Class 9 IMO 5 Years Book (2014-2018)

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ebook INTERNATIONAL MATHEMATICS OLYMPIAD

5

Years (2014-2018) Solved Papers

INSTANT

CLASS

9

Copyright © 2019 Science Olympiad Foundation. Printed with the permission of Science Olympiad Foundation. No part

of this publication may be reproduced, transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright holder. Ownership of an ebook does not give the possessor the ebook copyright. All disputes subject to Delhi jurisdiction only.

Disclaimer : The information provided in this book is to give you the path to success but it does not guarantee 100% success as the strategy is completely dependent on its execution and, it is based on previous years' papers of IMO exam.

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CLASS 9

Contents ÂÂ IMO 2014 - SET A ÂÂ IMO 2014 - SET B ÂÂ IMO 2015 - SET A ÂÂ IMO 2015 - SET B ÂÂ IMO 2016 - SET A ÂÂ IMO 2016 - SET B ÂÂ IMO 2017 - SET A ÂÂ IMO 2017 - SET B ÂÂ IMO 2018 - SET A ÂÂ IMO 2018 - SET B

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For Classes 6, 7, 8, 9, 10, 11 & 12 Class 6

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Class 9

Set A Year 2014

8th IMO - Set A

1

Logical Reasoning 1.

2.

3.

4.

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 of 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. 9 15 50 12 25 24 If the resultant of first row is x and that of second row is y, then find the value of x ÷ y. A. 18 B. 8 C. 5 D. 6 A cube of side 10 cm is coloured red with a 2 cm wide green strip along all the sides on all the faces. Now, the cube is cut into 125 smaller cubes of equal size. How many cubes have three green faces each? A. 0 B. 4 C. 6 D. 8

5.

If all the consonants starting from B are given sequentially the value of even numbers such as B = 2, C = 4 and so on, and all the vowels are given double the value of the preceding vowel and the value of A is 5, then what is the value of REASONING? A. 162 B. 177 C. 185 D. 187

6.

A set of three figures X, Y and Z shows a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Select the figure from the options which would resemble the unfolded form of paper.

7.

Pointing to a woman in a photograph, a man says "She is the grandmother of the son of my daughterin-law's mother-in-law." How is the woman related to the man? A. Mother B. Mother-in-law C. Sister D. Wife P, Q and R are three points on the ground. Point P is North of point Q and ∠PQR is 135° in anticlockwise direction. In what direction is point R from point Q? A. North-East B. North-West C. South-East D. South-West

A.

B.

C.

D.

Select the figure in which Figure (X) is exactly embedded as one of its part.

Figure (X)

8.

A.

B.

C.

D.

Two positions of a dice are shown below. What number will be opposite to the number 4? A. 5 6 1 B. 6 3 2 C. 3 4 4 D. 1

2

9.

8th IMO - Set A

Select a figure from the options which will replace the question mark to complete the given series.

?

A.



B.



C.



D.

10. A set of figures carrying certain characters, is given. Assuming that the characters in each set follow a similar pattern, then find the missing character. 7

3 6

315

6

4

A.



B.



C.



D.

14. Count the number of straight lines and squares in the given figure.

1

11 2402 8

2



4 1190

5

?





A. B. C. D.

1 2 6 10

11.

Find A. B. C. D.

the odd one out. 18 : 108 42 : 132 22 : 112 26 : 156

A. B. C. D.

21 18 17 19

straight straight straight straight

lines, lines, lines, lines,



A.

C.





squares squares squares squares

15. Select a figure from the options which satisfies the same conditions of placement of the dots as in Figure (X).

12. Which of the following Venn diagrams best represents the relationship amongst, "Honesty, Intelligence, Aptitude"?

7 8 8 8

Figure (X)

B.

A.



C.



B.

D.

13. There is a definite relationship between figures P and Q. Establish a similar relationship between figures R and S by selecting a suitable figure from the options that would replace (?) in figure R.



D.

8th IMO - Set A

3

MATHEMATICAL REASONING −1/ 2

1 9 −3×5 −    81 16. Find the value of −2 / 3  25  1  64  + +3    / 1 4 125  64   256    625 3/ 2

0

A.

15 13

B.

0

C.

16 5

D.

48 13

 1 1 1  24 22. If 2x = 4y = 8z and  + +  = , then the  2x 4 y 6z  7 value of z is A.

17. Evaluate: (2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) A. 8x3 – y3 + 27z3 – 18xyz B. 8x3 – y3 + 27z3 + 18xyz C. 8x3 + y3 + 27z3 + 18xyz D. 8x3 + y3 – 27z3 + 18xyz 18. In the given figure, DABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On the base BC a parallelogram DBCE of area same as that of DABC is constructed. Find the height DF of the parallelogram.

6.5

7.5

cm

cm

A

D

B A. B. C. D.

3 5 6 7

cm cm cm cm

19. If x 2 +

1

A. B. C. D. 20.

x

2

E C

7 cm

= 98, then find the value of x3 +

890 970 990 1110

Simplify : A. B. C. D.

F

3 2 4 0

2 1 3 + − 5+ 3 3+ 2 5+ 2

21. Euclid stated that all right angles are equal to each other in the form of a/an . A. Axiom B. Definition C. Postulate D. Proof

1

x3

.

C.

7 16 7 48

B. D.

7 32 7 64

23. In the given figure, ABCD is a rectangle. BD = BE, ∠BED = 40° and ∠EDA = 260°. Find ∠CDB. B A

260°

A. C.

25° 40°

D

C

B. D.

E

30° 45°

24. Fill in the blanks: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than right angles. A. Less, three B. More, two C. Less, two D. More, one 25. The weight, in kg, of 50 students are given below. 40 45 55 62 50 51 56 69 61 36 60 56 69 38 35 63 57 50 57 48 40 63 53 64 47 42 56 51 42 60 55 39 64 57 64 44 66 35 59 59 73 62 49 63 37 63 54 72 44 60 Find the mean, median and mode respectively for the given data. A. 55 kg, 57 kg, 64 kg B. 55 kg, 57 kg, 62 kg C. 53.92 kg, 56 kg, 63 kg D. None of these

4

8th IMO - Set A

26. Select the correct match. A. When x = 5, y = 2.5 and when y = 5, x = 10, then x and y are inversely proportional. B. When x = 10, y = 5 and when x = 20, y = 2.5, then xy = constant. C. If x and y vary inversely, then on decreasing x, y will decrease in proportion. D. If x and y vary directly, then on decreasing x , y will increase in proportion. 27. Study the given graph and answer the following question. y 4 3

l

2 1 –1 O –1

–4 –3 –2

1

3

2

x

4

–2

Calculate the area enclosed by the lines l, x = –3, y = –2 and y = –x + 2. A. 16 sq. units B. 19 sq. units C. 20 sq. units D. 22 sq. units 28. In the given figure, the shape of a solid copper piece (made up of two pieces with dimensions as shown in the figure) is shown. The face ABCDEFA is the uniform cross-section. Assume that the angles at A, B, C, D, E and F are right angles. Calculate the volume of the piece. A F

22 cm

2 cm

B

5 cm

C

8 cm

D

A. 528 cm3 C. 580 cm3

3 cm

E

B. D.

I

58°

H

B

C

115°

45°

G

F E

D

110°, 220° 120°, 235°

B. D.

120°, 225° 110°, 215°

30. The value of p upto 35 decimal places is given below: 3.14159265358979323846264338327950288 Find the probability of occurring 8 in it. A. 1/3 B. 1/5 C. 5/36 D. 1/7 31. John is of the same age as Mohan. Ram is also of the same age as Mohan. State the Euclid's axiom that illustrates the relative ages of John and Ram. A. First Axiom B. Second Axiom C. Third Axiom D. Fourth Axiom 32. The given question is followed by three statements. You have to study the question and all the three statements to decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the given question. What is the marked price of the suitcase? I. When a discount of 15% is offered, the profit earned is 10.5%. II. The cost price of the suitcase is ` 1500. III. The marked price is 30% above the cost price. A. I only B. Either I or III C. Any one of the three D. All I, II and III are required 33. The A(2, A. C.

area of the triangle formed by the points 0), B(6, 0) and C(4, 6) is . 24 sq. units B. 12 sq. units 10 sq. units D. None of these

34. In the given figure, AB || CD || EF. CE is joined and produced to G. If ∠BAC = 130°, ∠ACE = 140°, then find ∠DCE and ∠FEG respectively. A B

880 cm3 940 cm3

29. Study the figure shown here (not drawn to scale), If ABG is a straight line, then find ∠ABH and reflex ∠ABC respectively. A 60°

A. C.

A. C.

C

D

E G

F

50°, 130° 140°, 40°

B. D.

90°, 90° 45°, 135°

35. Find the value of a and b respectively, if

A. B. C. D.

5+ 3 = 47 a + 3b 7−4 3 2, 1 1, 27 11, 28 2, 38

8th IMO - Set A

5

EVERYDAY MATHeMATICS 36. A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in . A. 12 days B. 13 days C. D.

5 days 7 3 13 days 4 13

37. A sum of ` 1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is ` 106, then find the money lent at each rate. A. ` 750, ` 800 B. ` 600, ` 950 C. ` 650, ` 900 D. ` 850, ` 750 38. If 6 years are subtracted from the present age of Gagan and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Madan whose age is 5 years, then what is Gagan's present age? A. 48 years B. 60 years C. 84 years D. 96 years 39. A certain factory employed 600 men and 400 women and the average wage was ` 25.50 per day. If a woman got ` 5 less than a man, then what is the daily wage of a man and woman respectively? A. ` 25; ` 20 B. ` 27.50; ` 22.50 C. ` 30; ` 25 D. ` 32.50; ` 27.50 40. A man earns ` 20 on the first day and spends ` 15 on the next day. He again earns ` 20 on the third day and spends ` 15 on the fourth day. If he continues to save like this, then how soon will he have ` 60 in hand? A. On 17th day B. On 27th day C. On 30th day D. On 24th day

41. The price of rice is reduced by 2% per kg. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier? A. 48 kg B. 49 kg C. 50 kg D. 51 kg 42. In a bag, there are coins of 25 paise, 10 paise and 5 paise in the ratio of 1 : 2 : 3. If there are ` 30 in all, then how many 5 paise coins are there? A. 50 B. 100 C. 150 D. 200 43. A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in of a day? A. B. C. D.

1 4

1 4 19 41

44. The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is . A. 11 years B. 14 years C.

15 years

D.

15

2 years 7

45. Village X has a population of 68000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year. In how many years will the population of the two villages be equal? A. 12 B. 13 C. 14 D. 15

6

8th IMO - Set A

Achievers Section 46. Which of the following statements is INCORRECT? A. If the altitudes of a triangle are equal, then it is equilateral. B. If in a triangle, two sides are unequal, then the angle opposite to the longer side is greater than the angle opposite to the shorter side. C. In a triangle, side opposite to the larger angle is longer than the side opposite to the smaller angle. D. In a triangle, altitude from the vertex bisects the base. 47. The polynomial p(x) = x 4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find (a) the value of a. (b) the remainder when p(x) is divided by x + 2. (a) (b) A. 1 13 B. –3 48 C. 5 62 D. 8 43 48. Fill in the blanks. In coordinate geometry, the coordinate axes divide the plane into four parts called ___ P__. The point of intersection of the axes is called ___ Q__. The sign

of abscissa and ordinate will be same in ___ R__ and ___ S__ quadrants. P   Q R S A. Quadrant x-axis II III B. Quadrant origin I III C. Quadrant origin I IV D. Quadrant origin I II 49. Which of the following options hold? Statement-1 : If any two angles and non-included side of one triangle are equal to the corresponding angles and side of another triangle, then the triangles are congruent (AAS congruence criterion). Statement-2 : If in two right triangles, hypotenuse and one side of a triangle, are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent (RHS congruence criterion). A. Statement-1 is true but statement-2 is false. B. Statement-1 is false but statement-2 is true. C. Both the statements are true. D. Both the statements are false. 50. Which of the following statements is INCORRECT for a parallelogram? A. Opposite sides are equal. B. Opposite angles are equal. C. Opposite angles are bisected by the diagonals. D. Diagonals bisect each other.

