CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set L

Section I : Logical Reasoning

Question. Six people – Rohit, Suneet, Deepak, Vikas, Kanak and Manish–were all born on the same day of the year, but each was born in a different year, during a single six-year period.
I. Rohit is older than Deepak.
II. Suneet is older than both Vikas and Kanak.
III. Manish is 2 years older than Vikas.
IV. Rohit was born either in 1962 or in 1963.
V. The oldest member of the group was born in 1960.
If Manish is the oldest of the group, then which of the following must be true?
(A) Deepak was born in 1960.
(B) Rohit was born in 1962.
(C) Vikas was born in 1961.
(D) Suneet was born in 1961.
Answer : D

Question. Choose the correct option that will replace the question mark in the given number series.
11(1/9), 12(1/2), 14(2/7), 16(2/3), _?__
(A) 8(1/3)
(B) 19(1/2)
(C) 20
(D) 22(1/3)
Answer : C

Question. If Circle S stands for households having a scooter;
Circle T stands for households having a TV set;
Circle W stands for households having a washing machine;
Circle C stands for households having a car; then households having all the four items are represented by the region ____.

(A) 7
(B) 8
(C) 9
(D) 12
Answer : B

Question. If a meaningful word can be formed using the letters NWROD, each only once, then the fourth letter of that word is your answer. If more than one word can be formed, then 'Y' is your answer and if no such word can be formed, then 'Z' is your answer.
(A) Z
(B) R
(C) W
(D) Y
Answer : C

Question. Ajay left home for the bus stop 15 minutes earlier than usual. It takes 10 minutes to reach the stop. He reached the stop at 8.40 a.m. What time does he usually leave home for the bus stop?
(A) 8.30 a.m.
(B) 8.45 a.m.
(C) 8.15 a.m.
(D) None of these
Answer : C

Question. If '–' stands for 'division', '+' for 'multiplication', '÷' for 'subtraction' and '×' for 'addition', which one of the following equations is incorrect?
(A) 6 + 20 – 12 ÷ 7 – 1 = 3
(B) 6 – 20 ÷ 12 + 7 + 1 = 57
(C) 6 + 20 – 12 ÷ 7 × 1 = 4
(D) 6 ÷ 20 × 12 + 7 – 1 = 70
Answer : B

Question. Robin says, "If Jai gives me ₹ 40, he will have half as much as Atul, but if Atul gives me ₹ 40, then the three of us will all have the same amount." What is the total amount of money that Robin, Jai and Atul have between them?
(A) ₹ 240
(B) ₹ 320
(C) ₹ 360
(D) ₹ 420
Answer : C

Question. Choose the odd numeral group.
(A) 1 (–80) 9
(B) 6 (12) 2
(C) 7 (33) 4
(D) 11 (112) 3
Answer : B

Question. Find the missing number in the given figure.

(A) 13
(B) 14
(C) 20
(D) 21
Answer : B

Question. Select a figure from amongst the options which will continue the same series as established by the five figures.

Answer : C

Question. Which of the following is the correct option to find the code for "books" ?
Statement-1 : '253' means 'books are old'.
Statement-2 : '546' means 'man is old'.
Statement-3 : '378' means 'buy good books'.
(A) Only Statement- 1 is sufficient to answer the question.
(B) Only Statement- 2 is sufficient to answer the question.
(C) Only Statement- 3 is sufficient to answer the question.
(D) None of these.
Answer : D

Question. A family has a man, his wife, their four sons and their wives. The family of every son also has 3 sons and one daughter. Find out the ratio of number of male members to female members in the whole family.
(A) 4 : 1
(B) 8 : 3
(C) 3 : 1
(D) 17 : 9
Answer : D

Question. In the question there are seven figures, the first and last of which are unmarked and the remaining are marked as P, Q, R, S and T. These seven figures form a series. However, one of the five numbered figures does not fit into the series. Select that figure from the options.

(A) P
(B) R
(C) S
(D) Q
Answer : B

Question. Choose the figure which is different from the rest.

Answer : B

Question. What is the minimum number of line segments required to make the given figure?

(A) 10
(B) 12
(C) 14
(D) 16
Answer : C

Question. Select a figure from amongst the options, which when placed in the blank space of fig. (X) would complete the pattern.

Answer : A

Question. A square transparent sheet with a pattern is given. Figure out from amongst the options as to how the pattern would appear when the transparent sheet is folded at the dotted line.

