CBSE Class 10 Mathematics IMO Olympiad MCQs with Answers Set A

SECTION I : LOGICAL REASONING

Question. If in a certain code, 'O' is written as 'E', 'A' as 'C', 'M' as 'I', 'S' as 'O', 'N' as 'P', 'E' as 'M', 'I' as 'A', 'P' as 'N' and 'C' as 'S', then how will 'COMPANIES' be written in that code ?
(A) SEIACPAMO
(B) SMINCPAMO
(C) SEINCPAMO
(D) SEINCPMIO
Answer : C

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

(A) 20
(B) 23
(C) 25
(D) 28
Answer : B

Question. Select a figure amongst the four alternatives, which when placed in the blank space figure (X) would complete the pattern.

Answer : D

Question. B is to the South-West of A, C is to the East of B and South-East of A and D is to the North of C in line with B and A. In which direction of A is D located ?
(A) North
(B) East
(C) South-East
(D) North-East
Answer : D

Question. In the given question, there is a set of five figures labelled P, Q, R, S and T called the Problem Set. 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 : D

Question. If '¸' means '–', '–' means '´', '´' means '+' and '+' means '¸' then 20 ´ 60 ¸ 40 – 20 + 10 =
(A) 40
(B) 0
(C) 80
(D) 60
Answer : B

Question. The minimum number of straight lines required to form the given figure is ____.

(A) 13
(B) 15
(C) 12
(D) 11
Answer : D

Question. If 'W' means white, 'Y' means yellow, 'B' means black, 'G' means green, 'R' means red, which of the following will come next in the sequence given below ?
W, W Y, W Y B, W Y B G, W Y B G R, W, W Y, W Y B, W Y B __? __ .
(A) Red
(B) White
(C) Green
(D) Yellow
Answer : C

Question. The six faces of a cube have been marked with numbers 1, 2, 3, 4, 5 and 6 respectively. This cube is rolled down three times. The three positions are given in the figure below. Choose the figure that will be formed when the cube is unfolded.

Answer : C

Question. Letters of the words given below have been of jumbled up. Each letter has been numbered and each word is followed by four options. Choose the option which gives the correct order of the letters as indicated by the numbers to form words.
A M D E N R
1 2 3 4 5 6
(A) 1, 6, 2, 4, 3, 5
(B) 2, 1, 5, 3, 4, 6
(C) 3, 4, 5, 2, 1, 6
(D) 6, 4, 2, 1, 5, 3
Answer : D

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. Choose the correct option.

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

Question. In a certain code 'STREAM' is written as 'QSRNBF' and 'SUPERB' is written as 'OTRCSF'. How is 'BORING' written in that code ?
(A) QNAHOJ
(B) CPSJOH
(C) QNAOJH
(D) ANQJOH
Answer : A

Question. The given question consists of four figures marked (i), (ii), (iii) and (iv) called the Problem figures. Select a figure from the options which will continue the same series as established by the four problem figures.

Answer : A

Question. Introducing a man, Neeraj said, "His wife is the only daughter of my wife." How is Neeraj related to that man ?
(A) Father
(B) Grandfather
(C) Fatherinlaw
(D) Son
Answer : C

Question. A matrix of certain characters is given. These characters follow a certain trend row wise or column wise. Find the missing number.

(A) 13 11
(B) 15
(C) 16
(D) 9
Answer : C

Question. Choose the option which shows common feature in the relationship given.
Slap : Hit : Kick
(A) Each has no vowel
(B) They are the ways of striking a person
(C) They are exercises
(D) The terms are used in wrestling
Answer : B

Question. In a school, the following codes were used during physical exercise period. '1' means "start walking", '2' means "keep standing", '3' means "start running at the same stop", '4' means "sit down". How many times will a student who performs the following sequence without error from the beginning to the end has to start walking ?
1 2 3 4 2 3 2 4 4 3 2 2 1 2 4 3 1 4 4 1 2 3 1 1 4
(A) 6
(B) 7
(C) 4
(D) 5
Answer : D

DIRECTION (a & b) : The above building plan shows an office block for six officers A, B, C, D, E and F. Both B and C occupy offices to the right of the corridor (as one enters the office block) and A occupies an office to the left of the corridor. E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F's office is further down the corridor than A's, but on the same side.

Question a. If E sits in his office and faces the corridor, whose office is to his left ?
(A) A
(B) B
(C) C
(D) D
Answer : C

Question b. Whose office faces A's office ?
(A) B
(B) C
(C) D
(D) E
Answer : D

Question. Who is/are F's neighbour(s) ?
(A) A only
(B) A and D
(C) C only
(D) B and C
Answer : A

SECTION II : MATHEMATICAL REASONING

Question. If a, b are the roots of the equation √x² + x a + b = 0, then values of a and b are _____ .
(A) a = 1, b = 1
(B) a = 1, b = –2
(C) a = 2, b = 1
(D) a = 2, b = 2
Answer : B

Question. If a square and rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is _____ .
(A) Greater than 1
(B) Equal to 1
(C) Equal to 1/2
(D) Equal to 1/4
Answer : B

Question. In the given figure, AD = 4 cm, BD = 3 cm and CB = 12 cm. Find cot θ.

