CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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?

Q.2

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.3

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

Q.4

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

Q.5

The areas of two similar triangles are 81 cm² and 49 cm², respectively, then what will be the ratio of their corresponding medians?

Q.6

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

Q.7

If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:

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

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.10

W borrowed a certain sum of money from X at the rate of 10% per annum under simple interest and lent one-fourth of the amount to Y at 8% per annum under simple interest and the remaining amount to Z at 15% per annum under simple interest. If at the end of 15 years, W made a profit of $5850 in the deal, then find the sum that W had lent to Z.