# SOF - IMO Level 2 Sample Papers for Class 10

Class 10 sample paper & practice questions for the level 2 of International Mathematics Olympiad (IMO) are given below. Syllabus for level 2 is also mentioned for these exams. You can refer these sample paper & quiz for preparing for the exam. Q.1 Q.2 Q.3 Q.4 Q.5 Q.6 Q.7 Q.8 Q.9 Q.10
 Q.1 In four consecutive prime numbers that are in ascending order, the product of the first three is 385 and that of the last three is 1001. Find the largest given prime number? a) 17 b) 19 c) 13 d) 11
 Q.2 If the probability for A fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is? a) 0.38 b) 0.44 c) 0.94 d) 0.5
 Q.3 Find the least value of 2sin2θ + 3cos2θ? a) 3 b) 4 c) 2 d) 1
 Q.4 If one of the roots of quadratic equation 7y2 - 50y + k = 0 is 7, then what is the value of k? a) 1 b) 7 c) 50/7 d) 7/50
 Q.5 In a city of 5 million people, there are 1 million politicians. 10 persons are selected randomly from the city. What is the probability that at most three of them are politicians? a) 1.688 × (4/5)7 b) 2.096 × (4/5)7 c) 2.442 × (4/5)7 d) 4.192 × (4/5)7
 Q.6 A bucket of height 16 cm made up of metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 15 cm respectively. What is the slant height of the bucket? a) 15 cm b) 5 cm c) 12 cm d) 20 cm
 Q.7 A factory produces four different types of products, P, Q, R and S. The chances that a random piece of products P, Q, R and S is found to be defective are 20%, 30%, 5% and 10%, respectively. During an inspection, one piece of each product is randomly selected. What is the probability that exactly three of them are found to be defective? a) 0.005 b) 0.0057 c) 0.0103 d) 0.0124
 Q.8 A box contains 24 marbles, some are green and other are blue. If a marble is drawn at random from the box, the porbability that it is green is 2/3. Find the number of blue balls in the box? a) 13 b) 12 c) 16 d) 8
 Q.9 If α and β are the roots of the equation 4x2 - 19x + 12 = 0, find the equation having the roots 1/α and 1/β? a) 12x2 - 19x + 4 = 0 b) 4x2 + 19 + 12 = 0 c) 12x2 + 19x + 4 = 0 d) 4x2 + 19x - 12 = 0
 Q.10 The arc AB of the circle with centre at O and radius 10 cm has length 16 cm. What is the area of the sector bounded by the radii OA, OB and the arc AB? a) 40 sq cm b) 80 sq cm c) 20π sq cm d) 40π sq cm