CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

Which term is numerically greatest term in the expansion of (3 + 2x)⁴⁹, when x = 1/5?

Q.2

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.

Q.3

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

Q.4

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.5

A bag contains 63 cards (numbered 1, 2, 3, ….., 63). Two cards are picked at random from the bag (one after another and without replacement). What is the probability that the sum of the numbers of both the cards drawn is even?

Q.6

Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. Find the ratio of the area of the path to the flower bed.

Q.7

If cos x / (1 + cosec x) + cos x / (cosec x - 1) = 2, then which one of the following is one of the values of x?

Q.8

A certain strain of virus occurs three times every 25 minutes. In how much time will it become 729 times its initial value?

Q.9

If the first, second and last terms of an AP are a, b and c, respectively, then the sum is:

Q.10

The volume of the vessel, in the form of a right circular cylinder, is 448π cm³ and its height is 7 cm. What is the radius of its base?