CBSE Class 8 Mathematics IMO Olympiad MCQs with Answers Set 04

LOGICAL REASONING

Question. How many such numbers are there in the given arrangement, each of which is immediately preceded by a consonant and immediately followed by a vowel?
M % R 4 A T # J @ 7 D 5 © I F N 1 E $ 3 6 W U 2 H 8 * K 9 B Q
A. None
B. One
C. Two
D. Three
Answer : C

Question. If ‘*’ means ‘×’, ‘$’ means ‘+’, ‘#’ means ‘÷’ and ‘©’ means ‘–’, then what is the value of 360 # 24 $ 56 * 5 © 48 ?
A. 253
B. 242
C. 247
D. 285
Answer : C

Question. If all the digits are arranged in ascending order from left to right, while the other elements in the arrangement remain unchanged, which of the following will be fourteenth from the left end?
A E C B % 7 D $ E B 5 C ? 3 D E 9 @ 2 #
A. 2
B. 5
C. 3
D. 7
Answer : B

Question. If the animals which can walk are called swimmers, animals who crawl are called flyers, those living in water are called snakes and those which fly in the sky are called hunters, then what will a lizard be called?
A. Swimmers
B. Snakes
C. Flyers
D. Hunters
Answer : C

Question. Sunil Gavaskar was once asked to compare the battings of Sachin Tendulkar, Ravi Shastri, Rahul Dravid and Virender Sehwag. Gavaskar compared them and noted that
(i) each of the four players has a particular style of play: offensive, technically sound, stylish and perfectionist.
(ii) each of these players was famous for a particular shot: flick, cover drive, straight drive, square cut.
The final tally made by Gavaskar was lost. But he remembers that
(iii) Tendulkar was most famous for straight drive.
(iv) Neither Shastri nor Sehwag were technically sound.
(v) The batsman who is perfectionist is famous for his flick.
(vi) Sehwag is famous for square cuts.
(vii) Dravid has an offensive style.
Which of the following matches correctly a batsman with his famous shot and his batting style?
A. Dravid - cover drive - technically sound
B. Tendulkar - straight drive - stylish
C. Shastri - flick - perfectionist
D. Sehwag - cover drive - perfectionist
Answer : C

Question. Pointing to a man in a photograph, a woman says, “He is the only son of the only daughter-in-law of my only son’s father.” How is the man related to the woman?
A. Son
B. Father
C. Son-in-law
D. Grandson
Answer : D

Question. In the given figure, the triangle represents the students who passed in Physics, the rectangle represents the students who passed in Chemistry and the circle represents the students who passed in Mathematics in a class.

How many students passed in Mathematics only?
A. 3
B. 5
C. 4
D. 11
Answer : B

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

A. 585
B. 587
C. 755
D. 775
Answer : A

Question. Which of the following shows the correct net of the solid shown below?

Answer : C

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

Answer : B

Question. In which of the following options Fig. (X) is exactly embedded as one of its part?

Answer : D

Question. Select the correct mirror image of given combination, if the mirror is placed along MN.

Answer : B

Question. Select the odd one out.

Answer : D

Question. Which of the following options satisfies the same condition of placement of dots as in Fig. (X)?

Answer : A

Question. Select a figure from the options which will complete the series as established by the problem Figures.

Answer : A

MATHEMATICAL REASONING

Question. In the pentagon ABCDE, ∠ADE = 18°. If BC = CD, find ∠EDC and ∠CDB respectively.

A. 153°, 45°
B. 156°, 48°
C. 48°, 156°
D. 45°, 153°
Answer : A

Question. Solve : 0 1/2 x-5(02x - 2/25)= 3x
A. 1/35
B. 4/79
C. 2/35
D. 8/79
Answer : D

Question. Which of the following is CORRECT?
A. Addition is commutative for rational numbers.
B. Subtraction is commutative for rational numbers.
C. Multiplication is not commutative for rational numbers.
D. Division is commutative for rational numbers.
Answer : A

Question. The figure below shows a solid.

