CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set F

Logical Reasoning

Question. In the following letter series, some of the letters are missing which are given in that order as one of the options below it. Choose the correct option.
_ bcc _ ac _ aabb _ ab _ cc
A. aabca
B. abaca
C. bacab
D. bcaca
Answer : C

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 options that would replace the (?) in figure (4).

Answer : A

Question. P, Q, R, S, T and M are six houses of different heights and of different colours i.e., red, blue, white, orange, yellow and green, located on either sides of a road with three on each side. T, the tallest house, is exactly opposite to the red coloured house. The shortest house is exactly opposite to the green coloured house. M is the orange coloured house and is located between P and S. R, the yellow coloured house, is exactly opposite to P. Q, the green coloured house, is exactly opposite to M. P, the white coloured house, is taller than house R but shorter than houses S and Q.
What is the position of house P from top when the houses are arranged in descending order of their heights?
A. Third
B. Second
C. Fourth
D. Data inadequate
Answer : C

Question. Some equal cubes are arranged in the form of a solid block as shown in the given figure. All the visible surfaces of the block (except bottom) are then painted.

How many cubes have only one face painted?
A. 9
B. 45
C. 57
D. 62
Answer : C

Question. How many such consonants are there in the given arrangement, each of which is immediately preceded by a number but not immediately followed by a number?
F 4 © J 2 E % M P 5 W 9 @ I Q R 6 U H 3 Z 7 ★ A T B 8 V # G $ Y D
A. None
B. One
C. Two
D. Three
Answer : B

Question. How many such pairs of letters are there in the word ELEVATION each of which has as many letters between them as in the English alphabet?
A. Four
B. Five
C. Two
D. Three
Answer : A

Question. In which of the following options, Fig. (X) is exactly embedded as one of its part?

Answer : C

Question. In which of the following options, the two figures (I & II) fit into each other to form a complete square?

Answer : B

Question. In a certain code language ‘in ba pe’ means ‘he has won’, ‘le ki ba’ means ‘she has lost’ and ‘in se pe’ means ‘he always won’. Which word in that language
means ‘he’?
A. in
B. pe
C. se
D. Data inadequate
Answer : D

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

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

Question. The following question is based on the diagram given below.

(i) Rectangle represents males.
(ii) Triangle represents educated people.
(iii) Circle represents urban people.
(iv) Square represents civil servants.
Who among the following is uneducated urban male who is not a civil servant?
A. 8
B. 3
C. 11
D. 12
Answer : D

Question. Select the figure which satisfies the same conditions of placement of the dots as in Fig. (X).

Answer : A

Question. Two rows of numbers are given. The resultant of 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 on numbers in each row progress from left to right.
Rules:
(i) If an odd number is followed by another odd number, they are to be multiplied.
(ii) If an even number is followed by another even number, the first number is to be divided by the second even number.
(iii) If an even number is followed by the perfect square of an odd number, the first number is to be subtracted from the second number.
(iv) If an odd number is followed by an even number, the two are to be added.
(v) If an even number is followed by an odd number which is not a perfect square, the square of the odd number is to be added to the even number. 
96 16 81
11 15 18
If x and y are the resultant of first and second row respectively, then what is the value of y – 2x?
A. 108
B. 33
C. 105
D. 36
Answer : B

Question. There are seven figures, the first and last of which are unnumbered and the remaining five 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. Select the figure that does not fit into the series.

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

Question. There are two statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements disregarding commonly known fact.
Statements: (a) No circles are parabolas.
(b) No parabolas are hyperbolas.
Conclusions: I. No circles are hyperbolas.
II. No hyperbolas are circles.
III. No hyperbolas are parabolas.
A. Only III follows
B. Both I and II follow
C. All follow
D. None follows
Answer : A

MATHEMATICAL REASONING

Question. 85 children went to an amusement park where they could ride on the merry-go-round, roller coaster and giant wheel. It was known that 20 of them took all three rides and 55 of them took two of the three rides.
Each ride costs ₹ 1 and the total amount spent by the children in the park was ₹ 180. How many children took exactly one ride?
A. 10
B. 20
C. 25
D. 15
Answer : A

Question. If p and q are rational numbers and 5 + √11/3 - 2√11 = p + q√ 11, then find the values of p and q respectively.
A. 37/35, -13/35
B. 37/35, 13/35,
C. −37/35, -13/35
D. −37/35, 13/35
Answer : C

Question. For a group of 32 students, food lasts for 45 days.
For how many days will the same food last for 72 students ?
A. 13
B. 40
C. 20
D. 6
Answer : C

Question. Which of the following can be the coordinates of R, if PR = QR?