SPACE FOR ROUGH WORK

Class 9

Set B Year 2014

8th IMO - Set B

1

Logical Reasoning 1.

What should come next in the letter series given below? AABAB CAB C DAB C D EAB C D E FA B C D E F G A B C D E F G _?__ A. A B. I C. H D. B

2.

How many pairs of letters are there in the word NURSING which have as many letters between them as in the English alphabet? A. One B. Three C. Five D. Six

3.

Study the following arrangement carefully and answer the question given below : M J % 4TE K I 9 # PA$ Q 3 8 N 5 U 7W* B @DF1Z6H What should come in place of question mark in the following series based on the above arrangement? J 4 E  I # A  Q 8 5  7 * @  ? A. F16 B. DG C. F6 D. F1Z

4.

5.

6.

In a certain code 'ring a bell' is written as '5 8 2', 'did not ring' is written as '3 5 9' and 'not a reason' is written as '7 2 9'. What is the code for 'ring? A. 8 B. 2 C. 5 D. 3

7.

P, Q, R, S, T, U and W are sitting around a circle facing at the centre. S is third to the left of P who is second to the left of U. T is not a neighbour of either U or S. R is third to left of Q. Which of the following information represents the first person sitting to the immediate right of the second person? A. PQ B. UW C. RT D. PT

8.

A pile of cubes of equal size is arranged as shown in the figure. Now the block is dipped into a bucket full of red paint so that only the surfaces of the block get coloured. How many cubes are coloured on four faces only?

Ravi starts from his house and moves towards South. He walks 100 m, then turns left and walks 200 m, turns right and walks 500 m. How far is he from his house? A. B.

400 5 m 800 m

C.

200 10 m

D.

200 2 m

Four brothers go to a dance party. As they leave, each of the brothers accidentally takes a hat belonging to another brother and a coat belonging to a third brother. M takes the coat belonging to the brother whose hat is taken by P, while P's coat is taken by the brother who takes M's hat. S takes J's hat. Whose hat was taken by P? A. Can't say B. S C. M D. Either S or J

A. B. C. D. 9.

0 1 2 4

Find the missing character if the given matrix follows a certain rule row-wise or column-wise. 18

24

32

12

16

16

3

?

4

72

A. B. C. D.

2 3 4 5

96 128

2

8th IMO - Set B

10. In the given Venn diagram, triangle represents the healthy, square represents the old and circle represents the men. Which of the following regions represents the men who are healthy but not old? 7 12 4 3 5

A.

B.

C.

6

A. B. C. D. 11.

D.

1 2 3 7

Select the mirror image of Figure (X) from the given options, if the mirror is placed vertically to the right. F

E

14. There is a certain relationship between figures (i) and (ii). Establish the similar relationship between figures (iii) and (iv) by selecting a figure from the options which will replace the (?) in figure (iv).

?

F G E

(i)

F

E

F

G

E

D. G

G

12. Given below are the three figures (X), (Y) and (Z) showing a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Identify the unfolded form of piece of paper.

X

Y

Z

A.

B.

C.

D.

(ii)

(iii)

(iv)

A.

B.

J

J

C.

E

J

B. F

A.

J

J

G Figure (X)

13. The given question consists of Problem Figures followed by option figures. Select a figure which will continue the series. Problem Figures

C.

D. 15. Select the figure from the options which can be formed from the pieces given in Figure (X).

Figure (X)

A.

B.

C.

D.

8th IMO - Set B

3

MATHEMATICAL REASONING 16. In figure, ∠L = 62°, ∠LMN = 54°. If MO and NO are bisectors of ∠LMN and ∠LNM respectively of L DLMN, find ∠ONM and ∠MON. A. 27°, 121° B. 64°, 32° O C. 64°, 121° D. 32°, 121° M N 17. In the figure, it is given that A K B

35°

D

C 25° Z

x

E F

19. The value of A. B. C. D.

2 –1 3+ 2 1

A R

Q

B

6+2 3+2 2 +2 6 −

85.5 92.5 90.5 87.5

22. A bag contains 8 red and 4 green balls. Find the probability that the ball drawn is red when one ball is selected at random. A.

2 3

B.

1 3

C.

1 6

D.

5 6

23. In the given figure, ABCDEF is a regular hexagon and ∠AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?

(i) AB ^ BF and EF ^ BF (ii) AC = BC (iii) KD is perpendicular to BC and DE. Find the measure of x. A. 75° B. 30° C. 60° D. 45° 18. In a DABC, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm. The perimeter of the quad. ARPQ is A. 91 cm B. 60 cm C. 51 cm D. 70 cm

A. B. C. D.

C

P

1 5−2 6

is

20. If a + b + c = 15 and a2 + b 2 + c 2 = 83, find the value of a3 + b3 + c 3 – 3abc. A. 180 B. 71 C. 128 D. 95 21. Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be K% lower than the volume of B. The value of K must be

A.

1 12

B.

1 6

C.

1 24

D.

1 8

F

24. The value of expression

A.

−

C.

3 2

3 2

B

A

C

O D

E

(0.6)0 − (0.1) −1  3  3  2

−1

3

 3  1 ⋅  +  −   2  3

B.

2 3

D.

9 4

−1

is

25. In the given figure, square 2 is formed by joining the mid-points of square 1, square 3 is formed by joining the mid-points of square 2 and so on. In this way total five squares are drawn. The side of the square 1 is 'a' cm. What is the sum of perimeters of all the five squares ? A.

(4 2 + 1)a cm ( 2 + 1)

B.

5 a cm 6

C.

(7 + 3 2 )a cm

D.

None of these

1

2 4 5

3

4

8th IMO - Set B

26. In the given figure, O is the centre of the circle. The distance between P and Q is 4 cm. Find the ∠ROQ. A. 50° B. 60° C. 70° D. 35°

31. ABCD is a trapezium in which AB | | CD. Then AC2 + BD 2 is equal to

R

°

35

P

O 2 cm

Q

27. In the given figure, CD || AE and CY || BA. Then ar(BCZY ) = C

D

X

B

Z Y E

A

A. B. C. D.

ar(DZDC) ar(DCBY) ar(DEDZ) All of these

28. The given diagram shows a cylinder with a diameter of 10 cm 10 cm and height 15 cm. The 15 cm shaded portion in the form of a cone, with base diameter 10 cm and height 6 cm, is hollowed out. Find the volume of the remaining solid, in cm3. A. 300 p B. 345 p C. 295 p D. 325 p 29. The given diagram is drawn on a cartesian plane. Y S

R

O P(–3, –2)

X Q(2, –2)

PQRS is a square. The coordinates of S are A. (–3, 3) B. (3, – 3) C. (–3, –3) D. (–3, 2) 30. If a (a – A. B. C. D.

– b = 3, a + b + x = 2, then the value of b) [x 3 + 3(a + b)x 2 + 3x(a + b)2 + (a + b)3] is 84 48 32 24

A

A. B. C. D.

AD2 AD2 AD2 AD2

D

C

M

L

B

+ BC2 – 2AB⋅CD + BC2 + 2AB⋅CD – BC2 + 2AB⋅CD – BC2 – 2AB⋅CD

32. PQRS is the diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn with PQ and QS as diameters P S as shown in figure. Find the R Q ratio of the area of the shaded region to that of the unshaded region. A. 3 : 15 B. 15 : 13 C. 5 : 13 D. 13 : 5 33. Each side of DABC is 12 units. D is the foot of the perpendicular dropped from A on BC, E is the midpoint of AD. The length of BE is A.

36 3 units

B.

6 7 units

C.

3 3 units

D.

3 7 units

34. Divide the product of (4x 2 – 9) and (2x 2 – 3x + 1) by (4x 3 – 7x + 3). A. 2x – 3 B. 2x + 3 C. 2x D. 3x – 2 35. In the figure below, two straight lines PQ and RS intersect each other at O. If ∠POT = 75°, find the values of a, b and c respectively. A. 21°, 84°, 48° B. 48°, 84°, 21° C. 84°, 21°, 48° D. 57°, 21°, 48°

R 4b

P

Q

2c

O

75°

a b

T

S

8th IMO - Set B

5

EVERYDAY MATHeMATICS 36. 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B? A.

77

1 3

B.

77

2 3

C.

78

1 3

D.

78

2 3

37. One year ago, Sheela was four times as old as her daughter Sakshi. Six years hence, Sheela's age will exceed her daughter's age by 9 years. The ratio of the present ages of Sheela and her daughter is _____. A. 9 : 2 B. 11 : 3 C. 12 : 5 D. 13 : 4 38. A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. In the total transaction, his gain or loss will be _____. A. Neither loss nor gain B. 5% loss C. 5% gain D. 10% gain 39. If 18 binders bind 900 books in 10 days, how many binders will be required to bind 660 books in 12 days? A. 22 B. 14 C. 13 D. 11 40. The population of a town is increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is _____. A. 4.37% B. 5% C. 6% D. 50%

41. A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay ` 5400 interest only for the period. The principal amount borrowed by him was . A. ` 2000 B. ` 10,000 C. ` 15,000 D. ` 20,000 42. 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 43. A man bought goods worth ` 6000 and sold half of them at a gain of 10%. At what gain percent must he sell the remainder so as to get a gain of 25% on the whole? A. 25% B. 30% C. 35% D. 40% 44. Gauri went to the stationers and bought things worth ` 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? A. ` 15 B. ` 15.70 C. ` 19.70 D. ` 20 45. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in _____. A. 6 hrs B.

2 6 hrs 3

C.

7 hrs

D.

1 7 hrs 2

6

8th IMO - Set B

Achievers Section 46. Select the correct match. ( x − 2)( x − 4) Let f ( x) = x Column I A. B. C. D.

A. B. C. D.

Column II

f(x) is a polynomial As (x – 2), (x – 4), x are polynomials f(x) is an equation As it can be written as ax2 + bx + c p f(x) is a rational number As it is of the form , q q≠0 f(x) is not a polynomial As the exponents of x are not whole numbers.

48° 42° 56° 58°

49. The given figure, not drawn to scale, is made up of 3 circles and 3 squares. Find the total area of the 22 shaded parts. (Take p = ) 7

56 cm

13 cm

47. The marks scored by some students for a question in the Science test are shown in the table below. Marks

0

1

2

3

4

5

Number of students

3

2

3

5

x

1

(a) If the mode is 4, write down the smallest possible value of x. 1 (b) If the mean is 2 , find the value of x. 4 A. B. C. D.

(a) 6 5 6 6

(b) 2 2 4 3

28 cm

A. B. C. D.

Monday Thursday

Tuesday

C

(i) D

A

24°

F

E

1500 cm2 1680 cm2 1749 cm2 1149 cm2

50. The given pie chart shows the distance covered by Mohit from Monday to Thursday. The distance he covered on Tuesday was thrice the distance he covered on Wednesday. Mohit covered a distance of 201 km on Wednesday.

48. In the given figure, ABCD is a parallelogram and CEFD is a rhombus. ∠ADF = 90° and ∠CFD = 24°. Find ∠DAB. B

42 cm

Wednesday 1 12

What was the total distance he covered on the four days? (ii) What was the distance covered on Monday? (i)   (ii) A. 2142 km 1005 km B. 2214 km 1008 km C. 2124 km 1102 km D. 2412 km 1005 km

SPACE FOR ROUGH WORK

Class 9

Set A Year 2015

logical reasoning 1.

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. B. C. D.

2.

3.

4.

B.

11 7 15 9

C. D. 6.

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

7.

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

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. B. C. D.

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

A.

E G D T

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. B. C. D.

5.

21 22 23 24

A.

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).

B. C. D. 8.

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

A. B.

18

24

32

12

14

16

3

?

4

S

72 112 128 C. D. 2

A. B. C. D.

2 3 6 5 | 9th IMO | Class-9 | Set-A | Level 1

9.

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

?

A.

1.0 km

Fig. (X)

B.

