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	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.2	Find the unit digit in the product (2467)¹⁵³ x (341)¹⁷².
a)	4
b)	7
c)	6
d)	8

Q.3	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.4	If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68 and if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P?
a)	17
b)	12
c)	19
d)	15

Q.5	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.6	If the integer m and n are chosen at random between 1 and 100, then the probability that a number of the from 7^m + 7ⁿ is divisible by 5 equal to:
a)	1/8
b)	1/49
c)	1/4
d)	1/7

Q.7	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.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	If (secθ + tanθ)/(secθ − tanθ) = 2 ⁵¹/₇₉, then find the value of sinθ.
a)	65/144
b)	39/72
c)	'35/72
d)	'91/144

Q.10	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

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Answers to Sample Questions from Olympiad Success:

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

Answers to Sample Questions from Olympiad Success:

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

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