CBSE Class 10 Mathematics IMO Olympiad MCQs with Answers Set F

LOGICAL REASONING

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 operations of numbers progress from left to right.
Rules:
(i) If an even number is followed by another even number, they are to be added.
(ii) If an even number is followed by a prime number, they are to be multiplied.
(iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number.
(iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number.
(v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number.
36 13 39
77 30 7
Which will be the outcome if the resultant of the second row is divided by the resultant of the first row?
A. 12
B. 16
C. 8
D. 6
Answer : C

Question. The given square grid shows the plan of a playground.
The bench is North of the toy car.

The town council wants to plant a tree in the playground.
The location of the tree is to be North of the swing and South-West of the slide. Identify the position where the tree will be planted.
A. P
B. Q
C. R
D. S
Answer : A

Question. A dealer sold six cars – M, N, O, P, Q and R– during a period of Monday to Saturday, one car on each day.
(i) The car O was sold at least before three cars.
(ii) The car R was sold on Tuesday.
(iii) Both the cars N and Q were sold at least before one car.
(iv) The car P was sold immediately after the car O.
(v) At least four cars were sold after the car Q.
If Mr. Jindal is purchased a car sold on Wednesday, then the car purchased by him is
A. M
B. N
C. O
D. P
Answer : C

Question. 'X + Y means 'Y is brother of X'; 'X × Y' means 'Y is husband of X'; 'X – Y' means 'X is mother of Y'; and 'X ÷ Y' means 'X is father of Y'. Then which of the following expressions indicates 'P is grandmother of T'?
A. Q – P + R ÷ T
B. P × Q ÷ R – T
C. P × Q ÷ R + T
D. P + Q ÷ R – T
Answer : B

Question. A trader in order to code the cost price of an article used the letters of psicholazy in the form of '0 to 9' respectively. If an article was sold for ₹ 1015.58 to earn the 16% gain, then which of the following code stands for cost price?
A. AIL.HP
B. AIL.HS
C. Z YA.HO
D. Z AO.OP
Answer : D

Question. Find the missing figure from the options which will continue the series in given Problem Figures.

Answer : A

Question. An enterprising businessman earns an income of ₹ 1 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 10th day of business, his income is _______.
A. ₹ 29
B. ₹ 210
C. ₹ 10
D. ₹ 102
Answer : A

Question. There is a certain rule followed in all the three figures.
Identify the rule and find the missing number.

A. 6
B. 90
C. 540
D. 60
Answer : A

Question. Identify the wrong figure in the given series.

A. Q
B. S
C. R
D. T
Answer : D

Question. In a shop, the items were arranged in a shelf consisting of six rows. Biscuits are arranged above tins of chocolates but below the rows of packets of chips, cakes are at the bottom and the bottles of peppermints are below the chocolates. The topmost row had the display of jam bottles. Where exactly are the bottles of peppermints from the top?
A. 2nd
B. 3rd
C. 4th
D. 5th
Answer : D

Question. There is a certain relationship between figures P and Q. Identify the same relationship between figures R and S and find the missing figure from the options.

Answer : B

Question. Count the number of circles used to draw the given figure.

A. 20
B. 21
C. 25
D. 17
Answer : B

Question. Select the figure from the options in which Fig.(X) is exactly embedded as one of its part.

Answer : D

Question. There are three figures X, Y and Z showing a sequence of folding of a sheet of paper. Figure (Z) shows the manner in which the folded sheet has been cut. Select the figure from the options which would resemble the unfolded form of paper.

Answer : A

Question. A cube of side 10 cm is coloured red with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smallest cubes of equal size. How many cubes have at least two green faces?
A. 8
B. 27
C. 44
D. 63
Answer : C

MATHEMATICAL REASONING

Question. The given figure is created by using the arcs of quadrants with radii 1 cm, 2 cm and 3 cm. Find the total area of the shaded region. (Take π = 3.14)

A. 31.93 cm²
B. 15.96 cm²
C. 63.84 cm²
D. 13.68 cm²
Answer : D

Question. In the given figure (not drawn to scale), AG is parallel to CD and AG = (2/7)CD. The point B on AC is such that BC = (2/7)AC. If the line BG meets AD at F and the line through C is parallel to BG which meets AD at E, then find the value of FG/EC.

