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ICSE Class X Prelims 2024 : Mathematics (Garden High School, Kolkata)

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Pragyan Ghosh
Garden High School, Kolkata

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GARDEN HIGH SCHOOL CLASS X Prelims, 2023 24 Mathematics Time: 2 hours Full Marks: 80 This Question Paper has six printed pages. Answers must be written in the script/s provided. You will not be allowed to write for the first 15 minutes. This time must be spent in reading the Question Paper. The time given at the head of this Paper is the time allowed for writing answers. This Paper is divided into two Sections. Answer all the questions of Section A and any four of Section B. All working, including rough work, must be done and clearly shown in the right-hand margin of the page containing the answer. Omission of any essential working will result in deduction of marks. Maximum marks for a question or parts of a question are given in brackets [ ]. SECTION A (40 marks) Answer all the questions. Question No 1 Choose the correct answers to the questions from the given options: [15 1 = 15] 1 2 2 7 2 (a) If A = , B= , C = , D = [0 1], which of the following multiplication 3 4 9 3 1 of matrices is not possible? (i) AB (ii) BC (iii) CA (iv) CD (b) The quadratic equation, the roots of which are 3 and 2, is (i) x2 + 5x 6 = 0. (iii) x2 5x 6 = 0. (ii) x2 + 5x + 6 = 0. (iv) x2 5x + 6 = 0. (c) A man buys an article marked at 5000 at a discount of 15% on the marked price and the rate of GST charged is 18%. The tax paid by the man for this purchase is (i) 765. (iii) 825. (ii) 750. (iv) 900. (2) (d) Which of the following is/are not in Arithmetic Progression? A. 1, 52, 72, 73, B. 2, 22, 23, 24, C. 1, 1, 1, 2, 2, 2, 3, 3, 3, (i) only A (ii) only B (e) If, a, b, c, d are in proportion, then (i) c. a (ii) b. d (iii) A and B 3a2 + 8b2 3c2 + 8d2 (iv) B and C is equal to (iii) a. b (iv) c. d (f) The areas of two similar triangles are 225 cm2 and 289 cm2 respectively. If the largest side of the larger triangle is 17 cm, the largest side of the smaller triangle is (i) 16 cm. (ii) 15 cm. (iii) 14 cm. (iv) 19 cm. (g) The volumes of 2 spheres are in the ratio of 64 27. The ratio of their surface areas is (i) 3 4. (ii) 4 3. (iii) 9 16. (iv) 16 9. (iii) only B (iv) only C (h) Which of the following event(s) is an impossible event? A. Tossing a coin to get a tail B. Choosing 4 face cards of spades C. Rolling a die to get 4 (i) A, B and C (ii) only A (i) The locus of a point, which is equidistant from two given parallel lines is (i) a curved line. (ii) a circle. (iii) a line parallel to the given lines and not midway between them. (iv) a line parallel to the given lines and midway between them. (j) If two tangents are drawn from an external point to a circle, then: A. The lengths of the tangents are equal. B. The tangents subtend equal angles at the centre. C. The tangents are equally inclined to the line joining the point and the centre of the circle. Which of the above statements is correct? (i) only A (ii) only B (iii) A and B both (iv) A, B and C (3) (k) The length of the shadow of a tree is 3 times its height. The angle of elevation of the top of the tree is (i) 30 . (ii) 60 . (iii) 45 . (iv) 0 . (l) A company with 2000 shares of face value of 110 each declares an annual dividend of 10%. The dividend on one share is (i) 10. (ii) 21. (iii) 11. (iv) 20. (m) If two straight lines kx + 2y 7 = 0 and 8x + ky + 6 = 0 are parallel to each other, then the value of k is (i) 2. (ii) 4. (iii) 6. (iv) 8. (iii) 1. (iv) 4. (n) cos4 + sin4 + 2sin2 cos2 is equal to (i) 0. (ii) 2. (o) Assertion (A): The data 3, 7, 0, 9, 5, 8 has no mode. Reason (R): No number occurs more number of times than any other number. (i) A is true, R is false. (iii) Both A and R are false. (ii) A is false, R is true. (iv) Both A and R are true. Question No 2 (a) A person opened a recurring deposit account in a bank and deposited 700 for 5 years. At the time of maturity, he received 46270. Find the rate of interest per annum. [4] (b) A piece of canvas, the area of which is 551m2, is used to make a conical tent, the radius of the base of which is 7m. Assume that 1m2 of the canvas is used up for stitching margins. Find the volume of the