CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set B

Logical Reasoning

Question. What should come next in the letter series given below?
A A B A B C A B C D A B C D E A B C D E F A B C D E F G A B C D E F G _?_
A. A
B. I
C. H
D. B
Answer : C

Question. How many pairs of letters are there in the word NURSING which have as many letters between them as in the English alphabet?
A. One
B. Three
C. Five
D. Six
Answer : B

Question. Study the following arrangement carefully and answer the question given below :
M J % 4 T E K I 9 # P A $ Q 3 8 N 5 U 7 W * B @ D F © 1 Z 6 H
What should come in place of question mark in the following series based on the above arrangement?
J 4 E I # A Q 8 5 7 * @ ?
A. F16
B. D©G
C. F©6
D. F1Z
Answer : A

Question. Ravi starts from his house and moves towards South. 
He walks 100 m, then turns left and walks 200 m, turns right and walks 500 m. How far is he from his house?
A. 400√5 m
B. 800 m
C. 200√10 m
D. 200√2 m
Answer : C

Question. Four brothers go to a dance party. As they leave, each of the brothers accidentally takes a hat belonging to another brother and a coat belonging to a third brother. M takes the coat belonging to the brother whose hat is taken by P, while P's coat is taken by the brother who takes M's hat. S takes J's hat. Whose hat was taken by P?
A. Can't say
B. S
C. M
D. Either S or J
Answer : B

Question. In a certain code 'ring a bell' is written as '5 8 2', 'did not ring' is written as '3 5 9' and 'not a reason' is written as '7 2 9'. What is the code for 'ring?
A. 8
B. 2
C. 5
D. 3
Answer : C

Question. P, Q, R, S, T, U and W are sitting around a circle facing at the centre. S is third to the left of P who is second to the left of U. T is not a neighbour of either U or S. R is third to left of Q. Which of the following information represents the first person sitting to the immediate right of the second person?
A. PQ
B. UW
C. RT
D. PT
Answer : C

Question. A pile of cubes of equal size is arranged as shown in the figure. Now the block is dipped into a bucket full of red paint so that only the surfaces of the block get coloured. How many cubes are coloured on four faces only?

A. 0
B. 1
C. 2
D. 4
Answer : C

Question. Find the missing character if the given matrix follows a certain rule row-wise or column-wise.

A. 2
B. 3
C. 4
D. 5
Answer : B

Question. In the given Venn diagram, triangle represents the healthy, square represents the old and circle represents the men. Which of the following regions represents the men who are healthy but not old?

A. 1
B. 2
C. 3
D. 7
Answer : B

Question. Select the mirror image of Figure (X) from the given options, if the mirror is placed vertically to the right

Answer : B

Question. Given below are the three figures (X), (Y) and (Z) showing a sequence of folding of a piece of paper.
Figure (Z) shows the manner in which the folded paper has been cut. Identify the unfolded form of piece of paper.

Answer : C

Question. The given question consists of Problem Figures followed by option figures. Select a figure which will continue the series.

Answer : C

Question. There is a certain relationship between figures (i) and (ii). Establish the similar relationship between figures (iii) and (iv) by selecting a figure from the options which will replace the (?) in figure (iv).

Answer : D

Question. Select the figure from the options which can be formed from the pieces given in Figure (X).

Answer : C

MATHEMATICAL REASONING

Question. In figure, ∠L = 62°, ∠LMN = 54°. If MO and NO are bisectors of ∠LMN and ∠LNM respectively of ΔLMN, find ∠ONM and ∠MON.

A. 27°, 121°
B. 64°, 32°
C. 64°, 121°
D. 32°, 121°
Answer : D

Question. In the figure, it is given that

(i) AB ⊥ BF and EF ⊥ BF
(ii) AC = BC
(iii) KD is perpendicular to BC and DE.
Find the measure of x.
A. 75°
B. 30°
C. 60°
D. 45°
Answer : C

Question. In a ΔABC, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm. The perimeter of the quad. ARPQ is

A. 91 cm
B. 60 cm
C. 51 cm
D. 70 cm
Answer : C

Question. The value of

A. 2
B. –1
C. √3 + √2
D. 1
Answer : D

Question. If a + b + c = 15 and a² + b² + c² = 83, find the value of a³ + b³ + c³ – 3abc.
A. 180
B. 71
C. 128
D. 95
Answer : A

Question. Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be K% lower than the volume of B. The value of K must be

A. 85.5
B. 92.5
C. 90.5
D. 87.5
Answer : D

Question. A bag contains 8 red and 4 green balls. Find the probability that the ball drawn is red when one ball is selected at random.
A. 2/3
B. 1/3
C. 1/6
D. 5/6
Answer : A

Question. In the given figure, ABCDEF is a regular hexagon and ∠AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?

A. 1/12
B. 1/6
C. 1/24
D. 1/8
Answer : A

Question. The value of expression

A. − 3/2
B. 2/3
C. 3/2
D. 9/4
Answer : A

Question. In the given figure, square 2 is formed by joining the mid-points of square 1, square 3 is formed by joining the mid-points of square 2 and so on. In this way total five squares are drawn. The side of the square 1 is 'a' cm. What is the sum of perimeters of all the five squares ?

A. (4√2 + 1)a / (√2 + 1) cm
B. 5/6 a cm
C. (7 + 3 √2)a cm
D. None of these
Answer : C

Question. In the given figure, O is the centre of the circle. The distance between P and Q is 4 cm. Find the ∠ROQ.