A. 1/7
B. 3/7
C. 4/7
D. 2/7
Answer : D

Question. In the given figure (not drawn to scale), BD is a diameter of the circle with centre O. C and A are two points on the circle. BA and CD, when produced, meet at E. If ∠DOC = 60° and ∠ABD = 23°, then find ∠OBC.

A. 60°
B. 30°
C. 45°
D. 67°
Answer : B

Question. Which of the following have non-terminating repeating decimal?
A. 2/25
B. 2/7
C. 231/2²×5² ×7
D. 1323/6³ ×(35)²
Answer : B

Question. In the given figure (not drawn to scale), OABC is a quadrilateral with ABC on horizontal ground and O is vertically above A. M is the mid-point of BC. If ∠BAC = 90°, AB = AC = 16 cm and OA = 12 cm, calculate the length of OB.

A. 25 cm
B. 15 cm
C. 20 cm
D. 28 cm
Answer : C

Question. The given figure shows sector OAB with centre O and radius 54 cm. Another circle XYZ with centre P, is enclosed by the sector OAB. If ∠AOB = 60°. Find the area of OXPY.

A. 161 cm²
B. 461 cm²
C. 324 cm²
D. 561.2 cm²
Answer : D

Question. If two zeroes of the polynomial x⁴ – 6x³ – 26x² + 138x – 35 are 2 − √3 and 2 + √3, then find all the zeros.
A. –5, 7
B. –7, 5
C. 3, –5
D. 5, –3
Answer : A

Question. Solve : (sin⁴ θ – cos⁴ θ + 1) cosec²θ
A. 1
B. –2
C. 2
D. 0
Answer : C

Question. What is the value of the median of the data using the graph in the figure given below, of less than ogive and more than ogive?

A. 8
B. 4
C. 5
D. 17.5
Answer : C

Question. The number of zeroes for the given graph is ____.

A. 3
B. 2
C. 4
D. 1
Answer : A

Question. Find the mode (approx.) from the given frequency distribution.

A. 336.41
B. 307.20
C. 343.22
D. 342.72
Answer : D

Question. If the roots of the quadratic equation x² + px + q = 0 are tan 30° and tan 15° respectively, then the value of 2 + q – p is ______.
A. 0
B. 1
C. 2
D. 3
Answer : D

Question. Swati folded the three corners of a triangle. She managed to measure four of the angles as shown below before breaking her protractor. She needs help to figure out what the named angles are. Help her find f , g and h.

      f            g           h
A. 52°        44°        47°
B. 44°        52°        47°
C. 44°        47°        52°
D. 47°        44°        52°
Answer : B

Question. Kunal arranged some metal blocks at the bottom of a tank as seen in the figure below. Then he filled the 30 cm by 25 cm by 25 cm tank with water. If each block is 4 cm long, 3 cm wide and 5 cm tall, then how much water is needed to fill the tank to 80% of the tank's height?

A. 15000 cm³
B. 2280 cm³
C. 12720 cm³
D. 16470 cm³
Answer : C

Question. A number is chosen at random from 1 to 120. The probability of the number chosen being a multiple of 3 and 15 both is _____.
A. 1/15
B. 1/16
C. 1/17
D. 1/19
Answer : A

Question. In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If ∠OBA = 32°, then find the values of x and y respectively.

A. 32°, 58°
B. 58°, 48°
C. 58°, 58°
D. 42°, 58°
Answer : C

Question. In the given graph, line APB meets the x-axis at A and y-axis at B. P is the point (–4, 2) and AP : PB = 1 : 2. Find the coordinates of A and B respectively.

