CBSE Class 8 Mathematics IMO Olympiad MCQs with Answers Set G

LOGICAL REASONING

Question. Study the following arrangement carefully and answer the question given below.
                        P5MNB3OSLJ4U@ZCSICL9AX4TU*3EM 
How many such numbers are there in the above arrangement each of which is immediately followed by'a vowel and immediately preceded by a consonant?
A. None
B. One
C. Two
D. More than two
Answer : D

Question. The question consists of a set of three figures X, Y and Z showing a sequence of folding a piece of paper.
Fig. (Z) shows the manner in which the folded paper has been cut Select the figure from the options which would most closely resembles the unfolded form of Fig (Z).

Answer : B

Question. Sonali walks 20 m North. Then she turns right and walks 30 m. Then she again turns right and walks 35 m. In which direction and how many metres away is she from her original position?
A. 15 m. West
B. 15√5 m, South-East
C. 15√5 m. South-West
D. 15√3 m. South-East
Answer : B

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

Answer : C

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 operation on numbers progress from left to right.
Rules:
(1) 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.
(ii) 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 an even number the second one is to be subtracted from the first one
(v) If an odd number is followed by a prime odd number, the first number is to be divided by the second number
12      36     31
f        11      15

If x is the resultant of the first row, then what will be the resultant of the second row7

A. 5
B. 10
C. 45
D. 75
Answer : D

Question. Select a figure from the options which is exactly embedded in Fig. (X) as one of its parts.

Answer : C

Question. In a certain code language, the word CONFUSED is Written as EMNBEFTV How will the word SECLUDED be written in that language?
A. RDBKEFEV
B. KBDRCDCT
C. KBDREFEV
D. MDFTCDCT
Answer : C

Question. Choose the box that is similar to the box formed from the given Sheet (X) of paper.

A. (1) only
B. (2) and (3) only
C. (1), (2) and (4) only
D. (1), (2), (3) and (4)
Answer : B

Question. Eight friends A, B, C, D, E, F, G and H are sitting around a circle facing the centre. E is third to the left of G, who is on the immediate right of B, who is third to the left of A. H is second to the right of F, who is not an immediate neighbour of E. D is not an immediate neighbour of B.
Which of the following pairs has the first person on the immediate left of the second person?
A. GB
B. AF
C. CE
D. HD
Answer : D

Question. Pointing to a person, Puneet said, "His only brother is the father of my daughter's father". How is the person related to Puneet ?
A. Brother
B. Father
C. Uncle
D. Father-in-law
Answer : C

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 options which will replace (?) in figure (4).

Answer : C

Question. Select a figure from the options which will replace the (?) to complete the pattern in Fig. (X).

Answer : B

Question. Which of the following Venn diagrams best illustrates the relationship amongst, "Flute, Musical instruments, Violin"?

Answer : C

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

A. 80
B. 78
C. 70
D. 68
Answer : B

Question. Select the correct mirror image from the options for the given combination of letters and numbers, if mirror is placed along MN.

Answer : D

MATHEMATICAL REASONING

Question. If the vertices and faces of a solid are 34 and 18 respectively, then find the number of edges of the solid.
A. 48
B. 50
C. 52
D. 46
Answer : B

Question. The expenditure incurred on various things during the construction of a house are given below

Which of the following pie charts exhibits the given information?

Answer : C

Question. In the given figure, line RT is drawn parallel to SQ.
If ∠QPS = 100°, ∠PQS = 40°, ∠PSR = 85° and ∠QRS = 70°, then ∠QRT = ________.

A. 45°
B. 65°
C. 85°
D. 90°
Answer : B

Question. Find the value of p from 2/x + p = 3, when
5(7x+5)/3 - 23/3 = - (4x-2/3)
A. 0
B. 1
C. 2
D. 3
Answer : B

Question. One card is drawn from a well-shuffled deck of 52 cards. Find the probability that the number on the card drawn is a multiple of 5.
A. 4/52
B. 4/13
C. 7/52
D. 2/13
Answer : D

Question. What is the least number which should be subtracted from 0.000326 to make it a perfect square ?
A. 0.000002
B. 0.000004
C. 0.02
D. 0.04
Answer : A

