CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set M

Section I : Logical Reasoning

Question. Rahul told Anand, "Yesterday I defeated the only brother of the daughter of my grandmother." Whom did Rahul defeat?
(A) Son
(B) Father
(C) Brother
(D) Father-in-law
Answer : B

Question. In a row of boys, if P who is tenth from the left and Q who is ninth from the right interchange their positions, P becomes fifteenth from the left. How many boys are there in the row?
(A) 23
(B) 27
(C) 28
(D) 31
Answer : A

Question. A, B, C, D, E, F, G, H and I are nine houses. C is 2 km east of B. A is 1 km north of B and H is 2 km south of A. G is 1 km west of H while D is 3 km east of G and F is 2 km north of G. I is situated just in middle of B and C while E is just in middle of H and D.
Distance between A and F is _____.
(A) 1 km
(B) 1.41 km
(C) 2 km
(D) 3 km
Answer : A

Question. The two expressions on either side of the sign (=) will have the same value if two terms on either side or on the same side are interchanged. The correct terms to be interchanged have been given as one of the four alternatives under the expressions. Find the correct alternative in the given case.
7 × 2 – 3 + 8 ÷ 4 = 5 + 6 × 2 – 24 ÷ 3
(A) 2, 6
(B) 6, 5
(C) 3, 24
(D) 7, 6
Answer : D

Question. The given below input rearranges step-by-step in a particular order according to a set of rules. In this case the last step of arranged input is Step V.
Input : 85 16 36 04 19 97 63 09
Step I : 97 85 16 36 04 19 63 09
Step II : 97 85 63 16 36 04 19 09
Step III : 97 85 63 36 16 04 19 09
Step IV : 97 85 63 36 19 16 04 09
Step V : 97 85 63 36 19 16 09 04
Study the above arrangement carefully and then answer the following question.
Which of the following will be Step III for the input below ?
I nput : 09 25 16 30 32 18 17 06
(A) 32 30 25 09 16 18 17 06
(B) 32 30 09 25 16 18 17 06
(C) 32 09 25 16 30 18 17 06
(D) 32 30 09 25 16 19 17 06
Answer : A

Question. If a 1 mm thick paper is folded so that the area is halved at every fold, then what would be the thickness of the pile after 50 folds?
(A) 25 × 10⁶ km
(B) (52/10⁻⁶)km
(C) 50 × 2 × 10⁻⁶ km
(D) 250 × 10⁻⁶ km
Answer : D

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

Answer : A

Question. All surfaces of a cube are coloured. If a number of smaller cubes are taken out from it, each side is 1/4 the size of the original cube's side, find the number of cubes with only one side painted.
(A) 60
(B) 30
(C) 24
(D) 16
Answer : C

Question. Each of the vowels in the word 'MAGNIFY is replaced by number '2' and each consonant is replaced by a number which is the serial number of that consonant in the word, i.e., M by 1, G by 3 and so on. What is the total of all the numbers once the replacement is completed?
(A) 22
(B) 24
(C) 25
(D) 26
Answer : C

Question. Find out which of the following options replace the question mark in the figure matrix?

Answer : C

Question. Choose the correct mirror-image of the Fig.(X).

Answer : C

Question. What is the number of straight lines and the number of triangles in the given figure?

(A) 10 straight lines and 34 triangles
(B) 9 straight lines and 34 triangles
(C) 9 straight lines and 35 triangles
(D) None of these
Answer : D

Question. In the following diagram, the circle represents 'College Professors', the triangle represents 'Surgical Specialists', and rectangle represents 'Medical Specialists'.
What does B represent?

(A) Professors who are neither Medical nor Surgical Specialists.
(B) Professors who are not Surgical Specialists.
(C) Medical Specialists who are neither Professors nor Surgical Specialists.
(D) Professors who are not Medical Specialists.
Answer : C

Question. There are seven figures, the first and last of which are unnumbered and the remaining are numbered as 1, 2, 3, 4 and 5. These seven figures form a series. However, one of the five numbered figures does not fit into the series. Find the figure. 

(A) 4
(B) 5
(C) 3
(D) 2
Answer : A

Question. Select the pair of figures from the given options, which does not have a similar relationship to that in the given pair of Problem Figures.

