CBSE Class 10 Mathematics IMO Olympiad MCQs with Answers Set B

SECTION I : LOGICAL REASONING

Question. There are six persons A, B, C, D, E and F. C is the sister of F. B is the brother of E's husband. D is the father of A and grandfather of F. There are two fathers, three brothers and a mother in the group. Which of the following is a group of brothers?
(A) ABF
(B) ABD
(C) BFC
(D) BDF
Answer : A

Question. Anita, Mahima, Rajan, Lata and Deepti are five cousins. Anita is twice as old as Mahima. Rajan is half the age of Mahima. Anita is half the age of Deepti and Rajan is twice the age of Lata. If Mahima is 16 years old, then what is the age of Lata?
(A) 4 years
(B) 5 years
(C) 7 years
(D) 14 years
Answer : A

Question. If second Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then how many working days are there in that month?
(A) 25
(B) 22
(C) 24
(D) 23
Answer : C

Question. If the same function is applied to reach the results in each of the three sets of numbers given then which number will replace the question mark in the third set of numbers?

(A) 24
(B) 30 21 5
(C) 36 30 ?
(D) 40
Answer : B

Question. If the first and the second letters of the word UNPRECEDENTED are interchanged with the last and the second last letters and similarly the third and the fourth letters are interchanged with the third and the fourth letters from the last respectively and so on, then what will be the seventh letter to the right of the third letter from the left end ?
(A) C
(B) E
(C) P
(D) R
Answer : D

Question. Ravi wants to go to the university. He starts from his home which is in the East and comes to a crossing. The road to the left ends in a theatre, and straight ahead is the hospital. In which direction is the university if all the four places are in different directions ?
(A) North
(B) South
(C) East
(D) West
Answer : A

Question. Find out the wrong term in the number series.
105, 85, 60, 30, 0, – 45, – 90
(A) 105
(B) 60
(C) 0
(D) – 45
Answer : C

Question. Choose the numberletter group which is different from the others.
(A) M5S
(B) B9L
(C) T4Y
(D) F4J
Answer : D

Question. Select a figure from amongst the options which will continue the series established by the five problem figures.

Answer : B

Question. In the question, there are seven figures, the first and last of which are unmarked and the remaining are marked as P, Q, R, S and T. These seven figures form a series. However, one of the five marked figures does not fit into the series. Select that figure from the options.

(A) P
(B) Q
(C) R
(D) T
Answer : A

Question. In the given figure, if the triangle represents girls, the circle represents athletes, the rectangle represents boys and the square represents disciplined, then the boys who are athletes and disciplined are indicated by which number ?

(A) 1
(B) 2 8
(C) 6
(D) 10
Answer : B

Question. Five boys took part in a race. Raj finished before Mohit but behind Gaurav. Ashish finished before Sanchit but behind Mohit. Who won the race?
(A) Raj
(B) Gaurav
(C) Mohit
(D) Ashish
Answer : B

Question. In a certain coding system, '816321' means 'the brown dog frightened the cat'; '64851' means 'the frightened cat ran away'; '7621' means 'the cat was brown'; '341' means 'the dog ran'.
What is the code for 'the dog was frightened'?
(A) 5438
(B) 8263
(C) 8731
(D) None of these
Answer : C

Question. Choose that set of numbers from the options, that is similar to the given set : (9, 15, 21)
(A) (10, 14, 16)
(B) (7, 21, 28)
(C) (5, 10, 25)
(D) (4, 8, 12)
Answer : D

Question. Find the missing number?

(A) 8C
(B) 12B
(C) 16C
(D) 18C
Answer : A

Question. Find the odd one out.

Answer : D

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

Answer : D

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. When the given 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. Select a figure from the options which satisfies the same conditions of placement of the dots as in fig. (X).

