CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

Which among the following is a singleton set?

Q.2

How many 5-digit odd numbers can be formed using the digits 2, 3, 5, 7, 8, and 9 if every digit can occur at most once in any number?

Q.3

A square is drawn by joining midpoints of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If, the side of the first square is 16 cm, then what is the sum of the areas of all the squares?

Q.4

If p₁ and p₂ are two odd prime numbers such that p₁ > p₂, then p₁² - p₂² is:

Q.5

Solve and find the roots of the equation:
2(x² - 6) = 3(x - 4)

Q.6

For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:

Q.7

In the binomial expansion of (a - b)ⁿ, n ≥ 5 the sum of the 5^th and 6^th terms is zero. Find the value of a/b.

Q.8

The shadow of a pole standing on a horizontal plane is d metre longer when the Sun's altitude is α than when it is β. What is the height of the pole?

Q.9

The average weight of A, B and C is 84 kg. If D joins the group, the average weight of the group becomes 80 kg. If another man E who weighs 3 kg more than D replaces A, then the average of B, C, D and E becomes 79 kg. What is the weight of A ?

Q.10

A tower stands vertically on the ground. From a point on the ground which is 30 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45⁰. Find the height of the tower.