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	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.2	In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?
a)	4
b)	3
c)	5
d)	2

Q.3	Mark and Matt are born in two consecutive months of 2011. What is the probability that the numbers of months in which they are born have same number of days?
a)	1/22
b)	1/11
c)	1/6
d)	2/33

Q.4	1 yr ago, a mother was 4 times older to her son. After 6 yr. her age becomes more than double her son's age by 5 yr. Find the present ratio of their age.
a)	13: 12
b)	11: 3
c)	3: 1
d)	25: 7

Q.5	One-fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains and the remaining 15 are on the banks of a river. Find the total number of cows.
a)	6
b)	100
c)	36
d)	63

Q.6	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.7	A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point h m above the first, the depression of the foot of tower is 60°. What is the horizontal distance of the tower from the point?
a)	h cot 60°
b)	h cot 30°
c)	h/2 cot 60°
d)	h/2 cot 30°

Q.8	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.9	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.10	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

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Answers to Sample Questions from Olympiad Success:

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

Answers to Sample Questions from Olympiad Success:

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

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