CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set C

Logical Reasoning

Question. If the first and the second letters of the word MISJUDGEMENTS are interchanged with the last and the second last letters respectively, 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 fifth letter to the right of the third letter from the left end?
A. E
B. G
C. D
D. T
Answer : C

Question. The letter in the word ULTRAVIOLET are arranged in the alphabetical order and each letter is assigned numerical value equal to its serial number as in the English alphabet, what is the difference between the sum of odd-positioned numbers and that of evenpositioned numbers?
A. 11
B. 7
C. 15
D. 9
Answer : D

Question. Arun is fifth from the left end and Navin is twelfth from the right end in a row of children. If Navin shifts by three places towards Arun, he becomes tenth from the left end. How many children are there in the row?
A. 21
B. 22
C. 23
D. 24
Answer : D

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 fig. (4).

Answer : C

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

Answer : C

Question. A, B, C, D, E, F, G, H and K are sitting around a circle facing the centre. F is fourth to the right of A, who is third to the right of B. K is fourth to the left of B and third to the right of D. C is third to the right of H. E is second to the left of G.
What is E's position with respect to B?
A. Second to the left
B. Third to the right
C. Fourth to the right
D. Third to the left
Answer : D

Question. Which of the following Venn diagrams best represents the relationship amongst 'State, Country, Village'?

Answer : A

Question. Find the missing number, if same rule is followed row-wise or column-wise.

A. 2
B. 3
C. 6
D. 5
Answer : B

Question. Select a figure from the options, which when placed in the blank space of Fig.(X) would complete the pattern.

Answer : B

Question. Select the correct water image of given combination of letters and numbers.
                                                                S5L3T8

Answer : C

Question. In the given 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 on numbers progress 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 which is not a perfect square, 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 even number is to be subtracted from the odd number.
                                                    27 12 5
                                                    28 64 k
If the resultant of the first row is k, then what will be the resultant of the second row?
A. 42
B. 33
C. 108
D. 39
Answer : D

Question. A man travelled 400 metres straight from his office. He then turned left and travelled 500 metres straight, after which he turned left again and travelled for 400 metres straight. He then turned right and walked for another 600 metres straight. How far is he from his office?
A. 1.0 km
B. 1.1 km
C. 1.4 km
D. 1.8 km
Answer : B

Question. Which of the following is the tenth to the right of the nineteenth from the right end in the given arrangement?
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. M
B. T
C. A
D. 2
Answer : B

Question. Which of the following options satisfies the same condition of placement of dots as in Fig. (X)?

Answer : A

Question. Three different positions of a dice are shown below.
Which of the following colors will be opposite to the face having red color?

A. White
B. Pink
C. Brown
D. Violet
Answer : D

MATHEMATICAL REASONING

Question. Which of the following statements is INCORRECT?
A. There can be a real number which is both rational and irrational.
B. The sum of any two irrational numbers is not always irrational.
C. For any positive integers x and y, x < y ⇒ x² < y²
D. Every integer is a rational number.
Answer : A

Question. Find the value of l, so that y – 2p is a factor of y²/4p² - 2y + lp
A. 0
B. 1
C. 2
D. 3
Answer : C

Question. The number of dimensions, a point has
A. 0
B. 1
C. 2
D. 3
Answer : A

Question. The points, whose abscissa and ordinate have different signs, lie in _______ quadrants.
A. I and II
B. II and III
C. I and III
D. II and IV
Answer : D

Question. The figure below is the net of a prism made up of identical triangles. What is the total area of the faces of the prism, if the side of the square is 6 cm?

A. 75 cm²
B. 84 cm²
C. 95 cm²
D. 56 cm²
Answer : B

Question. The graph of line y = 6 is a line
A. Parallel to x-axis at a distance of 6 units from the origin.
B. Parallel to y-axis at a distance of 6 units from the origin.
C. Making an intercept of 6 units on the x-axis.
D. Making an intercept of 6 units on both the axes.
Answer : A

Question. Number of zeros of the zero polynomial is
A. 0
B. 1
C. 2
D. Infinite
Answer : D

Question. In the given figure, l ||BC and D is the mid-point of BC. 
If area (ΔABC) = x × area (ΔEDC), then find the value of x.

