CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set H

LOGICAL REASONING

Question. Read the following information carefully to answer the question.
Mr and Mrs Oberoi has three children Sakshi, Rashmi and Vishesh. Vishesh has married to Shikha who is daughter of Mr Sharma who is married to Rashi.
Sonu and Rocky are the children of Tarun and Rashi. Neha and Sidhi are daughters of Vishesh and Shikha. 
What is the relation of Sakshi to Neha?
A. Sister
B. Niece
C. Aunt
D. Daughter
Answer : C

Question. Find the missing number, if same rule is followed in all the three figures.

A. 3
B. 4
C. 5
D. 6
Answer : C

Question. Six students P, Q, R, S, T and U participated in a dancing competition wherein they won prizes ₹ 12000, ₹ 10000, ₹ 8000, ₹ 6000, ₹ 4000 and ₹ 2000 according to the position secured. The following information is known to us :
I. P won less money than Q.
II. The difference between the winning amount of R and U was ₹ 2000.
III. The difference between the winning amount of S and U was at least ₹ 4000.
IV. T won ₹ 8000 prize.
If P won ₹ 4000, then how much in total did R and U win?
A. ₹ 6000
B. ₹ 10000
C. ₹ 22000
D. ₹ 18000
Answer : C

Question. Sneha walks 2 km North from A to B. She turns right at 90° and goes 3 km upto C. She, then again turns right at 90° and goes 8 km upto D. Again she takes right turn at 90° and goes 3 km upto K. From K she takes right turn at 90° again and reaches at F after covering 4 km. Find the distance between A and F.
A. 2 km
B. 4 km
C. 6 km
D. 8 km
Answer : A

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

Answer : A

Question. Read the given information to answer the question that follows:
Seven people A, B, C, D, E, F and G are planning to enjoy boating. There are only two boats and the following conditions are to be kept in mind.
I. A will go in the same boat in which E is to go.
II. F cannot go in the boat in which C is to go, unless D is also accompanying.
III. Neither B nor C can be given the boat in which G is.
IV. The maximum number of persons in one boat can be four only.
If F and B are in one boat, which of the following statements is true?
A. G is in the other boat.
B. D is in the other boat.
C. C is in the other boat.
D. E is with F and B in one boat.
Answer : A

Question. Which of the following figures is exactly embedded in Fig. (X) as one of its parts?

Answer : B

Question. Given below are the three different positions of a dice. What shall come in the place of 'X'?

Answer : A

Question. Select the correct water image of Fig. (X).

Answer : D

Question. If first four letters of the English alphabet are written in reverse order; again next 5 letters are written in reverse order; again next 6 letters are written in reverse order; again next 7 letters are written in reverse order and finally, the remaining letters are also written in reverse order, then what will be the 9th letter to the right of the 7th letter from left end?
A. M
B. N
C. O
D. V
Answer : D

Question. In a certain code language, if 'DOWN' is written as '5@9#' and 'NAME' is written as '#6%3', then ‘%@53’ be the code for ______.
A. DAME
B. MADE
C. DOME
D. MODE
Answer : D

Question. Select the odd one out.

Answer : C

Question. A word and number arrangement machine when given an input line of words and numbers, rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement.
Input : 40 made butter 23 37 cookies salt extra 52 86 92 fell now 19
Step I : butter 19 40 made 23 37 cookies salt extra 52 86 92 fell now
Step II : cookies 23 butter 19 40 made 37 salt extra 52 86 92 fell now
Step III : extra 37 cookies 23 butter 19 40 made salt 52 86 92 fell now
Step IV : fell 40 extra 37 cookies 23 butter 19 made salt 52 86 92 now
Step V : made 52 fell 40 extra 37 cookies 23 butter 19 salt 86 92 now
Step VI : now 86 made 52 fell 40 extra 37 cookies 23 butter 19 salt 92
Step VII : salt 92 now 86 made 52 fell 40 extra 37 cookies 23 butter 19
Step VII is the last step of the arrangement. As per the rules followed in the given steps, find out the appropriate steps for the given input and answer the question follows.
Input : 32 proud girl beautiful 49 58 97 rich family 61 72 17 nice life
What is the position of 'nice' from the left end in the last step?
A. Fifth
B. Tenth
C. Seventh
D. Eighth
Answer : A

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

Answer : D

Question. How many squares are there in the given figure?