1.1 km

C.

1.4 km

D.

1.8 km

C.

13. Which of the following is the tenth to the right of the nineteenth from the right end in the given arrangement?

D. 10. Select the correct water image of given combination of letters and numbers. S5L3T8 A. B. C. D. 11.

12. 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?

8T3L5S S5L3T8

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.

F4©J2E%MP5W9@IQR6UH3Z7« ATB8V#G$YD A.

M

B.

T

C.

A

D.

2

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

Rules :

(iv)

(v)

C.

Brown

D.

Violet

n

Pink

ow

B.

Blue

Br

White

nk

A.

Red

Pi

9th IMO | Class-9 | Set-A | Level 1 |

Pink

e

42 33 108 39

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

k

If the resultant of the first row is k, then what will be the resultant of the second row? A. B. C. D.

D.

hit

64

C.

W

28

B.

Red

(iii)

A.

Blue

(ii)

If an odd number is followed by another composite odd number, they are to be multiplied. If an even number is followed by an odd number which is not a perfect square, they are to be added. 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. If an odd number is followed by a prime odd number, the first number is to be divided by the second number. If an odd number is followed by an even number, the even number is to be subtracted from the odd number. 27 12 5

Viol et

(i)

3

MATHEMATICAL REASONING 16. W h i c h o f t h e f o l l o w i n g s t a t e m e n t s i s INCORRECT?

C.

There can be a real number which is both rational and irrational. The sum of any two irrational numbers is not always irrational. For any positive integers x and y, x < y ⇒ x2 < y2

D.

Every integer is a rational number.

A. B.

17. Find the value of l, so that y – 2p is a factor of y3 − 2 y + lp. 4 p2 A. B. C. D.

0 1 2 3

18. The number of dimensions, a point has A. B. C. D.

0 1 2 3

19. The points, whose abscissa and ordinate have different signs, lie in _______ quadrants. A. B. C. D.

Making an intercept of 6 units on the x-axis. Making an intercept of 6 units on both the axes.

22. Number of zeros of the zero polynomial is A. B. C. D.

0 1 2 Infinite

23. In the given figure, l || BC and D is the mid-point of BC. If area (DABC) = x × area (DEDC), then find the value of x. A E l

B

A. B. C. D.

14 cm

1 2 3 4

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

75 84 95 56

cm2 cm2 cm2 cm2

A.

2+ 6 : 6

B.

3: 2+ 6

C.

6 :2+ 6

D.

6 :4+ 6

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

B.

4

Parallel to x-axis at a distance of 6 units from the origin. Parallel to y-axis at a distance of 6 units from the origin.

Q

W

21. The graph of line y = 6 is a line A.

C

D

I and II II and III I and III II and IV

20. 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. B. C. D.

C. D.

V C

U

A R S T B

Given that ∠BVD = 135° and AT = BR, then find ∠PCT and ∠ABD respectively. | 9th IMO | Class-9 | Set-A | Level 1

A. B. C. D.

135°, 135° 135°, 45° 45°, 135° 45°, 45°

31. 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?

26. The numbers 7.478478... and 1.101001000100001... are A. B. C. D.

Rational and irrational respectively Both rationals Both irrationals None of these

27. Factorise : x + 5x + 5x – 5x – 6 4

A. B. C. D.

2

3

2

2

(x – 1)(x + 6) (x – 1)(x + 2)3 (x2 – 1)(x + 3) (x + 2) (x – 1)(x + 2) (x2 + 3)

28. 'Lines are parallel if they do not intersect' is stated in the form of A. B. C. D.

An axiom A postulate A definition A proof

29. 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. B. C. D.

98 99 100 101

A.

20%

B.

30%

C. D.

45% 60%

32. 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

33. The graph of the linear equation y = x passes through the point A.

3 3  , −  2 2

B.

 3  0,  2

C.

(1, 1)

D.

 1 1  − ,  2 2

34. 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

30. F i n d t h e v a l u e s o f t h e i n t e g e r s a a n d b respectively, for which the solution of the equation

B.

Ordinate = 5

C.

Ordinate = –5

a+ b . 7

D.

Ordinate = 5 or –5.

x 24 = x 3 + 6 is A. B. C. D.

4, 2, 3, 9,

2 6 2 5

35. 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. R

Direction (31-32) : The pie chart below shows the number of fruits sold on a particular day at a fruit stall. Banana

Mango

Orange 58

Apple 25% 9th IMO | Class-9 | Set-A | Level 1 |

O

70°

Q

N

45° L

A.

80°

B.

60°

C.

70°

D.

50°

P

M

H

5

EVERYDAY MATHEMATICS 36. A t r i a n g u l a r p a r k i n a c i t y h a s d i m e n s i o n s 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 ` 4242 B. C. ` 1696.80 D. ` 1000 37. 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

38. 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. B. C. D.

45 : 56 50 : 61 99 : 125 None of these

39. 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

40. 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. B. C. D. 6

10 : 00 a.m. 3 : 00 a.m. 5 : 00 p.m. Both A and B

41. 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 42. 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 5 of its usual speed covers 7 45 km in 1 hour 40 mins 48 secs. What is the usual speed of the car?

43. A car travelling with



B.

6 km/hr 7 25 km/hr



C.

30 km/hr



D. None of these

A. 17

44. Roma took a loan of ` 16,000 against her insurance 1 policy at the rate of 12 % per annum. Calculate the 2 total compound interest that will be paid by Roma after 3 years. A. ` 6781.25 B. ` 6925.30 C. ` 4296.82 D. ` 3579.71 45. Cubical boxes of volume 15625 cm3 each are put in a cubical store of side 2.5 m.

(i)



(ii) What are the dimensions of the box ?



How many such boxes can be put in the store ? (i)

(ii)



A. 1250

15 cm



B.

1000

15 cm



C.

1250

25 cm

D. 1000

25 cm | 9th IMO | Class-9 | Set-A | Level 1

Achievers section 46. 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.

70, 105

B.

70, 150

C.

105, 70

D.

150, 70

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

4 cm

A

(a)

(b)

A.

144 p cm

2

5/18

B.

104 p cm2

5/18

C.

104 p cm

2

13/18

D.

144 p cm2

13/18

47. 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  b have p  −  = 0.  a

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.

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

Statement II : I f p ( x ) i s a p o l y n o m i a l o f 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.

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

B

F

9th IMO | Class-9 | Set-A | Level 1 |

D



E Column-I

(i)

Area (DBDE) =

(ii) Area (DFED) =

A. B. C. D.

(i) (i) (i) (i)

→ → → →

C

Column-II

(p) 2 × Area (DFED) (q)

1 × Area (DABC) 4

1 × Area (DAFC) 8 (r), (ii) → (p), (iii) → (q) (r), (ii) → (q), (iii) → (p) (q), (ii) → (p), (iii) → (r) (q), (ii) → (r), (iii) → (p)

(iii) Area (DBFE) =

Find the value of x and y respectively.

B

(r)

7

Class 9

Set B Year 2015

Logical Reasoning 1.

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).





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

5.

Select the odd one out.



A.





A.





B.







C.



D.

2.



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 ♣



(i)





B.



C.



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. B. C. D.

F B 8 D

3.

How many pairs of letters are there in the word OPERATION which have as many letters between them as in the English alphabet?



A. B. C. D.

4.

The following digits are coded as follows:

Four Seven Five More than seven

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. 2



D.

6.

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?



26375642961341639156923165 4321967163



A. B. C. D.

7.

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



A. B. C. D.

0 1 2 3

7

9

21

27

4

2

36

18

9

4

54

?

18 24 36 58 | 9th IMO | Class-9 | Set-B | Level 1

8.

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

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

S2O15OFDEC A. B. C. D. 9.

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

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

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

B. C.

A.

D. 10. M is sister of K. D is brother of K. F is mother of M. How is K related to F ? A. B. C. D. 11.

Son Daughter Son or Daughter None of these

C.

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

2 6

A. B. C. D.

3

5

B.

2 1

3

1

D. 15. Select the figure from the options, which when placed in the blank space of Fig. (X) would complete the pattern.

?

1 4 5 3

12. 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.

Fig. (X)

A. B.

What is P's position with respect to S? A. B. C. D.

Fourth to the left Fourth to the right Fifth to the left Sixth to the left

9th IMO | Class-9 | Set-B | Level 1 |

C. D. 3

MATHEMATICAL REASONING 3+ 2 3− 2 and b = , then find the value 3− 2 3+ 2 of a 2 + b 2 .

16. If a =

A. B.

40 6 96

C. D.

20 3 98

17. Which of the following statements is true? 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 (i)

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

A.

(–5, –4)

B.

(5, –4)

C.

(–4, 5)

D.

(–4, –5)

21. Which of the following is the factor of the polynomial p(x) = x 4 + 5x3 + 9x2 + 15x + 18? A.

x2 + 5x + 6

B.

x2 – 5x + 6

C.

x2 + 5x – 6

D.

x2 – 5x – 6

22. 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 p = 3.14) (i)

(ii)

A.

9 cm

10 cm

B.

10 cm

9 cm

C. D.

10 cm 6 cm

6 cm 10 cm

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

24°

141°

C

D

A. B. C. D.

x + y = 90° x – y = 90° t + 2y = 90° None of these

19. 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. B. C. D.

60 cm 13 30 cm 13 120 cm 13 10 cm

20. 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 4

75°

F

A.

25°

B.

75°

C.

100°

D.

141°

A

B

92°

G

24. If AB ||EF || DC and the area of DAFD is 42 cm2 , find the area of DBCE. A E D

A.

21 cm2

B.

42 cm2

C.

48 cm2

D.

84 cm2

B F C

| 9th IMO | Class-9 | Set-B | Level 1

25. 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

26. How many least number of distinct points determine a unique line? A. B. C. D.

1 2 3 4

27. Which of the following are solutions of the equation 2x + 3y = 12? A. B.

(3, 2) (2, 3)

C.

( 2 , 3)

D.

 2  3,  3

31. 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

32. 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

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

m c b a d e f

l

28. Factorize : p 3 (q – r)3 + q3 (r – p)3 + r 3 (p – q)3 A. B. C. D.

3pqr 3pqr(p – q)(q – r)(r – p) p3 + q3 + r3 – 3pqr None of these

29. 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. B. C. D.

Halved Three times Same as Four times

30. 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. B. C. D.

31.25 500 31.50 480

9th IMO | Class-9 | Set-B | Level 1 |

A.

∠a + ∠f = ∠c + ∠d

B.

∠a + ∠c + ∠e = 360° – ∠b – ∠d – ∠f

C.

180° – ∠c – ∠e = ∠b

D.

180° – ∠f = ∠d + ∠e

34. 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

35. 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 5

everyday MATHEMATIcs 36. 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

37. 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

38. 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

39. 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

40. 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 %

41. 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 6

A.

1 4

B.

1 10

C.

7 15

D.

8 15

42. 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

43. 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

44. 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%

45. 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 | 9th IMO | Class-9 | Set-B | Level 1

Achievers section 46. Read the following statements carefully. If the diagonals of a quadrilateral divide it into four triangles which are equal in area, then the quadrilateral must be a parallelogram.

(i)

(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.

True

True

False

47. Consider the following data. xi

12

13

14

15

16

17

18

fi

1

3

4

8

10

3

1

Match the Columns : Column I (i)

Column II

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

48. 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 49. 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 cm 2

B.

8 30 cm 2

C.

5 30 cm 2

D.

3 10 cm 2

50. 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 A X, 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

SPACE FOR ROUGH WORK

9th IMO | Class-9 | Set-B | Level 1 |

7

Class 9

Set A Year 2016

logical reasoning 1.

Two positions of a dice are given below. When 1 is at the top, which number will be at the bottom ?

(i)

A. C. 2.

(ii)

2 4

B. D.

3 6

5.

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 is to be answered. The operations on numbers progress from left to right. Rules : (i) If an even number is followed by another even number they are to be added. (ii) If an even number is followed by a prime number, they are to be multiplied. (iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number. (iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number. (v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number. 65 15

11 3

Select a figure from the option figures which will continue the same series as established by the five Problem Figures. Problem Figures C+

× +

A.

