CBSE Class 10 Mathematics IMO Olympiad MCQs with Answers Set D

LOGICAL REASONING

Question. There are five persons P, Q, R, S and T. One is a football player, one is a chess player and one is a hockey player. P and S are unmarried ladies and do not participate in any game. None of the ladies plays chess or football. There is a married couple in which T is the husband. Q is the brother of R and is neither a chess player nor a hockey player. Who is the football player?
A. P
B. Q
C. R
D. S
Answer : B

Question. How many such pairs of digits are there in the number 95137248 each of which has as many digits between them in the number as when they are arranged in ascending order?
A. None
B. One
C. Two
D. Three
Answer : D

Question. In a certain code language, 'bring the white board' is written as 'ka na di pa' and 'white and black board' is written as 'na di sa ra'. How is 'the' written in that code?
A. ka
B. pa
C. ka or pa
D. None of these
Answer : C

Question. Read the following information and answer the question given below it.
(i) L, M, N, O, P, Q, R and S are sitting around a circle facing the centre.
(ii) N, who is third to the left of P, is not a neighbour of R and M.
(iii) S is the neighbour of ‘O’ and ‘R’ and is third to the right of M.
(iv) L is not the neighbour of O, who is second to the left of N.
What is the position of Q?
A. Immediate right of R
B. Immediate left of N
C. Third to the right of M
D. Second to the left of S
Answer : B

Question. Two different positions of the same dice has been shown below. If digit 1 is on the top what will come just below it?

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

Question. Figures (i) and (ii) of the Problem Set bears a certain relationship. Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that would replace the question mark in fig.(iv).

Answer : C

Question. If 'tall' is equivalent to 'circle', 'army men' to 'triangle' and 'strong' to 'square', indicate which number will represent only strong army men?

A. 3
B. 4
C. 5
D. 6
Answer : B

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

Answer : D

Question. Three of the following four are alike in a certain way and so form a group. Which is the one that does not belong to that group?
A. 215
B. 247
C. 91
D. 65
Answer : A

Question. Group the given figures into three classes using each figure only once.

A. 1,2,5 ; 3,7,8; 4, 6, 9
B. 1, 7, 2; 3, 9, 6; 4, 5, 8
C. 2, 3, 8; 4, 6, 9; 1, 5, 7
D. 5, 6, 9; 3, 4, 1; 2, 7, 8
Answer : A

Question. Choose the option which most closely resembles the water-image of the given combination.

Answer : C

Question. Identify which one of the alternative figures completes the pattern in the given matrix.

Answer : A

Question. If it is possible to make a meaningful word from the second, fourth, seventh and tenth letters of the word UNDENOMINATIONAL, using each letter only once, third letter of the word would be your answer. If more than one such word can be formed your answer would be ‘X’, whereas if more than two such words can be formed your answer would be ‘Y’, and if no such word can be formed, answer would be ‘Z’.
A. X
B. Z
C. Y
D. N
Answer : C

Question. The following problem consists of a set of six figures, the first of which is unnumbered and marks the beginning of the series which is continued in the successive figures numbered from 1 to 5. However, the series will be established only if the positions of two of the numbered figures are interchanged.
The number of the earlier of the two figures is the answer. If no two figures need to be interchanged, then the answer is 5.

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

Question. Study the following arrangement carefully and answer the question given below:
4 K @ 1 E F © 2 H D % 3 8 B I M 6 * U W Y 5 $ 9 G J # 7 A
How many such consonants are there in the above arrangement, each of which is immediately preceded by a letter and immediately followed by a number?
A. None
B. One
C. Two
D. Three
Answer : C

Question. Mohit lives to the North of Rajesh who lives to the West of Tanuj. Arun who lives to the South of Mohit have his house in which direction with respect to Tanuj?
A. North-East
B. North
C. South-West
D. Can't be determined
Answer : D

Question. Find the suitable alternative to fit into the blank space in Fig. (X) in order to complete the pattern.

