CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set I

LOGICAL REASONING

Question. How many pairs of letters are there in the word RECREATION which have number of letters between them in the word one less than the number of letters between them in the English alphabet?
A. Two
B. Three
C. Four
D. More than four
Answer : C

Question. Select the correct water image of the given figure. Fig. (X)

Answer : A

Question. Which symbol will be on the face opposite to the face with symbol @, when the given figure is folded to form a cube?

A. *
B. #
C. ©
D. $
Answer : C

Question. A word-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 : page 15 easy 62 fire 52 desk 47
Step I : page 62 15 easy fire 52 desk 47
Step II : page 62 fire 15 easy 52 desk 47
Step III : page 62 fire 52 15 easy desk 47
Step IV : page 62 fire 52 easy 15 desk 47
Step V : page 62 fire 52 easy 47 15 desk
Step VI : page 62 fire 52 easy 47 desk 15
Step VI is the last step of the given input.
As per the rule followed in the above steps, which is the last step of given input?
Input : play 35 29 nice 17 clever task 75
A. Step V
B. Step VI
C. Step IV
D. Step VII
Answer : C

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

A. 7
B. 8
C. 9
D. 11
Answer : C

Question. Which of the following options satisfies the same conditions of placement of the dots as in the given figure?

Answer : C

Question. In a certain code language, CHOCOLATE is coded as AFMAPNCVG. How will SENSITIVE be coded in the same language?
A. UGPUKVKXG
B. QCLQKRGTC
C. QCLQJVKXG
D. UGPUJRGTC
Answer : C

Question. How many vowels are there in the given arrangement, each of which is immediately preceded by a symbol and immediately followed by a consonant?
F 4 @ J 2 E % M S 4 V 9 © A Q R 6 U T 3 Z 7 # U S B 8 V ★ G $ Y C
A. One
B. Two
C. Three
D. None of these
Answer : B

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

Answer : C

Question. Which of the following Venn diagrams best represents the relationship amongst, "Musicians, Non-smokers and Males"?

Answer : A

Question. Six friends are sitting in a circle facing the centre. Sneha is sitting opposite to Vaibhav. Kavya is sitting to the right of Vaibhav but to the left of Kirti. Monika is sitting to the left of Vaibhav. Priya is sitting to the right of Sneha and to the left of Monika. Now, Kirti and Priya, Monika and Vaibhav mutually interchange their positions.
Who will be sitting to the left of Monika?
A. Kavya
B. Priya
C. Kirti
D. Vaibhav
Answer : D

Question. Pointing to a lady in the garden, Priyansh said," She is the daughter of my grandfather's only son". How is Priyansh related to that lady?
A. Brother
B. Cousin
C. Uncle
D. Father
Answer : A

Question. The question consists of a 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 resembles the unfolded form of Fig. (Z) .

Answer : B

Question. There is a certain relationship between figures (1) and (2). Establish the same relationship between figures (3) and (4) by selecting a suitable figure from the given options that would replace the (?) in Fig. (4).

Answer : B

Question. Find the number of triangles formed in the given figure.

A. 22
B. 19
C. 18
D. None of these
Answer : A

MATHEMATICAL REASONING

Question. In a quadrilateral PQRS, diagonals PR and QS bisect each other at M. If ∠PMS = 90°, then quadrilateral PQRS is a ________.
A. Trapezium
B. Kite
C. Rhombus
D. Parallelogram
Answer : C

Question. Area of a given triangle is x1 square units. If the sides of this triangle be doubled, then the area of the new triangle becomes x² square units. Find the percentage increase in area.
A. 100%
B. 200%
C. 300%
D. None of these
Answer : C

Question. Consider the given statements carefully.
I. Any point on the x-axis is of the form (0, a).
II. The point (0, 0) lies on both the axes.
III. The point (3, –2) lies in the IIIrd quadrant.
Which of the above statements is/are true?
A. Both I and II
B. Only I
C. Only II
D. Both II and III
Answer : C

Question. If (3, –1) is a solution of the linear equation 4x – ky = 8x + 2y, then find the value of k.
A. 11
B. 13
C. 10
D. 15
Answer : C

Question. Which of the following statements is INCORRECT?
A. Things which coincide with one another are equal to one another.
B. Two distinct lines can have more than one point in common.
C. A circle can be drawn with any centre and any radius.
D. A straight line may be drawn from any one point to any other point.
Answer : B