A. 50°
B. 60°
C. 70°
D. 35°
Answer : C

Question. In the given figure, CD || AE and CY || BA. Then ar(BCZY) =

A. ar(ΔZDC)
B. ar(ΔCBY)
C. ar(ΔEDZ)
D. All of these
Answer : C

Question. The given diagram shows a cylinder with a diameter of 10 cm and height 15 cm. The shaded portion in the form of a cone, with base diameter 10 cm and height 6 cm, is hollowed out. Find the volume of the remaining solid, in cm³.

A. 300  π
B. 345  π
C. 295  π
D. 325  π
Answer : D

Question. The given diagram is drawn on a cartesian plane.

PQRS is a square. The coordinates of S are
A. (–3, 3)
B. (3, – 3)
C. (–3, –3)
D. (–3, 2)
Answer : A

Question. If a – b = 3, a + b + x = 2, then the value of (a – b) [x³ + 3(a + b)x² + 3x(a + b)² + (a + b)³] is
A. 84
B. 48
C. 32
D. 24
Answer : D

Question. ABCD is a trapezium in which AB | | CD. Then AC² + BD² is equal to

A. AD² + BC² – 2AB⋅CD
B. AD² + BC² + 2AB⋅CD
C. AD² – BC² + 2AB⋅CD
D. AD² – BC² – 2AB⋅CD
Answer : B

Question. PQRS is the diameter of a circle of radius 6 cm.
The lengths PQ, QR and RS are equal. Semi-circles are drawn with PQ and QS as diameters as shown in figure. Find the ratio of the area of the shaded region to that of the unshaded region.

A. 3 : 15
B. 15 : 13
C. 5 : 13
D. 13 : 5
Answer : C

Question. Each side of ΔABC is 12 units. D is the foot of the perpendicular dropped from A on BC, E is the midpoint of AD. The length of BE is
A. 36√3 units
B. 6√7 units
C. 3√3 units
D. 3√7 units
Answer : D

Question. Divide the product of (4x² – 9) and (2x² – 3x + 1) by (4x³ – 7x + 3).
A. 2x – 3
B. 2x + 3
C. 2x
D. 3x – 2
Answer : A

Question. In the figure below, two straight lines PQ and RS intersect each other at O. If ∠POT = 75°, find the values of a, b and c respectively.

A. 21°, 84°, 48°
B. 48°, 84°, 21°
C. 84°, 21°, 48°
D. 57°, 21°, 48°
Answer : C

EVERYDAY MATHeMATICS

Question. 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76.
What is the average percent marks of children of group B?
A. 77(1/3)
B. 77(2/3)
C. 78(1/3)
D. 78(2/3)
Answer : B

Question. One year ago, Sheela was four times as old as her daughter Sakshi. Six years hence, Sheela's age will exceed her daughter's age by 9 years. The ratio of the present ages of Sheela and her daughter is _____.
A. 9 : 2
B. 11 : 3
C. 12 : 5
D. 13 : 4
Answer : D

Question. A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. In the total transaction, his gain or loss will be _____.
A. Neither loss nor gain
B. 5% loss
C. 5% gain
D. 10% gain
Answer : C

Question. If 18 binders bind 900 books in 10 days, how many binders will be required to bind 660 books in 12 days?
A. 22
B. 14
C. 13
D. 11
Answer : D

Question. The population of a town is increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is _____.
A. 4.37%
B. 5%
C. 6%
D. 50%
Answer : B

Question. A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay ₹ 5400 interest only for the period. The principal amount borrowed by him was .
A. ₹ 2000
B. ₹ 10,000
C. ₹ 15,000
D. ₹ 20,000
Answer : C

Question. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits ₹ 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is
A. ₹ 120
B. ₹ 121
C. ₹ 122
D. ₹ 123
Answer : B

Question. A man bought goods worth ₹ 6000 and sold half of them at a gain of 10%. At what gain percent must he sell the remainder so as to get a gain of 25% on the whole?
A. 25%
B. 30%
C. 35%
D. 40%
Answer : D

Question. Gauri went to the stationers and bought things worth ₹ 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A. ₹ 15
B. ₹ 15.70
C. ₹ 19.70
D. ₹ 20
Answer : C

Question. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in _____.
A. 6 hrs
B. 6(2/3)hrs
C. 7 hrs
D. 7(1/2)hrs
Answer : C

Achievers Section

Question. Select the correct match.
Let f (x) = (x − 2)(x − 4)/x

Answer : D

Question. The marks scored by some students for a question in the Science test are shown in the table below.

(a) If the mode is 4, write down the smallest possible value of x.
(b) If the mean is 2(1/4), find the value of x.
   (a)      (b)
A. 6         2
B. 5         2
C. 6         4
D. 6         3
Answer : A

Question. In the given figure, ABCD is a parallelogram and CEFD is a rhombus. ∠ADF = 90° and ∠CFD = 24°. Find ∠DAB.

A. 48°
B. 42°
C. 56°
D. 58°
Answer : B

Question. The given figure, not drawn to scale, is made up of 3 circles and 3 squares. Find the total area of the shaded parts. (Take π = 22/7)

A. 1500 cm²
B. 1680 cm²
C. 1749 cm²
D. 1149 cm²
Answer : C

Question. The given pie chart shows the distance covered by Mohit from Monday to Thursday. The distance he covered on Tuesday was thrice the distance he covered on Wednesday. Mohit covered a distance of 201 km on Wednesday.

(i) What was the total distance he covered on the four days?
(ii) What was the distance covered on Monday?
          (i)             (ii)
A. 2142 km     1005 km
B. 2214 km     1008 km
C. 2124 km     1102 km
D. 2412 km     1005 km
Answer : D