IMO Maths Olympiad Online Mock Test Class 9 Set E

1. Given below is a question followed by three statements.
You have to study the question and the statements and decide which of the statements is/are necessary to answer the question.
What is Arun's present age ?
I. Five years ago, Arun's age was double that of his son's age at that time.
II. Present ages of Arun and his son are in the ratio of 11 : 6 respectively.
III. Five years hence, the respective ratio of Arun's age and his son's age will become 12 : 7.

2. Fill in the blanks and select the correct option.
(i) There is(are) P circle(s) passing through three non-collinear points.
(II) A continuous piece of a circle is called the Q of the circle.
(III) If two arcs of a circle are congruent, then their corresponding chords are R .
(IV) A line segment joining the centre to any point on the circle is called its S .
(V) The sum of either pair of opposite angles of a cyclic quadrilateral is T.

3.

4. Fill in the blanks.
(P) Any point lying on x-axis is of the form ____.
(Q) The abscissa of a point on y-axis is ____.
(R) The point at which the two coordinate axes meet is called the ____.
(S) The perpendicular distance of the point (4, 5) from x-axis is ____.
(T) The perpendicular distance of the point (3, 7) from y-axis is ____.

5. Following are the steps of construction of a DPQR, given that QR = 3 cm, ∠PQR = 45° and QP – PR = 2 cm. Arrange them and select the correct option.
(i) Make an angle XQR = 45° at point Q of base QR.
(ii) Join SR and draw the perpendicular bisector of SR say AB.
(iii) Draw the base QR of length 3 cm.
(iv) Let bisector AB intersect QX at P. Join PR.
(v) Cut the line segment QS = QP – PR = 2 cm from the ray QX.

6. After spending 40% in machinery, 25% in building, 15% in raw material and 5% on furniture, Harilal had a balance of Rs. 52200. The money with him was

7. A money lender borrows money at 4% p.a. and pays interest at the end of the year. He lends it at 6% p.a. compounded half-yearly and receives the interest at the end of the year. Thus, he gains Rs. 104.50 a year. The amount of money he borrows,

8. The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full?

9. In a mixture of 60 litres, the ratio of milk and water is 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is ________.

10. A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. The height of the embankment is ________.

11. A train travelling at 48 km/hr completely crosses another train having half its length and travelling in opposite direction at 42 km/hr, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is ________.

12. Average age of 6 sons of a family is 8 years. Average age of the sons together with their parents is 22 years. If the father is older than the mother by 8 years, then the age of the mother is

13. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

14. The cost price of an article A is Rs. 160 and selling price of another article B is Rs. 240. If the selling price of A will be equal to the cost price of B, then the profit after selling A is 20%. What is the profit on B?

15. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons is increased by ____ of the original share.

16. In the given figure, ‘O’ is the centre of circle, ∠CAO = 25° and ∠CBO = 35°. What is the value of ∠AOB?

17. If x = 1/2- √3, find the value of x³ – 2x² – 7x + 5.

18. Sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. Find its area.

19. Two men start from points A and B respectively, 42 km apart. One walks from A to B at 4 km/hr and another walks from B to A at a certain uniform speed. They meet each other after 6 hours. Find the speed of the second man.

20. In the figure shown, square 2 is formed by joining the mid-points of square 1, square 3 is formed by joining the mid-points of square 2 and so on. In this way total five squares are drawn. The side of the square 1 is 'a' cm. What is the sum of perimeters of all the five squares ?

21. Answer the questions on the basis of the information given below: Number of players participating in three different games in five different schools.   25% of the number of the players participating in hockey from School-5 are females. What is the number of the hockey players who are males in School-5?

22. Answer the questions on the basis of the information given below: Number of players participating in three different games in five different schools.   Number of players participating in Kho-Kho from School-4 is what percent of number of players participating in hockey from School-2?

23. Water flows in a tank 150 m × 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep?

24. In the given figure AB||CD and EF||DQ. Determine ∠PDQ, ∠AED and ∠DEF respectively.

25. Based on the given information, find the probability of people with age (60, 61 & 64) who can drive.

26.

27. Three statements are given below:
(i) In a ||gm, the angle bisectors of two adjacent angles enclose a right angle.
(ii) The angle bisectors of a ||gm form a rectangle.
(iii) The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.
Which is true?

28. Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

29. The perimeter of a triangle is 6p² – 4p + 9 and two of its sides are p² – 2p + 1 and 3p² – 5p + 3. Find the third side of the triangle.

30. In the given figure, it is given that Find the measure of x.

31. The mean of 25 numbers is 8. If 2 is added to every number, what will be the new mean?

32. Which of the following is a true statement?

33. A solid iron rectangular block of dimensions (2.2 m × 1.2 m × 1 m) is cast into a hollow cylindrical pipe of internal radius 35 cm and thickness 5 cm. Find the length of the pipe.

34.

35. The factors of 8a³ + b³ – 6ab + 1 are

36. A sheet of paper has been folded (either once or twice) and then the folded sheet has been cut. You have to select a figure from amongst the option figures, that would most closely resemble the unfolded form of Fig.(X).

37. Kalyani is mother-in-law of Veena who is sister-inlaw of Ashok. Dheeraj is father of Sudeep, the only brother of Ashok. How is Kalyani related to Ashok?

38. Select a figure from the options that illustrates the relationship amongst "pigeons, birds, dogs".

39. Select a figure from the options which when placed in the blank space of Fig. (X) would complete the pattern.

40. The positions of how many digits in the number will remain same after the digits within the number 2138574 are arranged in ascending order?

41. Find the water image of Fig. (X).

42. Code the group of digits as per the scheme and conditions given below Digit : 5 7 0 9 3 1 6 4 8 2
Letter/symbol : K E H $ Δ A J Q R @ Conditions :
(i) If the first as well as the last digit is odd their codes are to be interchanged.
(ii) If the first digit is even and the last digit is odd both are to be coded by the code for odd digit.
(iii) If the last digit is '0' it is to be coded by 'X'.
(iv) If the first as well as the last digit is even both are to be coded by '–'.
586403

43. Select a figure from the options which satisfies the same conditions of placement of the dots as in Fig. (X).

44. Eight friends Q, R, S, T, V, W, Y and Z are sitting around a circular table, facing the centre. There are three males and five females in the group of friends. No two males are immediate neighbours of each other.
(i) V sits second to the right of his wife.
(ii) S sits third to the right of V.
(iii) W sits second to the right of her husband Z. Z is not an immediate neighbour of V's wife.
(iv) T is a male and Y is not an immediate neighbour of V.
(v) R sits second to the right of Q.
Which of the following statements is true regarding T?

45. What is the minimum number of different colours required to paint the given figure such that no two adjacent regions have the same colour?

46. If it is possible to make a meaningful word with the second, fourth, eight and tenth letters of the word CONFIDENCE, which of the following will be second letter of that word? If more than one such word can be made, give 'S' as the answer. If no such word can be made, give 'P' as the answer.

47. Find the missing number, if a certain rule is followed row-wise or column-wise.

48. Select a figure from the option figures which will continue the same series as established by the five Problem Figures.

49. Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows is to be answered. The operations on numbers progress from left to right.
Rules :
(i) If an even number is followed by another even number they are to be added.
(ii) If an even number is followed by a prime number, they are to be multiplied.
(iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number.
(iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number.
(v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number.
65 11 12
15 3 11
What is the sum of the resultants of the two rows ?

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