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

Question. Find the ratio of the shaded area to the area of the quadrilateral ABCD.

A. 2 + √6 : √6
B. 3 : 2 + √6
C. √6 : 2 + √6
D. √6 : 4 + √6
Answer : C

Question. The figure below is made up of a square ABCD and two rhombuses, ATCP and DRBV.

Given that ∠BVD = 135° and AT = BR, then find ∠PCT and ∠ABD respectively.
A. 135°, 135°
B. 135°, 45°
C. 45°, 135°
D. 45°, 45°
Answer : D

Question. The numbers 7.478478... and 1.101001000100001... are
A. Rational and irrational respectively
B. Both rationals
C. Both irrationals
D. None of these
Answer : A

Question. Factorise : x⁴ + 5x³ + 5x² – 5x – 6
A. (x² – 1)(x² + 6)
B. (x – 1)(x + 2)3
C. (x² – 1)(x + 3) (x + 2)
D. (x – 1)(x + 2) (x² + 3)
Answer : C

Question. 'Lines are parallel if they do not intersect' is stated in the form of
A. An axiom
B. A postulate
C. A definition
D. A proof
Answer : C

Question. The mean of a set of seven numbers is 81. If one of the number is discarded, then the mean of the remaining numbers is 78. The value of discarded number is
A. 98
B. 99
C. 100
D. 101
Answer : B

Question. Find the values of the integer s a and b respectively, for which the solution of the equation x√24 = x√3 + √6 is a+√b/7.
A. 4, 2
B. 2, 6
C. 3, 2
D. 9, 5
Answer : A

Direction (a - b) : The pie chart below shows the number of fruits sold on a particular day at a fruit stall

Question a. The ratio of the number of mangoes sold to the number of apples sold is 6 : 5. What percentage of the total sales came from the sale of mangoes?
A. 20%
B. 30%
C. 45%
D. 60%
Answer : B

Question b. If the total number of fruits sold was 200. Then how many bananas were sold on that day?
A. 20
B. 30
C. 32
D. 48
Answer : C

Question. The graph of the linear equation y = x passes through the point
A. (3/2, - 3/2)
B. (0, 3/2)
C. (1, 1)
D. (- 1/2, 1/2)
Answer : C

Question. If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has
A. Abscissa = –5
B. Ordinate = 5
C. Ordinate = –5
D. Ordinate = 5 or –5.
Answer : D

Question. In the given figure (not drawn to scale), LMNO is a parallelogram and OPQR is a rhombus. Find ∠NMH given that LMH is a straight line.

A. 80°
B. 60°
C. 70°
D. 50°
Answer : A

EVERYDAY MATHEMATICS

Question. A triangular park in a city has dimensions 100 m × 90 m × 110 m. A contract is given to a company for planting grass in the park at the rate of ₹ 4,000 per hectare. Find the amount to be paid to the company. (Take √2 =1.414 )
A. ₹ 4532.90
B. ₹ 4242
C. ₹ 1696.80
D. ₹ 1000
Answer : C

Question. Reema bought x pens at ₹ 2.60 each and y greeting cards at 80 paise each. If the pens cost ₹ 12 more than the cards, then the given condition is represented by the equation _______.
A. 13x – 4y = 6
B. 13x – 4y = 60
C. 260x – 8y = 100
D. 260x – 8y = 12
Answer : B

Question. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is
A. 45 : 56
B. 50 : 61
C. 99 : 125
D. None of these
Answer : A

Question. Ajay has certain amount in his account. He gives half of it to his eldest son and one third of the remaining to his youngest son. What fraction of the original amount is left with him now?
A. 1/3
B. 2/3
C. 3/4
D. 1/6
Answer : A