C.

2

+

×

T

S

×

S

× CC

T

+C ××

B.

P

× ++ +

C

+ C

D.

×

6.

7.

12 11

What is the sum of the resultants of the two rows ? A. 366 B. 66 C. 264 D. 462 3.

4.

R

L

C

Find the missing number, if a certain rule is followed row-wise or column-wise. 7 4 5 A.

3

B.

4

C.

5

D.

6

8 3 29

7 3 19

6 ? 31

If it is possible to make a meaningful word with the second, fourth, eight and tenth letters of the word CONFIDENCE, which of the following will be second letter of that word? If more than one such word can be made, give 'S' as the answer. If no such word can be made, give 'P' as the answer. A.

O

B. C.

N S

D.

P

What is the minimum number of different colours required to paint the given figure such that no two adjacent regions have the same colour? A.

3

B.

4

C.

5

D.

6

Eight friends Q, R, S, T, V, W, Y and Z are sitting around a circular table, facing the centre. There are three males and five females in the group of friends. No two males are immediate neighbours of each other. (i)

V sits second to the right of his wife.

(ii) S sits third to the right of V. (iii) W sits second to the right of her husband Z. Z is not an immediate neighbour of V's wife. (iv) T is a male and Y is not an immediate neighbour of V. (v) R sits second to the right of Q.

×

Which of the following statements is true regarding T?

C

A.

T is an immediate neighbour of Z's wife.

B.

No male is an immediate neighbour of T.

C.

Q sits second to right of T.

D.

All are true.

+ C

| 10th IMO | Class-9 | Set-A | Level 1

8.

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

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

Fig. (X)

C.

D.

Code the group of digits as per the scheme and conditions given below. Digit : 5 7 0 9 3 1 6 4 8 2 Letter/symbol : K E H $ D A J Q R @ Conditions : 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 by the code for odd digit. (iii) If the last digit is '0' it is to be coded by 'X'. (iv) If the first as well as the last digit is even both are to be coded by '–'. 586403 A. KRJQHD B. DRJQHK C. DHJQRK D. KHJQRD

(i)

10. Find the water image of Fig. (X).

Fig. (X)

11.

A.

B.

C.

D.

The positions of how many digits in the number will remain same after the digits within the number 2138574 are arranged in ascending order? A. Nil B. Four C. Three D. Two

10th IMO | Class-9 | Set-A | Level 1 |

A.

×

C.

B.

D.

×

B. ×

9.

A.

13. Select a figure from the options that illustrates the relationship amongst "pigeons, birds, dogs". A.

B.

C.

D.

14. Kalyani is mother-in-law of Veena who is sister-inlaw of Ashok. Dheeraj is father of Sudeep, the only brother of Ashok. How is Kalyani related to Ashok? A. B. C. D.

Mother-in-law Aunt Wife None of these

15. A sheet of paper has been folded (either once or twice) and then the folded sheet has been cut. You have to select a figure from amongst the option figures, that would most closely resemble the unfolded form of Fig.(X).

Fig. (X)

A.

B.

C.

D.

3

MATHEMATICAL REASONING 16. The factors of 8a3 + b 3 – 6ab + 1 are A. B. C. D.

(2a + b – 1)(4a2 + b2 + 1 – 3ab – 2a) (2ab – b + 1)(4a2 + b2 – 4ab + 1 – 2a + b) (2a + b + 1)(4a2 + b2 + 1 – 2ab – b – 2a) (2a – 1 + b)(4a2 + 1 – 4a – b – 2ab)

4 17. If x +

A.

7

B. C. D.

18 6 12

1 x

4

= 47, find the value of x3 +

1

x3

20.5 24.5 22.4 18.4

B. C. D.

m m m m

Only a unique line can be drawn to pass through a given point. Infinitely many lines can be drawn to pass through two given points. If two circles are equal, then their radii are equal. A line has a definite length.

20. The mean of 25 numbers is 8. If 2 is added to every number, what will be the new mean? A. B. C. D.

10 6 8 12

A. B. C. D. 24.

Three statements are given below: (i) In a ||gm, the angle bisectors of two adjacent angles enclose a right angle. (ii) The angle bisectors of a ||gm form a rectangle. (iii) The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle. Which is true? A. (i) only B. (ii) only D. (ii) and (iii) only C. (i) and (ii) only

25. If

r

1   r +  4

9

3 ⋅ 3− r

3 3− r

= k , then the value of k is

A.

3

B.

32

C.

33

D.

r

3

Age (in years)

Number of persons of different age who can drive the car

60 61 62 63 64 65

16,090 11,490 8,012 5,448 3,607 2,320

AB ^ BF and EF ^ BF

(ii) AC = BC (iii) KD is perpendicular to BC and DE A K B

35°

D

Find the measure of x. A. 75° C. 60° 4

125 50 100 150

26. Based on the given information, find the probability of people with age (60, 61 & 64) who can drive.

21. In the given figure, it is given that (i)

+ 11p – 7 + 3p + 5 + 5p – 4 – 5p + 9

23. Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

19. Which of the following is a true statement? A.

8p2 2p2 3p2 5p2

A. B. C. D.

.

18. A solid iron rectangular block of dimensions (2.2 m × 1.2 m × 1 m) is cast into a hollow cylindrical pipe of internal radius 35 cm and thickness 5 cm. Find the length of the pipe. A. B. C. D.

22. The perimeter of a triangle is 6p 2 – 4p + 9 and two of its sides are p 2 – 2p + 1 and 3p 2 – 5p + 3. Find the third side of the triangle.

C

E x

25°

Z

B. D.

F

30° 45°

A.

36071 41490

B.

31187 46967

C.

31232 41149

D.

31232 41609

| 10th IMO | Class-9 | Set-A | Level 1

27. In the given figure AB ||CD and EF ||DQ. Determine ∠PDQ, ∠AED and ∠DEF respectively.

31. In the figure shown, square 2 is formed by joining the mid-points of square 1, square 3 is formed by joining the mid-points of square 2 and so on. In this way total five squares are drawn. The side of the square 1 is 'a' cm. What is the sum of perimeters of all the five squares ? 1

2



A. C.

34°, 68°, 68° 68°, 68°, 68°

B. D.

28. Water flows in a tank 150 m × 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep?

A. B. C. D.

4 3

68°, 34°, 68° 34°, 34°, 68°

50 hrs 150 hrs 100 hrs 200 hrs

Direction (29-30): Answer the questions on the basis of the information given below: Number of players participating in three different games in five different schools.

5



A.



C.



B.

5 a 6

(7 + 3 2 ) a

D.

None of these

(4 2 + 1)a ( 2 + 1)

32. Two men start from points A and B respectively, 42 km apart. One walks from A to B at 4 km/hr and another walks from B to A at a certain uniform speed. They meet each other after 6 hours. Find the speed of the second man.

A. B. C. D.

3 5 7 8

km/hr km/hr km/hr km/hr

33. Sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. Find its area.

A. B. C. D.

226 412 162 336

34. If x = 29. Number of players participating in Kho-Kho from School-4 is what percent of number of players participating in hockey from School-2?

A. B. C. D.

42 48 36 40



A. B. C. D.

2 1 4 3

cm2 cm2 cm2 cm2 1

2− 3

35. In the given figure, ‘O’ is the centre of circle, ∠CAO = 25° and ∠CBO = 35°. What is the value of ∠AOB? A

30. 25% of the number of the players participating in hockey from School-5 are females. What is the number of the hockey players who are males in School-5?

A. B. C. D.

15 18 30 27

10th IMO | Class-9 | Set-A | Level 1 |

, find the value of x3 – 2x2 – 7x + 5.



A. C.

55° 120°

B

O C

B. D.

110° Data insufficient

5

EVERYDAY MATHeMATICS 36. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons is increased by ____ of the original share. A.

1 9

B.

1 8

C.

1 7

D.

7 8

16.66% 50% 25% None of these

38. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman? A. B. C. D.

3:4 3:5 5:3 None of these

39. Average age of 6 sons of a family is 8 years. Average age of the sons together with their parents is 22 years. If the father is older than the mother by 8 years, then the age of the mother is A. B. C. D.

44 52 60 68

years years years years

40. A train travelling at 48 km/hr completely crosses another train having half its length and travelling in opposite direction at 42 km/hr, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is ________. A. B. C. D. 6

A.

2.46 m

B.

3.56 m

C.

4.66 m

D.

5.76 m

42. In a mixture of 60 litres, the ratio of milk and water is 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is ________.

37. The cost price of an article A is ` 160 and selling price of another article B is ` 240. If the selling price of A will be equal to the cost price of B, then the profit after selling A is 20%. What is the profit on B? A. B. C. D.

41. A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. The height of the embankment is ________.

400 450 560 600

m m m m

A.

20 litres

B.

30 litres

C.

40 litres

D.

60 litres

43. The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full? A.

2 7

B.

3 7

C.

4 7

D.

5 7

44. A money lender borrows money at 4% p.a. and pays interest at the end of the year. He lends it at 6% p.a. compounded half-yearly and receives the interest at the end of the year. Thus, he gains ` 104.50 a year. The amount of money he borrows, is A.

` 4500

B.

` 5000

C.

` 5500

D.

` 6000

45. After spending 40% in machinery, 25% in building, 15% in raw material and 5% on furniture, Harilal had a balance of ` 52200. The money with him was ________. A.

` 260000

B.

` 289000

C.

` 348000

D.

` 556000 | 10th IMO | Class-9 | Set-A | Level 1

Achievers section 46.

Following are the steps of construction of a DPQR, given that QR = 3 cm, ∠PQR = 45° and QP – PR = 2 cm. Arrange them and select the correct option.

(S) In a trapezium ABCD, it is given that AB||DC and the diagonals AC and BD intersect at O. Then, ar(DAOB) = ar(DCOD). (P)

(Q)   (R)   (S)

A.

F

T

F

T

(ii) Join SR and draw the perpendicular bisector of SR say AB.

B.

T

F

F

T

C.

T

F

T

F

(iii) Draw the base QR of length 3 cm.

D.

F

T

T

F

(i)

Make an angle XQR = 45° at point Q of base QR.

(iv) Let bisector AB intersect QX at P. Join PR. (v) Cut the line segment QS = QP – PR = 2 cm from the ray QX. A.

(iii) → (ii) → (i) → (v) → (iv)

B.

(iii) → (i) → (ii) → (v) → (iv)

C.

(iii) → (i) → (ii) → (iv) → (v)

D.

(iii) → (i) → (v) → (ii) → (iv)

(P) Any point lying on x-axis is of the form ____. (Q) The abscissa of a point on y-axis is ____. (R) The point at which the two coordinate axes meet is called the ____. (S) The perpendicular distance of the point (4, 5) from x-axis is ____. (T) The perpendicular distance of the point (3, 7) from y-axis is ____. (Q)

(R)

(S)

(T)

A.

(0, y)

1

origin

5

3

B.

(x, 0)

0

origin

5

3

C.

(x, 0)

0

origin

3

5

D.

(0, y)

1

origin

3

5

48. State True (T) or False (F). (P) In a DABC, if E is the midpoint of median AD, 1 then ar(DBED) = ar(DABC). 8 (Q) A parallelogram and a rectangle on the same base and between the same parallels are equal in area. (R) If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is 1 : 2. 10th IMO | Class-9 | Set-A | Level 1 |

Column II

Column I

47. Fill in the blanks.

(P)

49. A die is rolled. If the number on the die is even, then a coin is tossed once and if the number on the die is odd, then a coin is tossed twice. Match the events in Column I with their probabilities in Column II. 2 3

(P) Probability that 2 heads appears

(1)

(Q) Probability that at least 1 head appear

(2) 0

(R) Probability that a die shows an even number and a coin shows exactly two heads

(3)

1 6

(S) Probability that a die shows an odd number and a coin shows at least one tail

(4)

1 2

(P)

(Q)

(R)

(S)

A.

1

2

3

4

B.

3

1

2

4

C.

