CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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.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

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

Q.4

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.5

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.6

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.7

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

Q.8

In ∆ABC, ∠B = 90⁰. P, Q and R are the midpoints of AB, BC and AC, respectively. Which of the following options can be the vertices of a cyclic quadrilateral?

Q.9

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.10

f(x) = x⁴ - 2x³ + 3x² - ax + b is a polynomial such that when it is divided by (x - 1) and (x + 1), the remainders are 5 and 19, respectively. Determine the remainder when f(x) is divided by (x - 2).