SilverZone iOM Sample Paper Class 10

International Olympiad of Mathematics - iOM’ 22 CLASS : 10 SAMPLE QUESTIONS The Actual Question Paper Contains 40 Questions. The Duration of the Test Paper is 50 Minutes. 1. If the radius of a sphere is increased by 3 cm, its surface (A) p (B) p area is increased by 792 cm2. The radius of the sphere, before change is _____. Use p = p p (C) (D) (A) 7 cm (B) 14 cm (C) 9 cm (D) 10 cm 2. If 15 sin A + 8 cos A = 8, then find the value of 8 sin A – 7. The value of ends in ______. 15 cos A. (where p is a natural number) (A) 8 (B) 12 (C) 15 (D) 64 (A) 2 (B) 3 (C) 4 (D) 5 3. If the greatest common divisor of the numbers 2n + 13 8. If the positions of the first and the eighth letters of the and n + 7 is m, then find the value of 2m + 3. word REPRESENTATIVE are interchanged, similarly, the (A) 5 (B) 9 (C) 10 (D) 11 positions of the second and the ninth letters of the word 4. From a point p, inside of an equilateral triangle ABC, are interchanged and so on, which of the following will the perpendicular distances of the three sides are be the fourth to the left of the sixth from the left end cm, cm and cm, respectively. Find the after the rearrangement? semiperimeter of the triangle. (A) E (B) A (A) 27 cm (B) 18 cm (C) 54 cm (D) 36 cm (C) P (D) T 5. Find the median of the data a, ar, ar2, ..., arn where 9. Find the number of triangles in the figure given below. n is an odd number. (A) (1 + r) r (B) (1 – r) r (C) (1 + r) r (D) (1 – r) r 6. In the figure given below, two identical circles are intersecting each other at A and B. If O and O’ are their centres and OAO’B forms a square of side 1 cm, then (A) 18 (B) 20 find the area (in sq cm) of the shaded portion. (C) 22 (D) 24 10. A quadratic function f(x) attains a maximum of 4 at x = 1. The value of the function at x = 0 is 2. What is the value of f(x) at x = – 8? (A) – 150 (B) – 154 (C) – 158 (D) – 160 ANSWERS 1. (C) 2. (C) 3. (A) 4. (A) 5. (C) 6. (C) 7. (D) 8. (D) 9. (C) 10. (C) 13