Answer : D

Question. Study the information given below and answer the question that follow.
(i) A , B, C, D, E and F are six students in a class.
(ii) B and C are shorter than F but heavier than A.
(iii) D is heavier than B and taller than C.
(iv) E is shorter than D but taller than F.
(v) F is heavier than D.
(vi) A is shorter than E but taller than F.
Which of the following statements is true for F as regards height and weight?
(A) He is lighter than E and taller than E.
(B) He is heavier than B and taller than E.
(C) He is heavier than B but shorter than D.
(D) He is lighter than E and also shorter than E.
Answer : C

Question. In a shop, the items were arranged in a shelf consisting of six rows. Biscuits are arranged above the tins of chocolates but below the rows of packets of chips, cakes are at the bottom, and the bottles of peppermints are below the tins of chocolates. The topmost row had the display of jam bottles. Where exactly are the bottles of peppermints? Mention the place from the top.
(A) 2nd
(B) 3rd
(C) 4th
(D) 5th
Answer : D

Question. There is a definite relationship between figures P and Q. Establish a similar relationship between figures R and S by selecting a suitable figure from the answer set that would replace the question mark(?) in Fig.(S)

Answer : A

Question. There is a set of four figures labelled P, Q, R and S called the Problem Figures. Select a suitable figure, so that a series is formed by figures P, Q, R and S.

Answer : D

Question. Rewrite the word VOCALIST in the numeric form by writing its first four letters in the reverse order and then the next four letters in the reverse order by substituting I by 8, O by 1, L by 3, T by 2, V by 5, S by 7, A by 9 and C by 6.
(A) 96156873
(B) 96157683
(C) 96516783
(D) 96152783
Answer : D

Section II : Mathematical reasoning

Question. A rationalizing factor of 3 16 -3 4 +1 is ________.
(A) 3 4 +1
(B) 3 4 −1
(C) 3 4 + 2
(D) 3 4 − 2
Answer : A

Question. Consider the volumes of the following:
1. A parallelopiped of length 5 cm, breadth 3 cm and height 4 cm
2. A cube of each side 4 cm
3. A cylinder of radius 3 cm and length 3 cm
4. A sphere of radius 3 cm
The volumes of these in the decreasing order is ____.
(A) 1, 2, 3, 4
(B) 1, 3, 2, 4
(C) 4, 2, 3, 1
(D) 4, 3, 2, 1
Answer : D

Question. If the polynomial 16x⁴ – 24x³ + 41x² – mx + 16 be a perfect square, then the value of "m" is _____.
(A) 12
(B) –12
(C) 24
(D) –24
Answer : C

Question. If the roots of (p – q)² x² + 2 (p² – q²) x + k = 0 are equal, then k = ________.
(A) (p + q)²
(B) (p – q)²
(C) p² – q²
(D) 0
Answer : A

Question. In the given figure, O is the centre of the circle and XOY is a diameter. If XZ is any other chord of the circle, then which of the following is correct?

(A) XZ < OZ
(B) XY > XZ
(C) OX + OZ < XZ
(D) XZ + ZY < XY
Answer : B

Question. P is the mid-point of side AB to a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. Then BR is equal to ________.

(A) BQ
(B) (1/2)BQ
(C) 2BQ
(D) None of these
Answer : C

Question. In the given figure, AE = BC and AE || BC and CD = ED. If ∠A = 102°, then find the measure of ∠BDE.

(A) 138°
(B) 162°
(C) 24°
(D) None of these
Answer : C

Question. The number of numbers from 1 to 200 which are divisible by neither 3 nor 7 is ______.
(A) 115
(B) 106
(C) 103
(D) Less than 100
Answer : A

Question. There is a cone of height 12 cm, out of which a smaller cone (which is the top portion of the original cone) with the same vertex and vertical axis is cut out. What is the ratio of the volume of the larger (actual) cone to the remaining part of the cone, if the height of the smaller cone is 9 cm and AD/AB = DE/BC ?

(A) 3 : 1
(B) 9 : 1
(C) 64 : 37
(D) 16 : 7
Answer : C

Question. In a triangle ABC, O is the centre of incircle PQR, ∠BAC = 65°, ∠BCA = 75°, find ∠ROQ.
(A) 80°
(B) 120°
(C) 140°
(D) Can't be determined
Answer : C

Question. If x/(b-c)(b+c-2a) = y/(c-a)(c+a-2b) = z/(a-b)(a+b-2c), then the value of (x + y + z) is _______.
(A) a + b + c
(B) 0
(C) a² + b² + c²
(D) Can't be determined
Answer : B

Question. If a, b, g are such that α + β + γ = 2, α² + β² + γ² = 6, α³ + β³ + γ³ = 8, then α⁴ + β⁴ + γ⁴ is equal to ________.
(A) 10
(B) 12
(C) 18
(D) None of these
Answer : C

Question. In the given figure, ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ = (1/4)AC. Also, PQ when produced meets BC at R. Then CR = _______.