A. 24
B. 23
C. 27
D. None of these
Answer : D

MATHEMATICAL REASONING

Question. In the given figure, if ∠AOB = a/2 ,∠BOC = 5(a/2 - 10°) and ∠COD = a + 9°, then find ∠AEO + ∠EAO.

A. 127.75°
B. 130.75°
C. 129.50°
D. 115.75°
Answer : D

Question. If

then find x.
A. 3
B. 2
C. 1
D. 4
Answer : A

Question. The three vertices of a rectangle ABCD are A(2, 2), B(–3, 2) and C(–3, 5). Find the area of rectangle ABCD.
A. 15 sq. units
B. 35 sq. units
C. 20 sq. units
D. 25 sq. units
Answer : A

Question. In the given figure, if ABCD is a square and EF is parallel to diagonal BD and EM = FM, then which of the following is correct?
(i) DF = BE
(ii) AM bisects ∠BAD

A. Only (i)
B. Only (ii)
C. Both (i) and (ii)
D. Neither (i) nor (ii)
Answer : C

Question. Sahil and Kush are equidistant from the Park. Upon considering the park as origin, the position of Sahil is (0, 5). If the ordinate of the position of Kush is zero, then out of the following options what will be the position of the Kush?
A. (0, –5)
B. (5, 0)
C. (0, 0)
D. (5, 5)
Answer : B

Question. It is known that if a + b = 10, then a + b – c = 10 – c.
State the Euclid's axiom that best illustrates this statement.
A. If equals be subtracted from equals, the remainders are equal.
B. Things which are halves of the same thing are equal to one other.
C. The whole is greater than the part.
D. None of these
Answer : A

Question. In the given figure, ∠POT = 150° and O is the centre of circle. Find the measure of
(i) ∠RQT
(ii) ∠PUT

      (i)          (ii)
A. 75°          75°
B. 105°        75°
C. 105°      105°
D. 75°        105°
Answer : B

Question. In the given figure, a right circular cone of diameter r cm and height 12 cm rests on the base of a right circular cylinder of radius r cm. Their bases are in the same plane and the cylinder is filled with water upto a height of 12 cm. If the cone is removed, then find the height to which water level will fall.

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

Question. The diagonals of a parallelogram ABCD intersect at a point O. Through O, if a line is drawn to intersect AD at P and BC at Q, then PQ divides the parallelogram into _________ .

A. Two parts of equal area
B. Two parts of area in 2 : 1
C. Two parts of area in 1 : 3
D. Two parts of area in 4 : 3
Answer : A

Question. The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
5     3  10    20    25    11   13     7    12        31
1     9  10    12    17   18    11   32    17    16 2
7     9   7       8      3     5    12   15    18         3
12 14   2       9      6   15    15     7     6          2
Find the probability that an engineer lives :
(i) less than 6 km from their place of work.
(ii) at least 6 km from their place of work.
(iii) within 1 km from their place of work.
(iv) at most 7 km from their place of work.
     (i)    (ii)    (iii)    (iv)
A. 2/5   4/5   3/5   3/20
B. 3/5   1/5   2/5   3/20
C. 4/5   1/5     0    7/20
D. 1/5   4/5     0    7/20
Answer : D

Question. Simplify:

A. x^119/121
B. x^119/120
C. x^117/120
D. x^113/120
Answer : B

Question. In the given figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY = _________

A. 5 cm
B. 6 cm
C. 7 cm
D. 8 cm
Answer : C

Question. In the given figure, AB || CD and PQ, QR intersects AB and CD both at E, F and G, H respectively. Find the value of x.

