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ICSE Class X Prelims 2024 : Mathematics

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PERFECTION ACADEMY TEST TIME: - 180 MIN DATE: - 25/10/2023 SUB: - MATHS CLASS: - 10 ICSE MARKS: - 80 NAME: - _________________ Attempt all questions from Section A and any four questions from Section B SECTION A (40 Marks) (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options. [15] 1) If matrix A is of order 3 2 and matrix B is of order 2 2 then the matrix AB is of order: (a)3 2(b)3 1(c)2 3(d)1 3 2) The mean proportion between 9 and 16 is (a)25(b)144(c)7(d)12 3) A man deposited 500 per months for 6 months and received 3300 as the maturity value .the interest received by him is (a)1950(b)300(c)2000(d)none of these 4) The solution set representing the following number line is: 5) 6) 7) 8) 9) 10) 11) 12) (a) { : , 3 < 2} (b) { : , 3 < < 2} (c) { : , 3 < 2} (d) { : , 3 2} The first three terms of an arithmetic progression (A. P.) are 1, 9, 17, then the next two terms are: (a) 25 and 35 (b) 27 and 37 (c) 25 and 33 (d) none of these Ifx W then the solution set of the inequation > 7, is (a) {8, 9 ,10...} (b) {0, 1, 2, 3, 4, 5, 6} (c) {0, 1, 2 ,3...} (d) {- 8, - 9, - 10 ,...} The roots of the quadratic equation 4 7 + 2 = 0 are 1.390, 0.359. The roots correct to 2 significant figures are: (a) 1.39 and 0.36 (b) 1.3 and 0.35 (c) 1.4 and 0.36 (d) 1.390 and 0.360 1.5, 3 and 8 are in proportion, then x is equal to: (a)6 (b)4 (c)4.5 (d)16 If a polynomial 2 2 7 1 is divided by ( + 3), then the remainder is: (a)-4(b)38(c)-3(d)2 If 73 is the nth term of the arithmetic progression 3, 8, 13, 18 ..., then 'n' is: (a)13(b)14(c)15(d)16 The roots of the quadratic equation + 2 + 1 = 0 are: (a) Real and distinct (b) Real and equal (c) Distinct (d) Not real/ imaginary Which of the following statement is not true? (a) All identity matrices are square matrix (b) All null matrices are square matrix (c) For a square matrix number of rows is equal to the number of columns (d) A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix 1 13) If ( 2) is a factor of the polynomial 3 + 2 13 + , then 'k' is equal to (a)-10(b)26(c)-26(d)10 14) If the equation + 6 + = 0 has real and distinct roots, then: (a) < 9(b) > 9(c) 9(d) 9 15) The sum of the first twelve terms of an A.P. is three times the sum of the first six terms, then the ratio of the first term to the common difference is: (a)7:2(b)2:7(c)3:5(d)1:7 Question 2 (i) Mr. Arora has a two years recurring deposit account in State Bank of India. He deposits 1500 per month. If he receives 37,875 at the time of maturity, find the rate of interest. [4] (ii) Solve the following inequation and represent the solution set on the number line : 4 19 < 3 5 2 2 + 5 , [4] st (iii) Which term of the A.P. 8, 14, 20, 26, ..... will be 72 more than its 41 term ? [4] Question 3 (i) Using the Remainder Theorem find the remainders obtained when + ( + 8) + is divided by + 1 and 2. [4] (ii) A copper wire of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. [4] (iii) An observer on the top of a cliff, 200 m above the sea-level, observes the angles of depression of the two ships to be 45 and 30 respectively. Find the distance between the ships, if the ships are: [5] (i) on the same side of the cliff, (ii) on the opposite sides of the cliff. SECTION B (40 Marks) (Attempt any four questions from this Section.) Question 4 3 (i) Write down the equation of the line whose gradient is 2 and which passes through P, where P divides the line segment joining A(-2, 6) and B(3, 4) in the ratio 2: 3. [3] (ii) In an Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find the: (i) First term (ii) Common difference (iii) Sum of the first 20 terms [3] (iii) Find the missing frequency ( ) of the following distribution, if mode is 34.5 : [4] Marks obtained 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Number of students 4 8 10 8 Question 5 (i) Find the coordinates of point P which divides the join of A(6, - 5) and B(5, 3) in the ratio 2:5. [3] (ii) The volume of a metallic cylindrical pipe is 1408 cm . Its length is 14 cm and its external radius is 9 cm. Find its thickness. [3] 2 (iii) Use graph paper for this question. [4] The points A( 2, 3 , B(4, 5) and C( 7 ,2) are the vertices of AABC. (i) Write down the coordinates of A', B', C' if AA'B'C' is the image of AABC reflected in the origin. (ii) Write down the coordinates of A", B", C" if A"B"C" is the image of ABC when reflected in the X-axis. (iii) Mention the special name of the quadrilateral BCC"B" and find its area. Question 6 (i) If the sum of first m terms of an A.P. is same as the sum of its first n terms, show that the sum of its first (m+n) terms is zero. [3] 2 1 4 1 3 2 (ii) Let = [ [3] ], = [ ] and = [ ]. Determine 2 + 5 . 0 2 3 2 1 4 (iii) Prove that : ( ) ( ) ( + ) = 1. [4] Question 7 (i) Find the equation of a line: [3] (i) whose inclination is 45 and y-intercept is 5. (ii) with inclination = 60 and passing through (-2, 5). (iii) passing through the points (-3, 1) and (1, 5). (ii) Anu has a cumulative deposit account in a bank for 5 years at 9% p.a. At the time of maturity, she gets 51607.50. Find the monthly instalment. [3] 1 (iii) The slope of a line joining P(6, k) and Q(1-3k, 3) is 2 .Find (i) k, (ii) Mid-point of PQ, using 2 the value of k found in (i). [4] Question 8 (i) A bag contains 20 balls out of which x balls are blue. If one ball is drawn at random, find the probability of drawing a blue ball. If 10 more blue balls are added the bag, and a ball is drawn at random then the probability of getting a blue ball is double the probability obtained before . find x [3] (ii) Calculate the arithmetic mean, correct to one decimal place, for the following frequency distribution of marks obtained in a geometry test [3] Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 No of students 7 13 15 12 3 (iii) A train covers a distance of 300 km between two stations at a speed of km per hour Another train covers the same distance at a speed of ( 5) km per hour. If the first train takes 3 hours less than the second train, finds the speed of each train. [4] 3

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