(A) RB
(B) (1/3)CB
(C) (1/4)CB
(D) None of these
Answer : A

Question. In ΔABC, it is given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE. Then ar(ΔBOE) = ?

(A) 1/3 ar (ΔABC)
(B) 1/4 ar (ΔABC)
(C) 1/6 ar (ΔABC)
(D) 1/8 ar (ΔABC)
Answer : D

Question. Four dice are thrown simultaneously. Find the probability that all of them show the same faces.
(A) 1/216
(B) 15/16
(C) 15/36
(D) 1/2
Answer : A

Question. The construction of a ΔABC in which BC = 6 cm and ∠B = 50° is not possible when (AB – AC) is equal to ________.
(A) 5.6 cm
(B) 5 cm
(C) 6 cm
(D) 4.8 cm
Answer : C

Question. Which least number must be subtracted from 9999999 so that it will become the multiple
of 125?
(A) 124
(B) 4
(C) 24
(D) None of these
Answer : A

Question. When 5 is added to the numerator and denominator both of a (positive) fraction, then the new ratio of numerator to denominator becomes 11 : 15. What is the original ratio?
(A) 15 : 25
(B) 3 : 5
(C) 38 : 40
(D) Data inadequate
Answer : D

Question. AB and CD are two parallel lines and a transversal PQ intersects AB and CD at M and N respectively.
If the bisector of the interior angles form a quadrilateral, then formed quadrilateral is a ______.

(A) Rectangle
(B) Square
(C) Trapezium
(D) None of these
Answer : A

Question. A large solid sphere of diameter 15 m is melted and recast into several small spheres of diameter 3 m. What is the percentage increase in the surface area of the smaller spheres over that of the large sphere?
(A) 200%
(B) 400%
(C) 500%
(D) Can't be determined
Answer : B

Section III : Everyday Mathematics

Question. A bonus of ₹ 1000 is to be divided among three people so that Rohit receives twice as much as Sachin, who receives one-fifth as much as Gagan. How much money should Gagan receive?
(A) ₹ 100
(B) ₹ 250
(C) ₹ 375
(D) ₹ 625
Answer : D

Question. Samant bought a microwave oven and paid 10% less than the original price. He sold it with 30% profit on the price he had paid. What percentage of profit did Samant earn on the original price?
(A) 17%
(B) 20%
(C) 27%
(D) 32%
Answer : A

Question. Shekhar started a business investing ₹ 25,000 in 1999. In 2000, he invested an additional amount of ₹ 10,000 and Rajeev joined him with an amount of ₹ 35,000. In 2001, Shekhar invested another additional amount of ₹ 10,000 and Jatin joined them with an amount of ₹ 35,000. What will be Rajeev's share in the profit of ₹ 1,50,000 earned at the end of 3 years from the start of the business in 1999?
(A) ₹ 45,000
(B) ₹ 50,000
(C) ₹ 70,000
(D) ₹ 75,000
Answer : B

Question. A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?
(A) 30 days
(B) 35 days
(C) 40 days
(D) None of these
Answer : A

Question. Sixteen years ago, Tanya's grandfather was 8 times older to her. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Tanya's age to that of her grandfather?
(A) 1 : 2
(B) 1 : 5
(C) 3 : 8
(D) None of these
Answer : D

Question. David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was ₹ 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?
(A) ₹ 5000
(B) ₹ 6500
(C) ₹ 8000
(D) None of these
Answer : A

Question. In a bullet the gun powder is to be filled up inside the metallic enclosure. The metallic enclosure is made up of a cylindrical base and conical top with the base of radius 5 cm. The ratio of height of cylinder and cone is 3 : 2. A cylindrical hole is drilled through the metal solid with height twothird the height of metal solid. What would be the radius of the hole, so that the volume of the hole (in which gun powder is to be filled up) is one-third the volume of metal solid after drilling?
(A) √88/5 cm
(B) √55/8 cm
(C) 55/8 cm
(D) None of these
Answer : B

Question. A man gave 40% of the amount he had, to Rohan. Rohan in turn gave one-fourth of what he received from Aman to Sahil. After paying ₹ 200 to the taxi driver out of the amount he got from Rohan, Sahil now has ₹ 600 left with him. How much amount did Aman have?
(A) ₹ 4000
(B) ₹ 8000
(C) ₹ 12000
(D) Data inadequate
Answer : B

Question. A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month over the whole?
(A) 4500
(B) 4600
(C) 4680
(D) 4710
Answer : A

Question. Kamla has a triangular field with sides 240 m, 200 m, 360 m, where she grew wheat. In another triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions?(1 hectare = 10,000 m²).
(A) 6.10
(B) 5.32
(C) 8.27
(D) None of these
Answer : A