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ICSE Class X Prelims 2023 : Mathematics

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Chetan Pai
DAV Public School, BSEB Colony, Patna
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ICSE 10 PRELIM MARKS : 80 TIME : 2.30 hrs Date : SUBJECT : MATHS QUESTION PAPER Attempt all questions from Section A and any four questions from Section B. Section A (Attempt all questions from this Section) Question 1 Choose the correct answers to the questions from the given options: (i) 2 The remainder when 8 + 4 is divided by 2 + 1 is (a) 4 (ii) 1 8 (b) 8 1 4 (c) 3 1 6 (d) 2 1 4 2 The roots of the equation 2 + 6 + 3 = 0 are (a) imaginary and unequal (b) real and unequal (c) real and equal (d) imaginary and equal 3 2 (iii) Which of the following is not a factor of 4 + + 6 ? (a) ( 2) (b) ( + 1) (c) ( 1) (iv) (d) ( 3) is a type of .. (a) Zero matrix (c) Row matrix (v) [15] (b) Diagonal matrix (d) Rectangular matrix The 100th term of the sequence 3, 2 3, 3 3, .. is (a) 99 3 (b) 100 3 (c) 5050 3 (d) 50 3 2 (vi) Which of the following is a root of the equation 11 + 10 = 0 (a) = 1 (b) = 10 (c) = 11 (d) = 10 (vii) The coordinates of the image of the point (0, ) under reflection about the origin are (a) '( , 0) (b) '(0, ) (c) '(0, 0) (d) '(0, ) .... 2 .... (viii) The SGST paid by a customer to the shopkeeper for an article which is priced at Rs. 500 is Rs. 15. The rate of GST charged is (a) 1.5% (b) 3% (c) 5% (d) 6% (ix) In the given diagram the triangle PMN is similar to triangle UVW by the axiom (a) SSS (b) SAS (c) AAA (d) RHS (x) The volume of a right circular cone with height 15 m and base area 150 m2 is.. (a) 1125 m3 (b) 2250 m3 (c) 750 m3 (d) 650 m3 (xi) The coordinates of the midpoint M of (0, 4) and (0, 4) are (a) (0, 0) (b) (4, 0) (c) (0, 8) (d) (8, 0) (xii) The solution set for the given inequation is: 5 + 4 24, (a) {1, 2, 3, 4} (b) {0, 1, 2, 3, 4} (c) { 4, 3, 2, 1} (d) { 4, 3, 2, 1, 0, 1, 2, 3, 4} (xiii) In a badminton match between Rajesh and Joseph, the probability of winning of Rajesh is 0.58. Then the probability of Rajesh not winning is (a) 0.42 (b) 0.58 (c) 0.84 (d) 1.16 (xiv) If = and = then + = (a) (b) (c) (d) .... 3 .... (xv) In the given figure, if AOC = 160 , then value of is (a) 100 (b) 80 (c) 160 (d) 90 Question 2 (i) (ii) 2 2 2 Prove that (1 ) + (1 + ) = 2 What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional? (iii) The inner and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. Find the cost of painting it all over, at the rate of Rs. 1.50 per cm2. Question 3 (i) Rajesh opens a Recurring Deposit account with the Bank of Rajasthan and deposits Rs. 600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum. (ii) In triangle ABC, A = (3, 5), B = (7, 8), and C = (1, -10). Find the equation of the median through A. (iii) Use a graph sheet for this question. Take 2 cm = 1 unit along the axes. Plot the triangle OAB, where O (0, 0), A (3, -2), B (2, -3). (a) Reflect the triangle OAB through the origin and name it triangle OA B (b) Reflect the triangle OA B on the y-axis and name it triangle OA B (c) Reflect the triangle OA B on the -axis and name it triangle OA B (d) Join the points AA B B A A B B and give the geometrical name of the closed figure so formed. [4] [4] [4] [4] [4] [5] .... 4 .... Section B (Attempt any four questions from this Section) Question 4 (i) 3 2 Using factor theorem show that (3 + 2) is a factor of 3 + 2 3 2. 3 2 Hence, factorise the expression 3 + 2 3 2 completely. [3] (ii) Find the amount of bill for the following intrastate transaction of services provided by some consulting agency. [3] (iii) Using a graph sheet, draw a histogram for the following frequency distribution and find the mode. [4] Question 5 (i) Given , find + 2 3 (ii) In cyclic quadrilateral ABCD, DAC = 270, DBA = 500 and ADB = 330. [3] [3] Calculate : (i) DBC, DCB, CAB, (iii) Factorise the polynomial completely using Remainder theorem 3 2 2 7 3 + 18 [4] .... 5 .... Question 6 (i) ABCD is a rhombus. The coordinates of A and C are (3, 6) and (-1, 2) respectively. Find; (a) coordinates of the point of intersection of the diagonals AC and BD (b) equation of diagonal BD 2 [3] 2 (ii) Prove that + = . [3] (iii) The first and the last terms of an A.P. are 5 and 45, respectively. If the sum of its terms [4] is 1000, find; (a) number of terms (b) common difference of the A.P. Question 7 (i) A die is thrown once. Find the probability of getting: (a) an even number (b) a number between 3 and 8 (c) an even number or a multiple of 3 (ii) A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of [3] radius 0.5 cm. Find the number of spheres formed. (iii) ABCD is a cyclic quadrilateral in the circle with centre O. ST is a tangent. OBD = 250 and CBT = 300. Find BOD, BAD, BCD, BDC. Question 8 (i) Given , solve the inequation and graph the solution on the number line. 3 < (ii) [3] 1 2 2 3 [4] [3] 5 6 The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the Step Deviation Method. [3] .... 6 .... 3 2 (iii) The expression 4 + leaves remainders 0 and 30 when divided by + 1 and 2 3 respectively. Calculate the values of and . Hence factorise the expression completely. [4] Question 9 (i) A can do a piece of work in x days and B can do the same work in (x + 16) days. If both working together can do it in 15 days, calculate x. [4] (ii) Use a graph sheet for this question. The daily wages of 120 workers at a site are given. [6] Draw an ogive and hence estimate: (a) the median wages (b) the inter-quartile range of workers (c) the percentage of workers whole daily wages is above Rs. 475 Question 10 (i) Solve the following using the properties of proportion +1 + 1 +1 1 (ii) (ii) = [3] 4 1 2 Using a ruler and compass only, construct a triangle ABC in which BC = 4 cm, [3] ACB = 45 and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC. An aeroplane flying horizontally 1 km above the ground and going away from the [4] observer is observed at an elevation of 60 . After 10 seconds, its elevation is observed to be 30 . Find the uniform speed of the aeroplane in km per hour. All the Best

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Additional Info : ICSE Class X Mid-term 2023 : Math
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