CBSE Class 9 Mathematics IMO Olympiad MCQs with Answers Set D

Logical Reasoning

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 which will replace the (?) in fig. (4).

Answer : B

Question. Sandeep, Suraj and Swarn are in control of the following number-letter-symbol series respectively.
Sandeep : 7 F Q 8 D l ⇑ Z 1 O – A 2
Suraj : C ¤ 3 + 5 ♥ B ≠ Q ♣
Swarn : L T ⇐ 6 M ý 4 N 9 £
If the first five elements of Sandeep are picked up and written in reverse order followed by last five elements of Suraj and Swarn each, then which of the following elements will be 7th to the left of 5th element from the right end in the series formed?
A. F
B. B
C. 8
D. D
Answer : A

Question. How many pairs of letters are there in the word OPERATION which have as many letters between them as in the English alphabet?
A. Four
B. Seven
C. Five
D. More than seven
Answer : D

Question. The following digits are coded as follows:
Digit                 : 5    7   0  9  3  1   6  4  8   2
Letter/Symbol : K  E  H  $  D  A  J  Q  R  @
While coding the given number following conditions are also to be observed.
(i) If the first as well as the last digit is odd their codes are to be interchanged. 
(ii) If the first digit is even and the last digit is odd, both are to be coded as the code for odd digit.
(iii) If the last digit is '0' it is to be coded as 'X'.
(iv) If the first as well as the last digit is even both are to be coded as '–'.
586403
A. KRJQHD
B. DRJQHK
C. DHJQRK
D. KHJQRD
Answer : B

Question. Select the odd one out.

Answer : C

Question. How many such 6's are there in the following number series, each of which is immediately preceded by 1 or 5 and immediately followed by 3 or 9?
2 6 3 7 5 6 4 2 9 6 1 3 4 1 6 3 9 1 5 6 9 2 3 1 6 5 4 3 2 1 9 6 7 1 6 3
A. 0
B. 1
C. 2
D. 3
Answer : D

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

A. 18
B. 24
C. 36
D. 58
Answer : B

Question. Find the correct mirror-image of the given combination, if the mirror is placed vertically to the left.

Answer : A

Question. Which of the following Venn diagrams best represents the relationship amongst 'Beverages, Cold drinks, Pepsi'?

Answer : C

Question. M is sister of K. D is brother of K. F is mother of M. How is K related to F?
A. Son
B. Daughter
C. Son or Daughter
D. None of these
Answer : C

Question. Four positions of a dice are given below. Find the sum of numbers opposite to 6 and 4.

A. 1
B. 4
C. 5
D. 3
Answer : D

Question. P, Q, R, S, T, V, W and Z are sitting around a circle facing the centre. T is second to the right of R, who is third to the right of P. S is second to the left of P and fourth to the right of Q. Z is third to the right of V, who is not an immediate neighbour of P.
What is P's position with respect to S?
A. Fourth to the left
B. Fourth to the right
C. Fifth to the left
D. Sixth to the left
Answer : D

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

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

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

Answer : B

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

Answer : B

MATHEMATICAL REASONING

Question. If a = √3+√2/√3+√2 and b = √3+√2/√3+√2, then find the value of a² + b².
A. 40 6
B. 96
C. 20 3
D. 98
Answer : D

Question. Which of the following statements is true?
(i) In a DABC, if AB = AC, then altitude AD bisects BC. 
(ii) If the altitudes AD, BE and CF of DABC are equal, then DABC is equilateral.
(iii) If D is the midpoint of the hypotenuse AC of a right DABC, then BD = AC.
A. (i) only
B. (ii) only
C. Both (i) and (ii)
D. All are true
Answer : C

Question. A, B and C are three points on the circle whose centre is at O. Select the correct option.