Answer : D

SECTION II : MATHEMATICAL REASONING

Question. A person invested some amount at the rate of 10% simple interest and some other amount at the rate of 12% simple interest. He received yearly interest of ₹130. But if he had interchanged the amounts invested, he would have received ₹4 more as interest. How much amount did he invest at different rates ?
(A) ₹ 700 at 12%, ₹ 500 at 10%
(B) ₹ 700 at 10%, ₹ 500 at 12%
(C) ₹ 700 each at 10% and 12%
(D) ₹ 500 each at 10% and 12%
Answer : B

Question. In DPQR, PD⊥QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, then (a + b)(a – b) = _____.
(A) 1
(B) (c + d)(d – c)
(C) (c + d)(c – d)
(D) 0
Answer : C

Question. Two circles with radii a and b respectively touch each other externally. Let c be the radius of a circle that touches these two circles as well as a common tangent to these two circles. Then ___.
(A) - = 1/√a - 1/√b  = 1/√c
(B) 1/√a + 1/√b + 1/√c = 0
(C) 1/√a + 1/√b = 1/√c
(D) None of these
Answer : C

Question. DABC is right angled at A. DEFG is a square inscribed in triangle as side DE is on BC and G & F are two points at AB and AC respectively. Then DE 2 =

(A) BD x EC
(B) BD = 2EC
(C) BD = (1/2)
(D) None of these
Answer : A

Question. If from twice the greater of two positive numbers 16 is subtracted, the result is half the other number. If from half the greater number 1 is subtracted, the result is still half the other number. What are the numbers ?
(A) 16, 8
(B) 12, 10
(C) 6, 8
(D) 10, 8
Answer : D

Question. If P and Q are two points whose coordinates are (at², 2at) and (a/t², 2a/t)  respectively and S is the point (a, 0), then 1/SP+1/SQ is _____.
(A) Dependent of t
(B) Independent of t
(C) Independent of a
(D) None of these
Answer : B

Question. If T₁ , T₂ , T₃ , ......., T n are consecutive terms of an A.P., then 1/T₁T₂ + 1/T₂T₃ +......... + 1/T_n-1T_n = ____.
(A) n-1/T₁ · T_n
(B) n/T₁ · T_n 
(C) T₂(n-1)/T₁ · T_n
(D) None of these
Answer : A

Question. In the given figure, the diameters of two wheels have measures 2 cm and 4 cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angle.

(A) 4 cm each B
(B) 3 cm each
(C) 5 cm each
(D) 6 cm each
Answer : B

Question. In the given figure, three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm.
Find the approximate value of R.

(A) 5.4 cm
(B) 5.0 cm B C
(C) 4.0 cm
(D) 4.3 cm
Answer : D

Question. A number is selected at random from the numbers :
5, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 24, 25, 25, 27, 30, 30, 36, 37, 37, 39, 40, 40, 46.
Find the probability that the selected number is their average.
(A) 0
(B) 1
(C) 1/6
(D) 1/12
Answer : D

Question. A cone is cut into two parts by a horizontal plane passing through the midpoint of its axis. The ratio of the volume of the upper part to the volume of lower part is ____.
(A) 1 : 7
(B) 1 : 8
(C) 7 : 1
(D) 7 : 8
Answer : A

Question. The ratio of the areas of the right angled triangles ABC and DEF in which ∠A = 30°, ∠B = 90°, AC = 4 cm, ∠D = 60°, ∠E = 90° and DE = 4 cm is ___.
(A) 1 : 2
(B) 4 : 1
(C) 1 : 4
(D) 2 : 1
Answer : C

Question. If (x + a) is a factor of the polynomial x² + px + q and x² + mx + n, then a = ___.
(A) n-q/m-p
(B) m-q/n-p
(C) n-p/m-q
(D) None of these
Answer : A

Question. If A is the area of a rightangled triangle and b is one of the sides containing the right angle, then the length of altitude on the hypotenuse is ____.

Answer : A

Question. Find the interrelationship of the variables for the quadratic equation y = ax 2 + bx + c from given graph.

(A) a + b + c = 0
(B) a – b + c = 0
(C) 2a + b + c = 0
(D) 4a – 2b + c = 0
Answer : B

Question. The houses of a row are numbered consecutively from 1 to 49. If there is a x such that the sum of the numbers of the house preceding the house numbered x is equal to the sum of the numbers of the house following it. Find the value of x.
(A) 35
(B) 34
(C) 30
(D) 33
Answer : A

Question. If sinθ + cosθ = a and sinθ + cosθ/sinθ cosθ = b, then ____.
(A) b = 2a/a² - 1
(B) a = 2b/b² - 1
(C) ab = b² – 1
(D) a + b = 1
Answer : A

Question. In the given figure, PT is a tangent to the circle at T. If PA = 4cm and AB = 5 cm, find PT.