tent that can be made with the canvas. (c) Prove: sin 2sin3 2cos3 cos = tan [4] Question No 3 (a b) 3 ( b c) 3 (a) If a, b, c, d are in continued proportion, prove: (b) [4] = a d [4] In the adjoining figure, BAD = 65 , ABD = 70 and BDC = 45 . (i) Prove that AC is a diameter of the circle. (ii) Find ACB. [4] (4) (c) Use graph paper for this question. In the annual day of a school, the age-wise participation of students is shown in the following distribution: Age of students (in years) 5 7 7 9 9 11 11 13 13 15 15 17 17 19 Number of students 20 18 22 25 20 15 10 Draw an ogive for the above data and from it find the median age. [5] SECTION B (40 marks) Answer any four questions. Question No 4 8 2 12 (a) Given: X= 1 4 10 [3] (i) State the order of the matrix X. (ii) Find the matrix X. (b) Using the quadratic formula, solve the quadratic equation [3] x2 3(x + 3) = 0 and write the answer correct to 2 decimal places. (Mathematical tables may be used for this question.) (c) Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent. [4] Question No 5 (a) Using the step-deviation method, calculate the mean of the following distribution: Class interval Frequency 50 55 55 60 60 65 65 70 70 75 75 80 80 85 85 90 5 20 10 10 9 6 12 8 (b) The following items are bought from a departmental store: Items [3] [3] Quantity Selling Price Rate of GST Sugar 5 kg 40 per kg 5% Butter kg 400 per kg 12% Find the total amount to be paid for the above bill including the GST. (5) (c) ABCD is a trapezium in which AB is parallel to CD and AB = 2CD. The diagonals AC and BD intersect each other at O. If the area of AOB = 84 cm2, find the area of COD. [4] Question No 6 (a) Solve the following inequation and represent the solution set on a number line. 1 15 7x > 2x 27 , x N [3] The marks obtained in an examination are as follows: [3] (b) Use graph paper for this question. Marks Number of students 50 60 60 70 70 80 80 90 90 100 4 8 14 19 5 Draw a histogram for the above data and estimate the mode. (c) A vessel in the form of an inverted cone has radius 5 cm and height 8 cm. It is filled with water up to the rim. When lead shots each of which is a sphere of radius 0.5 cm are 1 dropped into the vessel, th of the water flows out. Find the number of lead shots 4 dropped into the vessel. [4] Question No 7 (a) A(2, 1), B(5, 3) and C( 1, 3) are the vertices of ABC. Find (i) the equation of the median AD. (ii) the equation of the altitude BE. [5] (b) Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the tower to be 30 and 38 respectively. Find the distance between them, if the height of the tower is 50m. Using tan52 = 1 2799 write the answer correct to 1 decimal place. [5] Question No 8 3 3 186 ? , are needed to get the sum 2 4 32 (b) Find the coordinates of the points of trisection of the line segment joining the points (a) How many terms of the G.P. 3, A(3, 1) and B( 3, 4). (c) [3] [3] In the adjoining figure, XY is the diameter of the circle and PQ is a tangent to the circle at Y. PAB is a straight line, AXB = 50 and ABX = 70 . Find BAY and CPY. [4] (6) Question No 9 (a) Using the properties of proportion, solve: x + 1 + x 1 x + 1 x 1 = [3] 4x 1 2 (b) An aeroplane left 30 minutes later than the scheduled time. In order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/h from its original speed. Find its original speed. [3] (c) Construct a triangle BCP, given BC = 5 cm, BP = 4 cm and PBC = 45 . Then, construct a rectangle ABCD, such that (i) P is equidistant from AB and BC. (ii) P is equidistant from C and D. Measure and write down the length of AB. [4] Question No 10 (a) If 2x3 + ax2 + bx 2 has a factor (x + 2) and leaves a remainder of 7 when divided by (2x 3), find the values of a and b. [3] (b) A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that the number on the stone is: [3] (i) a perfect square number. (ii) a number divisible by 5. (iii) a number divisible by 4 and 5. (c) Use graph paper for this question. [4] (i) Plot the point P(2, 4). Reflect it about the y-axis to get the image Q. Write down the coordinates of Q. (ii) The point Q is reflected about the x-axis to get the image R. Write down the coordinates of R. (iii) Write the geometrical name of the figure PQR. (iv) Find the area of the figure PQR.

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