3

2

1

4

D.

4

3

2

1

50. The volume of the space inside a right circular conical 2 3 m and its vertical height is 4 m. Find 7 the canvas required to make the tent and also find the cost of the canvas at the rate of ` 120 per m2 . tent is 138

A.

126.3 m2 , ` 15164.16

B.

126.3 m2 , ` 15156

C.

136.2 m2 , ` 16344

D.

142.3 m2 , ` 17076 7

Class 9

Set B Year 2016

logical reasoning 1.

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. B. C. D.

2.

aabca abaca bacab bcaca

How many cubes have only one face painted?

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).

A. C. 5.

? (1)

3.

(2)

(3)

A.

B.

C.

D.

What is the position of house P from top when the houses are arranged in descending order of their heights? A. B. C. D. 4.

2

Third Second Fourth Data inadequate

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.

B. D.

45 62

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? F4©J2E%MP5W9@IQR6UH3Z7 ATB8V#G$YD

(4)

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.

9 57

A. C. 6.

B. D.

One Three

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. C.

7.

None Two

Four Two

B. D.

Five Three

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

Fig. (X)

8.

A.

B.

C.

D.

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

B. I

C.

II

D.

| 10th IMO | Class-9 | Set-B | Level 1

9.

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. B. C. D.

in pe se Data inadequate

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



A. B. C. D.

1,4,7; 1,6,9; 1,4,7; 1,5,7;

3,6,9 2,4,7 2,6,9 2,6,9

; ; ; ;





7

12

4

10 6

13 14

11 5

(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. B. C. D.

8 3 11 12

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

Fig. (X)

A.



C.



B.

Rules:



(i)



(ii)



(iii)



(iv)



(v)

If an odd number is followed by another odd number, they are to be multiplied. If an even number is followed by another even number, the first number is to be divided by the second even number. 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. If an odd number is followed by an even number, the two are to be added. 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

3

9



2,5,8 3,5,8 3,5,8 3,4,8

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

8

13. 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.

D.

10th IMO | Class-9 | Set-B | Level 1 |

If x and y are the resultant of first and second row respectively, then what is the value of y – 2x?

A. C.

108 105

B. D.

33 36

14. 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. C.

1 3

1

2

3 B. D.

2 4

4

5

15. 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. B. C. D.

Only III follows Both I and II follow All follow None follows 3

MATHEMATICAL REASONING 16. 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. C.

10 25

B. D.

20 15

5 + 11 = p + q 11, 3 − 2 11 then find the values of p and q respectively.

17. If p and q are rational numbers and

A.

37 −13 , 35 35

C.

−37 −13 , 35 35

B.

37 13 , 35 35

D.

−37 13 , 35 35

3.

4. A. B. C. D.

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. Join AC and BC. Also join DC. ABCD is the required quadrilateral. Only 1 Both 2 and 3 Only 3 Both 2 and 4

21. 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

A

18. For a group of 32 students, food lasts for 45 days. For how many days will the same food last for 72 students ? A. C.

13 20

B. D.

40 6

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

Q

P

S

R

(i)

(ii)

(iii)

A.

30°

110°

50°

B.

15°

120°

45°

C.

15°

140°

45°

D.

30°

140°

50°

22. In DABC, 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 (DBOE).

4 3 2 P

A

1 –2

O

B

O

Q 2

4

x

O

–2 B

A. C.

(1, –1) (2, 3)

B. D.

(2, –2) (3, 3)

20. Which of the following steps is INCORRECT while constructing a quadrilateral ABCD, given t h a t AB = 5 cm, BC = 7 cm, AD = 4 cm, d i a g o n a l AC = 9 cm and diagonal BD = 6 cm. 1. 2.

4

Draw AB = 5 cm. With A and B as centres and 4 cm and 6 cm as radii respectively, draw arcs to cut each other at D.

E

D

C

A.

1 ar(DABC ) 3

B.

1 ar(DABC ) 4

C.

1 ar(DABC ) 6

D.

1 ar(DABC ) 8

23. 8(a – 2b)2 – 2a + 4b – 1 = A. B. C. D.

(2a (2a (2a (2a

– 4b – 1) (4a – 8b + 1) + 4b + 1) (4a – 8b + 1) – 4b – 1) (4a – 8b – 1) + 4b – 1) (4a + 8b + 1) | 10th IMO | Class-9 | Set-B | Level 1

24. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, then the value of a is . 2 B. 1 A. 3 5 4 C. D. 3 3 Direction (25 - 26) : Study the given graph and answer the following questions.

Number of students (in thousands)

(Number of students (in thousands) who opted for three different specializations during the five years in a University). Mathematics

English

Hindi

40 35 30 25 20 15 10 5 0

29. ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140°, then ∠BAC is equal to A. C.

80° 40°

B. D.

50° 30°

30. 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. B. C. D.

Mean of A = Mode of C Mean of C = Median of B Median of B = Mode of A Mean, Median and Mode of A are equal.

31. In the adjoining figure ∠CAB = 62°, ∠CBA = 76°, ∠ADE = 58° and ∠DFG = 66°, find ∠FGE. A 2013

2012

2014

2015

F

2016

Years

25. 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. C.

38 42

B. D.

28 46

26. 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. C.

2:3 11 : 7

B. D.

12 : 7 12 : 5

27. In the given figure, DABC is an equilateral triangle the length of whose side is equal to 10 cm and DDBC is right-angled at D and BD = 8 cm. Find the area of the shaded region. (Take 3 = 1.732) A A. B. C. D.

19.3 43.3 17.3 21.3

2

cm cm2 cm2 cm2

D B

C

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



0-20 20-30 30-40 40-50 50-60 60-70 70-100 7

10

10

20

20

15

Find the probability that a student obtained : (i) less than 20% marks. (ii) 60 or more marks. A. C.

(i)  (ii) 17/90 43/90 7/90  23/90

B. D.

10th IMO | Class-9 | Set-B | Level 1 |

(i)  (ii) 7/90  43/90 17/90 23/90

8

C

B

A. C.

E D

44° 36°

B. D.

G

34° None of these

32. Using Euler’s formula, find the values of P, Q, R and S respectively. Faces 6 Vertices P Edges 12 A. 8, 6, 24, 54 C. 6, 8, 24, 54

5 Q 9 B. D.

20 36 S 6, 8, 54, 24 8, 6, 54, 24

14 R 36

33. It is given that DABC ≅ DFDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then, which of the following is definitely true? A. B. C. D.

DF DF DE DE

= = = =

5 5 5 5

cm, cm, cm, cm,

∠F = 60° ∠E = 60° ∠E = 60° ∠D = 60°

34. 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. C.

13 m, 7 m 40 m, 30 m

B. D.

45 m, 37 m 50 m, 50 m

35. 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. C.

Two distinct Three distinct

B. D.

A unique None of these 5

EVERYDAY MATHeMATICS 36. 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%

A.

3

C.

5.6%

B.

5

D.

6.5%

C.

7

D.

Cannot be determined

37. 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

38. 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 .

42. Four different electronic devices make a beep after 1 every 30 minutes, 1 hour, 1 hours and 1 hour 2 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.

43. 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.

3 hrs 45 mins

B.

7 hrs 30 mins

A.

8

C.

7 hrs 45 mins

B.

6

D.

11 hrs 45 mins

C.

4

D.

2

39. 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 .

44. 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.

` 2000

A.

56 : 99 : 69

B.

` 2040

B.

99 : 56 : 69

C.

` 2100

C.

69 : 56 : 99

D.

` 2200

D.

99 : 69 : 56

40. 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?

6

41. 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?

45. 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.

` 12,000

A.

20%

B.

` 12,864

B.

39%

C.

` 15,600

C.

40%

D.

None of these

D.

50% | 10th IMO | Class-9 | Set-B | Level 1

Achievers section 1 of its breadth and 3 1 its height is of its length. The cost of whitewashing 2 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.

R.

A. B. C. D.

A. B. C. D.

46. Length of a mathematics lab is 1

` ` ` `

324 624 570 420

47. Match the following columns: Column I

Column II

(a)

A n g l e b i s e c t o r s o f a (p) parallelogram form a _____.

Parallelogram

(b)

The quadrilateral formed (q) by joining the mid-points of the pairs of adjacent sides of a square is a _____.

Rectangle

(c)

The quadrilateral formed (r) by joining the mid-points of the pairs of adjacent sides of a rectangle is a _____.

Square

(d)

The figure formed by (s) joining the mid-points of the pairs of adjacent sides of a quadrilateral is a _____.

Rhombus

A. B. C. D.

(a) (r) (q) (q) (s)

(b) (q) (r) (r) (r)

(c) (s) (p) (s) (q)

Q.

T.

True True False True

True False True True

False True False False

False False True True

True True False True

49. 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° 50. 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 ?

(d) (p) (s) (p) (p)

I. II. III.

48. State True or False and select the correct option. P.

S.

If D is the mid-point of the hypotenuse AC of a right DABC, then BD = AC. Perimeter of a triangle is equal to the sum of its three medians. If the altitudes AD, BE and CF of DABC are equal, then DABC is equilateral. P   Q   R S T

In a DABC in which AB = AC, the altitude AD bisects BC. The sum of any two sides of a triangle is greater than twice the median drawn to the third side.

A. B. C. D.

Five years ago, Arun's age was double that of his son's age at that time. Present ages of Arun and his son are in the ratio of 11 : 6 respectively. Five years hence, the respective ratio of Arun's age and his son's age will become 12 : 7. Only I and II Only II and III Only I and III Any two of the three

SPACE FOR ROUGH WORK

10th IMO | Class-9 | Set-B | Level 1 |

7

Class 9

Set A Year 2017

LOGICAL REASONING 1.

Find the missing number, if a certain rule is followed either row-wise or column-wise. 11 17 25 19

3 12 34 25

8 ? 19 11

A. 18 B. 16 C. 12 D. 20 2.

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



A. B. C. D.

5.

A cube is painted red on the two adjacent faces and black on the surfaces opposite to red surfaces and orange on the remaining faces. Now the cube is divided into 216 smaller cubes of equal size. How many smaller cubes will have no surface painted?



A. 36 B. 64 C. 60 D. 54

6.

The following letters are coded as follows.

Fig. (X)

A.



D.

3.

If all the symbols are dropped from the given arrangement, then which of the following will be the twelfth element to the left of E?



×2@M1N#RU5Y8JLT3HK7S$B W4E%H*DF



A. U B. J C. 8 D. L

4.

Group the given figures into three classes on the basis of their identical properties by using each figure only once.

2, 2, 2, 2,

4, 3, 3, 4,

9; 4; 5; 7;

3, 6, 4, 3,

5, 8, 8, 6,

8 9 9 9

Letters M R Z A T D E Q S I V Digit/Symbol 2 @ 3 5  1 $ 8 * # % While coding the given letters, following conditions are also to be observed.

7.

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



Fig. (X)

1

2

 C.

5

6

7

8

9

B.

 

D.



3

4



A.

8.

2

7; 7; 7; 8;





C.

6, 5, 6, 5,

Conditions : (i) If the first letter is a consonant and the last letter is a vowel, then their codes are to be interchanged. (ii) If both the first and the last letters are vowels, then both are to be coded as the code for the last letter. (iii) If both the first and the last letters are consonants, then both are to be coded as the code for the first letter. Find the code of ADMIRE. A. 5 1 2 # @ 5 B. 5 1 2 # @ $ C. $ 1 2 # @ $ D. $ 1 2 # @ 5



B.

1, 1, 1, 1,

If 'P @ Q' means 'P is brother of Q', 'P + Q' means 'P is wife of Q', 'P # Q' means 'P is daughter of Q' and 'P – Q' means 'P is father of Q', then which of the following expressions indicates that 'D is father-in-law of A'? | IMO | Class-9 | Set-A | Level 1

A. B. C. D. 9.

A+ A+ A+ A+

B@E–D#C E@B–C#D B@C#D–E B@C#E–D

C.

A square transparent Sheet (X) with a pattern and a dotted line on it is given. Select a figure from the options which shows the folded form of Sheet (X).