A. x + y = 90°
B. x – y = 90°
C. t + 2y = 90°
D. None of these
Answer : B

Question. The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. Find the length of perpendicular from the opposite vertex to the side whose length is 13 cm.
A. (60/13)cm
B. (30/13)cm
C. (120/13)cm
D. 10 cm
Answer : A

Question. If the perpendicular distance of a point P from the x-axis is 4 units in the negative direction of the y-axis, and the perpendicular distance of P from the y-axis is 5 unit in the positive direction of x-axis, then the coordinates of P are
A. (–5, –4)
B. (5, –4)
C. (–4, 5)
D. (–4, –5)
Answer : B

Question. Which of the following is the factor of the polynomial 
p(x) = x⁴ + 5x³ + 9x² + 15x + 18?
A. x² + 5x + 6
B. x² – 5x + 6
C. x² + 5x – 6
D. x² – 5x – 6
Answer : A

Question. The radius and height of a cone are in the ratio 3 : 4. If its volume is 301.44 cm³, then find 
(i) radius of the cone (ii) slant height of the cone.
(Take π = 3.14)
       (i)                  (ii)
A. 9 cm           10 cm
B. 10 cm           9 cm
C. 10 cm           6 cm
D. 6 cm           10 cm
Answer : D

Question. The figure below is not drawn to scale. Find ∠GCD, if AG || CF.

A. 25°
B. 75°
C. 100°
D. 141°
Answer : C

Question. If AB||EF||DC and the area of ΔAFD is 42 cm², find the area of ΔBCE.

A. 21 cm²
B. 42 cm²
C. 48 cm²
D. 84 cm²
Answer : D

Question. A card is drawn from a well shuffled pack of 52 cards, find the probability of getting a non-face card.
A. 10/13
B. 9/13
C. 12/13
D. 3/13
Answer : A

Question. How many least number of distinct points determine
a unique line?
A. 1
B. 2
C. 3
D. 4
Answer : B

Question. Which of the following are solutions of the equation 2x + 3y = 12?
A. (3, 2)
B. (2, 3)
C. ( 2, 3)
D. (3, 2/3)
Answer : A

Question. Factorize : p³(q – r)³ + q³(r – p)³ + r³(p – q)³
A. 3pqr
B. 3pqr(p – q)(q – r)(r – p)
C. p³ + q³ + r³ – 3pqr
D. None of these
Answer : B

Question. In a cylinder, radius of the base is tripled and height is made one-third, then the curved surface area will be ______ the area of the original cylinder.
A. Halved
B. Three times
C. Same as
D. Four times
Answer : C

Question. The mean of 16 items was found to be 30. On rechecking, it was found that two items were wrongly taken as 22 and 18 instead of 32 and 28 respectively.
Find the correct mean.
A. 31.25
B. 500
C. 31.50
D. 480
Answer : A

Question. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is ₹ 1. The sum (in ₹) is
A. 625
B. 630
C. 640
D. 650
Answer : A

Question. Two metallic right circular cones having their heights 4.1 cm and 4.3 cm respectively and the radii of their bases 2.1 cm each, have been melted together and recast into a sphere. Find the diameter of the sphere.
A. 2.1 cm
B. 3.5 cm
C. 4.2 cm
D. 6.2 cm
Answer : C

Question. In the given figure, l, m, n are straight lines. Which of the following is incorrect?

A. ∠a + ∠f = ∠c + ∠d
B. ∠a + ∠c + ∠e = 360° – ∠b – ∠d – ∠f
C. 180° – ∠c – ∠e = ∠b
D. 180° – ∠f = ∠d + ∠e
Answer : C

Question. Two numbers differ by 5. If their product is 336, then the sum of the two numbers is
A. 21
B. 28
C. 37
D. 51
Answer : C

Question. Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.
A. 1400
B. 1394
C. 1420
D. 1388
Answer : B

EVERYDAY MATHEMATICS

Question. The ratio of the incomes of P and Q is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves ₹ 1600, then the income of P is
A. ₹ 3400
B. ₹ 3600
C. ₹ 4000
D. ₹ 4400
Answer : C

Question. The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34.
Find the ages of the son and the father respectively (in years).
A. 6 and 39
B. 7 and 38
C. 9 and 36
D. 11 and 34
Answer : A