A. (–5, 0), (0, 5)
B. (–6, 0), (0, 6)
C. (–6, 0), (0, 5)
D. (6, –6), (–6, 6)
Answer : B

Question. Let Sn denote the sum of the first 'n' terms of an A.P. S_2n = 3Sn. Then, the ratio S_3n/S_n is equal to _____.
A. 4
B. 6
C. 8
D. 10
Answer : B

Question. If x² + px + q = 0 and x² + qx + p = 0 have a common root, then ______.
A. p = q
B. 1 + p + q = 0
C. p + q = 0
D. Both A and B
Answer : D

Question. If the area of the triangle given below is 20 sq. units, then what are the co-ordinates of point C?

A. (0, 40/a)
B. (a² + b², 0)
C. (20/b, 0)
D. (40/b, 0)
Answer : D

EVERYDAY MATHEMATICS

Question. A man walks a distance of 48 km in a given time.
If he walks 2 km an hour faster, he will perform the journey 4 hours before. Find his normal rate of walking.
A. 4 km/hr
B. 6 km/hr
C. 3 km/hr
D. 8 km/hr
Answer : A

Question. Mohan ate half a pizza on Monday. He ate half of what was left on Tuesday and so on. He followed this pattern for one week. How much of the pizza would he have eaten during the week?
A. 99.22%
B. 95%
C. 98.22%
D. 100%
Answer : A

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 2014 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. 2024
B. 2021
C. 2022
D. 2023
Answer : A

Question. The total monthly salary of 4 men and 2 women is ₹ 46,000. If a woman earns ₹ 500 more than a man, what is the monthly salary of a woman?
A. ₹ 6500
B. ₹ 7500
C. ₹ 8000
D. ₹ 9000
Answer : C

Question. The members in a welfare committee decided to collect as many paise from each member of the committee as is the number of members. If the total collection amounts to ₹ 96.04, then the number of members in the committee is _______.
A. 84
B. 98
C. 102
D. 92
Answer : B

Question. A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month over the whole?
A. 4500
B. 4600
C. 4680
D. 4710
Answer : A

Question. A housewife saved ₹ 2.50 in buying an item on sale. If she spent ₹ 25 for the item, then how much percent she saved in the transaction approximately?
A. 8%
B. 9%
C. 10%
D. 11%
Answer : B

Question. Rajeev buys goods worth ₹ 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
A. ₹ 6876.10
B. ₹ 6999.20
C. ₹ 6654
D. ₹ 7000
Answer : A

Question. Twenty women can do a work in sixteen days and sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
A. 3 : 4
B. 4 : 3
C. 5 : 3
D. Data inadequate
Answer : B

Question. A sum of money is borrowed and paid back in two annual installments of ₹ 882 each allowing 5% compound interest. The sum borrowed was _______.
A. ₹ 1620
B. ₹ 1640
C. ₹ 1680
D. ₹ 1700
Answer : B

ACHIEVERS SECTION

Question. Which of the following statements is true?
Statement-1 : The area of the equilateral triangle described on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles described on the other two sides of the triangle.
Statement-2 : The area of the equilateral triangle described on the side of right angled isosceles triangle is half of the area of the equilateral triangle described on its hypotenuse.
A. Only statement-1
B. Only statement-2
C. Both statement-1 and statement-2
D. Neither statement-1 nor statement-2
Answer : C

Question. Match the columns.

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

Question. Which of the following situations do not form an A.P.?
(i) The fee charged from a student every month by a school for the whole session when the monthly fee is ₹ 400.
(ii) The fee charged every month by a school from classes I to XII, when the monthly fee for class I is ₹ 250 and it increases by ₹ 50 for the next higher class.
(iii) The amount of money in the account of Sanchi at the end of every year when ₹ 1000 is deposited at simple interest at the rate of 10% per annum.
(iv) The number of bacteria in a certain food item after each second, when they double themselves in every second.
A. Only (i)
B. Only (ii)
C. Both (ii) and (iv)
D. Only (iv)
Answer : C

Question. Find the mean, mode and median respectively of the following data.

A. 51.72, 62, 61
B. 61, 62, 61
C. 61, 60, 61
D. 61.72, 61, 61
Answer : D

Question. Fill in the blanks.
Let a = p/q be a rational number such that p and q are P and the prime factorisation of q is not of the form 2ⁿ × 5^m, where n and m are whole numbers, then a has a decimal expansion which is Q and R .

Answer : C