D.

P

A

12. Going 90 m to the South, Gaurav turns left and goes another 35 m. Then turning to the North, goes 60 m and then turning to his right and goes 25 m. How far is he now from his starting point and in which direction? 30 5 m, North-East A. 30 5 m, South-East B. C. 38 m, South

Sheet (X)

40 3 m, North-West D. A.

B.

C.

D.

13. In the given Venn diagram, if circle represents 'Politicians', triangle represents 'Doctors' and rectangle represents 'Married people', then which of the following numbers represents the Married doctors who are not Politicians?

10. 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, 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 second one is to be subtracted from the first one. 83 32 17 33 m 8 If m is the resultant of the first row, then what will be the resultant of the second row? A. 3 C. 8 11.

B. 5 D. 10

1 2 7

A. 4 C. 2

4 5

3

6

B. 3 D. 5

14. A theatre has six performing ladies consisting of four vocal musicians, two dancers, one actress and three violinists. Gauri and Vandana are among the violinists while Jaya and Shailja do not known playing on violin. Shailja and Tanya are the dancers. Jaya, Shailja, Vandana and Tanya are all vocal musicians and two of them are also violinists. Pooja is an actress. Who amongst these lady artists is a dancer, a vocal musician and a violinist? A. Shailja B. Jaya C. Tanya D. Vandana 15. Select a figure from the options, which when placed in the blank space of Fig. (X) would complete the pattern.

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

? Fig. (X)

P x

A. IMO | Class-9 | Set-A | Level 1 |

C

B.

X

A.

B.

C.

D. 3

MATHEMATICAL REASONING 16.

The polynomial ax3 – 29x2 + 45x – 9 when divided by (3x – 1) leaves remainder 3. Find the value of a. Also, find the remainder when the given polynomial is divided by x – 2. A. B. C. D.

3, 6, 6, 9,

–19 –11 13 16

1 RB 2 D. None of these

C CR =

20. In the given figure, PQ || RS. If ∠QPM = 95° and ∠PMR = 30°, then find ∠MRS. Q

17. In the given figure (not drawn to scale), find the value of x, y and z respectively. A 50°

F z y

B

x

E

20°

C

D

S

R

P

M

A. 95° B. 135° C. 125° D. 85° 21. Study the given figure carefully. A point to be chosen randomly. Find the probability that the chosen point must be lying in the shaded region.

A. 90°, 50°, 110° B. 90°, 40°, 110° C. 40°, 90°, 110° D. 110°, 40°, 90°

6 cm

D

18. Which of the following triangles is formed by straight lines x + y = 2, x – y = 2 and y-axis?

C

6 cm

6 cm

y 2

x′

D –2

A

A B 2

O

C

x

9 C. 28 11 D. 28

19. In the given figure, ABCD is a parallelogram in which P is the midpoint of DC and Q is the point on AC 1 such that CQ = AC and PQ produced meet BC at 4 R, then P C D Q A A. CR = 1 CB 3 B. CR = RB 4

13 A. 26 11 B. 26

–2

y′

A. DAOB B. DABC C. DADC D. DADO

B

6 cm

22. In the figure, if ED = EC and ∠ADF = ∠BCG, then D ABE is a/an _________. F

C

G

E

A

R B

D

A. B. C. D.

B

Equilateral triangle Isosceles triangle Scalene triangle Non isosceles right angled triangle | IMO | Class-9 | Set-A | Level 1

23. If the medians of DPQR intersect at O, then ar (POQ) = P

L

M O

Q

N

R

A. ar (QOR) 1 B. ar (PQR) 3 C. Both A and B D. Neither A nor B 24. The given question is followed by three statements. Study the statements carefully and decide which of the following statement(s) is/are necessary to answer the question. What is the total surface area of cone? (I) The area of the base of the cone is 1386 cm2. (II) The curved surface area of the cone is 2310 cm2. (III) The volume of the cone is 3696 cm3. A. I and either II or III B. II and either I or III C. III and either I or II D. Any two of the three 25.

Which of the following is Euclid's third postulate? A.

A straight line may be drawn from any one point to any other point. B. A terminated line can be produced infinitely. C. A circle can be drawn with any centre and any radius. D. All right angles are equal to one another. 1  3 1  2 1  5 − 21 , then  x + 3  − 5  x + 2  +  x +  = 26. If x = x x x 2 ______. A. 0 B. 1 C. 2 D. –1 27. A design on a floor is made up of triangular tiles. The sides of each triangle being 24 cm, 32 cm and 40 cm. Find the cost of polishing all 170 tiles on the floor at the rate of ` 1.50 per cm2 . A. ` 97920 B. ` 65280 C. ` 99480 D. ` 89460 IMO | Class-9 | Set-A | Level 1 |

28. A capsule of medicine is in the shape of a cylinder of diameter 2.1 mm and height is three times the radius. How much approximate medicine (in mm3) is needed to fill this type of 30 capsules? A. 340.20 B. 327.30 C. 286.50 D. 267.30 29. The value of below.

2 upto 50 decimal places is given

2 = 1.411213562373095048801688724209698078 56967187537694 A number is chosen at random from the numbers after the decimal. Find the probability that chosen number will be a/an (i) Odd number. (ii) Prime number. (iii) Multiple of 2 (greater than 0). (i) (ii) (iii) A. 22/50 21/50 18/50 B. 24/50 18/50 21/50 C. 18/50 22/50 21/50 D. 23/50 18/50 21/50 30. If x =

a + 2b + a − 2b , then bx2 + b = a + 2b − a − 2b

A. ax B. 0 C. –ax D. –1

31. Which of the following statements is true? A.

If two parallelograms are on equal bases and between the same parallels, then the ratio of their areas is 1 : 2. B. A quadrilateral formed by joining the mid-point of the sides of a quadrilateral in order, is a parallelogram. C. If P is any point on the median AD of a DABC, then ar (DABP) ≠ ar (DACP). D. All of these

32. The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation 9C = 5F – 160°. If the temperature is 0°C, then what is the temperature in Fahrenheit and if the temperature is 0°F, then what is the temperature in Celsius? A. B. C. D.

32°F, 25°F, 25°F, 32°F,

17.78°C 16.50°C –16.50°C –17.78°C 5

3 1   1   33. Simplify: 5 8 3 + 27 3      (13 + 23 + 33 ) −3/ 2

1 4

  81 ×     16 

5 − 4

  25  ×    9   5 − 2

7912 6812 B. A. 625 625

A. 0.15

B. 0.75

C. 0.20

D. 0.004

35. If l||m and p is the transversal, then select the CORRECT match. p

4 3

6812 6912 D. C. 722 625

8 7

34. A die is thrown 500 times and the outcome of each throw is noted down. The given table shows the frequencies of the outcomes. Number of top face of die Frequency

1

2

3

4

5

6

150 75

46

94

35 100

What is the probability of getting the number 2?



5 6

1 2

l m

Column-I  Column-II

A. ∠1, ∠4, ∠6 & ∠7   Interior Angles B. ∠2, ∠3, ∠5 & ∠8   Exterior Angles C. ∠1 & ∠5, ∠2 & ∠6   Corresponding Angles ∠3 & ∠7, ∠4 & ∠8 D. ∠2 & ∠8, ∠3 & ∠5   Alternate Interior Angles ∠1 & ∠7, ∠4 & ∠6

EVERYDAY MATHEMATICS 36. Varun received ` 8000 as his share out of the total profit of ` 12,000 which he and his friend Karan earned at the end of one year. If Varun invested ` 30,000 for four months whereas Karan invested his amount for the whole year. What was the amount invested by Karan? A. ` 8,000 B. ` 5,000 C. ` 10,000 D. ` 15,000 37. In an experiment, a coin is tossed 500 times. If the tail turns up 280 times, then find the probability of getting a head. 11 A. 25 12 B. 25 14 C. 25 13 D. 25 38. A teak wood log is first cut in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is 1.104 m3. How many rectangular planks of size 2.3 m × 0.75 m × 0.04 m can be cut from the cuboid? 6

A. 16 B. 64 C. 68 D. 4

39. The average marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the average marks of all the students in the examination is 71, then find the ratio of the number of boys to the number of girls.

A. 1 : 3



B.

2:1



C.

1:2



D. 3 : 1

40. A train passes two persons walking in the same direction in which the train is going. These persons are walking at the rate of 5 km/hr and 8 km/hr respectively and the train passes them completely in 20 seconds and 25 seconds respectively. Find the speed of the train.

A. 20 km/hr



B.

28 km/hr



C.

18 km/hr



D. 15 km/hr

41. During a year, the population of a town increased by 8% and during the next year, the population decreased by 8%. If the total population is 9936 at the end of the second year, then what was the population in the beginning of the first year? A. 15000 B. 10000 C. 18000 D. 22000 | IMO | Class-9 | Set-A | Level 1

42. In a medical certificate, by mistake a candidate gave his height as 30% more than the actual height. In the interview panel, he clarified his height was 5 feet 6 inches. Find the approximate percentage correction made by the candidate from his stated height to his actual height. A. 25.52% B. 21.05% C. 23.07% D. 19.25% 43. A trader marks his goods 25% above the cost price. He then sells them at a discount of 25%. If the cost price is ` 500, then find the loss or gain percentage. A. B. C. D.

Loss, 5.25% Gain, 5.25% Gain, 7.15% Loss, 6.25%

44. A bill for ` 70 is paid by means of ` 10 notes and ` 20 notes. Five notes are used in all. If m is the number of ` 10 notes and n is the number of ` 20 notes, then _______. A. m + n = 5, 2m + n = 8 B. m – n = 5, m + 2n = 7 C. m + n = 5, m + 2n = 7 D. m – n = 5, m + 2n = 8 45. The compound interest on a certain sum for 2 years at 10% per annum is ` 525. Find the simple interest on the same sum for double the time at half the rate percent per annum. A. ` 400 B. ` 500 C. ` 600 D. ` 800

ACHIEVERS SECTION 46. Fill in the blanks and select the CORRECT option. Two cylindrical pots contain the same amount of milk. If their diameters are in the ratio 2 : 1, then the ratio of their heights is ___ P__.  The volume of a sphere is equal to ___ Q__ the volume of a cylinder which has same height and diameter. (Radius of sphere = radius of cylinder)  The slant height and base diameter of conical tomb are 25 m and 14 m respectively. The cost of white washing its curved surface at the rate of ` 210 per R__. 100 m2 is ___ P Q R A. 4 : 1 half ` 1100 B. 1 : 4 half ` 1100 C. 1 : 4 two-third ` 1155 D. 4 : 1 two-third ` 1155 

47. If the 11 observations are 24, 17, 13, 24, 26, 20, 26, 30, 8, 41, 24, then match the following : Column-I P.

Column-II

C. P → (ii), Q → (iv), R → (i), S → (iii) D. P → (i), Q → (ii), R → (iv), S → (iii) 48. Study the following statements carefully and select the CORRECT option. Cards marked with the consecutive odd numbers from 1 to 200 are put in a box and mixed thoroughly. One card is drawn at random from the box. Statement - 1 : Probability that drawn card is multiple of 3 is 1 . 2 Statement - 2 : Probability that drawn card is a perfect 2 square and a multiple of 9 both is . 3 A. Both Statement-1 and Statement-2 are true. B.

Both Statement-1 and Statement-2 are false.

C. Statement-1 is true but Statement-2 is false. D. Statement-1 is false but Statement-2 is true. 49. Which of the following is the solution of linear equations shown here?

Mean =

(i)

23.55

Q. Mode =

(ii)

23

(i) 4x + 3y = 24

R. If all 24 are replaced by 26, then new mean (approximately) =

(iii)

26

(ii) 3x – 4y = 1

S.

