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.

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

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.2

If A and B are complementary angles, then find the value of Sin A cos B + cos A sin B – tan A tan B + sec2 A – cot2 B.

a)

2

b)

-1

c)

0

d)

1

Q.3

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.4

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.5

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.6

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.7

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.8

What is the sum of all positive integers up to 1000, which are divisible by 5 and are not divisible by 2?

a) 10,050
b) 5000
c) 50,000
d) 5,050

Q.9

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.10

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

Your Score: 0/10



Answers to Sample Questions from Olympiad Success:
Q.1 )bQ.2 )dQ.3 )cQ.4 )dQ.5 )aQ.6 )bQ.7 )dQ.8 )cQ.9 )dQ.10 )d

Answers to Sample Questions from Olympiad Success:

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

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