Cmo sample-papers-for-class-10
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The document presents a sample paper for Class 10 Mathematics Olympiad, containing various problems ranging from algebra to geometry and probability. Each question has multiple-choice options, with solutions provided for each. It outlines the marking scheme, sections for achievers, and includes a link to the syllabus for further reference.
Cmo sample-papers-for-class-10
- 1. CLASS 10 SAMPLE PAPER CREST Mathematics Olympiad (CMO) 1 1. If √a > √b > √c > √d, where a, b, c and d are consecutive natural numbers, then which of the following is true? (a) √a – √b > √c – √d (b) √c – √d > √a –√b (c) √c – √d = √a – √b (d) None of the above 2. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction, then they meet in 5 hours. If they travel towards each other, then they meet in 1 hour. Find the speeds of both the cars. (a) 60 km/h, 40 km/h (b) 30 km/h, 45 km/h (c) 45 km/h, 60 km/h (d) 75 km/h, 90 km/h Class Topic/Section No. of Questions Marks per Questions Total Marks Practical Mathematics 25 1 25 1st to 4th Achievers Section 10 2 20 Grand Total 35 - 45 Practical Mathematics 40 1 40 5th to 10th Achievers Section 10 2 20 Grand Total 50 - 60 Syllabus for CMO is available at https://www.crestolympiads.com/cmo-syllabus Pattern And Marking Scheme
- 2. 2 3. A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1/4 m and a tread of 1/2 m. Calculate the total volume of concrete required to build the terrace. (a) 650 m3 (b) 750 m3 (c) 795 m3 (d) 845 m3 4. The co-ordinates of the mid-points of the sides of a triangle are (4, 2), (3, 3) and (2, 2). What will be the co-ordinates of the centroid of the triangle? (a) (3, 7/3) (b) (-3, -7/3) (c) (3, -7/3) (d) (-3, 7/3) 5. The decorative block shown in the figure given below is made of two solids, a cube and a hemisphere. The base of the block is a cube with the edge 5 cm and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (a) 150 cm2 (b) 160.86 cm2 (c) 162.86 cm2 (d) 163.86 cm2 CREST Olympiads – A digital initiative to enhance practical knowledge
- 3. 3 6. There are 35 cards numbered from 1 to 35. A card is selected at random. What is the probability that the drawing card will be a (i) multiple of 3 or 5. (ii) prime number (iii) multiple of 7, respectively? (a) 15/35, 9/35, 1/5 (b) 19/35, 12/35, 12/35 (c) 16/35, 11/35, 1/7 (d) 21/35, 10/35, 9/35 7. A TV tower stands vertically on a bank of a canal. From the point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60⁰. From another point 20 m away from this point on line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30⁰. Find the height of the tower. (a) 10√3 m (b) 10 m (c) 15 m (d) 24 m CREST Olympiads – A digital initiative to enhance practical knowledge
- 4. 4 8. An archery target has three regions formed by three concentric circles as shown in the figure given below. If the diameters of the circles are in the ratio 1: 2: 3, then find the ratio of the areas of three regions. (a) 1: 2: 4 (b) 1: 3: 4 (c) 1: 3: 5 (d) 2: 3: 4 9. Let ABC be a right-angled triangle in which AB = 3 cm, BC = 4 cm and angle B = 90⁰. BD is the perpendicular from B on AC. The circle through B, C and D is drawn. The steps of constructions of a pair of tangents from A to this circle is given below. Which of the following steps is incorrect? Step I: Draw triangle ABC and perpendicular BD from B on AC. Step II: Draw a circle with BC as a diameter. This circle will pass through D. Step III: Let O be the mid-point of BC. Join AO. Step IV: draw a circle with AO as diameter. This circle cuts the circle drawn in step II at B and P. Join AO, AP and AB are desired tangents drawn from A to the circle passing through B, C and D. (a) Only step I (b) Only step II (c) Only step III (d) Only step IV Achiever’s Section CREST Olympiads – A digital initiative to enhance practical knowledge
- 5. 5 10. If the four sides of a quadrilateral ABCD are tangential to a circle, then which of the following is true? (a) AC + AD = BD + CD (b) AB + CD = BC + AD (c) AB + CD = AC + BD (d) AC + AD = BC + AB 1. (b), 2. (a), 3. (b), 4. (a), 5. (d), 6. (c), 7. (a), 8. (c), 9. (d), 10. (b) Answers CREST Olympiads – A digital initiative to enhance practical knowledge