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Assembly of God Church School, Rupaidiha Preliminary Examination 2020-2021 Mathematics / ICSE X (Time 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 [ ]. ----------------------------------------------------------------------------------------------------------------------------- ------------------ Section-A [40 Marks] (Compulsory) (Attempt all questions from this Section) Question 1 (a) Find the value of k if 19x3 17x2 + k.x + 5 leaves a remainder 21 , when divided by 7x + 3. [3] (b) A wholesaler buys an item from the manufactures for Rs 24000. He marks the price of the item 25% above the cost price and sells it to a retailer at 10% discount. If the rate of GST is 8%, find the: (i) Marked price. (ii) GST paid by wholesaler to the government. [3] (c) ABC is a triangle and G (2, 1) is the centroid of the triangle. If A (-1, b), B (4, 2) and C (a, -2) then find a and b . Also find the equation of the line through G and parallel to AC. [4] Question 2 (a) Given 4 1 2 . = 6 , where M is a matrix and I is the unit matrix of order 1 2. (i) State the order of matrix M. (ii) Find the matrix M. [3] (b) Solve the following inequalities and represent your solution on the real number 1 1 1 2 2 2 line: 5 3 3 , . [3] (c) If q is the mean proportion between p and r, prove that 2 2 + 2 = 4 1 2 1 2 + 1 [4] 2 Question 3 (a) Solve the following equation: 2 + 3 + 1 = 1, . [3] (b) A bag contains 25 white balls, 16 yellow balls and 19 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is: [3] (i) a green ball, (ii) a white or yellow ball, (iii) neither a green ball nor a white ball. (c) The mean of the following distribution of is 24, find the value of a . Class interval 0 10 10 20 20 30 30 40 40 50 Frequency a 8 10 5 7 [4] Question 4 (a) Eliminate between the given equations: [3] x = a cot + b cosec , y = a cosec + b cot . (b) In the given figure O is the centre of the circle. Determine , If DA and DCare tangents and = 50 . [3] (c) A tent in the shape of cylinder surmounted by a conical top. If the height and the diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also find the cost of the canvas of the tent at the rate of Rs 250 per m2. [4] Section-B [40 Marks] (Attempt any four questions from this Section) Question 5 (a) If the sum of m terms of an A.P. be n and the sum of n terms be m, show that the sum of (m + n) terms is (m + n). [3] (b) In the figure given below AD is the diameter, O is the centre of the circle. AD is parallel to BC and = 32 . Find: (i) (ii) (iii) [3] (c) With the help of a graph paper, taking 2 cm = 1 unit along x axis and 2 cm = 1 unit along Y axis: [4] (i) Plot points A(0,3), B(2,3), C(3,0), D(2,-3) and E(0,-3). (ii) Reflect points B,C and D on Y axis and name them as B , C and D respectively. (iii) Write the equation of line B D . (iv) Name the figure BCDD C B B. Question 6 (a) In the given figure ABC and AMP are right andled at B and M respectively. Given AC = 10 cm, AP = 15 cm and PM = 12 cm. (i) Prove that ABC ~ AMP. (ii) Find AB and BC. [3] (b) A line passes through the point P(3,2). It meets the X-axis at point A and the Yaxis at point B, If PA:PB = 2:3, find the equation of the line that passes through the point P and is perpendicular to line AB. (c) If = +1+ 1 +1 1 [3] , then using the properties of proportion, show that 2 2 + 1 = 0. [4] Question 7 (a) A lot consists of 1440po bulbs, of which 20 are defective and the others and the others are good. Seema will buy a bulb if it is good, but will not buy if it is defective. The shpkeeper draws one bulb at random and gives it to her. What is the probability that : (i) she will buy it? (ii) She will not buy it? (b) Prove that: 1 sin = sec tan . 1+sin [3] [3]. (c) From a solid cylinder, whose height is 8 cmand radius is 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also find the total surface area of the remaining solid. [4] Question 8 (a) Given that , solve the inequationand graph the solution on the number line: 3 4 2 + 2. [3] 3 (b) Solve for x and y: + 4 1 2 = 7 2 2 11 [3] (c) Mrs. Teena Ambani has a recurring deposit account in a post office for three years at 7.5% p.a. simple interest. If she gets Rs 8,325 as interest at the time of maturity, find: (i) the monthly installment and (ii) the amount of maturity. [4] Question 9 (a) The 13th term of an AP is four times its 3rd term. If the fifth term is 16, then find the sum of its first 10 terms. [3] (b) Use remainder theorem to factorize the following polynomial. 2 3 + 5 2 11 14. [3] (c) Find the mean of the following distribution, using short cut method. x 0 10 10 20 20 30 30 40 40 50 f 10 6 8 12 5 [4] Question 10 (a) Solve the following equation for x and give your answer correct to 2 decimal places: 3x2 + 5x 9 = 0. [3] (b) Find the mode of the following frequency distribution, from the graph: [3] Class 20 30 30 40 40 50 50 60 60 70 70 80 Frequency 4 7 9 5 3 6 (c) The angle of elevation of a stationary cloud from a point 25 m above the lake is 30 and the angle of depressionof its reflection in the lake is 60 . What is the height of the cloud above the lake level? [4] Question 11 (a) In the given figure, AP and AQ are tangents to the circle with centre O. BC is tangent at point R on it. If OA = 17 cm and radius of crcle = 8 cm, find the perimeter of the triangle ABC. [4] (b) The table shows the distribution of the Marks obtained by 120 students in the Economics Examination. [6] Marks Number of students 0 10 5 10 20 9 20 30 16 30 40 22 40 50 26 50 60 18 60 70 11 70 80 6 80 90 4 90 100 3 Using graph paper, draw an ogive for the above distribution. Use your ogive to estimate. (i) The median. (ii) The interquartile range. (iii) The number of students who obtained more than 75% marks.
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