CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set N

LOGICAL REASONING

Question. If the words in the sentence, “She showed several sample snaps to Shikha's maternal sister” are rearranged in the alphabetical order, which will be the middle word?
A. Snaps
B. Sample
C. Several
D. Shikha's
Answer : D

Question. In a certain code REFERENDUM is written as HZZRBUCHDS and SIMULATION is written as ITEXXOSOHT. How is EXECUTIVES written in that code language?
A. NJNQMXAWGH
B. ITOEKHLQST
C. NJQNQXAWGF
D. NJRMQXAGWF
Answer : D

Question. Among six friends L, M, N, P, Q and S, each having a different height, N is taller than Q and P but shorter than M. P is taller than only Q while S is shorter than only L. Which of the following pairs represents the tallest and the shortest respectively among the five friends?
A. M, P
B. L, Q
C. P, Q
D. Can’t be determined
Answer : B

Question. Pointing to Mohit, Sana said, “His mother’s brother is the father of my son Nitin.” How is Mohit related to Sana?
A. Niece
B. Uncle
C. Nephew
D. Brother
Answer : C

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

Answer : C

Question. Two positions of a dice are shown below. If the face with 1 dot is at bottom, then the number of dots on the top is _______.

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

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

Answer : A

Question. Study the following arrangement carefully and answer the question given below.
1 H # U J 9 4 $ R 2 K • E L 9 H P A % T 3 F M T @ 7 G O S = 6 X
How many such symbols are there in the above arrangement, each of which is immediately followed by a vowel and not immediately preceded by a number?
A. One
B. Two
C. Three
D. Zero
Answer : B

Question. Priya starts from point N and moves 25 metres south, then she turns left and moves 30 metres, then she turns right and moves 15 metres to reach point P. What is the distance of P from N and which direction is she facing with respect to point N?
A. 50 metres South-West
B. 50 metres South-East
C. 45 metres South-East
D. 40 metres South
Answer : B

Question. There are two rows of numbers. 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 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, they are to be added.
(iii) If an even number is followed by a number which is the 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.
If x is the resultant of the first row, what is the resultant of the second row?
36 27 7
x 15 126
A. 125
B. 11
C. 9
D. 15
Answer : C

Question. Study the following information carefully and answer the question given below.
(i) In a family of 6 persons, there are two couples.
(ii) The Lawyer is the head of the family and has only two sons–Mrinal and Rakesh–both Teachers.
(iii) Mrs. Reena and her mother-in-law both are Lawyers.
(iv) Mrinal's wife is a Doctor and they have a son, Ajay.
What is/was Ajay's Grandfather's occupation?
A. Teacher
B. Lawyer
C. Doctor
D. Can't be determined
Answer : D

Question. Rohit is sixteenth from the front in a column of boys.
There are twice as many behind him as there are in front. How many boys are there between Rohit and fifth boy from the end of the column?
A. 26
B. 25
C. 10
D. Can't be determined
Answer : B

Question. Study the given diagram and identify the region representing girls who are employed and educated.

A. 5 only
B. 1, 4, 7
C. 4, 7
D. 4, 5, 6
Answer : A

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

Answer : C

Question. Select a figure from amongst the options which shows similar characteristics/properties as shown by the Problem figures.

Answer : C

Question. Which of the following is the correct mirror image of the given Fig. (X), if the mirror is placed vertically right ?

Answer : B

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

Answer : B

Question. Find the missing character, if the same rule is applied to (i), (ii) and (iii).

A. 184
B. 210
C. 241
D. 425
Answer : A

Question. The question is based on the following six numbers.
382 473 568 728 847 629
If 382 is written as 238, 473 as 347 and so on, then which of the following two numbers will have least difference between them?
A. 473 & 382
B. 629 & 728
C. 629 & 568
D. 728 & 847
Answer : D

Question. If 'A @ B' means 'A is added to B'; 'A * B' means 'A is multiplied by B'; 'A # B' means 'A is divided by B'; 'A $ B' means 'B is subtracted from A'; then number of boys (B) in a class is equal to one-fourth of three times the number of girls (G) in the class can be represented as ______.
A. B = (3 # G) *4
B. B = (3 * G) @4
C. B = (3 * G) # 4
D. B = (3 $ G) # 4
Answer : C

MATHEMATICAL REASONING

Question. The equations x – y = 1 and 2x + y = 8 are given.
The area bounded by these two lines and y-axis is ______.
A. 8 sq. units
B. 13.5 sq. units
C. 11 sq. units
D. 9 sq. units
Answer : B

Question. PS and QT are the medians of ΔPQR and QT||SU. If PR = 12 cm, find the value of RU.