Question. In a call centre at New Delhi, it is observed that it gets a call at an interval of every 10 minutes from California, at an interval of every 12 minutes from Texas, at an interval of 20 minutes from Washington DC and after every 25 minutes it gets a call from London. If in the early morning at 5 : 00 a.m. it has received the calls simultaneously from all the four destinations, then at what time again it will receive the calls at a time from all the places on the same day?
A. 10 : 00 a.m.
B. 3 : 00 a.m.
C. 5 : 00 p.m.
D. Both A and B
Answer : A

Question. M and N alone can do a work in 21 and 42 days respectively. In how many days they can complete the work, if they work on alternate days?
A. 14
B. 28
C. 42
D. 35
Answer : B

Question. 75 kg of wheat is being consumed in 30 days by 24 persons. How many persons will consume 50 kg of wheat in 40 days ?
A. 10
B. 12
C. 15
D. 18
Answer : B

Question. A car travelling with 5/7 of its usual speed covers 45 km in 1 hour 40 mins 48 secs. What is the usual speed of the car?
A. 17(6/7)km/hr
B. 25 km/hr
C. 30 km/hr
D. None of these
Answer : D

Question. Roma took a loan of ₹ 16,000 against her insurance policy at the rate of 12(1/2) % per annum. Calculate the total compound interest that will be paid by Roma after 3 years.
A. ₹ 6781.25
B. ₹ 6925.30
C. ₹ 4296.82
D. ₹ 3579.71
Answer : A

Question. Cubical boxes of volume 15625 cm³ each are put in a cubical store of side 2.5 m.
(i) How many such boxes can be put in the store?
(ii) What are the dimensions of the box?
       (i)         (ii)
A. 1250    15 cm
B. 1000    15 cm
C. 1250    25 cm
D. 1000    25 cm
Answer : D

Achievers section

Question. The figure below is made up of one big circle, two identical medium circles and two identical small circles.
The ratio of the radius of the small circle to the radius of the medium circle is 2 : 3.
(a) What is the total area of the unshaded part in the figure?
(b) What fraction of the big circle is shaded?

          (a)                (b)
A. 144 π cm²        5/18
B. 104 π cm²        5/18
C. 104 π cm²        13/18
D. 144 π cm²        13/18
Answer : B

Question. Study the statements carefully.
Statement I : If p(x) is a polynomial of degree ≥ 1 and ax + b is a factor of p(x), then we have p(-b/a) = 0
Statement II : If p(x) is a polynomial of degree ≥ 1 , then  polynomial
(x – a)(x – b) is a factor of p(x) iff
p(a) = 0 and p(b) = 0.
A. Both Statement I and Statement II are true.
B. Both Statement I and Statement II are false.
C. Statement I is true, Statement II is false.
D. Statement I is false, Statement II is true.
Answer : A

Question. ABCDE.... is part of a regular polygon which has interior angles of 160°. CDLM is a square.

Find the value of x and y respectively.
A. 70, 105
B. 70, 150
C. 105, 70
D. 150, 70
Answer : A

Question. In the figure, A and B are the centres of the two intersecting circles. Which Euclid’s axiom will prove that the ΔABC is an equilateral triangle?

A. If equals are added to equals, the wholes are equal.
B. Things which are double of the same things are equal to one another.
C. Things which are equal to the same thing are equal to one another.
D. If equals are subtracted from equals, the remainders are equal.
Answer : C

Question. In the given figure (not drawn to scale), ΔABC and DBDE are two equilateral triangles such that BD = CD and AE intersects BC at F. Then match the columns.

       Column-I                    Column-II
(i) Area (ΔBDE)     =      (p) 2 × Area (ΔFED)
(ii) Area (ΔFED)     =     (q) 1/4 × Area (ΔABC)
(iii) Area (ΔBFE)    =     (r) 1/8 × Area (ΔAFC)
A. (i) → (r), (ii) → (p), (iii) → (q)
B. (i) → (r), (ii) → (q), (iii) → (p)
C. (i) → (q), (ii) → (p), (iii) → (r)
D. (i) → (q), (ii) → (r), (iii) → (p)
Answer : D