A. 40°
B. 20°
C. 100°
D. None of these
Answer : B

Question. Which of the following is INCORRECT.

A. It is possible to construct an angle of 67.5° using ruler and compass only.
B. It is possible to construct a ΔPQR in which QR = 6 cm, ∠Q = 130° and ∠R = 50°.
C. It is possible to construct a ΔXYZ in which ∠X = 60°, ∠Y = 100° and ∠Z = 20°.
D. In a ΔABC, AB + BC > AC.
Answer : B

Question. The following are the steps involved in finding the value of a⁴ + 1/a⁴, when a + 1/a = 1 Arrange them in sequential order from the first to the last.

A. RPSQT
B. RSQPT
C. RQPST
D. RTSPQ
Answer : A

Question. In the rectangular coordinate system given below, the shaded region is bounded by two straight lines. Which of the following is not an equation of one of the boundary lines ?

A. x = 0
B. x = 1
C. x – y = 0
D. None of these
Answer : C

Question. If a = 5 + 2√6 and b = 1/a , then what will be the value of a² + b² and a³ + b³ ?
A. 98, 970
B. 98, 1000
C. 981, 985
D. 970, 560
Answer : A

Question. Which of the following experiments does not have equally likely outcomes?
A. Choosing a number at random from 1 to 7.
B. Tossing of a coin.
C. Choose a letter at random from the word SCHOOL.
D. None of these.
Answer : C

Question. The median of the following data : 0, 2, 2, 2, –3, 5, –1, 5, 5, –3, 6, 6, 5, 6 is n × 0.7. Find the value of n.
A. 4
B. 5
C. 6
D. 7
Answer : B

Question. In the given figure, P and Q are centres of two circles, intersecting at B and C and ACD is a straight line.
If ∠APB = 150° and ∠BQD = x then find the value of x.

A. 210°
B. 105°
C. 75°
D. 150°
Answer : D

EVERYDAY MATHEMATICS

Question. A machine M can print ten thousand books in 6 hours, machine N can print the same number of books in 8 hours while machine S can print them in 10 hours.
All the machines started at 10 a.m. while machine M is closed at 12 noon and the remaining two machines complete the work. Approximately at what time will the work be finished?
A. 12 : 30 p.m.
B. 1 : 00 p.m.
C. 2 : 00 p.m.
D. 2 : 30 p.m.
Answer : B

Question. In an examination in which maximum marks were 800, A gets 15% more than B, B gets 25% more than C and C gets 10% less than D. If A got 598 marks, then what percentage of full marks did D get (approximately)?
A. 45.8 %
B. 62.3 %
C. 57.8 %
D. None of these
Answer : C

Question. Priya has ₹ ( x³ + x² – 17x + 20). She wants to buy ice-cream cones each of cost ₹ (x – 3). After buying maximum number of ice-cream cones with her money, how much money is left with her?
A. ₹ 10
B. ₹ 50
C. ₹ 15
D. ₹ 5 
Answer : D

Question. A part of monthly expenses of a family on milk is fixed which is ₹ 700 and remaining varies with quantity of milk taken extra at the rate of ₹ 25 per litre. Taking quantity of milk required extra as x litres and total expenditure on milk as ₹ y, write a linear equation from the above information.
A. –25x + y = 700
B. 20x + y = 500
C. 20x + 10y = 300
D. x + 25y = 900
Answer : A

Question. In a class of 100 students, 23 students like dance and 39 students like computer. A student is selected at random. Find the probability that the selected student likes computer.
A. 39/100
B. 29/50
C. 19/50
D. 39/50
Answer : A

