CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set G

LOGICAL REASONING

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

A. 18
B. 16
C. 12
D. 20
Answer : B

Question. Select a figure from the options which satisfies the same condition of placement of the dots as in Fig. (X).

Answer : B

Question. If all the symbols are dropped from the given arrangement, then which of the following will be the twelfth element to the left of E?
× 2 @ M 1 N # R U 5 Y 8 © J L T 3 H K 7 S $ B W 4 E % H * D F
A. U
B. J
C. 8
D. L
Answer : C

Question. Group the given figures into three classes on the basis of their identical properties by using each figure only once.

A. 1, 6, 7; 2, 4, 9; 3, 5, 8
B. 1, 5, 7; 2, 3, 4; 6, 8, 9
C. 1, 6, 7; 2, 3, 5; 4, 8, 9
D. 1, 5, 8; 2, 4, 7; 3, 6, 9
Answer : 

Question. A cube is painted red on the two adjacent faces and black on the surfaces opposite to red surfaces and orange on the remaining faces. Now the cube is divided into 216 smaller cubes of equal size. How many smaller cubes will have no surface painted?
A. 36
B. 64
C. 60
D. 54
Answer : B

Question. The following letters are coded as follows

While coding the given letters, following conditions are also to be observed.
Conditions :
(i) If the first letter is a consonant and the last letter is a vowel, then their codes are to be interchanged.
(ii) If both the first and the last letters are vowels, then both are to be coded as the code for the last letter.
(iii) If both the first and the last letters are consonants, then both are to be coded as the code for the first letter.
Find the code of ADMIRE.
A. 5 1 2 # @ 5
B. 5 1 2 # @ $
C. $ 1 2 # @ $
D. $ 1 2 # @ 5
Answer : C

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

Answer : C

Question. If 'P @ Q' means 'P is brother of Q', 'P + Q' means 'P is wife of Q', 'P # Q' means 'P is daughter of Q' and 'P – Q' means 'P is father of Q', then which of the following expressions indicates that 'D is father-in-law of A'?

A. A + B @ E – D # C
B. A + E @ B – C # D
C. A + B @ C # D – E
D. A + B @ C # E – D
Answer : C

Question. A square transparent Sheet (X) with a pattern and a dotted line on it is given. Select a figure from the options which shows the folded form of Sheet (X).

Answer : A

Question. Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations on numbers progress from left to right.
Rules:
(i) If an odd number is followed by another composite odd number, they are to be multiplied.
(ii) If an even number is followed by an odd number, they are to be added.
(iii) If an even number is followed by a number which is a perfect square, the even number is to be subtracted from the perfect square.
(iv) If an odd number is followed by a prime odd number, the first number is to be divided by the second number.
(v) If an odd number is followed by an even number, the second one is to be subtracted from the first one.
                                                83 32 17
                                                33  m  8
If m is the resultant of the first row, then what will be the resultant of the second row?
A. 3
B. 5
C. 8
D. 10
Answer : A

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

Answer : D

Question. Going 90 m to the South, Gaurav turns left and goes another 35 m. Then turning to the North, goes 60 m and then turning to his right and goes 25 m. How far is he now from his starting point and in which direction?
A. 30√5 m, North-East
B. 30√5 m, South-East
C. 38 m, South
D. 40√3 m, North-West
Answer : B

Question. In the given Venn diagram, if circle represents 'Politicians', triangle represents 'Doctors' and rectangle represents 'Married people', then which of the following numbers represents the Married doctors who are not Politicians?

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

Question. A theatre has six performing ladies consisting of four vocal musicians, two dancers, one actress and three violinists. Gauri and Vandana are among the violinists while Jaya and Shailja do not known playing on violin.
Shailja and Tanya are the dancers. Jaya, Shailja, Vandana and Tanya are all vocal musicians and two of them are also violinists. Pooja is an actress. Who amongst these lady artists is a dancer, a vocal musician and a violinist?
A. Shailja
B. Jaya
C. Tanya
D. Vandana
Answer : C

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

Answer : C

MATHEMATICAL REASONING

Question. The polynomial ax³ – 29x² + 45x – 9 when divided by (3x – 1) leaves remainder 3. Find the value of a. Also, find the remainder when the given polynomial is divided by x – 2.
A. 3, –19
B. 6, –11
C. 6, 13
D. 9, 16
Answer : C

Question. In the given figure (not drawn to scale), find the value of x, y and z respectively.

A. 90°, 50°, 110°
B. 90°, 40°, 110°
C. 40°, 90°, 110°
D. 110°, 40°, 90°
Answer : B

Question. Which of the following triangles is formed by straight lines x + y = 2, x – y = 2 and y-axis?

