IMO Maths Olympiad Online Mock Test Class 11 Set F

1. Select the INCORRECT statement.

2. Fill in the blanks.
If ax² + bx + c = 0, a ≠ 0 is a quadratic equation and D = b² – 4ac is the discriminant of the equation, then

3. Which of the following graphs represents the given inequalities?
x + 2y ≤ 10, x + y ≤ 6, x ≤ 4, x ≥ 0 and y ≥ 0.

4. What is the probability that in a group of
(i) 2 people, both will have the same birthday?
(ii) 3 people, at least two will have the same birthday?
Assuming that there are 365 days in a year and no one has his/her birthday on 29th February.

5. Match the following.  

6.

7. Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team vcan lose and still win more than three-fourths to the total number of matches, if it is true that no match can end in a tie?

8. A survey shows that 89% of the Australians like butter whereas 79% like chocolate. It is known that they like atleast one of the two. What is the percentage of Australians who like both butter and chocolate?

9. A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speeds of the two trains.

10. Along a road lie an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then, the number of stones is ________.

11. A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area (approx.) which is exposed to the surroundings assuming that the dimples are hemispherical.

12. An urn contains 9 balls, 2 of which are white, 3 blue and 4 black. 3 balls are drawn at random from the urn. The chance that 2 balls will be of the same colour and the third of a different colour is ______.

13. A owns a house worth ` 10,000. He sells it to B at a profit of 15%. After some time, B sells it back to A at 15% loss. Find A's loss or gain percent.

14. From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. What is the height of the tower?

15. A guard of 12 men is formed from a group of 'n' soldiers. It is found that 2 particular soldiers A and B are 3 times as often together on guard as 3 particulars soldiers C, D and E. Then n is equal to ________.

16. which of the following remains constant with change in 'α'?

17. The number of divisors of the number

18. A chord AB of a circle of radius 15 cm makes an angle of 60° at the centre of the circle. Find the area of the major segment.

19. The sum of three numbers in G.P. is 42. If first two numbers are increased by 2 and third is decreased by 4 then resulting numbers form an A.P. The sum of the square of the numbers is _______.

20. Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is ______.

21. A pack of cards consists of 15 cards numbered 1 to 15. Three cards are drawn at random with replacement. Then, the probability of getting two odd and one even numbered card is ______.

22. Given below is the frequency distribution of the heights of players in a school. Find the height (approx.) of maximum number of students.

23. The ratio in which the line segment joining the points (4, –6) and (3, 1) is divided by the parabola y² = 4ax is ______.

24.

25.

26.

27. How many five-digit numbers divisible by 6 can be formed by using 0, 1, 2, 3, 4, 5 without repetition?

28. A cylindrical container whose diameter is 12 cm and height is 15 cm, is filled with ice cream. The whole ice cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of it base, then the diameter of the ice cream cone is _______.

29. If z = a + ib satisfies arg (z – 1) = arg (z + 3i), then (a – 1) : b = ________.

30. The two points on the line x + y = 4 that lie at a unit distance from the line 4x + 3y = 10 are ______.

31.

32. Out of 800 boys in a school, 224 played cricket; 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is _____.

33. In the given figure, BDC is a tangent to the given circle at point D such that BD = 30 cm and CD = 7 cm. The other tangents BE and CF are drawn respectively from B and C to the circle and meet when produced at A making BAC a right triangle.
Find :
(i) AF
(ii) Radius of the circle.

34.

35. Find the coordinates of the points which trisect the line segment AB, given that A (2, 1, –3) and B (5, –8, 3).

36. Which of the following figures will complete the pattern given in Fig. (X)?

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

38. Study the statements carefully.
'P © Q' means 'P is not greater than Q'.
'P % Q' means 'P is not smaller than Q'.
'P * Q' means 'P is neither smaller than nor equal to Q'.
'P @ Q' means 'P is neither greater than nor equal to Q'.
'P $ Q' means 'P is neither greater than nor smaller than Q'.
Assuming the following statements to be true, you have to decide which of the following conclusions is/are definitely true.
Statement : T © N, K $ N, N @ Z
Conclusions : I. Z * T
II. N % T

39. Which of the following options satisfy the same condition of placement of dots as in Fig. (X)?

40. Select a figure from the options in which Fig. (X) is exactly embedded as one of it parts.

41. Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules. The operations of the numbers progress from left to right.
(i) If a two digit odd number is followed by a prime number, then the first number is to be multiplied by the prime number.
(ii) If an even number is followed by another even number, then the first number is to be divided by the second number.
(iii) If an odd number is followed by a composite odd number, then the first number is to be added to the second number.
(iv) If an even number which is multiple of 5 is followed by another number which is a multiple of 5, then the second number is to be subtracted from the first number.
(v) If a number which is perfect square is followed by another number which is a perfect square, then the resultant number is the product of the square roots of the two numbers. 50 25 49
p 9 4 If p is the resultant of the first row, then what is the resultant of the second row?

42. Study the given Venn diagram and answer the question that follows. Which of the following regions represent unmarried people who are educated and employed?

43. The question consists of set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Select a figure from the options which would most closely resemble the unfolded form of Fig. (Z).

44. A word and number arrangement machine when given an input line of words and numbers rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement:
Input : now 41 28 for join 37 go 61
Step I : 61 now 41 28 for join 37 go
Step II : 61 for now 41 28 join 37 go
Step III : 61 for 41 now 28 join 37 go
Step IV : 61 for 41 go now 28 join 37
Step V : 61 for 41 go 37 now 28 join
Step VI : 61 for 41 go 37 join now 28
Step VII : 61 for 41 go 37 join 28 now
As per the rules followed in the above steps, find the last step for the given input.
Input : wood 21 chair 56 34 now 11 desk

45. Which of the following options will continue the same series as established by the Problem Figures?

46. How many such pairs of letters are there in the word PROGESTERONE each of which has as many letters between them as in the English alphabet?

47. Study the given information carefully and answer the question that follows. B, C, D, F, G, H and J are seven students studying in three colleges P, Q and R. There are three boys and four girls. There is at least one boy and one girl in each college. Three of them are in Commerce discipline and two each in Arts and Science. B and her sister G are in Science discipline but in different colleges. F studies Arts in college Q and he does not study with either J or C. D is not in Commerce and he studies in college R only with B. H studies in the same college with her friend G. In which college only arts and science students study?

48. Two positions of a dice are given. Find the number of dots on the face opposite to face having 4 dots.

49. Find the correct mirror image of Fig. (X), if the mirror is placed vertically to the left.

50. The following numbers are coded as follows: While coding the given numbers following conditions are also to be observed. 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 the 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 @.
Find the code of 2684903.