (iv) Name the figure formed by BCDEE D C B c) Using ruler and a compass only construct a semi-circle with diameter BC = 7cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ADC and write it down. QUESTION 10 a) Three numbers whose sum is 15 are in A.P. If 8, 6, 4 be added to them respectively, the resultant numbers are in G.P. Find the numbers. b) A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the fig. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article. c) Calculate the mean of the following table by using step deviation method only Profit per shop(in Rs.) No. of Shops 0 100 100 200 200 300 300 400 400 500 500 600 12 18 27 20 17 6 QUESTION 11 a) b) In the given figure AB = 7 cm and BC = 9 cm, (i) prove that ACD DCB (ii) Find the length of CD. c) Find the ratio in which the line joining (-2,5) and (-5,-6) is divided by the line y = -3. Hence the point of intersection. ******** ALL THE BEST ******** P age |4
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