Question. Which of the following statements is INCORRECT?
A. If a and b are consecutive rational numbers where a < b, then a+b/2 < b.
B. x+y/2 is a rational number which lies between x and y.
C. Rational numbers are associative under subtraction.
D. The rational numbers 5/3 and -1/3 are lying on the opposite sides of '0' on the number line.
Answer : C

Question. If the height of a cylinder becomes 1/2 of the original height and the radius is doubled, then volume of cylinder becomes ________ of its original volume.
A. 2 times
B. 1/2 times
C. 1/4 times
D. 3 times
Answer : A

Question. If (a² + b²)³ = (a³ + b³)² and ab ≠ 0, then a (a/b + b/a)⁶ is equal to ________.
A. a⁶+b⁶/a³b³
B. 64/729
C. 1
D. a⁶+a³b³+b³/a²b⁴+a⁴b²
Answer : B

Question. The difference between compound interest and simple interest on a sum for 2 years at 8% p.a. is ₹ 768. Find the sum.
A. ₹ 110000
B. ₹ 120000
C. ₹ 100000
D. ₹ 170000
Answer : B

Question. The area of a quadrilateral is 342 sq. m. The perpendiculars from two of its opposite vertices to the diagonal are 12 m and 12 m. What is the length of the diagonal?
A. 28.6 m
B. 25.3 m
C. 28.5 m
D. 22.5 m
Answer : C

Question. In the given figure (not drawn to scale), ABCD is a rhombus and ALMC is a square, AC = BC. Find ∠MBC.

A. 60°
B. 75°
C. 30°
D. 45°
Answer : B

Question. Solve for x: (i) 2(x + 5) – (x – 6) = 3(x + 7) – 3
(ii) (3x + 4)² + (3x – 2)² = (6x + 5) (3x – 2) + 12
    (i)      (ii)
A. 1         2
B. –1     –2
C. 2         0
D. 0         1
Answer : B

Question. Find the total area of shaded region in the given figure.

A. 400 cm²
B. 404 cm²
C. 396 cm²
D. 275 cm²
Answer : B

Question. If in the five digit number 1b6a3, a is the greatest single digit perfect cube and twice of it exceeds b by 7, then the sum of the number and its cube root is ________.
A. 18700
B. 11862
C. 19710
D. 25320
Answer : C

Question. Select the CORRECT match

Answer : B

Direction (a - b): Study the following graph carefully and answer the questions given below:
Total number of Students Appeared and Qualified from Various Schools at a Scholarship Exam

Question. The average number of students qualified in the examination from schools C and D is what percent of the average number of students appeared for the examination from the same schools? (Rounded off to 2 digits after decimal.)
A. 58.62 %
B. 73.91 %
C. 62.58 %
D. 58.96 %
Answer : B

Question. What is the ratio of the number of students qualified in the scholarship examination from school A and the number of students qualified in the examination from school B?
A. 8 : 3
B. 5 : 7
C. 7 : 3
D. 7 : 5
Answer : D

Question. There are two boxes shown in the figure. Which box requires more amount of material to be made?

A. Box (i)
B. Box (ii)
C. Both requires equal amount of material
D. Can't be determined
Answer : B

Question. Which of the following is the net of a hexagonal prism?

Answer : A

EVERYDAY MATHEMATICS

Question. A loan was repaid in two annual instalments of ₹ 3630 each. If the rate of interest be 10% per annum compounded annually, then find the sum that was borrowed.
A. ₹ 5200
B. ₹ 6100
C. ₹ 6300
D. ₹ 5600
Answer : C

Question. The perimeter of a rectangular garden is 420 cm. If its length is increased by 20% and breadth is decreased by 40%,we get the same perimeter. Then, the length and breadth of the new formed rectangular garden, respectively are
A. 115 cm and 95 cm
B. 168 cm and 42 cm
C. 210 cm and 210 cm
D. 95 cm and 115 cm
Answer : B

Question. Sakshi sold a book for ₹ 27.50 with a profit of 10%.
If she had sold it for ₹ 25.75, then what would have been the percentage of profit or loss she earned ?
A. Profit, 3%
B. Loss, 5%
C. Profit, 5%
D. Loss, 3%
Answer : A

