CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set K

SECTION I : LOGICAL REASONING

Question. If TEMPLE is coded as VHQURL, how would you code CHURCH?
(A) EKYWIO
(B) EKUWIO
(C) EKYWIN
(D) EKYWJO
Answer : A

Question. When the following figure is folded to form a cube, how many dots would lie opposite the face bearing five dots ?

(A) 1
(B) 2
(C) 3
(D) 4
Answer : C

Question. In the given question, select a figure from amongst the four options, which when placed in the blank space of figure. (X) would complete the pattern.

Answer : B

Question. Ravi travelled 4 km straight towards South. He turned left and travelled 6 km straight, then turned right and travelled 4 km straight. How far is he from the starting point ?
(A) 8 km
(B) 10 km
(C) 12 km
(D) 18 km
Answer : B

Question. How many minimum number of straight lines are need to form this figure ?

(A) 6
(B) 11
(C) 9
(D) 10
Answer : B

Question. If ⬜ means 'greater than'; Δ means 'less than'; '–' means 'not equal to'; '+' means 'equal to', Find the relationship that can definitely be deduced on the basis of two relationship given below.
3A + 2B and B + 3C
(A) C ⬜ A
(B) 3C + 2A
(C) A ⬜ C
(D) 2C + A
Answer : D

Question. In the given question, there are seven figures, the first and last of which are unnumbered and the remaining are numbered as 1, 2, 3, 4 and 5. These seven figures form a series. However, one of the five numbered figures does not fit into the series. The number of that figure is the answer.

(A) 1 only
(B) 2 only
(C) 3 only
(D) 5 only
Answer : C

Question. In the following alphabetical series, which letter will be 10 th letter from the left of 15 th letter from the right side ?
A B C D ............ Z.
(A) U
(B) B
(C) V
(D) W
Answer : B

Question. In the given question, there is a set of five figures labelled P, Q, R, S and T called the Problem Set. Figure (R) contains a question mark. Select a suitable figure from the options which will substitute this question mark so that a series is formed by the figures P, Q, R, S and T.

Answer : C

Question. Introducing a girl, Amit said, "This girl is the wife of the grandson of my mother." How is Amit related to the girl ?
(A) Father
(B) Fatherinlaw
(C) Grandfather
(D) Husband
Answer : B

Question. Let J = 1, K = 2, L = 5, M = 7, N = 11, O = 13, P = 17. Find the letter to be inserted in the box so that the relation given below holds.
(N X ? + M ) ÷ K = 31
(A) L
(B) P
(C) J
(D) O
Answer : A

Question. If '+' denotes '=', '–' denotes '≠', '×' denotes '>', '÷' denotes '<', 'Δ' denotes '>' and '⬜' denotes '<'. a ⬜ b × c equals to
(A) a x b ÷ c
(B) a Δ b ÷ c
(C) b Δ a X c
(D) a ⬜ b Δ c
Answer : D

Question. If B says that his mother is the only daughter of A's mother, how is A related to B ?
(A) Son
(B) Father
(C) Brother
(D) Uncle
Answer : D

Question. The given question consists of four Problem Figures marked P, Q, R and S. Select a figure from the given options which will continue the series established by the four Problem Figures.

Answer : B

Question. If FLARE is coded as 21, 15, 26, 9, 22, how would BREIF be coded in the same language?
(A) 25, 9, 22, 21, 18
(B) 5, 37, 11, 19, 13
(C) 13, 19, 11, 37, 5
(D) 25, 9, 22,18, 21
Answer : D

Question. How many 3's are immediately preceded by 9 but not immediately followed by 5 in the following number series ?
934593593643933539539375759395
(A) 4
(B) 3
(C) 5
(D) 6
Answer : C

Question. Find the missing number from amongst the given options at the place of sign of interrogation (?).

(A) 10
(B) 15
(C) 20
(D) 25
Answer : B

Question. A person walks 1 mile to West, turns left and walks 1 mile and turns left and walks 1 mile, and again turns left and walks 1 mile. What is the direction he is facing now ?
(A) North
(B) South
(C) East
(D) West
Answer : A

DIRECTION (a & b) : Read the following information and then answer the questions given below :
Seven boys A, B, C, D, E, F and G are standing in a line.
(i) G is between A and E.
(ii) F and A have one boy between them.
(iii) E and C have two boys between them.
(iv) D is to the immediate right of F.
(v) C and B have three boys between them.

Question a. Who is second from left ?
(A) C
(B) G
(C) E
(D) A
Answer : C

Question b. C is standing between ____ .
(A) A and F
(B) D and G
(C) A and D
(D) F and G
Answer : A

SECTION II : MATHEMATICAL REASONING

Question. In a parallelogram ABCD, AP and CQ are drawn perpendicular to the diagonal BD. On measuring it is found that ∠PAB = 65° and ∠DAB = 75° then the measure of ∠QCD is ____ .
(A) 90°
(B) 75°
(C) 65°
(D) 10°
Answer : C

Question.

(A) 7/18
(B) 49/54
(C) 2/3
(D) 1/6
Answer : A

Question. If A = x% of y and B = y% of x, then which of the following statements is true ?
(A) A is smaller than B.
(B) Relationship between A and B cannot be determined.
(C) If x is smaller than y, then A is greater than B.
(D) None of these
Answer : D

Question. In the given figure, the sides of ΔPQR are 30 m, 24 m and 18 m and sides of ΔABC are 25 m, 24 m and 7 m as shown. Find the area of the shaded region.