(iv)

If all 24 are replaced by 26, then new mode =

(iii) 8y – 6x = 4 (i) (ii) (iii) 24

A. P → (i), Q → (ii), R → (iii), S → (iv) B. P → (iv), Q → (iii), R → (ii), S → (i) IMO | Class-9 | Set-A | Level 1 |

A. B. C. D.

(9, (9, (3, (3,

– 4) 4) 4) 4)

(–1, –1) (–1, –1) (3, 2) (–3, 2)

(2, (2, (2, (2,

–2) 2) 2) 2) 7

50. State T for true and F for false and select the CORRECT option. 3+ 2 5

= p + q 5 , where p and q are rational 4−2 5 numbers, then values of p and q respectively are –8 and 7/2.

P. If

Q. 2. 6 − 0.82 is equal to 182/99. R. If a = 2 + 3 + 5 and b = 3 + 3 − 5 , then a2 + b2 – 4a – 6b – 3 is equal to 0.

S. If x = 3 5 + 2 2 and y = 3 5 − 2 2 , then the value of (x2 – y2)2 is 240. P Q R S A. T F F F B. F F T T C. T T F T D. F T T F

SPACE FOR ROUGH WORK

8

| IMO | Class-9 | Set-A | Level 1

Class 9

Set B Year 2017

LOGICAL REASONING 1.

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.

A. B. C. D. 5.

What is the relation of Sakshi to Neha? A. Sister B. Niece C. Aunt D. Daughter 2.

9

105

7

36

4

2

6

4

6

9

?

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 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.

3

2

A.

B.

C.

D.

6.

4

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. A will go in the same boat in which E is to go. 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?

I. II.

3.

2

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).

1

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

4.

km km km km

?

Find the missing number, if same rule is followed in all the three figures. 72

2 4 6 8

A. B. C. D. 7.

G is in the other boat. D is in the other boat. C is in the other boat. E is with F and B in one boat.

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

Fig. (X) A.

B.

C.

D.

| IMO | Class-9 | Set-B | Level 1

8.

Given below are the three different positions of a dice. What shall come in the place of 'X'? 4

X 2

3

6 6

4

1

5



A. 1 B. 2 C. 4 D. 5

9.

Select the correct water image of Fig. (X). 3

5

9

9

13. 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?

Fig. (X)

6

5 C. 6

6 B. 5 5 9 3 D. 3 5 9

3

9

3

6

6



A.

10. 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



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

11. 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. B. C. D.

DAME MADE DOME MODE

C.

1 1 2 2 TP l V J l P T AJ V 3 JV 4 4

VJ 1 2 l A MP T

BT P B 2 T P DV J l l A A M M

B B D G VJ HT P P T   I J V A. B. A A 5 5

12. Select the odd one out. A.

A. Fifth B. Tenth C. Seventh D. Eighth

B.

D.

IMO | Class-9 | Set-B | Level 1 |

B B D PT DJ V PT F J V C. G D. A A 5 M

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

A. 24 B. 23 C. 27 D. None of these 3

MATHEMATICAL REASONING 16.

a a  ,∠BOC = 5  − 10°   2 2 and ∠COD = a + 9°, then find ∠AEO + ∠EAO.

In the given figure, if ∠AOB =

B

C

A

O

D

E

A. 127.75° B. 130.75° C. 129.50° D. 115.75° x

2x

64 = , then 729

A. 3 B. 2 C. 1 D. 4 18. The three vertices of a rectangle ABCD are A(2, 2), B(–3, 2) and C(–3, 5). Find the area of rectangle ABCD. 15 35 20 25

sq. sq. sq. sq.

(i) DF = BE (ii) AM bisects ∠BAD Only (i) Only (ii) Both (i) and (ii) Neither (i) nor (ii)

A

D F M C

E

B

20. 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. B. C. D. 4

(0, (5, (0, (5,

–5) 0) 0) 5)

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

(i) ∠RQT (ii) ∠PUT (i) A. 75° B. 105° C. 105° D. 75°

S 150°

P

(ii) 75° 75° 105° 105°

O

T Q

R

U

23. 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.

units units units units

19. 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?

A. B. C. D.

A.

22. In the given figure, ∠POT = 150° and O is the centre of circle. Find the measure of

a b 4 3+5 2 a+b 6 and     17. If = b a 15 48 + 18 find x.

A. B. C. D.

21. 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. B. C. D.

3 2 1 4

cm cm cm cm

24. 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

P

D O

B

A. B. C. D.

Two Two Two Two

parts parts parts parts

of of of of

Q C

equal area area in 2 : 1 area in 1 : 3 area in 4 : 3 | IMO | Class-9 | Set-B | Level 1

25. The distance (in km) of 40 engineers from their residence to their place of work were found as follows: 5 19 7 12

3 10 9 14

10 12 7 2

20 17 8 9

25 18 3 6

11 11 5 15

13 32 12 15

7 17 15 7

12 16 18 6

31 2 3 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 26. Simplify:

5

x 4 4 x3 3 x 2 x .

C F B



A.



It is possible to construct a D PQR in which QR = 6 cm, ∠Q = 130° and ∠R = 50°. C. It is possible to construct a DXYZ in which ∠X = 60°, ∠Y = 100° and ∠Z = 20°. D. In a DABC, AB + BC > AC.



It is possible to construct an angle of 67.5° using ruler and compass only.

B.

30. The following are the steps involved in finding the value of a 4 +

1 1 , when a + = 1. Arrange them in a4 a

sequential order from the first to the last. a2 + P.

1 1 + 2 = 1 ⇒ a 2 + 2 = −1 2 a a

Q.

 1 (a 2 ) 2 +  2  + 2 = 1 a 

27. 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

Z



T.

a4 +

y (0, 1)

O

28. 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 G E

H

80°

C x

Q

120°

F D B

IMO | Class-9 | Set-B | Level 1 |

1 = −1 a4

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

C

D

cm cm cm cm

A. 40° C. 100°

1  2  a +  = 1 a

31. 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 ?

B X

Y

R

2

R.

2

D. x113/120

P

E

P

D

 2 1 2 S.  a + 2  = ( −1) a

C. x117/120

5 6 7 8

Q

2

x119/120 B.

A. B. C. D.

A



A. x119/121



29. Which of the following is INCORRECT.

B. 20° D. None of these

1

2

x

A. x = 0  B. x=1 C. x–y=0 D. None of these 1 32. If a = 5 + 2 6 and b = , then what will be the a value of a 2 + b 2 and a3 + b 3 ?

A. 98, 970 B. 98, 1000 C. 981, 985 D. 970, 560 5

33. 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. 34.

35. 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.

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. 210° B. 105° C. 75° D. 150°

A. 4 B. 5 C. 6 D. 7

EVERYDAY MATHEMATICS 36. 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. B. C. D.

12 : 30 p.m. 1 : 00 p.m. 2 : 00 p.m. 2 : 30 p.m.

37. 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. B. C. D.

45.8 % 62.3 % 57.8 % None of these

38. 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 39. 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 6

C. 20x + 10y = 300 D. x + 25y = 900 40. 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. 39 29 A. B. 100 50 19 39 C. D. 50 50 41. 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 m 2 cloth costs ` 10. A. ` 22 B. ` 2200 C. ` 220 D. ` 200 42. 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 43. 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. B. C. D.

9% 6% 8% 12 % | IMO | Class-9 | Set-B | Level 1

44. 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. B. C. D.

2 1 2 1

min min min min

30 45 12 30

sec sec sec sec

45. 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. B. C. D.

26 42 45 46

minutes 18 seconds minutes 36 seconds minutes minutes 12 seconds

ACHIEVERS SECTION 46. By using a given figure of quadrilateral ABCD, match the columns.

P. Q. R. S.

A. B. C. D.

Column-I If ABCD is a parallelogram, then sum of the angles x, y and z is If ABCD is a rhombus, where ∠D = 130°, then the value of x is If ABCD is a rhombus, then the value of w is If ABCD is a parallelogram, where x + y = 130°, then the value of ∠B is P (1) (3) (2) (2)

Q (2) (4) (1) (4)

R (3) (2) (4) (3)

Column-II (1) 25° (2) 180° (3) 50° (4) 90°

S (4) (1) (3) (1)

47. Simplify: (i)

4 5 2 − + −3 / 7 −1/ 4 (2187) (13312 ) −1/ 3 (256) 1

1

1

 x a  ab  x b  bc  x c  ca (ii)  b  ⋅  c  ⋅  a  x  x  x  (i) A. 270 B. 330 C. 330 D. 270

(ii) xabc 0 1

1 abc x

48. 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). IMO | Class-9 | Set-B | Level 1 |

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. 49. 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. The area of an equilateral triangle is 81 3 cm 2 , then its height is 9 3 cm. 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 R.

50. Fill in the blanks. (i) (ii) (iii) (iv) A. B. C. D.

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 . 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. The largest sphere is carved out of a cube of side 7 cm. Then the volume of the sphere is R . Curved surface area of the hollow cylinder of radii r1 and r2 and height h is S . P Q R S 3 2:3 6000 189.67 cm 2ph(r1 – r2) 3:2 6000 179.66 cm3 2ph(r1 – r2) 2:3 5000 189.67 cm3 2ph(r1 + r2) 3:2 5000 179.67 cm3 2ph(r1 + r2) 7

Class 9

Set A Year 2018

LOGICAL REASONING 1.

How many pairs of letters are there in the word RECREATION which have number of letters between them in the word one less than the number of letters between them in the English alphabet?



A. Two B. Three C. Four D. More than four

2.

Select the correct water image of the given figure.

Input : play 35 29 nice 17 clever task 75

A. B. C. D.

5.

Find the missing number, if a certain rule is followed either row-wise or column-wise. 7 5 2 109

A.

B.



C.

D.

6.

Fig. (X)

3.

Which symbol will be on the face opposite to the face with symbol @, when the given figure is folded to form a cube? #

Step V Step VI Step IV Step VII

15 8 12 2 ? 3 183 168

A. 7 B. 8 C. 9 D. 11 Which of the following options satisfies the same conditions of placement of the dots as in the given figure?

•

@

*

$

A.

B.

C.

D.

© A. * B. # C. © D. $ 4.

A word-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 :  page 15 easy 62 fire 52 desk 47 Step I :  page 62 15 easy fire 52 desk 47 Step II :  page 62 fire 15 easy 52 desk 47 Step III :  page 62 fire 52 15 easy desk 47 Step IV :  page 62 fire 52 easy 15 desk 47 Step V :  page 62 fire 52 easy 47 15 desk Step VI :  page 62 fire 52 easy 47 desk 15 Step VI is the last step of the given input. As per the rule followed in the above steps, which is the last step of given input? 2

7.

In a certain code language, CHOCOLATE is coded as AFMAPNCVG. How will SENSITIVE be coded in the same language?



A. UGPUKVKXG B. QCLQKRGTC C. QCLQJVKXG D. UGPUJRGTC

8.

How many vowels are there in the given arrangement, each of which is immediately preceded by a symbol and immediately followed by a consonant? F 4 @ J 2 E % M S 4V9 ©AQ R 6 UT3 Z 7 # U S B 8V G $YC



A. One B. Two C. Three D. None of these | IMO | Class-9 | Set-A | Level 1

9.



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

A.

C.

13. The question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Select a figure from the options which would most closely resembles the unfolded form of Fig. (Z) .

B.



X Y Z

D.



10. Which of the following Venn diagrams best represents the relationship amongst, "Musicians, Non-smokers and Males"? A.

B.

C.

D.



A.

B.

C.

D.

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

11. Six friends are sitting in a circle facing the centre. Sneha is sitting opposite to Vaibhav. Kavya is sitting to the right of Vaibhav but to the left of Kirti. Monika is sitting to the left of Vaibhav. Priya is sitting to the right of Sneha and to the left of Monika. Now, Kirti and Priya, Monika and Vaibhav mutually interchange their positions.

Who will be sitting to the left of Monika? A. Kavya B. Priya C. Kirti D. Vaibhav

(1)

(2)

(3)

(4)

A.

B.

C.

D.

15. Find the number of triangles formed in the given figure.

12. Pointing to a lady in the garden, Priyansh said," She is the daughter of my grandfather's only son". How is Priyansh related to that lady?

