CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

Ken and Paul can complete a job in 40 days and 50 days, respectively. They worked on alternative days to complete it. Find the minimum possible time in which they could have completed it.

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 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, find the value of 'b'.

Q.4

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

Q.5

A three-digit number was chosen at random. Find the probability that its hundred's digit, ten's digit and unit's digit are consecutive integers in descending order.

Q.6

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.7

The average mark obtained by the students in a class is 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?

Q.8

If the sum of the roots of the equation ax² + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct?

Q.9

Find the values of a and b for which 3x³ - ax² - 74x + b is a multiple of x² + 2x - 24.

Q.10

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.