A. ΔAOB
B. ΔABC
C. ΔADC
D. ΔADO
Answer : B

Question. In the given figure, ABCD is a parallelogram in which P is the midpoint of DC and Q is the point on AC such that CQ = AC 1/4 and PQ produced meet BC at R, then

A. CR = (1/3)CB
B. CR = RB
C CR = (1/2)RB
D. None of these
Answer : B

Question. In the given figure, PQ || RS. If ∠QPM = 95° and∠PMR = 30°,  then find ∠MRS.

A. 95°
B. 135°
C. 125°
D. 85°
Answer : C

Question. Study the given figure carefully. A point to be chosen randomly. Find the probability that the chosen point must be lying in the shaded region

A. 13/26
B. 11/26
C. 9/28
D. 11/28
Answer : D

Question. In the figure, if ED = EC and ∠ADF = ∠BCG, then ΔABE is a/an _________.

A. Equilateral triangle
B. Isosceles triangle
C. Scalene triangle
D. Non isosceles right angled triangle
Answer : B

Question. If the medians of ΔPQR intersect at O, then ar (POQ) =

A. ar (QOR)
B. 1/3 ar (PQR)
C. Both A and B
D. Neither A nor B
Answer : C

Question. The given question is followed by three statements.
Study the statements carefully and decide which of the following statement(s) is/are necessary to answer the question.
What is the total surface area of cone?
(I) The area of the base of the cone is 1386 cm².
(II) The curved surface area of the cone is 2310 cm².
(III) The volume of the cone is 3696 cm³.
A. I and either II or III
B. II and either I or III
C. III and either I or II
D. Any two of the three
Answer : D

Question. Which of the following is Euclid's third postulate?
A. A straight line may be drawn from any one point to any other point.
B. A terminated line can be produced infinitely.
C. A circle can be drawn with any centre and any radius.
D. All right angles are equal to one another.
Answer : C

Question. If x =

A. 0
B. 1
C. 2
D. –1
Answer : A

Question. A design on a floor is made up of triangular tiles.
The sides of each triangle being 24 cm, 32 cm and 40 cm. Find the cost of polishing all 170 tiles on the floor at the rate of ₹ 1.50 per cm².
A. ₹ 97920
B. ₹ 65280
C. ₹ 99480
D. ₹ 89460
Answer : A

Question. A capsule of medicine is in the shape of a cylinder of diameter 2.1 mm and height is three times the radius.
How much approximate medicine (in mm3) is needed to fill this type of 30 capsules?
A. 340.20
B. 327.30
C. 286.50
D. 267.30
Answer : B

Question. The value of √2 upto 50 decimal places is given below.
√2 = 1.41121356237309504880168872420969807856967187537694
A number is chosen at random from the numbers after the decimal. Find the probability that chosen number will be a/an
(i) Odd number.
(ii) Prime number.
(iii) Multiple of 2 (greater than 0).
        (i)      (ii)     (iii)
A. 22/50 21/50 18/50
B. 24/50 18/50 21/50
C. 18/50 22/50 21/50
D. 23/50 18/50 21/50
Answer : B

Question. If x =

A. ax
B. 0
C. –ax
D. –1
Answer : A

Question. Which of the following statements is true?
A. If two parallelograms are on equal bases and between the same parallels, then the ratio of their areas is 1 : 2.
B. A quadrilateral formed by joining the mid-point of the sides of a quadrilateral in order, is a parallelogram.
C. If P is any point on the median AD of a ΔABC, then ar (ΔABP) ≠ ar (ΔACP).
D. All of these
Answer : B

Question. The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation 9C = 5F – 160°.
If the temperature is 0°C, then what is the temperature in Fahrenheit and if the temperature is 0°F, then what is the temperature in Celsius?
A. 32°F, 17.78°C
B. 25°F, 16.50°C
C. 25°F, –16.50°C
D. 32°F, –17.78°C
Answer : D

Question. Simplify

A. 7912/625
B. 6812/625
C. 6912/625
D. 6812/722
Answer : C

Question. A die is thrown 500 times and the outcome of each throw is noted down. The given table shows the frequencies of the outcomes.

What is the probability of getting the number 2?
A. 0.15
B. 0.75
C. 0.20
D. 0.004
Answer : A

Question. If l||m and p is the transversal, then select theCORR ECT match.

