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IMO Mock Test – Class 10
IMO Mock Tests for Class 10 is designed for International Math Olympiad Preparation.
The IMO Class 10 online mock test paper is free for all students.
This paper has 50 questions.
Time allowed is 60 minutes.
There are 3 sections: 20 questions in section I, 20 in section II and 10 in section III.
The IMO Mock tests for Class 10 given here will help the student get an accurate idea of the types of questions asked in the International Math Olympiad and also help prepare timing and accuracy.
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Question 1 of 49
1. Question
Category: Logical ReasoningUsing 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.

Question 2 of 49
2. Question
Category: Logical ReasoningIf 323 × 41 = 14323; 137 × 72 = 27731 and 48 × 87 = 7884, then 34 × 75 = ?

Question 3 of 49
3. Question
Category: Logical ReasoningThere 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.

Question 4 of 49
4. Question
Category: Logical ReasoningIf the expressions ‘E < J ≤ H > Z’, ‘H ≤ Y’ and ‘E > F’ are true, which of the following conclusions will be definitely false ?

Question 5 of 49
5. Question
Category: Logical ReasoningSix 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?

Question 6 of 49
6. Question
Category: Logical ReasoningIn 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 ?

Question 7 of 49
7. Question
Category: Logical ReasoningFind the missing number in the adjoining figure.

Question 8 of 49
8. Question
Category: Logical ReasoningSelect a figure from amongst the four alternatives, which when placed in the blank space of the given figure would complete the pattern.

Question 9 of 49
9. Question
Category: Logical ReasoningIn 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 twentysixth from the left and there were three boys between Kewal and Satish after shifting, what was the position of Rohan in the row ?

Question 10 of 49
10. Question
Category: Logical Reasoning‘+’ stands for division, ‘÷’ stands for multiplication, ‘×’ stands for subtraction and ‘–’ stands for addition. Which one of the following equations is correct ?

Question 11 of 49
11. Question
Category: Logical ReasoningAt 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 ?

Question 12 of 49
12. Question
Category: Logical ReasoningAll 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 ?

Question 13 of 49
13. Question
Category: Logical ReasoningIn 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’ ?

Question 14 of 49
14. Question
Category: Logical ReasoningWhich letter will be sixth to the left of the nineteenth letter from the right end of the English alphabet series ?

Question 15 of 49
15. Question
Category: Logical ReasoningIf 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 _____.

Question 16 of 49
16. Question
Category: Logical ReasoningFind the figure from the options which will continue the series established by the problem figures.

Question 17 of 49
17. Question
Category: Logical ReasoningRohit 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 ?

Question 18 of 49
18. Question
Category: Logical ReasoningThe adjoining diagram represents those students who play cricket, football and kabaddi. Study the diagram and identify the students who play all the three games.

Question 19 of 49
19. Question
Category: Logical ReasoningIn the adjoining figure, find out how the figure will look like after rotation.

Question 20 of 49
20. Question
Category: Logical ReasoningIn the adjoining figure, count the number of triangles and squares.

Question 21 of 49
21. Question
Category: Mathematical ReasoningA 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 _____.

Question 22 of 49
22. Question
Category: Mathematical ReasoningIn the given figure, ABCD and AEFG are squares. Then in ΔAGE and ΔADC which of the following holds ?

Question 23 of 49
23. Question
Category: Mathematical ReasoningAn equilateral triangle is inscribed in a circle of circumference equal to perimeter of a square with side 22 cm. Find its side.
7√3 cm

Question 24 of 49
24. Question
Category: Mathematical ReasoningL.C.M. of two prime numbers x and y (x > y) is 161. The value of 3y – x is _____.

Question 25 of 49
25. Question
Category: Mathematical ReasoningIf a quadratic polynomial of the form x2 + ax + b has no linear term and the constant term is negative, then _____.

Question 26 of 49
26. Question
Category: Mathematical ReasoningFind 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.

Question 27 of 49
27. Question
Category: Mathematical ReasoningIf 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 = _____.

Question 28 of 49
28. Question
Category: Mathematical ReasoningA 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 f the river ?

Question 29 of 49
29. Question
Category: Mathematical ReasoningIf (2, –2), (–2, 1) and (5, 2) are vertices of a right angled triangle, then the area of the triangle is _____.

Question 30 of 49
30. Question
Category: Mathematical ReasoningIf area of a parallelogram with sides ‘l’ and ‘b’ is ‘A’ and that of a rectangle with sides ‘l’ and ‘b’ is ‘B’, then _____.

Question 31 of 49
31. Question
Category: Mathematical ReasoningIf the roots of a quadratic equation are (p/q – q/p), then the equation is _____.

Question 32 of 49
32. Question
Category: Mathematical ReasoningIf x = √7 − √5, y = √5 − √3, z = √3 − √7 , then find the value of x^{3} + y^{3} + z^{3} – 2xyz.

Question 33 of 49
33. Question
Category: Mathematical ReasoningA hemispherical container with radius 6 cm contains 325 ml of milk. Calculate the volume of milk that is needed to fill the container completely. (π = 3.142)

Question 34 of 49
34. Question
Category: Mathematical ReasoningWithout using trigonometric tables, evaluate the following :
cos^{2}20° + cos^{2}70°/sec^{2}50° – cot^{2}70°+ 2 cosec^{2} 58° – 2 cot 58° tan 32° – 4 tan 13° tan 37° tan 45° tan 53° tan 77° 
Question 35 of 49
35. Question
Category: Mathematical ReasoningIf 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 ?

Question 36 of 49
36. Question
Category: Mathematical ReasoningIf 3+5+7+….+n terms/5+8+11+….+10 terms = Volume of cylinder with diameter 7 units and height 2/11units , then thevalue of n is _____.

Question 37 of 49
37. Question
Category: Mathematical ReasoningA 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.

Question 38 of 49
38. Question
Category: Mathematical ReasoningPoint A is on xaxis, point B is on yaxis and the point P lies on line segment AB, such that P = where n = 2 and AP : PB = 5 : 3. Find the coordinates of points A and B.

Question 39 of 49
39. Question
Category: Mathematical ReasoningIn the right triangle shown here, AB + AD = BC + CD, if AB = x, BC = h and CD = d, then x is equal to _____.

Question 40 of 49
40. Question
Category: Everyday MathematicsA 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 ?

Question 41 of 49
41. Question
Category: Everyday MathematicsRaghav buys a watch for ` 1,20,000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of ` 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. 
Question 42 of 49
42. Question
Category: Everyday MathematicsA, 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 ? 
Question 43 of 49
43. Question
Category: Everyday MathematicsAssume 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 ?

Question 44 of 49
44. Question
Category: Everyday MathematicsOne 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 ____. 
Question 45 of 49
45. Question
Category: Everyday MathematicsVidushi and Sanya distributed ₹ 100 each in charity. Vidushi distributes money to 5 more people than Sanya and Sanya gives ₹ 1 more than Vidushi to each person. How many people are recipients of the charity ?

Question 46 of 49
46. Question
Category: Everyday MathematicsRahman bought 30 stamps consisting of 20 paise and 30 paise stamps. Given that the stamps cost ₹ 7.80 altogether, how many 20 paise stamps did he buy ?

Question 47 of 49
47. Question
Category: Everyday MathematicsTo 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 ?

Question 48 of 49
48. Question
Category: Everyday MathematicsRaju has 64 small cubes of 1 cm^{3}. 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 ?

Question 49 of 49
49. Question
Category: Everyday MathematicsThe 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?