CBSE Class 8 Mathematics IMO Olympiad MCQs with Answers Set 15

MATHEMATICS

Question. Three different containers contain different quantities of mixtures of milk and water, whose measurements are 403 kg, 434 kg and 465 kg. What biggest measure must be there to measure all the different quantities exactly?
A. 1 kg
B. 7 kg
C. 31 kg
D. 41 kg
Answer : C

Question. Three rational numbers lying between −3/4 and 1/2 are
A.−1/2, 0, 3/4 ,
B. −1/4, 1/4, 3/4
C. −1/4, 0, 1/4,
D. −5/4, 0, 1/4
Answer : C

Question. Solve for x : x+6/x+5 - 2x-1/x-4 + x+4/x-2 = 0.
A. 3
B. –2
C. 2
D. 1
Answer : B

Direction (a and b) : Study the following graph carefully and answer the questions given below :

Question a. The total number of girls in colleges D and E together are approximately what per cent of the total number of girls in colleges A, B and C together?
A. 87%
B. 75%
C. 70%
D. 88%
Answer : A

Question b. What is the respective ratio of the number of boys in college D to the number of boys in college B?
A. 5 : 4
B. 8 : 9
C. 4 : 5
D. 9 : 8
Answer : C

Question. In the given figure (not drawn to scale), AFGB, CFE and CGD are straight lines. Find y.

A. 90°
B. 86°
C. 94°
D. 92°
Answer : C

Question. Select the correct statement.
A. A cuboid has 4 faces.
B. A cylinder has 2 flat faces.
C. A sphere has 1 vertex.
D. A cone has no vertex.
Answer : B

Question. Which of the following figures do not satisfy any of the following properties?
– All sides are equal.
– All angles are right angles.
– Opposite sides are parallel.

A. P
B. Q
C. R
D. S
Answer : A

Question. Three unbiased coins are tossed. What is the probability of getting at least two tails?
A. 1/4
B. 1/2
C. 3/8
D. 7/8
Answer : B

Question. If two quantities x and y vary directly with each other, then
A. x/y remains constant.
B. x – y remains constant.
C. x + y remains constant.
D. x × y remains constant.
Answer : A

Question. If x = 1/(3/2)^-2 x (2/3)^-4, then find the value of x^–3.
A. (2/3)¹⁰
B. (2/3)^-12
C.(2/3)^-6
D. (2/3)⁸
Answer : C

Question. The perimeters of a square and a rectangle are equal.
If their areas are respectively A m2 and B m², then which of the following is a true statement?
A. A < B
B. A ≤ B
C. A < B/2
D. None of these
Answer : D

Question. − 3/8 + 1/7 = 1/7 + (-3/8) is an example to show that
A. Addition of rational numbers is commutative.
B. Rational numbers are closed under addition.
C. Addition of rational numbers is associative.
D. Rational numbers are distributive under addition.
Answer : A

Question. In the given figure (not drawn to scale), ABC and CDEare straight lines, ∠ACE is a right angle, DF||CG||BH. Find y.

A. 62°
B. 28°
C. 52°
D. 38°
Answer : A

Question. By what least number 25920 be divided to obtain a number which is a perfect cube ?
A. 35
B. 25
C. 15
D. 5
Answer : C

Question. The greatest among (√7 − √5), (√5 − √3),(√9 − √7) and (√11 − √9) is _______.
A. (√7 − √5)
B. (√5 − √3)
C. (√9 − √7)
D. (√11 − √9)
Answer : B

Question. The value of (856+167)² + (856-167)² / 856x856+167x167 is equal to
A. 1
B. 2
C. 689
D. 1023
Answer : B

Question. If x + 0 = 0 + x = x, which is rational number, then 0 is called _____.
A. Identity for addition of rational numbers
B. Additive inverse of x
C. Multiplicative inverse of x
D. Reciprocal of x
Answer : A

Question. Solve for x : 3/x+1 - 2/x-1 = 5/x²-1
A. 10
B. 12
C. 8
D. 9
Answer : A

Question. If two quantities p and q vary inversely with each other, then
A. p/q remains constant.
B. p + q remains constant.
C. p × q remains constant.
D. p – q remains constant.
Answer : C