Question. A man bought a house for ₹ 5 lakhs and rents it. He puts 12(1/2)% of each month's rent aside for repairs, pays ₹ 1660 as annual taxes and realises 10% on his investment thereafter. What is the monthly rent of the house ?
A. ₹ 2460
B. ₹ 2500
C. ₹ 4920
D. ₹ 5000
Answer : C

Question. A group of students decided to collect as many paise from each member of the group as is the number of members. If the total collection amounts to ₹ 59.29, then the number of members in the group is _______.
A. 57
B. 67
C. 77
D. 87
Answer : C

Question. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
A. 38 L
B. 40 L
C. 39.5 L
D. 38.5 L
Answer : D

Question. Riya started a business investing ₹ 25000. After 3 months, Sneha joined her with a capital of ₹ 30,000.
At the end of the year, they made a profit of ₹ 19000.
What will be the Riya's share in the profit ?
A. ₹ 9423
B. ₹ 12500
C. ₹ 14000
D. ₹ 10000

Answer : D

Question. In a simultaneous throw of two dice, what is the probability of getting a doublet ?
A. 1/4
B. 5/6
C. 1/6
D. 2/3
Answer : C

Question. A mixture contains milk and water in the ratio 5:1.
On adding 5 litres of water, the ratio of milk to water becomes 5:2. Find the quantity of milk in the original mixture.
A. 16 litres
B. 22.75 litres
C. 25 litres
D. 32.5 litres
Answer : C

Question. The mean weight of 120 students in a class is 56 kg.
If the mean weight of boys and that of the girls in the class are 60 kg and 50 kg respectively, then the number of boys in the class are_____.
A. 72
B. 38
C. 64
D. 57
Answer : A

ACHIEVERS SECTION

Question. Find the value of P, Q, R and S respectively

      P         Q            R               S
A. 12      1526       1500       1467.25
B. 15      1496       1800       1525.38
C. 12      1496       1200       189.15
D. 12      1496       1200       1389.32
Answer : C

Question. PQRS is a rectangle of dimensions 12 cm and 5 cm.
PMNR is a rectangle drawn in such a way that the diagonal PR of the first rectangle is one of its sides and side opposite to it is touching the first rectangle at S as shown in figure. What is the ratio of the area of rectangle PQRS to that of PMNR?

A. 3 : 1
B. 2 : 3
C. 1 : 1
D. 5 : 4
Answer : C

Question. Arrange the following steps in correct order in constructing a quadrilateral PQRS, given PS = 3.2 cm, PQ = 5.6 cm, ∠P = 60°, ∠Q = 75° and ∠R = 90°.
Step 1: At Q, draw ∠YQP = 75°, so that YQ intersects MS at R.
Step 2: With P as centre and radius 3.2 cm, draw an arc to cut PX at S.
Step 3: Draw PQ = 5.6 cm.
Step 4: At P, draw ∠XPQ = 60°.
Step 5: At S, draw ∠MSP = 135°.
A. 3, 4, 1, 5, 2
B. 3, 1, 2, 5, 4
C. 3, 2, 1, 5, 4
D. 3, 4, 2, 5, 1
Answer : D

Question. Fill in the blanks.
(i) The range of the data: 15, 4, 16, 20, 5, 6, 16, 8, 2, 1, 19, 0, is ___P__.
(ii) Probability of an impossible event is ___Q__.
(iii) The number of times a particular observation occurs in given data is called ___R__.
(iv) In a single throw of two dice, the probability of getting a total of 11 is ___S__.
     P       Q           R                S
A. 18      1      frequency       1/12
B. 20      0      frequency       1/18
C. 19      0      class mark      1/9     
D. 20      1      raw data         1/18
Answer : B

Question. Read the statements carefully and select the correct option.
Statement-1: The value of

Statement-2: The expression (x–2p y3q)6 ÷ (x3 y–1)–4p, after simplification becomes independent of both x and y.
A. Both Statement-1 and Statement-2 are true.
B. Statement-1 is true but Statement-2 is false.
C. Statement-1 is false but Statement-2 is true.
D. Both Statement-1 and Statement-2 are false.
Answer : B