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ICSE Class X Prelims 2023 : Mathematics (Ashoka Universal School (AUS), Chandsi, Nashik)

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Vitrag Sabadra
Ashoka Universal School (AUS), Chandsi, Nashik
10th

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Ashoka Universal School, Arjun Nagar Academic Year 2022-2023 Grade X (Pre - Board II) Marks: 80 Mathematics Time: 2:30 Hours. 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 (Attempt all the questions from this section) Q. 1 Choose the correct answers to the questions from the given options: [15] (i) If a shopkeeper buys goods worth Rs. 1000 and sells at a profit of 10 %. If rate of GST is 5 %, then bill amount is: (a) Rs.1050 (b) Rs. 1155 (c) Rs. 1080 (d) Rs. 1000 (ii) The solution set representing following number line is: (a) { : , 2 < < 2} (c) { : , 2 < 2} (b) { : , 2 < 2} (d) { : , 2 2} (iii) The nature of the root of the equation 4x 12x 9 = 0 is: (a) real and equal (b) real and distinct (c) non real roots (d) none of the above (iv) If g(x) = x+1 is a factor of h(x) = 5 3 + 2 8 12, then value of p is: (a) -8 (b) 5 (c) 9 (d) 12 (v) Two matrices A and B are multiplied to get A if: (a) both have same order (b) both are rectangular (c) number of columns in matrix A is equal to the number of rows in matrix B (d) number of columns in matrix B is equal to the number of columns in matrix A (vi) If the nth term of an A.P. is 7- 4n, then its 6th term is : (a) 17 (b) -17 (c) 18 (d) -18 (vii) The point (0, 6) is invariant in line: (a) = 0 (b) = 6 (d) = 6 (c) = 0 (viii) If the vertices of a triangle are (-1, 4), (5, 2) and (-4, -15) then the centroid of the triangle is : (a) (-3, -3) (b) (-3, 0) (c) (0, 3) (d) (0, -3) (ix) If D, E, and F are midpoints of the sides BC, CA and AB respectively, then two triangles ABC and DEF are: (a) congruent (b) similar (c) neither similar nor congruent (d) both similar and congruent (x) The tangent to a circle of radius 10 cm from an external point P, is of length 24 cm. The distance of point P from the center of the circle is: (a) 26 cm (b) 13 cm (c) 34 cm (d) 14 cm (xi) The number of balls of radius 1cm that can be made from a sphere of radius 10 cm is (a) 100 (b) 1000 (c) 10000 (d) 100000 (xii) An ogive curve is used to determine (a) range (b) mean (c) mode (d) median (xiii) When a die is thrown, the probability of getting an odd number less than 3 is: 1 (a) 6 1 (b) 3 (c) 1 2 (xiv) The 30th term of an A.P. 10, 7, 4, ..is: (a) 87 (b) 77 (c) 77 +3 4 a) x = 2, y= 7 (xv) If 4 5 4 = , then the value of x and y are: + 3 9 b) x = 7, y= 2 c) x = 3, y= 6 (d) 0 (d) 87 d) x = -2, y= 7 Q. 2 (i) Mrs. Chopda deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is 8 % per annum and Mrs. Chopda gets Rs. 8088 from the bank after 3 years, find the value of his monthly instalment. [4] (ii) A line AB meets x-axis at A and y-axis at B. Point P (4, -1) divides AB in the ratio 1 : 2. (a) Find the coordinates of A and B. (b) Find the equation of the line through P and perpendicular to AB. [4] (iii) The entire surface area of a solid cone of base of radius 3 cm and height 4 cm is equal to the entire surface area of a solid right circular cylinder of diameter 4 cm. Find the ratio of their: [4] (a) curved surfaces (b) volume Q. 3 (i) If = 9 10, find the value of (a) 5 +3 5 3 (b) 2 2 3 2 [4] 2 2 + 3 2 (ii) 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. [4] (iii) The point P (3, 4) is reflected to P in the x-axis; and O is the image of O (the origin) when reflected in the line PP . Using graph paper (Take 1 cm = 1 unit) give: [5] (a) The coordinates of P and O (b) The length of segment PP and OO . (c) The perimeter of the quadrilateral POP O (d) The geometrical name of the figure POP O . Section B (Attempt any FOUR questions from this section) Q. 4 (i) Using ruler and compasses only: Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter on both sides of its centre, each at a distance of 7 cm on opposites of its centre. Draw tangents to the circle from each of these two points P and Q. [3] (ii) Draw a Histogram for the given data, using a graph paper: Weekly wages (in Rs.) 2000300040003000 4000 5000 No. of workers 4 8 12 Estimate the mode from the graph. [3] 50006000 6 60007000 7 (iii) If term of an A.P. is q and the term is p, show that term is (p + q - n). 70008000 5 [4] Q. 5 (i) The price of a bicycle is Rs. 3136 inclusive of GST at the rate of 12 % on its listed price. A buyer asks for a discount on the listed price so that after charging GST, the selling price becomes equal to the listed price. Find the amount of discount which the seller has to allow for the deal. [3] (ii) Find the set of values of x satisfying 5 7 + 3 3 5 and 5 4 . 4 Also graph the solution set on the number line. [3] (iii) In the adjoining figure, AB = AC. If PM AB and PN AC, show that PM PC = PN PB. [4] Q.6 (i) ABC is a triangle and G (4, 3) is the centroid of the triangle. If A, B and C are the points (1, 3), (4, b) and C (a, 1) respectively, find the values of a and b. Also find the length of side BC. [3] (ii) In the given figure, ABC is a triangle in which = 30 . Show that BC equals the radius of the circumcircle of whose centre is O. [3] (iii) If Tina were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now? [4] Q. 7 (i) Sixteen cards are labelled as a, b, c, d, e, f........m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is: [3] (a) a vowel (b) a consonant (c) none of the letters of the word median . (ii) Find two numbers whose mean proportional is 16 and the third proportional is 128. [3] (iii) If 4 + 2 = 1, prove that 4 + 2 = 1 [4] 3 Q. 8 (i) If = [ 0 [3] 0 ] , = [ 4 0 ] and AB = A + B, find the values of , . (ii) The surface area of a solid metallic sphere 2464 2 . It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate: (a) the radius of the sphere. (b) the number of cones recast. (take = [3] 22 ) 7 (iii) The mean of the following frequency distribution is 50 and the sum of all the frequencies is 120. Find the value of p and q. [4] Class-Interval Frequency 0-20 17 20-40 p 40-60 32 60-80 q 80-100 19 Q. 9 (i) If a polynomial ( ) = 4 2 3 + 3 2 leaves remainders 5 and 19 when divided by (x-1) and (x+1) respectively, find the values of a and b. Hence, determine the remainder when f(x) is divided by (x -2). [4] (ii) Draw ogive for the following distribution: [6] Monthly 600-700 700-800 income (in Rs.) No. of 40 68 employees Hence determine: (a) The median income (b) The lower and upper quartiles (c) The inter quartile range. 800-900 900-1000 1000-1100 1100-1200 1200-1300 86 120 90 40 26 Q. 10 (i) Three consecutive natural numbers are such that the squares of the middle number exceeds the difference of the square of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence find the three numbers. [3] (ii) Prove that: 3 + 3 sin + + 3 3 sin (iii) In the figure, PAT is tangent at A. If = 50 and = , find : a) b) ) =2 [3] [4]

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