Question. Which of these is equal to (3)^-3 - (√81)/√25 + (√64)^-2/3/(16)^-1/4?
A. 1/54
B. − 1/54
C. 341/270
D. − 341/270
Answer : D

Question. The value of

A. –1
B. 0
C. 1
D. 1/2
Answer : C

Question. The length of a rectangular field is 11 m more than its width. If the length is decreased by 12 m and the width is increased by 10 m, the area decreases by 24 m². Find the original length and width of the field respectively.
A. 18 m, 7 m
B. 9 m, 5 m
C. 7 m, 5 m
D. 12 m, 5 m
Answer : A

Question. In the given figure (not drawn to scale), ABCD is a trapezium with AB parallel to DC, ADE is an isosceles triangle with AD = AE. Find ∠AEB and ∠EAB respectively.

A. 105°; 34°
B. 105°; 41°
C. 41°; 105°
D. 105°; 54°
Answer : B

Question. Two dice are thrown simultaneously. Find the probability of getting a multiple of 4 as the product of numbers.
A. 1/2
B. 7/12
C. 1/12
D. 5/12
Answer : D

Question. The compound interest on a sum at 12% p.a. for 2 years is ₹ 1590. What will be the simple interest on this sum?
A. ₹ 1500
B. ₹ 1540
C. ₹ 1470
D. ₹ 1530
Answer : A

Question. A machine was sold at a gain of 10%. Had it been sold at ₹ 80 less, the seller would have lost 10%.
What was the cost price of the machine?
A. ₹ 350
B. ₹ 400
C. ₹ 450
D. ₹ 520
Answer : B

Question. The areas of three adjacent faces of a cuboid are in the ratio 2 : 3 : 4 and its volume is 9000 cm3. The smallest side has a length ______.
A. 10 cm
B. 15 cm
C. 20 cm
D. 30 cm
Answer : B

Question. Which of the following is not the net of a solid?

Answer : C

Question. Which of the following statements is true? 
(i) Points (3, 4) and (4, 3) represent the same point on the graph.
(ii) The y coordinate of any point lying on the x axis will be 0.
A. only (i)
B. only (ii)
C. Both (i) and (ii)
D. Neither (i) nor (ii)
Answer : B

Question. Arrange the given steps in CORRECT order while constructing a rhombus ABCD in which diagonal AC = 6.6 cm and AB = 5 cm.
1. Join AB, BC, CD and DA.
2. Again with C as centre and radius equal to 5 cm, draw two arcs one above the line segment AC and another below the line segment AC cutting the first two arcs at point D and B respectively.
3. With A as centre and radius equal to 5 cm, draw an arc above the line segment AC and another below AC.
4. Draw AC = 6.6 cm.
5. Then, ABCD is the required rhombus.
A. 1 → 2 → 3 → 4 → 5
B. 2 → 3 → 4 → 1 → 5
C. 3 → 2 → 1 → 4 → 5
D. 4 → 3 → 2 → 1 → 5
Answer : D

Direction (a and b) : The given pie chart shows the break-up of the cost of construction of a house. Assuming that the total cost of construction is ₹ 600000, answer the questions given below.

Question a. The amount spent on cement is _____.
A. ₹ 200000
B. ₹ 160000
C. ₹ 120000
D. ₹ 100000
Answer : C

Question b. The amount spent on cement, steel and supervision is what percent of the total cost of construction?
A. 40%
B. 45%
C. 50%
D. 55%
Answer : C

Question. The figure shows a solid.

Answer : D

Question. Simplify : 3xy(9xy + 14x) – 27x²y² + 42x²y
A. 0
B. 84x²y
C. 54x²y²
D. 1
Answer : B

Question. Identify the INCORRECT step while constructing a quadrilateral ABCD, given that
AB = 4.3 cm, BC = 5 cm, CD = 4.5 cm, ∠B = 60° and ∠C = 120°.
Steps of Construction
1. Draw AB = 4.3 cm.
2. At B, draw ∠XBA = 60°.
3. With B as centre and radius equal to 5 cm, draw an arc cutting BX at C.
4. At C draw ∠YCB = 120°.
5. With C as centre and diameter equal to 4.5 cm, draw an arc cutting CY at D.
6. Join AD.
ABCD is the required quadrilateral.
A. Step 3
B. Step 4
C. Step 5
D. Both A and C
Answer : C