Question. A closed rectangular box of length, breadth and height are 3 m, 2 m and 1 m respectively. Find the cost of cloth to cover box completely, if 1 m2 cloth costs ₹ 10.
A. ₹ 22
B. ₹ 2200
C. ₹ 220
D. ₹ 200
Answer : C

Question. The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, then find his lowest score.
A. 55
B. 60
C. 62
D. Can't be determined
Answer : B

Question. Nitesh borrows a sum of ₹ 1200 at the beginning of a year. After 4 months, ₹ 1800 more is borrowed at a rate of interest double the previous one. At the end of a year, the sum of interest on both the loans is ₹ 216. What is the first rate of interest per annum?
A. 9 %
B. 6 %
C. 8 %
D. 12 %
Answer : B

Question. Two trains A and B start running together from the same point in the same direction at 40 kmph and 64 kmph respectively. If the length of each train is 300 m, then how long will it take for the train B to cross train A?
A. 2 min 30 sec
B. 1 min 45 sec
C. 2 min 12 sec
D. 1 min 30 sec
Answer : D

Question. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?
A. 26 minutes 18 seconds
B. 42 minutes 36 seconds
C. 45 minutes
D. 46 minutes 12 seconds
Answer : C

ACHIEVERS SECTION

Question. By using a given figure of quadrilateral ABCD, match the columns.

Column-I                                                                                                            Column-II
P. If ABCD is a parallelogram, then sum of the angles x, y and z is                    (1) 25°
Q. If ABCD is a rhombus, where ∠D = 130°, then the value of x is                     (2) 180°
R. If ABCD is a rhombus, then the value of w is                                                  (3) 50°
S. If ABCD is a parallelogram, where x + y = 130°, then the value of ∠B is        (4) 90°
      P   Q   R   S
A. (1) (2) (3) (4)
B. (3) (4) (2) (1)
C. (2) (1) (4) (3)
D. (2) (4) (3) (1)
Answer : C

Question. Simplify:

      (i)       (ii)
A. 270      xabc
B. 330       0
C. 330       1
D. 270       1/x^abc
Answer : C

Question. Read the statements carefully and select the correct option.
Statement-I : If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x) and g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x). q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).
Statement-II : 3x2 + x – 1 = (x + 1) (3x – 2) + 1.
A. Both Statement-I and Statement-II are true.
B. Both Statement-I and Statement-II are false.
C. Statement-I is true but Statement-II is false.
D. Statement-I is false but Statement-II is true.
Answer : A

Question. Read the statements carefully and state 'T' for true and 'F' for false.
P. The area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm is 18 cm2.
Q. An advertisement board is in the form of an isosceles triangle with its sides equal to 12 m, 10 m and 10 m. The cost of painting it at ₹ 2.25 per m2 is ₹ 112.
R. The area of an equilateral triangle is 81 3 2 cm , then its height is 9 3cm.
S. The lengths of the three sides of a triangular field are 40 m, 24 m and 32 m respectively. The area of the triangle is 384 m².
    P Q R  S
A. F T  T  F
B. F F  T  T
C. T T  F  F
D. T F  T  F
Answer : B

Question. Fill in the blanks.
(i) A sphere is placed inside the cylinder and touches all the faces of cylinder, then ratio of the volume of cylinder to the volume of sphere is P .
(ii) Q bricks will be required to construct a wall 10 m long, 6 m high and 22.5 cm thick, if each brick measures 25 cm by 12 cm by 9 cm.
(iii) The largest sphere is carved out of a cube of side 7 cm. Then the volume of the sphere is R .
(iv) Curved surface area of the hollow cylinder of radii r₁ and r₂ and height h is S .
      P         Q             R                      S
A. 2:3     6000    189.67 cm³    2ph(r₁ – r₂)
B. 3:2     6000    179.66 cm³    2ph(r₁ – r₂)
C. 2:3     5000    189.67 cm³    2ph(r₁ + r₂)
D. 3:2     5000    179.67 cm³    2ph(r₁ + r₂)
Answer : D