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.

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Sample Questions from Olympiad Success:

Q.1

Q.2

Q.3

Q.4

Q.5

Q.6

Q.7

Q.8

Q.9

Q.10

Q.1	The area of a sector of a circle of radius 36 cm is 72π cm². Find the length of the corresponding arc of the sector.
a)	2π cm
b)	π cm
c)	4π cm
d)	3π cm

Q.2	If the hypotenuse of a right triangle is 41 cm and the sum of the other two sides is 49 cm, find the difference between the other sides.
a)	30 cm
b)	29 cm
c)	31 cm
d)	32 cm

Q.3	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.4	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.5	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.6	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.7	A box contains 24 marbles, some are green and other are blue. If a marble is drawn at random from the box, the probability 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.8	A box contains 3 white and 2 red balls. If we draw one ball and then the second ball without replacing the first ball. Find the probability of drawing red ball in the second drawn.
a)	2/5
b)	8/25
c)	3/5
d)	21/25

Q.9	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.10	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

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Answers to Sample Questions from Olympiad Success:

Q.1 )c	Q.2 )c	Q.3 )d	Q.4 )d	Q.5 )b	Q.6 )d	Q.7 )d	Q.8 )a	Q.9 )c	Q.10 )a

Answers to Sample Questions from Olympiad Success:

Q.1 : c | Q.2 : c | Q.3 : d | Q.4 : d | Q.5 : b | Q.6 : d | Q.7 : d | Q.8 : a | Q.9 : c | Q.10 : a

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