Question. A grocer buys 80 kg of rice at ₹ 13.50 per kg and mixes it with 120 kg of rice available at ₹ 16 per kg.
At what rate per kg should he sell the mixture to gain 20% on the whole?
A. ₹ 12
B. ₹ 18
C. ₹ 15
D. ₹ 16
Answer : B

Question. A cylinder has a diameter of 14 cm and the area of its curved surface is 220 sq. cm. The volume of the cylinder is ______. 
A. 770 cm³
B. 1000 cm³
C. 1540 cm³
D. 6622 cm³
Answer : A

Question. The point (3, 4) is at a distance of _____.
A. 3 units from both the axis
B. 4 units from both the axis
C. 4 units from the x axis and 3 units from y axis
D. 3 units from x axis and 4 units from y axis
Answer : C

Question. A rectangular block 6 cm × 12 cm × 15 cm is cut into exact number of equal cubes. The least possible number of cubes will be _______.
A. 6
B. 11
C. 33
D. 40
Answer : D

Question. In the given figure (not drawn to scale), ABCD is a parallelogram and GBEF is a rectangle. Find x and y respectively.

A. 30°, 27°
B. 30°, 23°
C. 23°, 30°
D. 30°, 21°
Answer : B

Question. Factorise : 4x² + 12xy + 9y² – 8x – 12y
A. (2x – 3y) (2x – 3y – 4)
B. (2x + 3y) (2x + 3y – 4)
C. (2x – 3y) (2x + 3y – 2)
D. (2x + 3y) (3x + 2y – 4)
Answer : B

Question. Megha plants 15376 mango trees in her garden and arranges them so that there are as many rows as there are mango trees in each row. The number of rows is
A. 124
B. 126
C. 134
D. 144
Answer : A

Question. The perimeters of a circular field and a square field are equal. If the area of the square field is 12100 m², the area of the circular field will be ______.
A. 15500 m²
B. 15400 m²
C. 15200 m²
D. 15300 m²
Answer : B

Question. In the given graph, the coordinates of point x are

A. (0, 2)
B. (2, 3)
C. (3, 2)
D. (3, 0)
Answer : C

ACHIEVERS SECTION

Question. Find the area of the following polygon, if
AL = 10 cm, AM = 20 cm, AN = 50 cm, AO = 60 cm,
AD = 90 cm, FM = 20 cm, EO = 60 cm, CN = 40 cm and BL = 30 cm.

A. 337.5 cm²
B. 384 cm²
C. 5500 cm²
D. 5050 cm²
Answer : D

Question. Quotient and remainder when x⁴ – 3x³y – 8xy³ + 8x²y² + 8y⁴ is divided by x² + 2y² – xy is
A. x² – 2xy + 4y² and 0
B. x² – 4xy + 5y² and 2
C. x² – 6xy + 4y² and –2
D. x² + 2xy – 4y² and 0
Answer : A

Question. The given question is followed by two statements. You have to study the question and the two statements given to decide which of the statement(s) is/are required to
answer the question.
What is the area of the right-angled triangle?
I. Length of the hypotenuse is 10 cm.
II. Perimeter of the triangle is four times its base.
A. Only I
B. Only II
C. Both I and II
D. Data inadequate
Answer : C

Question. The following statements are true about triangle XYZ.

• The measure of each angle is evenly divisible by 12.
The measure of angle Z is greater than the measure of angle Y.
• The measure of angle Y is greater than the measure of angle X.
• The measure of angle X is greater than 40°.
Which of the following is true for all four statements for angles X, Y and Z?
A. m∠X = 72°, m∠Y = 60°, m∠Z= 84°
B. m∠X = 48°, m∠Y = 60°, m∠Z = 84°
C. m∠X = 50°, m∠Y = 60°, m∠Z = 70°
D. m∠X = 48°, m∠Y = 60°, m∠Z = 72°
Answer : D

Question. Match the columns.

A. (i) – (a), (ii) – (b), (iii) – (c)
B. (i) – (b), (ii) – (c), (iii) – (a)
C. (i) – (c), (ii) – (a), (iii) – (b)
D. (i) – (b), (ii) – (a), (iii) – (c)
Answer : B