Question. In a class test in Mathematics, 10 students scored 73 marks each, 12 students scored 60 marks each and 8 students scored 40 marks each. The mean of their scores is ______.
A. 47 marks
B. 59 marks
C. 54 marks
D. 57 marks
Answer : B

Question. A bank offers 5 % compound interest calculated on half-yearly basis. A customer deposits ₹ 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is
A. ₹ 120
B. ₹ 121
C. ₹ 122
D. ₹ 123
Answer : B

Question. A man walked diagonally across a square lot. 
Approximately, what was the percent saved by not walking along the edges?
A. 20 %
B. 24 %
C. 30 %
D. 33 %
Answer : C

Question. P can do a work in 15 days and Q in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is
A. 1/4
B. 1/10
C. 7/15
D. 8/15
Answer : D

Question. A machine was sold at a gain of 10%. Had it been sold at ₹ 80 less, the seller would have lost 10%.
What is the cost price of the machine?
A. ₹ 350
B. ₹ 400
C. ₹ 450
D. ₹ 520
Answer : B

Question. One-third of the boys and one-half of the girls of a college participated in a social work project. If the number of participating students is 300 out of which 100 are boys, what is the number of students in the college?
A. 500
B. 600
C. 700
D. 800
Answer : C

Question. Piyush earned 40% more money than Aakash. Aakash earned 20% less than Manan. Piyush earned more than Manan by
A. 10%
B. 12%
C. 20%
D. 25%
Answer : B

Question. A farmer travelled a distance of 61 km in 9 hours.
He travelled partly on foot at the rate 4 km/ hr and partly on bicycle at the rate 9 km/hr. The distance travelled on foot is
A. 14 km
B. 15 km
C. 16 km
D. 17 km
Answer : C

ACHIEVERS SECTION

Question. Read the following statements carefully.
(i) If the diagonals of a quadrilateral divide it into four triangles which are equal in area, then the quadrilateral must be a parallelogram.
(ii) Three altitudes of an equilateral triangle are equal in length.
(iii) If triangles of equal areas have a common base, then their vertices must lie on a line parallel to the base.
Which of the options hold?
      (i)          (ii)         (iii)
A. True     True      False
B. True     False    False
C. True    True      True
D. False  True      True
Answer : A

Question. Consider the following data 

Match the Columns :
          Column I               Column II
(i) Mean of the data is        (p) 16
(ii) Median of the data is    (q) 15
(iii) Mode of the data is      (r) 15.2
A. (i) → (r), (ii) → (q), (iii) → (p)
B. (i) → (r), (ii) → (p), (iii) → (q)
C. (i) → (q), (ii) → (r), (iii) → (p)
D. None of these
Answer : A

Question. Fill in the blanks :
A __P_ is breadthless length. A __Q__ is a line which lies evenly with the points on itself. A __R_ is that which has length and breadth only. A __S_ is a surface which lies evenly with the straight lines on itself.
       P                 Q                      R                        S
A. Line        Straight line       Surface          Curved surface
B. Point       Straight line       Surface         Curved surface
C. Line        Straight line       Surface         Plane Surface
D. Point      Straight line        Surface         Plane Surface
Answer : C

Question. Find the area of a triangle having perimeter 32 cm, one side 11 cm and difference of other two sides is 5 cm.
A. √30 cm²
B. 8√30 cm²
C. 5√30 cm²
D. 3√10 cm²
Answer : B

Question. Arrange the following steps of constructions of a DABC whose base AB = 5 cm, ∠A = 30° and AC – BC = 2.5 cm in correct sequence.
Step 1 : Draw ∠ BAX = 30°
Step 2 : Join BD.
Step 3 : Join BC to obtain the required DABC.
Step 4 : Draw the perpendicular bisector of BD which cuts AX at C.
Step 5 : From ray AX, cut off line segment
AD = 2.5 cm (= AC – BC)
Step 6 : Draw base AB = 5 cm.
A. 1, 2, 3, 5, 6, 4
B. 6, 1, 2, 5, 4, 3
C. 6, 2, 1, 5, 3, 4
D. 6, 1, 5, 2, 4, 3
Answer : D