# 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 For what value of k, the equation x2 + 2(k - 4) x + 2k = 0 has equal roots? a) 12 and 2 b) 6 and 4 c) 10 and 4 d) 8 and 2
 Q.2 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.3 If the integer m and n are chosen at random between 1 and 100, then the probability that a number of the from 7m + 7n is divisible by 5 equals? a) 1/8 b) 1/49 c) 1/4 d) 1/7
 Q.4 A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between which of the following option? a) 390 cm2 and 400 cm2 b) 360 cm2 and 370 cm2 c) 380 cm2 and 390 cm2 d) 370 cm2 and 380 cm2
 Q.5 What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? a) 1,49,700 b) 1,52,897 c) 1,64,749 d) 1,64,850
 Q.6 An elevator starts with 5 passengers and stops at 8 different floors. Find out the probability of all the 5 passengers alighting at different floors? a) 101/512 b) 107/512 c) 109/512 d) 105/512
 Q.7 A piece of equipment cost a certain factory 600,000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost? a) 2,00,000 b) 1,05,000 c) 4,05,000 d) 6,50,000
 Q.8 What will come in place of the question mark (?) in the following number series?1727, 1333, 997, ?, 507 a) 733 b) 752 c) 754 d) 775
 Q.9 Two 15 m strings are tied to a peg between two poles 9 m and 12 m long  from their types. What is the distance between the poles? a) 18 m b) 21 m c) 20 m d) 23 m
 Q.10 The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression? a) 44 b) 22 c) 18 d) 42