CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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.2

The following steps are involved in finding a number, if the positive number is less than its square by 30. Arrange them in sequential order:
(A) x² - x - 30 = 0
(B) x = 6
(C) x² - x = 30
(D) (x + 5) (x - 6) = 0

Q.3

Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:

Q.4

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?

Q.5

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.6

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

Q.7

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.8

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.9

The volume of a pyramid whose base is an equilateral triangle is 12 cm³. If the height of the pyramid is 3√3 cm, then find the length of each side of the base:

Q.10

The arithmetic mean of the squares of the first n natural number is: