IMO Maths Olympiad Online Mock Test Class 10 Set B

1. The Gurgaon office of Microsoft has 1500 executives. O f these 900 subscribe to the Hindustan Times and 750 subscribe to The Hindu. 150 subscribe to both Hindustan Times and The Hindu. If an executive is picked at random, what is the probability that he has subscribed to Hindustan Times?

2. Raju has 64 small cubes of 1 cm³. He wants to arrange all of them in a cuboidal shape, such that the surface area will be minimum. What is the diagonal of this larger cuboid ?

3. To win an election, a candidate needs 3/4 of the votes cast. If, after 2/3 of the votes have been counted, a candidate has 5/6 of what he needs, then what part of the remaining ratio does he still need ?

4. Rahman bought 30 stamps consisting of 20 paise and 30 paise stamps. Given that the stamps cost Rs. 7.80 altogether, how many 20 paise stamps did he buy ?

5. Vidushi and Sanya distributed Rs. 100 each in charity. Vidushi distributes money to 5 more people than Sanya and Sanya gives Rs. 1 more than Vidushi to each person. How many people are recipients of the charity ?

6. One fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains, and of the remaining, 15 are on the bank of a river. The total number of cows is ____.

7. Assume that a mango and its seed, both are spherical. The radius of the seed is 2/5 of the thickness of the pulp. The seed lies exactly at the centre of the fruit. What per cent of the total volume of the mango is its pulp ?

8. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point ?

9. Raghav buys a watch for Rs. 1,20,000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of Rs. 5000 each. If the rate of interest is 12% and he pays with the instalment the interest due on the unpaid amount, find the total cost of the watch.

10. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought ?

11. In the right triangle shown here, AB + AD = BC + CD, if AB = x, BC = h and CD = d, then x is equal to _____.

12.

13. A bag contains tickets marked with numbers 179, 180, 172, 127, 155, 115, 143, 122, 175, 222, 232, 162, 112, 132, 192, 182, 174, 132, 32, 131. A ticket is drawn at random. Find the probability that the ticket drawn has an even digit at ten’s place.

14. If 3+5+7+........+n terms / 5+8+11+...........+10 terms = Volume of cylinder with diameter 7 units and height 2/11 units , then the value of n is _____.

15. If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have ?

16. Without using trigonometric tables, evaluate the following

17. A hemispherical container with radius 6 cm contains 325 ml of milk. Calculate the volume of milk that is needed to fill the container completely.
(Pi = 3.142)

18. If x = √7 − √5, y = √5 − √3, z = √3 − √7 , then find the value of x³ + y³ + z³ – 2xyz.

19. If the roots of a quadratic equation are (p/q, q/p), then the equation is _____.

20. If area of a parallelogram with sides ‘l’ and ‘b’ is ‘A’ and that of a rectangle with sides ‘l’ and ‘b’ is ‘B’, then _____.

21. A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 is _____.

22. If (2, –2), (–2, 1) and (5, 2) are vertices of a right angled triangle, then the area of the triangle is _____.

23. A bridge across a river makes an angle of 30° with the river bank (Fig. given). If the length of the bridge across the river is sum of the arithmetic progression 5, 10, 15, ....., 55, what is the width of the river ?

24. If l is the last term, d is the common difference and ‘s’ is the sum of n terms of an A.P. be connected by the equation 8ds = (d + 2l)2, then d = _____.

25. Find the values of x and y in the given rectangle if its length is cube root of 2197 and width is one less than the fourth multiple of first prime number.

26. If a quadratic polynomial of the form x² + ax + b has no linear term and the constant term is negative, then _____.

27. L.C.M. of two prime numbers x and y (x > y) is 161. The value of 3y – x is _____.

28. An equilateral triangle is inscribed in a circle of circumference equal to perimeter of a square with side 22 cm. Find its side.

29. In the given figure, ABCD and AEFG are squares. Then in ΔAGE and ΔADC which of the following holds ?

30. A set of numbers consists of four 5’s, six 7’s, ten 9’s, eleven 12’s, three 13’s, two 14’s. The approximate difference between mean and median of this set of numbers is _____.

31. In the adjoining figure, count the number of triangles and squares.

32. In the adjoining figure, find out how the figure will look like after rotation.

33. The adjoining diagram represents those students who play cricket, football and kabaddi. Study the diagram and identify the students who play all the three games.

34. Rohit walked 25 m towards south. Then he turned to his left and walked 20 m. He then turned to his left and walked 25 m. He again turned right and walked 15 m. At what distance is he from the starting point and in which direction?

35. Find the figure from the options which will continue the series established by the problem figures.

36. If animals that live on land and the animals that live in water are represented by two big circles and animals that live both in water and on land are represented by a small circle, the combination of these three can be best represented as _____.

37. Which letter will be sixth to the left of the nineteenth letter from the right end of the English alphabet series ?

38. In a certain code language, ‘123’ means ‘bright little boy’, ‘145’ means ‘tall big boy’ and ‘637’ means ‘beautiful little flower’. Which digit in that language means ‘bright’ ?

39. All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes. How many small cubes will be formed having no face coloured ?

40. At a farm, there are hens, cows, bullocks and keepers to look after them. There are 69 heads less than legs. The number of cows is double than that of the bullocks but the number of cows and hens is the same. There is one keeper per 10 birds and cattle. The total number of hens plus cows and bullocks and their keepers does not exceed 50. How many cows are there ?

41. ‘+’ stands for division, ‘÷’ stands for multiplication, ‘×’ stands for subtraction and ‘–’ stands for addition. Which one of the following equations is correct ?

42. In a row of 40 boys, Satish was shifted 10 places to the right of Rohan and Kewal was shifted 10 places to the left of Vilas. If Vilas was twenty-sixth from the left and there were three boys between Kewal and Satish after shifting, what was the position of Rohan in the row ?

43. Select a figure from amongst the four alternatives, which when placed in the blank space of the given figure would complete the pattern.

44. Find the missing number in the adjoining figure.

45. In a shop, there were 4 dolls of different heights A, B, C and D. D is neither as tall as A nor as short as C. B is shorter than D but taller than C. If Mani wants to purchase the tallest doll, which one should she purchase ?

46. Six people A, B, C, D, E and F are sitting on the ground in a hexagonal shape. All the sides of the hexagon so formed are of same length. A is not adjacent to B or C; D is not adjacent to C or E; B and C are adjacent; F is in the middle of D and C. Which of the following is not a correct neighbour pair?

47. If the expressions ‘E < J ≤ H > Z’, ‘H ≤ Y’ and ‘E > F’ are true, which of the following conclusions will be definitely false ?

48. There is a matrix followed by four answer figures. In the matrix there are eight designs and one space is left blank as shown by a question mark. Find which answer figures will replace the question mark.

49. If 323 × 41 = 14323; 137 × 72 = 27731 and 48 × 87 = 7884, then 34 × 75 = ?

50. Using first, third, sixth and seventh digits of the number 9 3 4 2 6 1 8 5, one time each, how many numbers of two digits are possible which are perfect squares of a number. What is that number? If two such numbers are possible then answer 11, if no such number is possible then answer zero.