CBSE Class 10 Mathematics IMO Olympiad MCQs with Answers Set C

SECTION-I : LOGICAL REASONING

Question. Study the following information carefully to answer the given question.
M K K I D N E T T Q O B F H A A G T U U X W L S R I
Each of these letters gets a numerical value based on its position in the above arrangement, such as, 1 for M, 2 for K, 4 for I and so on.
Value of A is exactly equal to the total value of which of the following pairs?
(i) DO (ii) QE (iii) MH
(A) Only (i)
(B) Only (ii)
(C) Only (iii)
(D) Both (i) and (ii)
Answer : C

Question. Seven villages A, B, C, D, E, F and G are situated as follows: E is 2 km to the west of B. F is 2 km to the north of A. C is 1 km to the west of A. D is 2 km to the south of G. G is 2 km to the east of C. D is exactly in the middle of B and E.
How far is E from F (in km)?
(A) 4
(B) 20
(C) 5
(D) 26
Answer : A

Question. In the given diagram, the circle stands for educated, square for hard-working, triangle for urban and the rectangle for honest people. Different regions in the diagram are numbered from 1 to 12. Region 4 is best described as consisting of ______.

(A) People who are non-urban, honest, uneducated and hard-working.
(B) People who are uneducated, urban, honest and hard-working.
(C) People who are uneducated, urban, hard-working and dishonest.
(D) People who are urban, hard-working, honest and educated.
Answer : B

Question. Read the following information carefully to answer the given question.
Fifty books belonging to different subjects, viz. History (8), Geography (7), Literature (13), Psychology (8) and Science (14), are placed on a shelf. They are arranged in an alphabetical order subject to the condition that no two books of the same subject are placed together so long as books of other subjects are available. Unless otherwise mentioned, all counting is done from the left.
Counting from the right end, the fifth book from the right of 39th book is ______.
(A) History
(B) Psychology
(C) Geography
(D) Science
Answer : A

Question. If the word TERMINATION is coded as 12345671586, what should be the code for the word MOTION?
(A) 438586
(B) 458586
(C) 481586
(D) 485186
Answer : C

Question. Read the following information carefully and answer the question given below it .
(i) A, B, C, D and E are five friends. (ii) B is elder to E, but not as tall as C.
(iii) C is younger to A, and is taller to D and E. (iv) A is taller to D, but younger than E.
(v) D is elder to A but is shortest in the group.
Which of the following statements is correct about B?
(i) B is not the tallest.
(ii) B is shorter to E.
(iii) When they are asked to stand in ascending order with respect to their heights, B is in the middle.
(A) Only (i)
(B) Only (i) and (ii)
(C) (i), (ii) and (iii)
(D) All are incorrect
Answer : A

Question. Pointing to a photograph, a person tells his friend, "She is the grand daughter of the elder brother of my father." How is the girl in the photograph related to this man?
(A) Niece
(B) Sister
(C) Aunt
(D) Sister-in-law
Answer : A

Question. Study the following information and answer the question given below it.
The admission ticket for an exhibition bears a password which is changed after every clock hour based on set of words chosen for each day. The following is an illustration of the code and steps of rearrangement for subsequent clock hours. The time is 9 a.m. to 3 p.m.
Batch I (9 a.m. to 10 a.m.) : is not ready cloth simple harmony burning
Batch II (10 a.m. to 11 a.m.) : ready not is cloth burning harmony simple
Batch III (11 a.m. to 12 noon) : cloth is not ready simple harmony burning
Batch IV (12 noon to 1 p.m.) : not is cloth ready burning harmony simple
Batch V (1 p.m. to 2 p.m.) : ready cloth is not simple harmony burning
Batch VI (2 p.m. to 3 p.m.) : is cloth ready not burning harmony simple
If the password for Batch I was – 'rate go long top we let have', which batch will have the password–'go rate top long have let we'?
(A) II
(B) III
(C) IV
(D) V
Answer : C

Question. N ranks fifth in a class. S is eighth from the last. If T is sixth after N and just in the middle of N and S, then how many students are there in the class?
(A) 23
(B) 24
(C) 25
(D) 26
Answer : B

Question. Which one of the four interchanges in signs and numbers would make the given equation correct ?
4 × 6 – 2 = 14
(A) × to ÷, 2 and 4
(B) – to ÷ , 2 and 6
(C) – to +, 2 and 6
(D) × to +, 4 and 6
Answer : C

Question. A total of 324 coins of 20 paise and 25 paise make a sum of ₹ 71. The number of 25 paise coins is _______.
(A) 120
(B) 124
(C) 144
(D) 200
Answer : B

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

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
(B) 2
(C) 4
(D) 5
Answer : D

Question. There is a set of five figures labelled P, Q, R, S and T called the Problem figures. Fig. (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 taken in order.