It has _____ rectangular faces, _____ triangular faces, _____ vertices and _____ edges.
A. 2, 3, 6, 9
B. 2, 3, 9, 6
C. 3, 2, 9, 6
D. 3, 2, 6, 9
Answer : D

Question. A die is rolled once. Find the probability that the number on the uppermost face will be
(a) 5
(b) not 5
     (a)         (b)
A. 5/6         1/6
B. 1/2         3/2
C. 1/6         5/6
D. 3/4         1/4
Answer : C

Question. In the given figure, the side of the square ABPQ is 10 cm. EF = 2.5 cm, C and D are halfway between the top and bottom sides of the figure. What is the area of the shaded portion?

A. 41.82 cm²
B. 43.75 cm²
C. 46.70 cm²
D. None of these
Answer : B

Question. Which of the following steps is INCORRECT while constructing a quadrilateral ABCD in which AB = 4.6 cm, BC = 5.3 cm, ∠A = 60°, ∠B = 100° and ∠C = 120°.
Steps of construction :
Step I : Draw AB = 4.6 cm.
Step II : Draw BC = 5.3 cm, making ∠BAC = 100°.
Step III : Draw CX making ∠BDC = 120°.
Step IV : At A draw a line AD making ∠BAD = 60° and meeting CX at D.
Then ABCD is the required quadrilateral.
A. Only Step II
B. Only Step III
C. Both Step I and Step II
D. Both Step II and Step III
Answer : D

Question. Given that (3x – 1)(x + p) = 3x² + qx – 2, find the value of p + q – pq.
A. 3
B. 4
C. –3
D. –5
Answer : C

Question. Evaluate : 3√0.729 ÷ √0.0009 × (0.25)^1/2 − 3√3.375
A. 135
B. 1.35
C. 0.135
D. 13.5
Answer : D

Question. The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides of the polygon.
A. 10
B. 36
C. 6
D. 3
Answer : A

Question. The pie chart below shows the number of students attending a poetry recital. If there were 105 Primary 5 students, how many students attended the poetry recital in all?

A. 400
B. 500
C. 600
D. 700
Answer : B

Question. Find the sum of p, q, r and s.

A. 90°
B. 110°
C. 200°
D. 210°
Answer : C

Question. Number of prime factors in 6¹² x (35)²⁸ x (15)¹⁶ / (14)¹² x (21)¹¹ is
A. 56
B. 66
C. 112
D. None of these
Answer : B

Question. Find the area of square whose diagonals are of length 12 cm.
A. 82 cm²
B. 72 cm²
C. 136 cm²
D. 75 cm²
Answer : B

Question. Which of the following expression has (7p – q – 3r) as one of its factors?
A. 49p² – q² – 9r² – 14pq
B. p² + 49q² – 9r² – 14pq
C. 49p² + q² – 9r² + 14pq
D. 49p² + q² – 9r² – 14pq
Answer : D

Question. What is the least number which when divided by 5, 6, 8, 9, 12 gives remainder 1 in each case and exactly divisible by 13?
A. 361
B. 721
C. 1801
D. 3601
Answer : D

Question. Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 33957. The numbers are _____.
A. 14, 21, 28
B. 12, 15, 17
C. 14, 18, 21
D. 21, 28, 32
Answer : A

Question. If x - 1/x = 3, then find the value of x⁴ + 1/x⁴
A. 121
B. 119
C. 117
D. 101
Answer : B

Question. Which of the following is FALSE?
A. A quadrilateral is a rectangle if its opposite sides are equal and its diagonals are equal.
B. A quadrilateral is a square if its all sides are equal and the diagonals are equal.
C. A quadrilateral is a parallelogram but not a rectangle, if its opposite sides are equal but the diagonals are not equal.
D. A quadrilateral is a rhombus but not a square if its all sides are equal and the diagonals are also equal.
Answer : D

Question. The figure below is made up of a triangle, a rhombus and a parallelogram. BCF, ICE and HCD are straight lines. If ∠CIA = 128° and ∠FGH = 50°, then find ∠ECD.

