CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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.2

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

Q.3

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

Q.4

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.5

Write the general term in the expansion of (x² -y)⁶:

Q.6

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

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

Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to a unit. The distance between their feet is equal to b units. Find the area of the rhombus.

Q.9

If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?

Q.10

If the coefficients of r^th term and (r + 1)^th term in the expansion of (1 + x)²⁰ are in the ratio 1:2, what is the value of r?