Answer : A

Question. In the following 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 of numbers progresses from left to right.
Rules:
(i) 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.
(iii) 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 a prime odd number, the first number is to be divided by the second number.
(v) If an odd number is followed by an even number, the second one is to be subtracted from the first one.
                        58    17   5
                        85     5    n
If n is the resultant of the first row what is the resultant of the second row?
A. 255
B. 32
C. 49
D. 34
Answer : A

Question. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the option that would replace the question mark (?) in fig. 4.

Answer : B

Question. Pointing to a woman in a photograph a man says; “She is the only daughter of my father’s mother-in-law”. How is the woman related to the man?
A. Daughter
B. Mother
C. Daughter-in-law
D. Mother-in-law
Answer : B

MATHEMATICAL REASONING

Question. Determine the value of k so that the following linear equations have no solution.
(3k + 1)x + 3y – 2 = 0
(k² + 1)x + (k – 2)y – 5 = 0
A. –1
B. –2
C. 1
D. 4
Answer :A 

Question. Find the value of sec39°/cosec51° + 2/√3 tan17° tan38° tan60° tan52° tan73° – 3(sin²31° + sin²59°)
A. –1
B. 0
C. 1
D. 2
Answer : B

Question. Let f (x) = x² + bx + c where b, c are integers. If f (x) is a factor of both x4 + 6x² + 25 and 3x⁴ + 4x² + 28x + 5, then the value of f(1) is _____
A. 1
B. 2
C. 3
D. None of these
Answer : D

Question. A, B, C are three towns connected by straight roads from A to B, B to C and C to A. AB = 5 km, BC = 6 km and CA = 7 km. Two cyclists start simultaneously from A and go in different roads with same speed. They meet at D, then BD = _______.
A. 2 km
B. 4 km
C. 6 km
D. 8 km
Answer : B

Question. Triangle ABC is equilateral of side length 8 cm. Each arc shown in the diagram is an arc of a circle with the opposite vertex of the triangle as its centre. The total area enclosed within the entire figure shown (in cm²) ________.

A. 48(p − √3)
B. 30 √3π
C. 32(π − √3)
D. 90 π
Answer : C

Question. Solve for x : x² + x – (a + 1)(a + 2) = 0
A. (a + 1), (– a + 2)
B. (a + 1), (a + 2)
C. (– a + 1), (a + 2)
D. (a + 1), – (a + 2)
Answer : D

Question. The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length AD.

A. 19 cm
B. 20 cm
C. 25 cm
D. 30 cm
Answer : A

Question. The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of cloud in the lake is 60°. Find the height of the cloud.
A. 100 m
B. 120 m
C. 60 m
D. 125 m
Answer : B

Question. A bag contains 12 balls out of which x are white. If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that of drawing a white ball before adding the balls. Find the value of x.
A. 1
B. 6
C. 3
D. 7
Answer : C

Question. Find the area of the quadrilateral ABCD whose vertices are respectively A(1, 1), B(7, –3), C(12, 2) and D(7, 21).
A. 125 sq. units
B. 110 sq. units
C. 148 sq. units
D. 132 sq. units
Answer : D

Question. A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, calculate the speed per hour with which the boy is cycling.
A. 15.82 km/hour
B. 15.84 km/hour
C. 15.96 km/hour
D. 20 km/hour
Answer : B

Question. A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed as shown in figure. What fraction of water overflows?

A. 3/8
B. 8/3
C. 5/4
D. 6/7
Answer : A

Question. The sum of 5^th and 9th terms of an A.P. is 72 and the sum of 7^th and 12^th terms is 97. Find the A.P. 
A. 5, 10, 15, 20 ......
B. 15, 30, 45, 60 .......
C. 6, 11, 16, 21, 26, .....
D. 2, 4, 6, 8, 10 ......
Answer : C

Question. Find the median of the following data.