(A) 7 cm
(B) 6 cm
(C) 8 cm
(D) 2 cm
Answer : B

Question. Consider a cylinder of height n cm and radius 3/π cm. A string of width h cm, when wound around the cylinder without keeping any space between two turns, covers the lateral surface of the cylinder completely. What is the required length of the string ?
(A) (6n/h)cm
(B) (12h/n)cm
(C) (36n/h)cm
(D) None of these
Answer : A

Question. If α and β are roots of the equation A(x² + m²) + Amx + cm² x² = 0, then A(α²+β²) + Aαβ + cα² β² =____.
(A) 0
(B) 1
(C) –1
(D) None of these
Answer : A

SECTION III : EVERYDAY MATHEMATICS

Question. Piyush gave onefourth of the amount he had to Mahesh. Mahesh in turn gave half of what he received from Piyush to Suraj. If the difference between the remaining amount with Piyush and the amount received by Suraj is ₹ 500, how much money did Mahesh receive from Piyush ?
(A) ₹ 100
(B) ₹ 200
(C) ₹ 400
(D) Data inadequate
Answer : B

Question. 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age difference of 2 years), the present average age of the family is the same. The present age of the youngest child is ____.
(A) 1 years
(B) 2 years
(C) 3 years
(D) 5 years
Answer : C

Question. A, B and C start cycling around a circular path in the same direction at same time. Circumference of the path is 1980 m. If the speed of A is 330 m/min, speed of B is 198 m/min and C is 220 m/min and they start from the same point, then after what time interval will they be together at the starting point?
(A) 30 mins
(B) 9 mins
(C) 90 mins
(D) 60 mins
Answer : C

Question. A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is ₹ 250 per quintal, the total monthly expenses are ₹ 1000 and when it is ₹ 240 per quintal, the total monthly expenses are ₹ 980. Find the total monthly expenses of the family when the cost of wheat is ₹ 350 per quintal.
(A) ₹ 1100
(B) ₹ 1200
(C) ₹ 1300
(D) ₹ 1500
Answer : B

Question. In the Maths Olympiad at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes :
(i) One of them made a mistake in the constant term and got the roots as 5 and 9.
(ii) The other committed an error in the coefficient of x and he got the roots as 12 and 4. In the meantime, they realised that they were wrong and together they managed to get it right. Find the quadratic equation.
(A) x² + 4x + 14 = 0
(B) 2x² + 7x – 24 = 0
(C) x² – 14x + 48 = 0
(D) 3x² – 17x + 52 = 0
Answer : C

Question. Hari wishes to determine the distance between two objects A and B, but there is an obstacle between these two objects which prevents him from making a direct measurement. He devises an clever way to overcome this difficulty.
First he fixes a pole at a convenient point O so that from O, both A and B are visible. Then he fixes another pole at the point D on the line AO (produced) such that AO = DO. In a similar way he fixes a third pole at the point C on the line BO (produced) such that BO = CO. Then he measures CD which is equal to 170 cm.
The distance between the objects A and B is ____.

(A) 170 cm
(B) 340 cm
(C) 85 cm
(D) None of these
Answer : A

Question. A, B, C are three points on the same horizontal line and CT is a vertical pole. The angle of elevation of T, as seen from A, is x° and the angle of elevation of T, as seen from B is y°(y° > x°). If AB = d, then the height of the pole is ____.
(A) d cos x° cos y°/sin(y° - x°)
(B) d tan x° tan y°/tan y° - tan x°
(C) d cos x° cos y°/cos(y° - x°)
(D) d sin x° sin y°/cos(y° - x°)
Answer : B

Question. A bucket is 40 cm in diameter at the top, 28 cm in diameter at the bottom and 21 cm deep. The cost of tin sheet used in making the bucket, if the cost of tin is ₹ 1.50 per sq. dm is ____.
(A) ₹ 32.25
(B) ₹ 40.25
(C) ₹ 44.25
(D) None of these
Answer : C

Question. There are 100 transistors in a box. 20 of them are defective. At random two transistors are taken one by one consecutively without replacement. What is the probability that both of them are good ?
(A) 316/495
(B) 19/495
(C) 16/99
(D) 32/99
Answer : A

Question. A boy is standing on the ground and flying a kite with 100 m length of string at an elevation of 30°. Another boy is standing on the roof of a 10 m high building and is flying his kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet. 
(A) 50√3 m
(B) 40√2 m
(C) 50 m
(D) 100 m
Answer : B