Answer : B

Question. If the first and third letters in the word NECESSARY are interchanged, also the fourth and the sixth letters, and the seventh and the ninth letters are interchanged, then which of the following would be the seventh letter from the left?
(A) A
(B) Y
(C) R
(D) E
Answer : B

Question. Choose the correct option that will replace the question mark in the given letter-number series.
C4X, F9U, I16R, _?_
(A) K25P
(B) L25P
(C) L25O
(D) L27
Answer : C

Question. A child is looking for his father. He went 90 metres in the East before turning to his right. He went 20 metres before turning to his right again to look for his father at his uncle's place 30 metres from this point. His father was not there. From there he went 100 metres to the North before meeting his father in a street. How far from the starting point did the son meet his father?
(A) 80 metres
(B) 100 metres
(C) 140 metres
(D) 260 metres
Answer : B

Section II : Mathematical reasoning

Question. When in a frequency distribution class widths are not same and we have to draw histogram then,
(A) We mark class size as width and the given frequency as length and draw the rectangle.
(B) We reduce class size to minimum class size keeping the length same.
(C) We find the proportionate lengths of the class corresponding to minimum width and draw the rectangle.
(D) None of these
Answer : C

Question. An experiment is performed 350 times and there are three possible events A, B and C in the experiment. Possible occurrences of the three events are recorded. Which one of the records is possible?
(A) A : 176, B : 80, C : 98
(B) A : 90, B : 0, C : 250
(C) A : 200, B : 100, C : 50
(D) A : 110, B : 110, C : 110
Answer : C

Question. Which of the following is the correct match with respect to the given question?
'ABCD' is a rhombus such that ∠ACB = 40° then ∠ADB is ______.
     Column-I               Column-II
(a) 70°             (i) A s ∠ADB = 1/2 (180° – 40°)
(b) 45°             (ii) ∠C + ∠D = 900
(c) 50°             (iii) ∠BCD = 80° ⇒ ∠ADC = 100° ∴ ∠ADB = (1/2) x 100°
(d) 60°             (iv) A ll sides are equal
(A) (a) → (i)
(B) (c) → (iii)
(C) (d) → (iii)
(D) (b) → (iv)
Answer : B

Question. In a gym, in one exercise you have to continuously toss solid cylindrical dumbbells and catch them. Cylindrical dumbbells are of length 1 m and base diameter also 1 m. If density of the material used is 4 kg per m3, then the weight tossed is _____.
(A) 3.14 kg
(B) p/2 kg
(C) 4p kg
(D) 12.56 kg
Answer : A

Question. Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. The median of the data is 24. The mean of the data is _____.
(A) 20
(B) 23.9
(C) 25
(D) 27
Answer : B

Question. The value of

(A) 1
(B) –1
(C) 2
(D) –2
Answer : A

Question. If (3x – 1)⁷ = a₇x⁷ + a6x6 + a₅x⁵ + .... + a₁x + a0, then a₇ + a₆ + a₅ + ..... + a₁ + a₀ = ____.
(A) 0
(B) 1
(C) 128
(D) 64
Answer : C

Question. In the given figure, AB = 14 cm, radius of incircle of ΔABC is 4 cm,
AF = 6 cm, AE = 6 cm and BD = 8 cm. Find AC and BC.

(A) 14 cm, 16 cm
(B) 11 cm, 13 cm
(C) 12 cm, 14 cm
(D) 13 cm, 15 cm
Answer : D

Question. Which of the following statements is incorrect ?
(A) All prime numbers greater than 2 are odd.
(B) If x ≥ 0, then x³ ≥ 0
(C) Two times a natural number is always even.
(D) For any x, 2x + 1 > 3
Answer : D

Question. If the perpendicular distance of a point P from the x-axis is (7776)1/6 and the foot of the perpendicular lies on the negative side of x-axis, the point P always has _____.
(A) Negative y-coordinate
(B) Positive y-coordinate
(C) Negative x-coordinate
(D) Positive x-coordinate
Answer : C

Question. Sum of three altitudes of a triangle is _______ the sum of the three sides of the triangle.
(A) Less than
(B) G reater than
(C) Equal to
(D) Can't be determined
Answer : A

Question. Match the columns :
       Column I             Column II
(a) A solid has          (p) 0 dimension
(b) A surface has      (q) 1 dimension
(c) A point has          (r) 2 dimensions
                                (s) 3 dimensions
(A) (a) → r, (b) → q, (c) → p
(B) (a) → r, (b) → p, (c) → q
(C) (a) → s, (b) → p, (c) → q
(D) (a) → s, (b) → r, (c) → p
Answer : D

Question. Sixteen cylindrical cans, each with a radius of 1 unit, are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and the walls of the box, then which of the following could be the interior area of the bottom of the box in square units?
(A) 16
(B) 32
(C) 64
(D) 128
Answer : C