A. 78°
B. 52°
C. 50°
D. 128°
Answer : A

EVERYDAY MATHEMATICS

Question. The perimeter of floor of a rectangular hall is 250 m.
If its height is 6 m, find the cost of painting its four walls at the rate of ₹ 20 per m².
A. ₹ 95000
B. ₹ 65000
C. ₹ 50000
D. ₹ 30000
Answer : D

Question. Rita and Mita together can do a work in 4 days. Rita alone takes 6 days to do the same work. In how many days can Mita alone do the work?
A. 10
B. 8
C. 14
D. 12
Answer : D

Question. A school collected ₹ 2,02,500 as fees from students. 
If each student paid as much money as there were students, find the number of students in the school.
A. 210
B. 320
C. 250
D. 450
Answer : D

Question. Two-thirds of a consignment was sold at a profit of 6% and the rest at a loss of 3%. If there was an overall profit of ₹ 540, the value of the consignment was _______.
A. ₹ 15000
B. ₹ 16000
C. ₹ 18000
D. None of these
Answer : C

Question. Find the sum of money invested, if the difference between simple and compound interest (compounded annually) on the sum of money for 2 years at 10% per annum is ₹ 65.
A. ₹ 6500
B. ₹ 6565
C. ₹ 65065
D. ₹ 65650
Answer : A

Question. One litre of water is evaporated from 6 litres of a solution containing 5% salt. The percentage of salt in the remaining solution is
A. 4(4/9)%
B. 5(5/7)%
C. 5%
D. 6%
Answer : D

Question. 10 years ago, Simran's mother was four times older than Simran. After 10 years, the mother will be twice older than the daughter. The present age of Simran is
A. 5 years
B. 10 years
C. 20 years
D. 30 years
Answer : C

Question. The ratio of the perimeter of a rectangular field to the perimeter of a triangular field is 5 : 3. The breadth of the rectangular field is half its length and the sum of the length and the breadth of the rectangular field is 75 cm. Find the perimeter of the triangular field.
A. 40 cm
B. 60 cm
C. 90 cm
D. 110 cm
Answer : C

Question. A man constructed a room. The area of four walls of the room is 57.4 m². If the room is 5 m long and 3.2 m wide, find the volume of the room.
A. 74 m³
B. 42 m³
C. 56 m³
D. 65 m³
Answer : C

Question. What is the greatest possible length of a scale that can be used to measure exactly the rods of lengths 3 m, 5 m 10 cm and 12 m 90 cm?
A. 10 cm
B. 20 cm
C. 25 cm
D. 30 cm
Answer : D

ACHIEVERS SECTION

Question. Study the following statements carefully.
Statement I : The simplest form of
(−3/2 x 4/5) + (9/5 x -10/3) - (1/2 x 3/4) is 7(23/40)
Statement II : When denominator is positive integer and H.C.F. of numerator and denominator is more than
1, then rational number is in standard form.
A. Both Statement I and Statement II are true.
B. Both Statement I and Statement II are false.
C. Statement I is true, Statement II is false.
D. Statement I is false, Statement II is true.
Answer : B

Question. In the given figure (not drawn to scale), if ABCD is a parallelogram, then find
(i) a + b
(ii) c + d
(iii) a + b + c + d + e

       (i)           (ii)          (iii)
A. 100°        120°        280°
B. 120°        180°        270°
C. 100°        100°        280°
D. 150°        130°        270°
Answer : C

Question. Match the Columns

A. (i) → (r), (ii) → (s), (iii) → (p), (iv) → (q)
B. (i) → (r), (ii) → (q), (iii) → (s), (iv) → (p)
C. (i) → (q), (ii) → (p), (iii) → (s), (iv) → (r)
D. (i) → (s), (ii) → (r), (iii) → (p), (iv) → (q)
Answer : A

Question. Fill in the blanks.
The diagonals of a rectangle are __P__ in length.
A square is a __Q__ with equal sides.
Also, the diagonals of a square are __R__ of each other.
         P                   Q                                R
A. Equal          Rectangle          Perpendicular bisector
B. Equal          Trapezium         Perpendicular bisector
C. Not equal    Polygon            Perpendicular bisector
D. Not equal    Kite                   Perpendicular bisector
Answer : A

Question. Study the bar graph and answer the following questions.

(a) How many students are interested in music and drama clubs altogether?
(b) How many more students are there in the literary club as compared to the debating club?
    (a)     (b)
A. 80     20
B. 80     10
C. 90     30
D. 80     30
Answer : B