A. 6 cm
B. 2.5 cm
C. 4 cm
D. 3 cm
Answer : D

Question. In the given figure, O is the centre of the circle. If ∠AOB = 90°, find m ∠APB.

A. 130°
B. 150°
C. 135°
D. Can’t be determined
Answer : C

Question. In a class, teacher gave two identical cardboard pieces which are in the shape of a parallelogram to two groups. First group was asked to find area of parallelogram using AB as base. Then, another group was asked to find height h of the parallelogram with AD as base.

What is the height of the parallelogram in group II?
A. 4.8 cm
B. 4 cm
C. 5.6 cm
D. 8.4 cm
Answer : A

Question. In the adjoining figure, the value of x is

A. 110°
B. 130°
C. 120°
D. 125°
Answer : C

Question. Find the value of p, if the mean of the following distribution is 7.5.

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

Question. In the given figure, AB is a diameter of a circle with centre O. If ADE and CBE are straight lines, meeting at E such that ∠BAD = 35° and ∠BED = 25°, find ∠BDC.

A. 25°
B. 30°
C. 35°
D. 115°
Answer : B

Question. In the given figure, the radius of each of the smallest circles (C₁, C₂, C₃, C₄, C₅, C₆ and C₇) is 1/12 of the radius of the biggest circle B1. The radius of each of the middle sized circles (P₁, P₂, P₃ and P₄) is three times the radius of the smallest circle. The area of the shaded portion is _____ times the area of the biggest circle.

A. 23/48
B. 53/48
C. 14/23
D. 51/91
Answer : B

Question. A triangle has sides with lengths 13 cm, 14 cm and 15 cm. A circle whose centre lies on the longest side touches the other two sides. The radius of the circle is (in cm) ______

A. 43/9
B. 49/9
C. 56/9
D. 63/15
Answer : C

Question. PQR is a triangle in which PQ = 5.6 cm, PR = 4.8 cm and QR = 6.2 cm. M is the midpoint of PQ and N is the midpoint of PR. Calculate the perimeter of trapezium MNRQ.
A. 12.5 cm
B. 16.5 cm
C. 18.5 cm
D. 14.5 cm
Answer : D

Question. The area of the triangle formed by the 2x + 3y = 6 and the coordinate axes is
A. 1 sq. unit
B. 2 sq. units
C. 3 sq. units
D. 4 sq. units
Answer : C

Question. A bar code is formed using 25 black and certain white bars. White and black bars alternate. The first and the last are black bars. Some of the black bars are thin and others are wide.

The number of white bars is 15 more than the thin black bars.
The number of thick black bars is _____.
A. 14
B. 15
C. 16
D. 17
Answer : C

Question. In the given figure, PQRS is a cyclic quadrilateral.

Find the value of x.
A. 100°
B. 180°
C. 270°
D. 120°
Answer : A

Question. In the given figure, PQRS is a parallelogram, PO and QO are, respectively, the angle bisectors of ∠P and ∠Q. Line LOM is drawn parallel to PQ. Which of the following is true?

A. PL = QM
B. LO = OM
C. OM = QM
D. All of these
Answer : D

Question. OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If OE =2 5cm, find the area of the rectangle.

A. 20 cm²
B. 4 5 cm²
C. 40 cm²
D. 80 cm²
Answer : C

EVERYDAY MATHEMATICS

Question. Karan tells his daughter Alia, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". If present ages of Alia and Karan are x and y years respectively, represent this situation algebraically.
A. 7x – y = 42; y – 3x = 6
B. x – y = 42; y – 3x = 6
C. x – 7y = 6; y – x = 4
D. x – 7y = 42; 3y – x = 6
Answer : A

Question. A cylindrical road roller made of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the roller if 1 c.c. of iron weighs 8 gm.
(p = 3.14)
A. 1425.6 kg
B. 1424.304 kg
C. 1567.06 kg
D. 1424.034 kg
Answer : B