A. (1, –1)
B. (2, –2)
C. (2, 3)
D. (3, 3)
Answer : C

Question. Which of the following steps is INCORRECT
while constructing a quadrilateral ABCD, given that AB = 5 cm, BC = 7 cm, AD = 4 cm, diagonal AC = 9 cm and diagonal BD = 6 cm.
1. Draw AB = 5 cm.
2. With A and B as centres and 4 cm and 6 cm as radii respectively, draw arcs to cut each other at D.
3. Join AD and BC. With A and B as centres and
9 cm and 7 cm as radii, respectively, draw arcs to cut each other at C. 
4. Join AC and BC. Also join DC. ABCD is the required quadrilateral.
A. Only 1
B. Both 2 and 3
C. Only 3
D. Both 2 and 4
Answer : C

Question. In the figure given below, PQRS is a trapezium. AB is parallel to PQ and cuts PR at O. If ∠PSR = 90°, ∠ABR = 110° and ∠QPR = 40°, find (i) ∠PRQ (ii) ∠AOR (iii) ∠OPA

     (i)   (ii)   (iii)
A. 30° 110° 50°
B. 15° 120° 45°
C. 15° 140° 45°
D. 30° 140° 50°
Answer : D

Question. In ΔABC, it is given that D is the midpoint of BC, E is the midpoint of BD and O is the midpoint of AE.
Then, find ar (ΔBOE).

A. 1/3 ar(ΔABC)
B. 1/4 ar(ΔABC)
C. 1/6 ar(ΔABC)
D. 18 ar(ΔABC)
Answer : D

Question. 8(a – 2b)² – 2a + 4b – 1 =
A. (2a – 4b – 1) (4a – 8b + 1)
B. (2a + 4b + 1) (4a – 8b + 1)
C. (2a – 4b – 1) (4a – 8b – 1)
D. (2a + 4b – 1) (4a + 8b + 1)
Answer : A

Question. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, then the value of a is ________.
A. 2/3
B. 1
C. 4/3
D. 5/3
Answer : D

Direction (a - b) : Study the given graph and answer the following questions.
(Number of students (in thousands) who opted for three different specializations during the five years in a University).

Question a. The total number of students who opted for English in the years 2012 and 2015 together are approximately what per cent of the total number of students who opted for all three subjects in the same years?
A. 38
B. 28
C. 42
D. 46
Answer : D

Question b. What is the respective ratio between the number of students who opted for Mathematics in the years 2012 and 2016 together and the number of students who opted for Hindi in the years 2013 and 2015 together?
A. 2 : 3
B. 12 : 7
C. 11 : 7
D. 12 : 5
Answer : A

Question. In the given figure, ΔABC is an equilateral triangle the length of whose side is equal to 10 cm and ΔDBC is right-angled at D and BD = 8 cm. Find the area of the shaded region. (Take √3 = 1.732)

A. 19.3 cm²
B. 43.3 cm²
C. 17.3 cm²
D. 21.3 cm²
Answer : A

Question. Given below are the marks scored by a group of 90 students in a Mathematics test of 100 marks.

(i) less than 20% marks.
(ii) 60 or more marks.
(i) (ii) (i) (ii)
A. 17/90 43/90
B. 7/90 43/90
C. 7/90 23/90
D. 17/90 23/90
Answer : C

Question. ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠A DC = 140°, then ∠BAC is equal to
A. 80°
B. 50°
C. 40°
D. 30°
Answer : B

Question. A, B, C are three sets of values of x given below.
A : 2, 3, 7, 1, 3, 2, 3
B : 7, 5, 9, 12, 5, 3, 8
C : 4, 4, 11, 7, 2, 3, 4
Which one of the following options is correct?
A. Mean of A = Mode of C
B. Mean of C = Median of B
C. Median of B = Mode of A
D. Mean, Median and Mode of A are equal.
Answer : D

Question. In the adjoining figure ∠CAB = 62°, ∠CBA = 76°, ∠ADE = 58° and ∠DFG = 66°, find ∠FGE.

A. 44°
B. 34°
C. 36°
D. None of these
Answer : B

Question. Using Euler’s formula, find the values of P, Q, R and S respectively.

A. 8, 6, 24, 54
B. 6, 8, 54, 24
C. 6, 8, 24, 54
D. 8, 6, 54, 24
Answer : A

Question. It is given that ΔABC ≅ ΔFDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then, which of the following is definitely true?
A. DF = 5 cm, ∠F = 60°
B. DF = 5 cm, ∠E = 60°
C. DE = 5 cm, ∠E = 60°
D. DE = 5 cm, ∠D = 60°
Answer : C

Question. The length and breadth of a hall are in the ratio 4 : 3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at ₹ 6.60 per square metre is ₹ 5082. Find the length and breadth of the hall.
A. 13 m, 7 m
B. 45 m, 37 m
C. 40 m, 30 m
D. 50 m, 50 m
Answer : C

Question. Based on Playfair’s axiom, for every line l and for every point P not lying on l, there exists _____ line(s) passing through P and parallel to l.
A. Two distinct
B. A unique
C. Three distinct
D. None of these
Answer : B