A. 64
B. 48.93
C. 63.43
D. 66.43
Answer : D

Question. Evaluate :

A. 1/√3
B. 2/√3
C. √3
D. 1
Answer : B

EVERYDAY MATHEMATICS

Question. The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
A. 4 km/hr
B. 5 km/hr
C. 6 km/hr
D. 7 km/hr
Answer : B

Question. Two cars start together in the same direction from the same place. The first goes with uniform speed of 10 km/h. The second goes at a speed of 8 km/h in the first hour and increases the speed by 1/2 km in each succeeding hour. After how many hours will the second car overtake the first car if both cars go non-stop?
A. 9 hours
B. 10 hours
C. 12 hours
D. None of these
Answer : A

Question. An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.
A. 115.47 metres
B. 200 metres
C. 215.47 metres
D. 315.47 metres
Answer : D

Question. Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize?
A. 19/20
B. 1/25
C. 1/20
D. 17/20
Answer : C

Question. Water is being pumped out through a circular pipe whose internal diameter is 7 cm. If the flow of water is 72 cm per second, how many litres of water are being pumped out in one hour?
A. 2772 litres
B. 9979 litres
C. 9979.2 litres
D. 9297.4 litres
Answer : C

Question. A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft. by 8 ft. What would be the size (in inches) of the tile required that has to be cut and how many such tiles are required respectively?
A. 24, 20
B. 20, 24
C. 20, 43
D. 41, 6
Answer : A

Question. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens. Find the original number of pens and pencils respectively.
A. 28, 12
B. 12, 28
C. 27, 13
D. 13, 27
Answer : D

Question. Two poles of height 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
A. 12 m
B. 13 m
C. 14 m
D. 15 m
Answer : B

Question. A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, find the value of each prize.
A. ₹ 100, ₹ 120, ₹ 140, ₹ 160, ₹ 80, ₹ 40, ₹ 20
B. ₹ 160, ₹ 140, ₹ 120, ₹ 100, ₹ 80, ₹ 40, ₹ 20
C. ₹ 160, ₹ 140, ₹ 120, ₹ 100, ₹ 80, ₹ 60, ₹ 40
D. ₹ 380, ₹ 360, ₹ 340, ₹ 320, ₹ 300, ₹ 280, ₹ 260
Answer : C

Question. In an examination the ratio of the number of successful candidates and unsuccessful candidates is 4 : 1. Had 20 more candidates appeared and 2 more passed, the ratio of successful candidates to unsuccessful candidates would have been 2 : 1. Find the number of candidates who appeared in the examination originally.
A. 85
B. 92
C. 34
D. 17
Answer : A

ACHIEVERS SECTION

Question. CAB is an angle whose measure is 70°. ACFG and ABDE are squares drawn outside the angle.
The diagonal FA meets BE at H. Then the measure of the angle EAH is _____.

A. 45°
B. 25°
C. 65°
D. 70°
Answer : B

Question. Study the statements carefully and select the correct option.
Statement-1 : The distance between two points (x¹, y¹) and (x², y²) is √(x¹ - x²)² + (y¹ - y²)²
Statement-2 : The point(s) on the x-axis which has its distances from the points (7, 6) and (–3, 4) in the ratio 1 : 2 is (35/3, 0) or (–9, 0).
A. Both the statements are true.
B. Statement-1 is true but statement-2 is false.
C. Statement-1 is false but statement-2 is true.
D. Both the statements are false.
Answer : B

Question. Fill in the blanks.
A P to a circle is a line that meets the circle at only one point. It is a special case of Q , when the two end points of its corresponding chord R .
There is only one S at a point of circle.

Answer : B

Question. Match the columns

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

Question. If the volume of a sphere is increased by 95(5/16)% without changing the shape, what will be the percentage increase in the surface area?
A. 56.25%
B. 50 %
C. 28.56%
D. Remains same
Answer : A