(A) 12
(B) 4/3
(C) 4/5
(D) 12/5
Answer : D

Question. The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at ____ .
(A) (0, 13)
(B) (0, –13)
(C) (0, 12)
(D) (13, 0)
Answer : A

Question. How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length ?
(A) 9.8 secs
(B) 12.1 secs
(C) 12.42 secs
(D) 14.3 secs
Answer : B

Question. Calculate the area of the designed region in figure common between the two quadrants of circles of radius 8 cm each.

(A) 32 cm²
(B) (256/7) cm²
(C) 182 cm²
(D) (352/7) cm²
Answer : B

Question. The value of 0.0396 ÷ 2.51 correct to 2 significant figures is ____ .
(A) 0.015
(B) 0.0157
(C) 0.016
(D) 0.017
Answer : C

Question. A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower (approximately) ?
(A) 14 mins 35 secs
(B) 15 mins 49 secs
(C) 16 mins 26 secs
(D) 18 mins 5 secs
Answer : C

Question. Find the diameter of a wheel that makes 113 revolutions to go 2 km 26 decametres.
(A) 4(4/13)metres
(B) 6(4/11)metres
(C) 12(4/11)metres
(D) 12(8/11)metres
Answer : B

Question. If r is the ratio of the roots of the equation ax² + bx + c = 0, then (r+1)²/r =
(A) 1
(B) b²/ac
(C) ac/b²
(D) b² – 4ac
Answer : B

Question. In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors of 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been _____.
(A) 24
(B) 144
(C) 292
(D) 584
Answer : D

Question. If √5+1/√5-1 and b = √5-1/√5+1, the value of (a²+ab+b²/a²-ab+b²) is ____ .
(A) 3/4
(B) 4/3
(C) 3/5
(D) 5/3
Answer : B

Question. Find the least multiple of 23, which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively.
(A) 3002
(B) 3013
(C) 3024
(D) 3036
Answer : B

Question. Twothird of a positive number and 25/216 of its reciprocal are equal. The number is ____.
(A) 5/12
(B) 12/5
(C) 25/144
(D) 144/25
Answer : A

Question. What is the unit digit in {( 6374)¹⁷⁹³ X (625)³¹⁷ X (341)⁴⁹¹} ?
(A) 0
(B) 2
(C) 3
(D) 5
Answer : A

Question. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?
(A) 1/2
(B) 3/4
(C) 3/8
(D) 5/16
Answer : B

Question. The value of (0.2 + 0.3 + 0.4 + 0.9 + 0.39) is
(A) 0.57
(B) 1(20/33)
(C) 2(1/3)
(D) 2(13/33)
Answer : D

Question. A computer is available for ₹ 39, 000 cash or ₹ 17, 000 as cash down payment followed by 5 monthly installments of ₹ 4, 800 each. Bank also gives loan at the rate of 24% per annum to purchase the computer. Which option is better ?
(A) Full cash payment
(B) Payment in Installments
(C) Both are equal
(D) Can't be determined
Answer : A

Question. It costs ₹ x each to make the first thousand copies of a compact disc and ₹ y to make each subsequent copy. If z is greater than 1000, how much will it cost to make z copies of the compact disc ?
(A) zx – zy
(B) 1000x + yz
(C) 1000 (x – y) + yz
(D) 100 (z – y) + xz
Answer : C

Question. In the given figure, ABCD is a rectangle in which line segments AP and AQ are drawn as shown. Find the length of (AP + AQ).

(A) 60 cm
(B) 30 cm
(C) 180 cm
(D) 120 cm
Answer : C

SECTION III : EVERYDAY MATHEMATICS

Question. 200 logs are stacked in the following manner : 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows 200 logs are placed and how many logs are in the top row respectively ?

(A) 25, 4
(B) 18, 12
(C) 15, 3
(D) 16, 5
Answer : D

Question. The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq. metres, its volume is _____ .
(A) 3180 m³
(B) 4620 m³
(C) 5240 m³
(D) 3250 m³
Answer : B

Question. Priyansh speaks truth in 75% cases and Mohit in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident ?
(A) 5%
(B) 15%
(C) 35%
(D) 45%
Answer : C

Question. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was ₹ 4.20 and that of Y was ₹ 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?
(A) 2010
(B) 2011
(C) 2012
(D) 2013
Answer : B

Question. Ankit, Armaan and Abhay start at the same time in the same direction to run around a circular stadium. Ankit completes a round in 252 seconds, Armaan in 308 seconds and Abhay in 198 seconds, all starting at the same point. After what time will they meet again at the starting point ?
(A) 26 minutes 18 seconds
(B) 42 minutes 36 seconds
(C) 45 minutes
(D) 46 minutes 12 seconds
Answer : D

Question. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is ____.
(A) 400 kg
(B) 560 kg
(C) 600 kg
(D) 640 kg
Answer : C

Question. A man at the top of a tower is watching a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 60 metres from tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water ?
(A) 32 km/hr
(B) 36 km/hr
(C) 38 km/hr
(D) 40 km/hr
Answer : A

Question. Water boils at 212°F or 100°C and melts at 32°F or 0°C. If the temperature of a particular day is 35°C, it is equivalent to _____.
(A) 85°F
(B) 90°F
(C) 95°F
(D) 99°F
Answer : C

Question. How many pieces of 85 cm length can be cut from a rod 42.5 metres long ?
(A) 30
(B) 50
(C) 60
(D) 40
Answer : B

Question. A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq. feet per day, then approximately what time will be taken by the cow to graze the whole field ?
(A) 2 days
(B) 6 days
(C) 18 days
(D) 24 days
Answer : B