SilverZone iOM Sample Paper Class 12

International Olympiad of Mathematics- iOM’22 CLASS : 12 SAMPLE QUESTIONS The Actual Question Paper Contains 40 Questions. The Duration of the Test Paper is 50 Minutes. 1. The degree of the differential equation 4. Let and ; . satisfying = a (x – y) is Then, _____. _____. (A) There exists more than one but finite (A) 1 (B) 2 number of B’s such that AB = BA (C) 3 (D) 4 (B) There cannot exist any B such that AB = BA 2. dx is equal to ______. (C) There exist infinitely many B’s such that AB = BA (D) There exists exactly one B such that AB = BA (A) +C 5. The minimum value of is ______. (B) +C (A) e (B) (C) (C) e2 (D) e3 6. A is one of 6 horses entered for a race and is (D) to be ridden by one of two jockeys B and C. It is 2 : 1 that B rides A, in which case all the horses are equally likely to win. If C rides A, 3. The value of tan–1 is _______. his chance of winning is trebled. What are the odds against winning of A? p p (A) 5 : 18 (B) 5 : 13 (A) (B) (C) 18 : 5 (D) 13 : 5 p p 7. What should come next in the letter series (C) (D) given below? c b a a c b a a b c b a a b c c b a a b c d c b a a (A) a (B) b (C) c (D) d 3

International Olympiad of Mathematics- iOM’ 22 8. A lizard, at an initial distance of 21 cm 10. Consider a pyramid OPQRS located in the first behind an insect, moves from rest with an octant (x 0, y 0, z 0) with O as origin and acceleration of 2 cm/sec2 and pursues the OP and OR along the X-axis and the Y-axis, insect which is crawling uniformly along a respectively. The base OPQR of the pyramid straight line at a speed of 20 cm/sec. Then, is a square with OP = 3. The point S is directly the lizard will catch the insect after _______. above the mid-point T of diagonal OQ such (A) 24 sec (B) 1 sec that TS = 3. Then, _______. (C) 21 sec (D) 20 sec (A) the acute angle between OQ and OS is p. 9. In a certain code language, ‘3a, 2b, 7c’ means ‘Truth is Eternal’, ‘7c, 9a, 8b, 3a’ means (B) the equation of the plane containing the ‘Enmity is not Eternal’ and ‘9a, 4b, 2b, 6b’ is x – y = 0. means ‘Truth does not perish’. Which of the (C) the length of the perpendicular from p following means ‘enmity’ in that language? to the plane containing the is . (A) 3a (B) 7c (C) 8b (D) 9a (D) the perpendicular distance from O to the straight line containing RS is . ANSWERS 1. (A) 2. (B) 3. (C) 4. (C) 5. (A) 6. (D) 7. (B) 8. (C) 9. (C) 10. (B) 4