Answer : C

Question. There is a definite relationship between figures P and R. Establish a similar relationship between figures Q and S by selecting a suitable figure from the options that would replace the question mark (?) in fig. (S).

Answer : A

Question. Which term comes next in the given series?
AC, FH, KM, PR, ?
(A) UW
(B) VW
(C) UX
(D) TV
Answer : A

Question. Count the number of pentagons in the given figure.

(A) 16
(B) 12
(C) 8
(D) 4
Answer : B

Question. Choose the correct mirror-image of the Fig. (X) from amongst the four options given along with it, if the mirror is placed along M1 M2.

Answer : B

Question. A cube, painted yellow on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only ?
(A) 1
(B) 6
(C) 8
(D) 12
Answer : B

Question. Find out which of the options will complete the figure matrix.

Answer : A

SECTION-II : MATHEMATICAL REASONING

Question. The value of

(A) 7/8
(B) 0
(C) 11/16
(D) 1
Answer : B

Question. If ax – 1 = bc, by – 1 = ca and cz – 1 = ab then xy + yz + zx = ______.
(A) xyz
(B) x²y²z²
(C) 2xyz
(D) 1/(xyz)
Answer : A

Question. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs ₹ 216 and one full and one half reserved first class tickets cost ₹ 327. What is the cost of basic first class full fare and the reservation charge?
(A) ₹ 105 and ₹ 6
(B) ₹ 216 and ₹ 12
(C) ₹ 210 and ₹ 12
(D) ₹ 210 and ₹ 6
Answer : D

Question. If p and q are the roots of the equation x² – bx + c = 0, then what is the equation if the roots are (pq + p + q) and (pq – p – q)?
(A) x² – 2cx + (c² – b²) = 0
(B) x² – 2bx + (b² + c²) = 0
(C) 3cx² – 2(b + cx + c²) = 0
(D) x² + 2bx – (c² – b²) = 0
Answer : A

Question. Given intersecting chords, find x.

(A) 20°
(B) 40°
(C) 60°
(D) 80°
Answer : C

Question. If ABC is a right angled triangle with ∠A = 90° and 2s = a + b + c, where a > b > c and notations have their usual meanings, then which one of the following is correct?
(A) (s – b) (s – c) > s(s – a)
(B) (s – a) (s – c) > s(s – b)
(C) (s – a) (s – b) < s(s – c)
(D) 4s(s – a) (s – b) (s – c) = bc
Answer : C

Question. Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at random from the basket. Which of the following is the probability that the fruit is an apple?
(A) 0.32
(B) 0.4
(C) 0.46
(D) 0.58
Answer : D

Question. A is three times as old as B. Four years ago, C was twice as old as A. In four years time, A will be 31. What are the present ages of B and C respectively?
(A) 9, 46
(B) 9, 50
(C) 10, 46
(D) 10, 50
Answer : B

Question. If α , β and γ are in A.P., then cot β = _______.
(A) sin α - sin γ/cos γ - cos α
(B) sin γ - sin α/cos γ - cos α
(C) sin α - sin γ/2(cos α - cos γ)
(D) 2(sin γ - sin α)/cos γ - cos α
Answer : A

Question. Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
(A) 60 mins 15 secs
(B) 50 mins 15 secs
(C) 51 mins 12 secs
(D) 49 mins 8 secs
Answer : C

Question. Points A, B, C and D are midpoints of the sides of square JETS. If the area of JETS is 36 sq. cm, then the area of ABCD is ________.

