Indian Talent Olympiad - IMO PDF Sample Papers for Class 10
Class 10 sample paper & practice questions for International Maths Olympiad (IMO) level 1 are given below. Syllabus for level 1 is also mentioned for these exams. You can refer these sample paper & quiz for preparing for the exam.
Q.1 |
A container has milk and water in the ratio 4: 1. The volume of the contents is increased by 40% by adding water to it. From this solution, 5 L are drawn out and replaced with 5 L of milk. If the solution now has five parts milk and three parts water, find the initial volume of the container. |
| a) |
28.56 L |
| b) | 14.28 L |
| c) | 15 L |
| d) | 24 L |
Q.2 |
Ankit and Anuj started simultaneously from X and Y respectively. Each person started towards the starting point of the other XY = 18 km. The speeds of Ankit and Anuj throughout their journeys were 5 kmph and 4 kmph respectively. On reaching X or Y, each turned back immediately to resume the journey to his starting point. Find the total distance travelled by Ankit before meeting Anuj for the second time. (in m) |
| a) |
30 |
| b) | 27 |
| c) | 24 |
| d) | 33 |
Q.3 |
If H.C.F. of two numbers is 68 and 85 is 17. What is the L.C.M. of two numbers? |
| a) | 340 |
| b) | 350 |
| c) | 360 |
| d) | 370 |
Q.4 |
A dealer bought 80 cricket bats for ₹ 50 each. He sells 20 of them at a gain of 5%. What must be the gain percentage of the remaining bats, so as to get 10% gain on the whole? |
| a) |
3 2/11 % |
| b) | 12 1/2 % |
| c) | 11 2/3 % |
| d) | 4 2/3 % |
Q.5 |
Identify the similar pair of words as given below: Stone: Sculpture:: |
| a) |
Mural: Painting |
| b) | Opera: Stage |
| c) | Canvas : Easel |
| d) | Clay: Pottery |
Q.6 |
Identify the identical figures from the following options given.  |
| a) |
(1, 5, 7), (3, 6, 8), (2, 4, 9) |
| b) | (1, 4, 7), (2, 6, 8), (3, 5, 9) |
| c) | (1, 5, 7), (2, 6, 8), (3, 4, 9) |
| d) | (5, 7, 9), (2, 6, 8), (1, 3, 4) |
Q.7 |
If f(x) = x² – 5x – 14, find the value of f(7). |
| a) |
-1 |
| b) | 1 |
| c) | 0 |
| d) | 3 |
Q.8 |
A tangent to a circle (centre O) drawn from an exterior point T to the circle and touches the circle at a point P on the circumference. Which of the following statement is TRUE? |
| a) |
∠TPO > 90° |
| b) | ∠TPO < 180° |
| c) | ∠TPO < 90° |
| d) | ∠TPO = 90° |
Q.9 |
If –4 is a root of the equation x² + px – 4 = 0 and the quadratic equation x² + px + k = 0 has equal roots, find the value of k. |
| a) | 9/8 |
| b) | 9/4 |
| c) | 9/5 |
| d) | 9/3 |
Q.10 |
In figure AB = 8 cm, BC = 12 cm and AE = 6 cm. Find area of the rectangle BCDE.  |
| a) |
120 cm² |
| b) | 190 cm² |
| c) | 220 cm² |
| d) | 150 cm² |
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Sample PDF of Indian Talent Olympiad - International Maths Olympiad (IMO) PDF Sample Papers for Class 10:
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Answers to Sample Questions from Olympiad Success:
Q.1 : a | Q.2 : a | Q.3 : a | Q.4 : c | Q.5 : d | Q.6 : c | Q.7 : c | Q.8 : d | Q.9 : b | Q.10 : a
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