Question. A bag contains 8 yellow, 3 pink, 2 green and 7 red candies of similar size. A candy is taken out randomly from the bag. What is the probability that the chosen candy is of red colour?
A. 1/4
B. 3/20
C. 7/20
D. 4/5
Answer : C

Question. In the given figure, ΔDABC and ΔPBC are two isosceles triangles on the same base BC and vertices A and P are on the same side of BC. If A and P are joined, then

A. ∠BPA = 1/2 ∠BAC 
B. ∠BAP = 1/2 ∠BAC
C. ∠CPA = 1/2 ∠BAC
D. ∠BAP = 2∠BAC
Answer : B

Question. The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, then what is the value of r in terms of x?
A. (x²/2π) units
B. (x/2√π) units
C. (√2x/π) units
D. (x/√π) units
Answer : B

Question. What could be the possible values of X, if 2345691X32 is divisible by 3 (where X is a digit)?
A. 1
B. 4
C. 7
D. All of these
Answer : D

Question. In the given figure (not drawn to scale), ABCD and PQRS are parallelograms. Find the value of x.

A. 70°
B. 80°
C. 30°
D. 40°
Answer : D

Question. The denominator of

is_________.
A. a²
B. b²
C. a² – b²
D. 4a² - 2-b²/b
Answer : B

Question. If p = 2 −√3, q = √3 − 7 and r = √7 − √4, then find the value of p³ + q³ + r³.
A. 0
B. 3(3√3 + √7 − 8)
C. 3√3 − 2√7
D. None of these
Answer : B

Question. Three identical spherical balls fit snugly into a cylindrical can. The radius of each of the spherical ball equals the radius of the can and the balls just touch the bottom and the top of the can. What fraction of the volume of the can is taken up by the balls?
A. 3/5
B. 4/3
C. 3/2
D. 2/3
Answer : D

Direction (a - b) : The given bar graph represents the petrol and diesel cars sold in a mega city from 2010 to 2015. Study the graph carefully and answer the following questions.

Question a. Find the difference between the number of petrol cars sold in 2010 and 2011 together and the number of diesel cars sold in 2015.
A. 3200
B. 2800
C. 2500
D. 3000
Answer : D

Question b. In which year, the total sale of petrol and diesel cars altogether was maximum?
A. 2012
B. 2011
C. 2013
D. 2014
Answer : B

Question. In the given figure (not drawn to scale), AB and BC are two chords of the circle with centre O. Find the value of x.

A. 170°
B. 70°
C. 150°
D. None of these
Answer : A

Question. Study the given statements carefully and select the correct option.
P. Two congruent figures have equal areas and vice versa.
Q. Parallelograms on the same base (or equal bases) and between the same parallels are equal in area.
R. If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is equal to the area of the parallelogram.
S. Triangles on the same base (or equal bases) and having equal areas lie between the same parallels.
A. Only P and Q are true.
B. Only Q and S are true.
C. Only P and R are false.
D. Both B and C
Answer : D

Question. In the given figure, ABCD is a rhombus whose diagonals intersect at O. If E and F are mid-points of AO and BO respectively, then find the length of EF.

A. 10 cm
B. 5 cm
C. 8 cm
D. 9 cm
Answer : B

Question. The traffic police recorded the speed (in km/hr) of 10 motorcyclists as 32, 45, 46, 55, 65, 38, 45, 41, 39 and 62. Later on, an error in recording instrument was found. Find the correct average speed of the motorcyclists, if the instrument recorded 3 km/hr less in each case.
A. 49.9 km/hr
B. 48.5 km/hr
C. 43.8 km/hr
D. 49.8 km/hr
Answer : D

Question. In the given figure (not drawn to scale), ABCD is a quadrilateral. If AE || DC, BE || AD and AE intersects BC at F, then find ∠EBF.

A. 43°
B. 72°
C. 51°
D. 27°
Answer : D

EVERYDAY MATHEMATICS

Question. Amit scored 73 marks in Mathematics. He scored 56% marks in English and x marks in Science. Maximum marks in each subject were 150. The overall percentage of marks obtained by him was 54%. How many marks did he score in Science?
A. 84
B. 86
C. 89
D. 73
Answer : B

Question. A box contains 125 adapter chargers out of which 45 are defective and rest are good. Priyanka will buy a charger, if it is good. The shopkeeper draws one charger at random and gives it to her. What is the probability that she will buy it?
A. 9/25
B. 16/25
C. 4/25
D. None of these
Answer : B