Question. ABCD is a parallelogram. The diagonals AC and BD intersect at a point O. If E, F, G, and H are the mid-points of AO, DO, CO and BO respectively, then the ratio of (EF + FG + GH + HE) to (AD + DC + CB + BA) is ______.
(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 1 : 4
Answer : B

Question. If a+b+c = 0, then a²/bc + b²/ca + c²/ab is equal to _____.
(A) 0
(B) 1
(C) 3
(D) 2
Answer : C

Question. If x = 3√9, y = 4√11, z = 6√17 then ______.
(A) x > y > z
(B) y > z > x
(C) z > y > x
(D) x < y = z
Answer : A

Question. The string of length n is wound on the exterior four walls of a cube of side 'a' cm starting at point C and ending at point D exactly above C, making 4 turns equally spaced. The side of the cube is ______.
(A) a = 2n/√255
(B) a = (n)²/16
(C) a = n/√257
(D) a =2√15n
Answer : C

Question. If ABCD is a parallelogram, E is the mid-point of AB and CE bisects ∠BCD, then ∠DEC is _____.

(A) 60°
(B) 90°
(C) 100°
(D) 120°
Answer : B

Question. Let U be the upper class boundary of a class in a frequency distribution and M be the mid-point of the class. Which one of the following is the lower class boundary of the class?
(A) M + M + U / 2
(B) U + M + U / 2
(C) 2M – U
(D) M – 2U
Answer : C

Question. Here the steps of construction of an equilateral triangle one of whose altitudes measures 5 cm are given. In these steps, one step is wrong. Which step does not fit in the steps of construction ?
STEPS OF CONSTRUCTION :
(i) Draw a line XY.
(ii) Mark any point P on it.
(iii) From P, draw PQ ⊥ XY.
(iv) From P, set off PA = 5 cm cutting PQ at A.
(v) Construct ∠PAB = 60° and ∠PAC = 60°, meeting XY at B and C respectively. Then, ΔABC is the required equilateral triangle.
(A) (i) only
(B) (ii) only
(C) (v) only
(D) (iii) only
Answer : C

Section III : Everyd ay Mathematics

Question. On Charvi's birthday, Tanya was asked to buy birthday caps. Caps were of different dimensions, so she was confused; she came back home and measured Charvi's head with her palm. Two of her palms totally covered the head with a little more space to be neglected. So she went to the shop again and measured with her palm and bought birthday caps. The width of her palm was 7 cm. Can you guess the plane area of head the cap will cover?
(A) 44 cm
(B) 88 cm
(C) 154 cm²
(D) 2156 cm²
Answer : C

Question. 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 ?
(A) 2/7
(B) 3/7
(C) 4/7
(D) 5/7
Answer : B

Question. The problem given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is / are necessary to answer the question.
How many marks did Tarun secure in English ?
(i) The average marks obtained by Tarun in four subjects including English are 60.
(ii) The total marks obtained by him in English and Mathematics together are 170.
(iii) The total marks obtained by him in Mathematics and Science together are 180.
(A) I and II only
(B) II and III only
(C) I and III only
(D) None of these
Answer : D

Question. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
(A) 2 : 3 : 4
(B) 6 : 7 : 8
(C) 6 : 8 : 9
(D) None of these
Answer : A

Question. A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same was 38 cm when folded along the other set of sides. What is the area of the paper?
(A) 140 cm²
(B) 240 cm²
(C) 560 cm²
(D) None of these
Answer : A

Question. The given bar-graph here shows the percentage distribution of the total production of a car manufacturing company into various models over two years. Study the graph carefully and answer the question. Percentage of six different types of cars manufactured by a company over two years 

Difference between total number of cars of models P, Q and T manufactured in 2000 and 2001 is____.
(A) 2,45,000
(B) 2,27,500
(C) 2,10,000
(D) 98,000
Answer : D

Question. A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, then how much beverage is contained in the vessel from the bowl ?
(A) 66(2/3)%
(B) 78(1/2)%
(C) 100%
(D) More than 100% (i.e., some liquid will be left in the bowl).
Answer : C

Question. A pineapple costs ₹ 7. A watermelon costs ₹ 5. X spends ₹ 38 on these fruits. The number of pineapples purchased is _____.
(A) 2
(B) 3
(C) 4
(D) Data inadequate
Answer : C

Question. Due to an increase of 30% in the price of eggs, 3 less eggs are available for ₹ 7.80. The present rate of eggs per dozen is _____.
(A) ₹ 8.64
(B) ₹ 8.88
(C) ₹ 9.36
(D) ₹ 10.40
Answer : C

Question. A housewife saved ₹ 2.50 in buying an item on sale. If she spent ₹ 25 for the item, approximately how much percent did she save in the transaction ?
(A) 8%
(B) 9%
(C) 10%
(D) 11%
Answer : B