IMO Maths Olympiad Online Mock Test Class 11 Set D

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4. If 2x² – 3xy + y² + x + 2y – 8 = 0, then dy/dx is equal to

5. If tan 3x- tan 2x / 1+ tan3x tan 2x = then is equal to

6. A light house, facing north, sends out a fanshaped beam of light extending from north-east to north-west. An observer on a steamer, sailing due west at a uniform speed, first sees the light when he is 5 km away from the light house and continues to see it for 30√2 minutes. Speed of the steamer is ________ .

7. If there are three athletic teams in a school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is ________ .

8. The probability that an MBA aspirant will join IIM is 2/5 and that he will join XLRI is 1/3. Find the probability that he will join IIM or XLRI.

9. Mr. John has x children by his first wife and Ms. Bashu has x + 1 children by her first husband. They marry and have children of their own. The whole family has 10 children. Assuming that two children of the same parents do not fight, find the maximum number of fights that can take place among children.

10. A bacteria gives birth to two new bacterias in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. Initially there is one newly born bacteria at time t = 0, then find the total number of live bacterias just after 10 seconds.

11. A ball is dropped from a height of 96 feet and it rebounds 2/3 of the height it falls. If it continues to fall and rebound, find the total distance that the ball can travel before coming to rest.

12. In an examination 43% passed in Maths, 48% passed in Physics and 52% passed in Chemistry. Only 8% students passed in all the three. 14% passed in Maths an Physics and 21% passed in Maths and Chemistry and 20% passed in Physics an Chemistry. Number of students who took the exam is 200. A student is declared pass in the exam only if he/she clears any two subjects. The number of students who were declared passed in this exam is ________ .

13. A bicycle wheel makes 5000 revolutions in moving 11 km. What is the radius of the wheel?

14. Amit throws three dice in a special game of Ludo. If it is known that he needs 15 or higher in this throw to win, then find the chance of his winning the game.

15. A spherical cannon ball, 28 cm in diameter, is melted and cast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone correct upto two places of decimal.

16. Let f(x + y) = f(x) f(y) and f(x) = 1 – sin 2x g(x), where g(x) is continuous. Then f′(x) equals

17. If A, B, C are 3 non-empty sets, then (A ∩ B) ∩ (B ∩ C) ∩ (C ∩ A) is equal to

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19. If a sec α – c tan α = d and b sec α + d tan α = c, then

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21. Three numbers are in A.P. such that their sum is 18 and sum of their squares is 158. The greatest number among them is

22. The equation (x – b) (x – c) + (x – a) (x – b) + (x – a) (x – c) = 0 has all its roots

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24. If x, 2y, 3z are in A.P. and x, y, z are in G.P., then common ratio of G.P. is

25. If x-4/x² - 5x +6 can be expanded in the ascending powers of x, then the coefficient of x³ is

26. A book contains 1000 pages numbered consecutively. A page is selected at random, find the probability that the sum of the digits of the number of a page is 9, is

27. If z² + z + 1 = 0, where z is a complex number, then the value of

28. Let A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}. Then A ∩ B is give by

29. Let α and β be the roots of the equation x² + x + 1 = 0, then the equation whose root are α¹⁹, β⁷ is

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33. For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

34. A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is

35. The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

36. The sheet of paper shown in the Fig. (X), is folded to form a box. Choose from amongst the options, the boxes that are similar to the box that will be formed.

37. If in a certain language, ‘nero qaro’ means ‘cloth fine’; ‘eta hisa’ means ‘water clear’ and ‘soha hisa neru’ means ‘clear fine weather’, which word in that language means ‘clear’?

38. Select the one which satisfies the same conditions of placement of the dot as in Fig.(X).

39. Find the minimum number of straight lines required to make the given figure.

40. A pair of numbers have a certain relationship to each other. Select the pair from the options in which the numbers are similarly related as in the given pair.
6 : 180

41. How many meaningful words can be formed using the first, the third, the sixth and the seventh letters of the word DREAMLAND using each letter only once in each word?

42. Read the following information to answer the given question.
(i) A, B, C, D, E, F and G are sitting in a circle facing at the centre and playing cards.
(ii) B is neighbour of A and D.
(iii) G is not between F and E.
(iv) F is to the immediate right of A.
(v) G is third to the left of A.
Which of the following does not have the pair persons sitting adjacent to each other?

43. A matrix of certain characters is given. These characters follow a certain trend, rowwise or column-wise. Find out this trend and choose the missing character from the given options.

44. Find out how many such pairs of letters are there in the given word each of which has as many letters between them in the word as in the English alphabet.
ENTHUSIASTIC

45. The given equation becomes correct due to the interchange of two signs. One of the options under it specifies the interchange of signs in the equation which when made will make the equation correct. Find the correct option.
5 + 6 ÷ 3 – 12 × 2 = 17

46. Two positions of a dice are shown below. Identify the number at the bottom when the number at the top is ‘3’.

47. In a row of girls facing North, Reena is 10th to the left of Pallavi, who is 21st from the right end. If Megha, who is 17th from the left end, is fourth to the right of Reena, how many girls are there in the row?

48. Which of the following diagrams correctly represents Elephants, Wolves, Animals?

49. A man is performing yoga with his head down and legs up. His face is towards the north. In which direction will his left hand be ?

50. Five friends A, B, C, D and E are standing in a row facing South but not necessarily in the same order. Only B is between A and E, C is immediate right to E and D is immediate left to A. On the basis of above information, which of the following statements is definitely true?