Question. Aman had four number cards. The number on the first card is twice the second, that on the second is onethird of the third and that on the third is five times the fourth. The average of the numbers is 24.75. Find the largest number amongst them.
A. 9
B. 25
C. 30
D. None of these
Answer : D

Question. A man gets a simple interest of ₹ 2500 on a certain principal at the rate of 10% per annum in 5 years. What compound interest will the man get on twice the principal in two years at the same rate?
A. ₹ 1500
B. ₹ 2100
C. ₹ 1750
D. ₹ 1350
Answer : B

Question. A three-wheeler scooter charges ₹ 15 for the first kilometer and ₹ 7.50 each for every subsequent kilometer. For a distance of x km, an amount of ₹ y is paid. Which of the following shows the linear equation representing the given information?
A. 7.50 x – 7.50 = y
B. 15 + 7.50 x = y
C. 7.50 x + 7.50 = y
D. 15 – 7.50 x = y
Answer : C

Question. Along a path, 25 conical pillars are constructed. Each pillar has radius 15 cm and height 20 cm. Find the total cost of painting these pillars at the rate of ₹ 50 per cm2. [Take π = 3.14]
A. ₹ 201752.50
B. ₹ 2052325
C. ₹ 3214325.50
D. ₹ 1471875
Answer : D

Question. Two spinning machines A and B can together produce 50000 m of cloth in 20 hours. If machine B alone can produce the same amount of cloth in 25 hours, then how much cloth can machine A produce alone in 20 hours?
A. 18000 m
B. 15000 m
C. 10000 m
D. 25000 m
Answer : C

Question. The traffic light at three different signal points change after every 15 seconds, 30 seconds and 45 seconds respectively. If all change simultaneously at 8:15:20 hours, then when will they again change simultaneously?
A. 8:16:20 hours
B. 8:18:35 hours
C. 8:18:45 hours
D. 8:16:50 hours
Answer : D

Question. A person at first has enough money to buy 80 sunglasses worth ₹ 700 each. If the cost of each sunglasses gets increased by ₹ 50, then how many sunglasses can he buy with the same amount of money (approx.).
A. 80
B. 74
C. 82
D. 75
Answer : B

Question. The manufacturer of a machine sells it to a trader making a profit of 15% on its manufacturing cost, the trader sells it to the vendor, making a profit of 5% and vendor sell it to the actual user at a profit of 10%. If the actual user pays ₹ 531.30 for it, then find the manufacturing cost.
A. ₹ 400
B. ₹ 800
C. ₹ 600
D. ₹ 360
Answer : A

ACHIEVERS SECTION

Question. Read the statements carefully and select the correct option.
Statement-I : A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe whose cross-section is 25 cm2, at the rate of 16 km per hour. The rise in the level of water in the tank in 45 minutes is 2.5 cm. 
Statement-II : If V is the volume of cuboid of dimensions a, b and c and A is its surface area, then A/V = 2[a + b + c].
A. Statement-I is true but Statement-II is false.
B. Statement-I is false but Statement-II is true.
C. Both Statement-I and Statement-II are true.
D. Both Statement-I and Statement-II are false.
Answer : D

Question. ABC is a triangle. D is a point on AB such that AD = (1/4)AB and E is a point an AC such that AE = (1/4)AC. Then DE = ________
A. BC
B. 2 BC
C. (1/4)BC
D. (1/2)BC
Answer : C

Question. Study the given co-ordinate system carefully. Which of the following options hold true?

P. The coordinates of points B and D are (3, –5) and (– 6, –3) respectively.
Q. Point A is at the distance of 6 units from y-axis.
R. BG is parallel to y-axis.
S. Point E and G lie on x-axis.
A. Only P and S
B. Only P and Q
C. Only R and S
D. P, Q, R and S
Answer : C

Question. Match the following:

A. P→(b); Q→(c); R→(d); S→(a)
B. P→(c); Q→(b); R→(a); S→(d)
C. P→(d); Q→(a); R→(c); S→(b)
D. P→(a); Q→(b); R→(d); S→(c)
Answer : A

Question. A die having numbers 1, 2, 4, 6, 7 and 8 on its faces, is rolled once. Find the probability of getting
(i) an even prime number.
(ii) a number greater than 3.
(iii) a multiple of 2 which is less than 4.
     (i)    (ii)    (iii)
A. 1/6   1/3   2/3
B. 1/3   1/2   1/3
C. 1/6   1/2   1/6
D. 1/6   2/3   1/6
Answer : D