IMO Maths Olympiad Online Mock Test Class 9 Set D

1. There is a definite relationship between figures (1) and (2). Establish a similar relationship between figures (3) and (4) by selecting a suitable figure from the options which will replace the (?) in fig. (4).

2. Find the area of a triangle having perimeter 32 cm, one side 11 cm and difference of other two sides is 5 cm.

3. Fill in the blanks :
A ___P_ is breadthless length. A ___Q__ is a line which lies evenly with the points on itself. A ___R_ is that which has length and breadth only. A ___S_ is a surface which lies evenly with the straight lines on itself.

4. Consider the following data. Match the Columns :
Column I Column II
(i) Mean of the data is (p) 16
(ii) Median of the data is (q) 15
(iii) Mode of the data is (r) 15.2

5. Read the following statements carefully.
(i) If the diagonals of a quadrilateral divide it into four triangles which are equal in area, then the quadrilateral must be a parallelogram.
(ii) Three altitudes of an equilateral triangle are equal in length.
(iii) If triangles of equal areas have a common base, then their vertices must lie on a line parallel to the base.
Which of the options hold?

6. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at the rate 4 km/ hr and partly on bicycle at the rate 9 km/hr. The distance travelled on foot is

7. Piyush earned 40% more money than Aakash. Aakash earned 20% less than Manan. Piyush earned more than Manan by

8. One-third of the boys and one-half of the girls of a college participated in a social work project. If the number of participating students is 300 out of which 100 are boys, what is the number of students in the college?

9. A machine was sold at a gain of 10%. Had it been sold at Rs. 80 less, the seller would have lost 10%. What is the cost price of the machine?

10. P can do a work in 15 days and Q in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is

11. A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

12. A bank offers 5 % compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is

13. In a class test in Mathematics, 10 students scored 73 marks each, 12 students scored 60 marks each and 8 students scored 40 marks each. The mean of their
scores is ______.

14. The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. Find the ages of the son and the father respectively
(in years).

15. The ratio of the incomes of P and Q is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs. 1600, then the income of P is

16. Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.

17. Two numbers differ by 5. If their product is 336, then the sum of the two numbers is

18. In the given figure, l, m, n are straight lines. Which of the following is incorrect?

19. Two metallic right circular cones having their heights 4.1 cm and 4.3 cm respectively and the radii of their bases 2.1 cm each, have been melted together and recast into a sphere. Find the diameter of the sphere.

20. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum (in Rs. ) is

21. The mean of 16 items was found to be 30. On rechecking, it was found that two items were wrongly taken as 22 and 18 instead of 32 and 28 respectively. Find the correct mean.

22. In a cylinder, radius of the base is tripled and height is made one-third, then the curved surface area will be ______ the area of the original cylinder.

23. Factorize : p³(q – r)³ + q³(r – p)³ + r³(p – q)³

24. Which of the following are solutions of the equation
2x + 3y = 12?

25. How many least number of distinct points determine a unique line?

26. A card is drawn from a well shuffled pack of 52 cards, find the probability of getting a non-face card.

27. If AB||EF ||DC and the area of ΔAFD is 42 cm2, find the area of ΔBCE.

28. The figure below is not drawn to scale. Find ∠GCD, if AG || CF.

29. The radius and height of a cone are in the ratio 3 : 4. If its volume is 301.44 cm3, then find
(i) radius of the cone (ii) slant height of the cone.

30. Which of the following is the factor of the polynomial p(x) = x⁴ + 5x³ + 9x² + 15x + 18?

31. If the perpendicular distance of a point P from the x-axis is 4 units in the negative direction of the y-axis, and the perpendicular distance of P from the y-axis is 5 unit in the positive direction of x-axis, then the coordinates of P are

32. The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. Find the length of perpendicular from the opposite vertex to the side whose length is 13 cm.

33. A, B and C are three points on the circle whose centre is at O. Select the correct option.

34. Which of the following statements is true?
(i) In a ΔABC, if AB = AC, then altitude AD bisects BC.
(ii) If the altitudes AD, BE and CF of DABC are equal, then ΔABC is equilateral.
(iii) If D is the midpoint of the hypotenuse AC of a right ΔABC, then BD = AC.

35.

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

37. Select the figure which satisfies the same condition of placement of the dots as in Fig. (X).

38. Group the given figures into three classes using each figure only once.

39. P, Q, R, S, T, V, W and Z are sitting around a circle facing the centre. T is second to the right of R, who is third to the right of P. S is second to the left of P and fourth to the right of Q. Z is third to the right of V, who is not an immediate neighbour of P. What is P's position with respect to S?

40. Four positions of a dice are given below. Find the sum of numbers opposite to 6 and 4.

41. M is sister of K. D is brother of K. F is mother of M. How is K related to F?

42. Which of the following Venn diagrams best represents the relationship amongst 'Beverages, Cold drinks, Pepsi'?

43. Find the correct mirror-image of the given combination, if the mirror is placed vertically to the left.
S 2 O 1 5 O F D E C

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

45. How many such 6's are there in the following number series, each of which is immediately preceded by 1 or 5 and immediately followed by 3 or 9?
2 6 3 7 5 6 4 2 9 6 1 3 4 1 6 3 9 1 5 6 9 2 3 1 6 5 4 3 2 1 9 6 7 1 6 3

46. Select the odd one out.

47. The following digits are coded as follows:
Digit : 5 7 0 9 3 1 6 4 8 2
Letter/Symbol : K E H $ Δ A J Q R @ While coding the given number following conditions are also to be observed. (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 as the code for odd digit.
(iii) If the last digit is '0' it is to be coded as 'X'.
(iv) If the first as well as the last digit is even both are to be coded as '–'.
586403

48. How many pairs of letters are there in the word OPERATION which have as many letters between them as in the English alphabet?

49. Sandeep, Suraj and Swarn are in control of the following number-letter-symbol series respectively. If the first five elements of Sandeep are picked up and written in reverse order followed by last five elements of Suraj and Swarn each, then which of the following elements will be 7th to the left of 5th element from the right end in the series formed?

50. How many pairs of letters are there in the word NURSING which have as many letters between them as in the English alphabet?