(A) 3 sq. cm
(B) 7.5 sq. cm
(C) 9 sq. cm
(D) 18 sq. cm
Answer : D

Question. The mean of 1, 3, 4, 5, 7 and 4 is m. The numbers 3, 2, 2, 4, 3, 3 and p have mean m – 1 and median q, then p + q = ______.
(A) 7
(B) 6
(C) 5
(D) 4
Answer : A

Question. What approximate value should come in place of the question mark (?) in the following equation?
158.25 × 4.6 + 21% of 847 + ? = 950.935045
(A) 35
(B) 44
(C) 50
(D) 45
Answer : D

Question. If the ratio of mean and median of a certain data is 2 : 3, then find the ratio of its mode and mean.
(A) 2 : 5
(B) 3 : 2
(C) 5 : 2
(D) 1 : 2
Answer : C

Question. In the given diagram, ABCD is a square, diagonal BD is extended through D to E. AD = DE and AE is drawn. What is m∠DAE?

(A) 22.5°
(B) 45°
(C) 112.5°
(D) 135°
Answer : A

Question. What is the probability of getting at least one six in a single throw of three unbiased dice?
(A) 1/6
(B) 125/216
(C) 1/36
(D) 91/216
Answer : D

Question. ABC is a right angled triangle, right angled at A. A circle is inscribed in it and the lengths of the two sides containing the right angle are 12 cm and 16 cm. Find the area of the circle.
(A) 25.56 sq. cm
(B) 50.28 sq. cm
(C) 75.65 sq. cm
(D) 20.34 sq. cm
Answer : B

Question. A person of height 2 m wants to get a fruit which is on the top of a pole of height 10/3 m if he stands at distance of (4/√3) m from the foot of the pole, then the angle at which he should throw the stone, so that it hits the fruit is _____.
(A) 15°
(B) 30°
(C) 45°
(D) 60°
Answer : B

Question. The point (–4, –2) lies on a circle. What is the length of the radius of this circle, if the centre is located at (–8, –10)?
(A) 48
(B) 80
(C) 108
(D) 288
Answer : B

Question. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is ______.
(A) 15360
(B) 153600
(C) 30720
(D) 307200
Answer : B

SECTION-III : EVERYD AY MATHEMATICS

Question. In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is ______.
(A) 20 m
(B) 22 m
(C) 24 m
(D) 26 m
Answer : B

Question. 3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is _____.
(A) 1 year
(B) (11/2)years
(C) 2 years
(D) 3 years
Answer : C

Question. Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's sister is ______.
(A) 32 years
(B) 36 years
(C) 38 years
(D) 40 years
Answer : C

Question. In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 95 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class?
(A) 65.5
(B) 72.5
(C) 75
(D) 85
Answer : C

Question. Padma purchased 30 kg of rice at the rate of ₹ 17.50 per kg and another 30 kg rice at a certain rate. She mixed the two and sold the entire quantity at the rate of ₹ 18.60 per kg and made 20% overall profit. At what price per kg did she purchase the lot of another 30 kg rice?
(A) ₹ 12.50
(B) ₹ 13.50
(C) ₹ 14.50
(D) ₹ 15.50
Answer : B

Question. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
(A) 5 : 7 : 8
(B) 28 : 49 : 64
(C) 38 : 28 : 21
(D) None of these
Answer : D

Question. Simi can do a work in 3 days, while Meeta can do the same work in 2 days. Both of them finish the work together and get ₹ 150. What is the share of Simi?
(A) ₹ 30
(B) ₹ 60
(C) ₹ 70
(D) ₹ 75
Answer : B

Question. A bicycle can be purchased on cash payment of ₹ 1500. The same bicycle can also be purchased at the down payment (initial payment, at the time of purchasing) of ₹ 350 and rest can be paid in 3 equal installments of ₹ 400 for next 3 months. The rate of SI per annum charged by the dealer is _____.
(A) 23(9/17)%
(B) 17(9/23)%
(C) 13(9/17)%
(D) None of these
Answer : D

Question. The question given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
A solid metallic cone is melted and recast into a sphere. What is the radius of the sphere?
I . The radius of the base of the cone is 2.1 cm.
II . The height of the cone is four times the radius of its base.
III . The height of cone is 8.4 cm.
(A) Only I and II
(B) Only II and III
(C) Only I and III
(D) Any two of three
Answer : D

Question. Yash invested a certain sum of money at 8% p.a. simple interest for ‘n’ years. At the end of ‘n’ years, Yash got back 4 times his original investment. What is the value of n?
(A) 50 years
(B) 25 years
(C) 12 years 6 months
(D) 37 years 6 months
Answer : D