(A) 132 m²
(B) 180 m²
(C) 841 m²
(D) 216 m²
Answer : A

Question. The average of first 50 natural numbers is ____ .
(A) 12. 25
(B) 21.25
(C) 25
(D) 25.5
Answer : D

Question. The average annual income (in ₹) of certain agricultural workers is S and that of other workers is T. The number of agricultural workers is 11 times that of other workers. Then the average monthly income (in ₹) of all the worker is
(A) S+T/2
(B) S+11T/2
(C) 1/11S+T
(D) 11S+T/12T
Answer : D

Question. The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. The ages of the son and the father (in years) are respectively ____ .
(A) 6 and 39
(B) 7 and 38
(C) 9 and 36
(D) 11 and 34
Answer : A

Question. Find the sum : 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132
(A) 7/8
(B) 11/12
(C) 15/16
(D) 1/12
Answer : B

Question. Mehul does not like the colour on the wooden ball he has. So he wants to scratch and remove the colour so that he can put the new one, how much area he has to scratch, if diameter of ball is r cm.
(A) 4πr² cm²
(B) πr² cm²
(C) (4/3)πr³ cm³
(D) (1/6)πr³ cm³
Answer : B

Question. Which of the following polynomials has (x + 1) as a factor?
(i) x³ + x² + x + 1
(ii) x⁴ + x³ + x² + x + 1
(iii) x⁴ + 3x³ + 3x² + x + 1
(iv) x³ – x² – (2+√2)x +√2
(A) (i)
(B) (iii)
(C) (ii) and (iv)
(D) (i) and (ii)
Answer : A

Question. If 3x – 4y + z = 7; 2x – z + 3y = 19; x + 2y + 2z = 24, then what is the value of z ?
(A) 4
(B) 5
(C) 6
(D) 8
Answer : B

Question. In a quadrilateral ABCD, bisectors of angles A, B, C and D form another quadrilateral EFGH as shown,
If ∠HEF = 70° and ∠ GHE = 80°, then ∠HGF and ∠GFE are ____ .

(A) ∠HGF = 80°, ∠GFE = 70°
(B) ∠HGF = 70°, ∠GFE = 80°
(C) ∠HGF = 110°, ∠GFE =90°
(D) ∠HGF = 110°, ∠GFE = 100°
Answer : D

Question. When a commodity is sold for ₹ 34.80, there is a loss of 25%. What is the cost price of the commodity?
(A) ₹ 26.10
(B) ₹ 43
(C) ₹ 43.20
(D) ₹ 46.40
Answer : D

Question. If O is centre of circle as shown in figure, find ∠RTQ and ∠RQT respectively.

(A) 45°, 110°
(B) 110°, 45°
(C) 100°, 50°
(D) 50°, 100°
Answer : A

Question. What is the unit digit in the product (3 ⁶⁵ x 6 ⁵⁹ x 7 ⁷¹) ?
(A) 1
(B) 2
(C) 4
(D) 6
Answer : C

Question. Reciprocal of an irrational number is ____ .
(A) An irrational number
(B) A rational number
(C) A whole number
(D) A natural number
Answer : B

Question. If a x b = ab/a+b, find the value of 3 x (3 x (– 1)).
(A) –3
(B) –1.5
(C) – 1
(D) 2/3
Answer : A

Question. Find the value of (489+375)² - (489-375)²/(489x375)´
(A) 144
(B) 864
(C) 2
(D) 4
Answer : D

Question. On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is ____ .
(A) 47619
(B) 47719
(C) 48619
(D) 47649
Answer : A

Question. Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm x  8 cm x 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use % = 3.14]
(A) 488 cm³
(B) 490 cm³
(C) 492 cm³
(D) 494 cm³
Answer : D

SECTION III : EVERYDAY MATHEMATICS

Question. P and Q started a business investing ₹ 85,000 and ₹ 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively ?
(A) 3 : 4
(B) 3 : 5
(C) 15 : 23
(D) 17 : 3
Answer : D

Question. The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A ?
(A) 12 years
(B) 24 years
(C) 6 years
(D) 7 years
Answer : A

Question. The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on ₹ 4000 for 2 years at 10% per annum. The sum placed on simple interest is ____ .
(A) ₹ 1550
(B) ₹ 1650
(C) ₹ 1750
(D) ₹ 2000
Answer : C

Question. The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is _____ .
(A) 1 : 2
(B) 2 : 3
(C) 3 : 4
(D) 3 : 5
Answer : B

Question. Income of a company doubles after every one year. If the initial income was ₹ 4 lakhs, what would be the income after 5 years?
(A) ₹ 1.24 crores
(B) ₹ 1.28 crores
(C) ₹ 2.56 crores
(D) None of these
Answer : B

Question. One diagonal of a parallelogram is 70 cm and the perpendicular distance of this diagonal from either of the outlying vertices is 27 cm. The area of the parallelogram (in sq. cm) is _____ .
(A) 1800
(B) 1836
(C) 1890
(D) 1980
Answer : C

Question. If the measured value of the radius is 1.5% larger, the percentage error (correct to one decimal place) made in calculating the volume of a sphere is _____ .
(A) 2.1
(B) 3.2
(C) 4.6
(D) 5.4
Answer : C

Question. Two dice are tossed. The probability that the sum of numbers on two dice is a prime number is ____ .
(A) 1/6
(B) 5/12
(C) 1/2
(D) 7/9
Answer : B

Question. If the volumes of two cones are in the ratio of 1 : 4 and their diameters are in the ratio of 4 : 5, then the ratio of their respective heights is _____ .
(A) 1 : 5
(B) 5 : 4
(C) 5 : 16
(D) 25 : 64
Answer : D

Question. A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10 times the original diameter, then the time required by A to go round the new path once, travelling at the same speed as before, is ____.
(A) 20 mins
(B) 25 mins
(C) 50 mins
(D) 100 mins
Answer : C