EVERYDAY MATHEMATICS

Question. Sam purchased 20 dozens of toys at the rate of ₹ 375 per dozen. He sold each one of them at the rate of ₹ 33. What was his profit percentage?
A. 3.5%
B. 4.5%
C. 5.6%
D. 6.5%
Answer : C

Question. Water flows through a cylindrical pipe of diameter 5 mm at the rate of 10 m per minute and falls into a conical vessel having 40 cm as the diameter of its base and 24 cm as its height. How long will it take to fill the vessel?
A. 48 mins 15 secs
B. 51 mins 2 secs
C. 52 mins 1 sec
D. 51 mins 12 secs
Answer : D

Question. A man takes 5 hours 45 mins in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways, is _____..
A. 3 hrs 45 mins
B. 7 hrs 30 mins
C. 7 hrs 45 mins
D. 11 hrs 45 mins
Answer : C

Question. From the salary of a worker, 10% is deducted as house rent, 15% of the rest he spends on children's education and 10% of the balance, he spends on clothes. After this expenditure, he is left with ₹ 1377. His salary is _____..
A. ₹ 2000
B. ₹ 2040
C. ₹ 2100
D. ₹ 2200
Answer : A

Question. A man borrows ₹ 12,500 at 20% compound interest. At the end of every year he pays ₹ 2000 as part repayment. How much does he still owe after three such installments?
A. ₹ 12,000
B. ₹ 12,864
C. ₹ 15,600
D. None of these
Answer : D

Question. 10 women can complete a work in 7 days and 10 children take 14 days to complete the same work. How many days will 5 women and 10 children take to complete the same work?
A. 3
B. 5
C. 7
D. Cannot be determined'
Answer : C

Question. Four different electronic devices make a beep after every 30 minutes, 1 hour, 1(1/2) hours and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at _____. .
A. 12 midnight
B. 3 a.m.
C. 6 a.m.
D. 9 a.m.
Answer : D

Question. If the price of erasers is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee?
A. 8
B. 6
C. 4
D. 2
Answer : B

Question. Incomes of A, B and C are in the ratio 7 : 9 : 12 and their expenditures are in the ratio 8 : 9 : 15. If A's saving is 1/4 of his income, then the ratio of savings of A, B and C is _____..
A. 56 : 99 : 69
B. 99 : 56 : 69
C. 69 : 56 : 99
D. 99 : 69 : 56
Answer : A

Question. A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is above the cost price by _____..
A. 20%
B. 39%
C. 40%
D. 50%
Answer : D

ACHIEVERS SECTION

Question. Length of a mathematics lab is 11/3 of its breadth and its height is 1/2 of its length. The cost of whitewashing the walls at the rate of ₹ 2.60 per m2 is ₹ 291.20.
Find the cost of tiling the floor at the rate of ₹ 6.75 per m².
A. ₹ 324
B. ₹ 624
C. ₹ 570
D. ₹ 420
Answer : A

Question. Match the following columns:

    (a) (b) (c) (d)
A. (r) (q) (s) (p)
B. (q) (r) (p) (s)
C. (q) (r) (s) (p)
D. (s) (r) (q) (p)
Answer : C

Question. State True or False and select the correct option.
P. In a DABC in which AB = AC, the altitude AD bisects BC.
Q. The sum of any two sides of a triangle is greater than twice the median drawn to the third side.
R. If D is the mid-point of the hypotenuse AC of a right DABC, then BD = AC.
S. Perimeter of a triangle is equal to the sum of its three medians.
T. If the altitudes AD, BE and CF of DABC are equal, then DABC is equilateral.
       P            Q         R         S           T
A. True      True     False    False    True
B. True      False    True     False    True
C. False    True     False    True      False
D. True     True     False    True      True
Answer : A

Question. Fill in the blanks and select the correct option.
(i) There is(are) P circle(s) passing through three non-collinear points.
(II) A continuous piece of a circle is called the Q of the circle.
(III) If two arcs of a circle are congruent, then their corresponding chords are R .
(IV) A line segment joining the centre to any point on the circle is called its S .
(V) The sum of either pair of opposite angles of a cyclic quadrilateral is T .
         P            Q               R                   S           T
A. Infinite     Chord     Not equal      Diameter    360°
B. Two          Arc        Equal            Diameter     360°
C. One         Chord    Equal            Radius        180°
D. One         Arc        Equal            Radius        180°
Answer : D

Question. Given below is a question followed by three statements.
You have to study the question and the statements and decide which of the statements is/are necessary to answer the question.
What is Arun's present age ?
I. Five years ago, Arun's age was double that of his son's age at that time.
II. Present ages of Arun and his son are in the ratio of 11 : 6 respectively.
III. Five years hence, the respective ratio of Arun's age and his son's age will become 12 : 7.
A. Only I and II
B. Only II and III
C. Only I and III
D. Any two of the three
Answer : D