Answer : C

EVERYDAY MATHEMATICS

Question. Varun received ₹ 8000 as his share out of the total profit of ₹ 12,000 which he and his friend Karan earned at the end of one year. If Varun invested ₹ 30,000 for four months whereas Karan invested his amount for the whole year. What was the amount invested by Karan?
A. ₹ 8,000
B. ₹ 5,000
C. ₹ 10,000
D. ₹ 15,000
Answer : B

Question. In an experiment, a coin is tossed 500 times. If the tail turns up 280 times, then find the probability of getting a head.
A. 11/25
B. 12/25
C. 14/25
D. 13/25
Answer : A

Question. A teak wood log is first cut in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is 1.104 m3. How many rectangular planks of size 2.3 m × 0.75 m × 0.04 m can be cut from the cuboid?
A. 16
B. 64
C. 68
D. 4
Answer : A

Question. The average marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the average marks of all the students in the examination is 71, then find the ratio of the number of boys to the number of girls.
A. 1 : 3
B. 2 : 1
C. 1 : 2
D. 3 : 1
Answer : B

Question. A train passes two persons walking in the same direction in which the train is going. These persons are walking at the rate of 5 km/hr and 8 km/hr respectively and the train passes them completely in 20 seconds and 25 seconds respectively. Find the speed of the train.
A. 20 km/hr
B. 28 km/hr
C. 18 km/hr
D. 15 km/hr
Answer : A

Question. During a year, the population of a town increased by 8% and during the next year, the population decreased by 8%. If the total population is 9936 at the end of the second year, then what was the population in the beginning of the first year?
A. 15000
B. 10000
C. 18000
D. 22000
Answer : B

Question. In a medical certificate, by mistake a candidate gave his height as 30% more than the actual height. In the interview panel, he clarified his height was 5 feet 6 inches. Find the approximate percentage correction made by the candidate from his stated height to his actual height.
A. 25.52%
B. 21.05%
C. 23.07%
D. 19.25%
Answer : C

Question. A trader marks his goods 25% above the cost price.
He then sells them at a discount of 25%. If the cost price is ₹ 500, then find the loss or gain percentage.
A. Loss, 5.25%
B. Gain, 5.25%
C. Gain, 7.15%
D. Loss, 6.25%
Answer : D

Question. A bill for ₹ 70 is paid by means of ₹ 10 notes and ₹ 20 notes. Five notes are used in all. If m is the number of ₹ 10 notes and n is the number of ₹ 20 notes, then _______.
A. m + n = 5, 2m + n = 8
B. m – n = 5, m + 2n = 7
C. m + n = 5, m + 2n = 7
D. m – n = 5, m + 2n = 8
Answer : C

Question. The compound interest on a certain sum for 2 years at 10% per annum is ₹ 525. Find the simple interest on the same sum for double the time at half the rate percent per annum.
A. ₹ 400
B. ₹ 500
C. ₹ 600
D. ₹ 800
Answer : B

ACHIEVERS SECTION

Question. Fill in the blanks and select the CORRECT option.
• Two cylindrical pots contain the same amount of milk. If their diameters are in the ratio
2 : 1, then the ratio of their heights is ___ P__.
• The volume of a sphere is equal to __Q___ the volume of a cylinder which has same height and diameter. (Radius of sphere = radius of cylinder)
• The slant height and base diameter of conical tomb are 25 m and 14 m respectively. The cost of white washing its curved surface at the rate of ₹ 210 per 100 m2 is ___R__.
        P          Q                 R
A. 4 : 1    half              ₹ 1100
B. 1 : 4    half              ₹ 1100
C. 1 : 4    two-third      ₹ 1155
D. 4 : 1    two-third      ₹ 1155
Answer : C

Question. If the 11 observations are 24, 17, 13, 24, 26, 20, 26, 30, 8, 41, 24, then match the following :

Answer : C

Question. Study the following statements carefully and select the CORRECT option.
Cards marked with the consecutive odd numbers from 1 to 200 are put in a box and mixed thoroughly. One card is drawn at random from the box.
Statement - 1 : Probability that drawn card is multiple of 3 is 1/2.
Statement - 2 : Probability that drawn card is a perfect square and a multiple of 9 both is 2/3.
A. Both Statement-1 and Statement-2 are true.
B. Both Statement-1 and Statement-2 are false.
C. Statement-1 is true but Statement-2 is false.
D. Statement-1 is false but Statement-2 is true. 
Answer : B

Question. Which of the following is the solution of linear equations shown here?
(i) 4x + 3y = 24
(ii) 3x – 4y = 1
(iii) 8y – 6x = 4
       (i)             (ii)           (iii)
A. (9, – 4)   (–1, –1)     (2, –2)
B. (9, 4)      (–1, –1)     (2, 2)
C. (3, 4)      (3, 2)         (2, 2)
D. (3, 4)      (–3, 2)       (2, 2)
Answer : C

Question. State T for true and F for false and select the CORRECT option. 
If 3+2√5/4 - 2√5 = p + q√5 
= p + q , where p and q are rational numbers, then values of p and q respectively are – 8 and 7/2.
Q. 2.6 − 0.82 is equal to 182/99.
R. If a = 2 +√3 + √5 and b = 3 + √3 − √5, then a² + b² – 4a – 6b – 3 is equal to 0.
S. If x = 3√5 + 2√2 and y = 3√5 − 2√2, then the value of (x² – y²)² is 240.
    P Q R S
A. T F F F
B. F F T T
C. T T F T
D. F T T F
Answer : D