IMO Maths Olympiad Online Mock Test Class 11 Set A

1. If P = (1, 0), Q = (–1, 0) and R = (2, 0) are three given points then the locus of a point S satisfying the relation SQ² + SR² = 2SP² is

2.

3. If the standard deviation of a variable x is σ, then the standard deviation of another variable ax+b/c is

4. Statement 1 : The chance of drawing all aces from a pack of cards in exactly 5 trials is Statement 2 : There are four aces in a pack of cards.

5. Statement 1 : The expression aⁿ⁺¹ + bⁿ⁺¹ / aⁿ + bⁿ is G.M. of a and b. So n is zero.
Statement 2 : If a and b are two numbers of opposite signs, then G.M. between them does not exist.

6. A and B take turn in throwing two dice; the first to throw 9 is being awarded. Find the ratio of probabilities of their winning if A has the first throw.

7. An airgun can take a maximum of 4 shots at a balloon at some distance. The probabilities of hitting the balloon at the first, second, third and fourth shot are 0.1, 0.2, 0.3 and 0.4 respectively. What is the probability that the balloon is hit?

8. 5 men and 4 women are to be seated in a row so that the women occupy the even places. How many such arrangements are possible?

9. Vibhor joined as an area manager of Quick Corporation in the pay scale of Rs. 12,000 – 500 – 18,500. Minimum how many years he has to work in the corporation to avail the salary Rs. 18,500 per month?

10. A bouncing tennis ball rebounds each time to a height equal to one half the height of the previous bounce. If it is dropped from a height of 16 m, find the total distance it has travelled when it hits the ground for the 10th time.

11. In a car agency one day 120 cars were decorated with three different accessories viz., power window, AC and music system. 80 cars were decorated with power windows, 84 cars were decorated with AC and 80 cars were decorated with music systems. What is the minimum and maximum number of cars which were decorated with all of three accessories?

12. A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.

13. Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it?

14. A man sells chocolates which are in the boxes. Only either full box or half a box of chocolates can be purchased from him. A customer comes and buys half the number of boxes which the seller had plus half a box more. A second customer comes and purchases half the remaining number of boxes plus half a box. After this the seller is left with no chocolate boxes. How many chocolate boxes the seller had initially?

15. A student of 5th standard started writing down the counting numbers as 1, 2, 3, 4, … and then he added all those numbers and got the result 500. But when I checked the result I have found that he had missed a number. What is the missing number?

16. Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is allowed) are

17. Value of 2(sin⁶ Θ + cos⁶Θ) – 3(sin⁴ Θ + cos⁴ Θ) + 1 is

18. How any different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

19. If three dice are thrown together, then the probability that the sum of the numbers appearing on them is 13, is

20. If x = 3 + i, then x³ – 3x² – 8x + 15 =

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24. If in the expansion of (1 + x)^m (1 – x)ⁿ, the coefficient of x and x² are 3 and –6 respectively, then m is

25. If iz⁴ + 1 = 0, then z can take the value

26. If two sets A and B are having 44 elements in common. Number of elements common to A × B and B × A is

27. A parabola has the origin at its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

28. If A, B, C are non-empty sets and (A × B) ∪ (B × A) = C × C, then

29. Find the value of (1 + 2ω + ω²)³ⁿ – (1 + ω + 2ω²)³ⁿ.

30. Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the equation _________.

31. If a, b, c are the p^th , q^th and r^th terms of both an A.P. and also of a G.P.; then a^{b – c} ⋅ b^{c – a} ⋅ c^{a – b} =

32. If tan²Θ – (1 + √3 ) tanΘ + √3 = 0, then the general value of Θ is

33.

34. Two consecutive sides of parallelogram are 4x + 5y = 0 and 7x + 2y = 0. If the equation of one diagonal is 11x + 7y = 9, then the equation of other diagonal is

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36. Find the missing number in the given below number pattern.

37. Nitin was counting down from 32. Sumit was counting upwards the numbers starting\ from 1 and he was calling out only the odd numbers. What common number will they call out at the same time if they were calling out at the same speed?

38. If ‘air’ is called ‘green’, ‘green’ is called ‘blue’, ‘blue’ is called ‘sky’, ‘sky’ is called ‘yellow’, ‘yellow’ is called ‘water’ and ‘water’ is called ‘pink’, that what is the colour of clear sky?

39. In an imaginary language, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are substituted by a, b, c, d, e, f, g, h, i and j, & 10 is written as ba. bee + fg – (ca × h/be) is equal to

40. How many such symbols are there in the below arrangement which are not immediately preceded by a number and also not immediately followed by a letter?

41. There is a certain relationship between each pair given on either side of : : . Identify the relationship and find the missing term from the options.
C : 16 : : F : ?

42. A, B, C, D and E are five friends. E is shorter than A but taller than D. B is the tallest. C is shorter than B and taller than A. Who has two persons taller and two persons shorter than him?

43. In the following question, arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence.
1. Credential 2. Creed 3. Crease 4. Cremate
5. Credible

44. In a certain code language, ‘They are good girls’ is written as ‘$*?#’, ‘Birds are beautiful’ is written as ‘£?@’ and ‘Beautiful girls walk fast’ is written as ‘+@↑#’, then what is the code for ‘Birds’ in that code language?

45. A man is facing north. He turns 45° in the clockwise direction and then another 180° in the same direction and then 270° in the anti-clockwise direction. Which direction is he facing now?

46. What is the sum of the numbers common in square, triangle, ellipse and rectangle, square, triangle?

47. Study the following information carefully and answer the given question :
(i) B and E are good in Maths and Science.
(ii) A and B are good in Science and Computer.
(iii) A, D and C are good in Computer and History.
(iv) C and A are good in Computer and English.
(v) D and E are good in History and Maths.
Who is good in Computer, History and English, but not in Science?

48. There is a certain relationship between each pair given on either side of : : . Identify the relationship and find the missing term from the options.
49 : 81 : : 121 : ?

49. If Neha says, “Ayushi’s father Rajan is the only son of my father-in-law Manan, then how is Beena, who is the sister of Ayushi, related to Manan?

50. Two positions of a dice are shown below. When number 1 is on the top, what number will be at bottom?