Question. In a cricket match, a batsman hits a boundary 8 times out of 40 balls he plays. Find the probability that he didn't hit a boundary.
A. 4/7
B. 0.10
C. 0.8
D. 5/7
Answer : C

Question. Pratik invested an amount of ₹ 12,000 at the rate of 10 % p.a. simple interest and another amount at the rate of 20 % p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14 % p.a. Find the total amount invested.
A. ₹ 20,000
B. ₹ 22,000
C. ₹ 24,000
D. ₹ 25,000
Answer : A

Question. The largest possible length of a tape which can measure 525 cm, 1050 cm and 1155 cm length of clothes in a minimum number of attempts without measuring the length of a cloth in a fraction of the tape's length is ______.
A 25 cm
B. 105 cm
C. 75 cm
D. 50 cm
Answer : B

Question. When a barrel is 40% empty it contains 80 litres more than when it is 20% full. The full capacity of the barrel (in litres) is _____.
A. 200 litres
B. 300 litres
C. 358 litres
D. 400 litres
Answer : A

Question. A heap of wheat is in the form of a cone, whose diameter is 10.5 m and height 7 m. Find the lateral surface area of wheat in the heap.
A. 202.25 m²
B. 202.125 m²
C. 200.25 m²
D. None of these
Answer : D

Question. Three fair coins are tossed simultaneously. Find the probability of getting atleast two heads.
A. 3/8
B. 7/8
C. 1/2
D. 1/4
Answer : C

Question. There are only five people in Aman's family. Aman, his wife, a son and two daughters. The younger daughter’s age is (4/5)^th of the elder daughter’s age.
The age of eldest daughter is 3/8 times that of her father Aman and the age of the son is (1/5)^th that of his father Aman. 4 years ago the age of his wife was 8 times that of his son and now the sum of the ages of the younger daughter and wife is same as the sum of the ages of Aman and his son. The average age of the family is
A. 22.2 years
B. 25.4 years
C. 21.2 years
D. 23 years
Answer : A

Question. The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
A. 91
B. 910
C. 1001
D. 1911
Answer : A

ACHIEVERS SECTION

Question. Rearrange the following steps of constructing a triangle when the base angles say ∠B and ∠C and its perimeter BC + CA + AB is given
(1) Draw perpendicular bisectors PQ of AX and RS of AY.
(2) Draw a line segment, say XY equal to BC + CA + AB.
(3) Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.
(4) Make angles LXY equal to ∠B and MYX equal to ∠C.
(5) Bisect ∠LXY and ∠MYX. Let these bisectors intersect at a point A.
A. 1 → 3 → 5 → 4 → 2
B. 2 → 4 → 5 → 1 → 3
C. 5 → 4 → 3 → 2 → 1
D. 2 → 3 → 5 → 4 → 1
Answer : B

Question. Which of the following statements is INCORRECT?
A. A linear equation in two variables has infinitely many solutions.
B. The graph of every linear equation in two variables is a straight line.
C. The graph of x = a is a straight line parallel to the y-axis.
D. Every point on the graph of a linear equation in two variables is a solution of the linear equation. Every solution of the linear equation may not be a point on the graph of the linear equation.
Answer : D

Question. Fill in the blanks.
A circle is the collection of all points in a plane which are P from a fixed point in the plane.
The fixed point is called Q of the circle and fixed distance is called R of the circle. A circle divides the plane on which it lies into S parts.
         P                        Q                R               S
A. Equal                  radius         centre         two
B. Equidistant         centre         radius         three
C. Distanc               ecentre       radius         two
D. Normal               radius          centre        four
Answer : B

Question. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. The perimeter of the parallelogram is _______ than that of the rectangle.

A. Greater
B. Lesser
C. Equal
D. Can't be determined
Answer : A

Question. If a + b = 10 and ab = 21, a > 0 & b > 0 then
 Column-I        Column-II
(i) a³ – b³        (p) 58
(ii) a² + b²       (q) 40
(iii) a² – b²       (r) 316
A. (i)–(r), (ii)–(q), (iii)–(p)
B. (i)–(p), (ii)–(q), (iii)–(r)
C. (i)–(r), (ii)–(p), (iii)–(q)
D. (i)–(p), (ii)–(r), (iii)–(q)
Answer : C