A. Brother B. Cousin C. Uncle D. Father

A. 22 B. 19 C. 18 D. None of these

MATHEMATICAL REASONING 16. In a quadrilateral PQRS, diagonals PR and QS bisect each other at M. If ∠PMS = 90°, then quadrilateral PQRS is a ________. A. Trapezium

B. Kite

C. Rhombus

D. Parallelogram

IMO | Class-9 | Set-A | Level 1 |

17. Area of a given triangle is x1 square units. If the sides of this triangle be doubled, then the area of the new triangle becomes x2 square units. Find the percentage increase in area.

A. C.

100% 300%

B. D.

200% None of these 3

18.

Consider the given statements carefully. I. Any point on the x-axis is of the form (0, a). II. The point (0, 0) lies on both the axes. III. The point (3, –2) lies in the IIIrd quadrant. Which of the above statements is/are true? A. Both I and II B. Only I C. Only II D. Both II and III

19. If (3, –1) is a solution of the linear equation 4x – ky = 8x + 2y, then find the value of k.

A.

Things which coincide with one another are equal to one another. B. Two distinct lines can have more than one point in common. C. A circle can be drawn with any centre and any radius. D. A straight line may be drawn from any one point to any other point.



21. A bag contains 8 yellow, 3 pink, 2 green and 7 red candies of similar size. A candy is taken out randomly from the bag. What is the probability that the chosen candy is of red colour? 1 A. 4 3 B. 20 7 C. 20 4 D. 5

x2 A. units 2π x B. units 2 π

24. What could be the possible values of X, if 2345691X32 is divisible by 3 (where X is a digit)? A. 1

B. 4 C. 7



D. All of these

25. In the given figure (not drawn to scale), ABCD and PQRS are parallelograms. Find the value of x.



A.

70°

B. 80° C. 30° D. 40°

22. In the given figure, DABC and DPBC are two isosceles triangles on the same base BC and vertices A and P are on the same side of BC. If A and P are joined, then A

B

1 ∠BPA = ∠BAC A. 2 1 ∠BAP = ∠BAC B. 2

a + a 2 − b2 a − a 2 − b2 26. T h e d e n o m i n a t o r o f + a − a 2 − b2 a + a 2 − b2 is_________. A. a2 B. b2 C. a 2 – b 2 4a 2 − 2b 2 D. b 27. If p = 2 − 3 , q = 3 − 7 and r = 7 − 4, then find the value of p 3 + q3 + r 3.

P

4

23. The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, then what is the value of r in terms of x?

2x units C. π x D. units π

A. 11 B. 13 C. 10 D. 15

20. Which of the following statements is INCORRECT?

1 ∠BAC 2 ∠BAP = 2∠BAC D. ∠CPA = C.

C

A. 0

(

3 3 3 + 7 −8 B. C. 3 3−2 7 D. None of these

) | IMO | Class-9 | Set-A | Level 1

28. Three identical spherical balls fit snugly into a cylindrical can. The radius of each of the spherical ball equals the radius of the can and the balls just touch the bottom and the top of the can. What fraction of the volume of the can is taken up by the balls?



3 4 A. B. 5 3



3 2 C. D. 2 3

Number of cars sold (in thousands)

Direction (29-30) : The given bar graph represents the petrol and diesel cars sold in a mega city from 2010 to 2015. Study the graph carefully and answer the following questions.



Petrol Cars Diesel Cars

5

33. In the given figure, ABCD is a rhombus whose diagonals intersect at O. If E and F are mid-points of AO and BO respectively, then find the length of EF. D

2

A

0 2010

2011

2012 2013 Years

2014

C 16 cm

O

1 2015

A. 3200 B. 2800 C. 2500 D. 3000

30. In which year, the total sale of petrol and diesel cars altogether was maximum?



Parallelograms on the same base (or equal bases) and between the same parallels are equal in area. R. If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is equal to the area of the parallelogram. S. Triangles on the same base (or equal bases) and having equal areas lie between the same parallels. A. Only P and Q are true. B. Only Q and S are true. C. Only P and R are false. D. Both B and C

4 3

29. Find the difference between the number of petrol cars sold in 2010 and 2011 together and the number of diesel cars sold in 2015.



Q.

A. 2012 B. 2011 C. 2013 D. 2014

31. In the given figure (not drawn to scale), AB and BC are two chords of the circle with centre O. Find the value of x.

B 12 cm



A. B. C. D.

10 cm 5 cm 8 cm 9 cm

34. The traffic police recorded the speed (in km/hr) of 10 motorcyclists as 32, 45, 46, 55, 65, 38, 45, 41, 39 and 62. Later on, an error in recording instrument was found. Find the correct average speed of the motorcyclists, if the instrument recorded 3 km/hr less in each case.

A. B. C. D.

49.9 48.5 43.8 49.8

km/hr km/hr km/hr km/hr

35. In the given figure (not drawn to scale), ABCD is a quadrilateral. If AE || DC, BE || AD and AE intersects BC at F, then find ∠EBF. D



A. 170° B. 70° C. 150° D. None of these

32. Study the given statements carefully and select the correct option.

P.

Two congruent figures have equal areas and vice versa.

IMO | Class-9 | Set-A | Level 1 |

110° A

C 97° F

E

73° B

A. 43° B. 72° C. 51° D. 27° 5

EVERYDAY MATHEMATICS 36. Amit scored 73 marks in Mathematics. He scored 56% marks in English and x marks in Science. Maximum marks in each subject were 150. The overall percentage of marks obtained by him was 54%. How many marks did he score in Science?

A. 84 B. 86 C. 89 D. 73

41. Along a path, 25 conical pillars are constructed. Each pillar has radius 15 cm and height 20 cm. Find the total cost of painting these pillars at the rate of ` 50 per cm2 . [Take p = 3.14] A. ` 201752.50 B. ` 2052325 C. ` 3214325.50 D. ` 1471875

37. A box contains 125 adapter chargers out of which 45 are defective and rest are good. Priyanka will buy a charger, if it is good. The shopkeeper draws one charger at random and gives it to her. What is the probability that she will buy it?

42. Two spinning machines A and B can together produce 50000 m of cloth in 20 hours. If machine B alone can produce the same amount of cloth in 25 hours, then how much cloth can machine A produce alone in 20 hours?

9 A. 25 16 B. 25 4 C. 25 D. None of these



A. 18000 m



B.

15000 m



C.

10000 m



D. 25000 m

38. Aman had four number cards. The number on the first card is twice the second, that on the second is onethird of the third and that on the third is five times the fourth. The average of the numbers is 24.75. Find the largest number amongst them.

A. 9 B. 25 C. 30 D. None of these

39. A man gets a simple interest of ` 2500 on a certain principal at the rate of 10% per annum in 5 years. What compound interest will the man get on twice the principal in two years at the same rate? A. ` 1500 B. ` 2100 C. ` 1750 D. ` 1350 40. A three-wheeler scooter charges ` 15 for the first kilometer and ` 7.50 each for every subsequent kilometer. For a distance of x km, an amount of ` y is paid. Which of the following shows the linear equation representing the given information?

A. B. C. D. 6

7.50 x – 7.50 = y 15 + 7.50 x = y 7.50 x + 7.50 = y 15 – 7.50 x = y

43. The traffic light at three different signal points change after every 15 seconds, 30 seconds and 45 seconds respectively. If all change simultaneously at 8:15:20 hours, then when will they again change simultaneously?

A. 8:16:20 hours



B.

8:18:35 hours



C.

8:18:45 hours



D. 8:16:50 hours

44. A person at first has enough money to buy 80 sunglasses worth ` 700 each. If the cost of each sunglasses gets increased by ` 50, then how many sunglasses can he buy with the same amount of money (approx.). A. 80

B.

74

C. 82

D.

75

45. The manufacturer of a machine sells it to a trader making a profit of 15% on its manufacturing cost, the trader sells it to the vendor, making a profit of 5% and vendor sell it to the actual user at a profit of 10%. If the actual user pays ` 531.30 for it, then find the manufacturing cost. A. ` 400 B. ` 800 C. ` 600 D. ` 360 | IMO | Class-9 | Set-A | Level 1

ACHIEVERS SECTION 46. Read the statements carefully and select the correct option.

S. Point E and G lie on x-axis.

A. Only P and S





B.

Only P and Q



C.

Only R and S



D. P, Q, R and S



Statement-I : A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe whose cross-section is 25 cm 2 , at the rate of 16 km per hour. The rise in the level of water in the tank in 45 minutes is 2.5 cm.

49. Match the following:

Statement-II : If V is the volume of cuboid of dimensions a, b and c and A is its surface area, then A = 2[a + b + c]. V



A. Statement-I is true but Statement-II is false.



B.

Statement-I is false but Statement-II is true.



C.

Both Statement-I and Statement-II are true.



D. Both Statement-I and Statement-II are false.

Column-I (a)

3

Q. I f x = 3 – 2 2 , t h e n 1 x− = _________. x

(b)

−1 3

R. If x = 2 + 3 , then

(c)

±2

(d)

196

P.

The value of m for which 1 9

−1  −3 2    1    = 3m , is   32        

47. ABC is a triangle. D is a point on AB such that 1 AD = A B and E is a point an AC such that 4 1 AE = AC. Then DE = ________ 4 A. BC

2

 2 1  x + 2  = ______. x S.

B. 2 BC 1 C. BC 4

Column-II

x −2

x −4

 b If  a  =   b  a x = __________.

, then

1 D. BC 2



A.

P→(b); Q→(c); R→(d); S→(a)



B.

P→(c); Q→(b); R→(a); S→(d)



C.

P→(d); Q→(a); R→(c); S→(b)

48. Study the given co-ordinate system carefully. Which of the following options hold true?



D.

P→(a); Q→(b); R→(d); S→(c)

50. A die having numbers 1, 2, 4, 6, 7 and 8 on its faces, is rolled once. Find the probability of getting (i) an even prime number. (ii) a number greater than 3. (iii) a multiple of 2 which is less than 4. (i)

(ii)

(iii)

A.

1 6

1 3

2 3

B.

1 3

1 2

1 3

The coordinates of points B and D are (3, –5) and (– 6, –3) respectively.

C.

1 6

1 2

1 6

Q. Point A is at the distance of 6 units from y-axis.

D.

1 6

2 3

1 6



P.

R. BG is parallel to y-axis. IMO | Class-9 | Set-A | Level 1 |

7

SPACE FOR ROUGH WORK

8

| IMO | Class-9 | Set-A | Level 1

Class 9

Set B Year 2018

LOGICAL REASONING 1.



If it is possible to make only one meaningful English word with the first, fourth, fifth, ninth and eleventh letters of the word TRANSLOCATION(using each letter only once), then which of the following will be the third letter of the word formed? If no such word can be formed, then give 'X' as your answer and if more than one such word can be formed, then give 'Z' as your answer.

B.

C.

D.

5.

A. X B. T C. Z D. I 2.

A.

Starting from a point, Rohit walked 15 m South. Then, he turned left and walked 10 m. Again, he turned left and walked 15 m. After that he turned right and walked 5 m. At last he turned left and walked another 20 m. How far is he now and in which direction from the starting point?



A. B. C. D.

25 20 15 25

3.

Given question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Select a figure from the options that would most closely resembles the unfolded form of Fig. (Z).

m, m, m, m,

South-East North-East South-West North-East

If '–' stands for 'multiplication', '+' stands for 'division', '×' stands for 'addition' and '÷' stands for 'subtraction', 1 then find the value of 142 + 2 ÷ 31 × 10 – . 2 A. 7/3 B. 45 C. 39 D. 5/2 6.

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

OP73ER29ATI4ON OP73ER29ATI4ON A. N O 4 I TA 92 R E 37 P O B. OP73ER2 ATI4ON C. D. O 4 I TA 92 R E 3 P O 7.

Group the given figures into three classes on the basis of their identical properties by using each figure only once.

A

L

W

E

V

N

T

M

Z

4

X A.

C.

4.

2

Y

Z

B.

2

1

7

1,3,8; 1,6,9; 1,5,7; 1,2,3;

2,5,7; 2,5,7; 2,3,4; 4,6,8;

5

8

3

6

9



A. B. C. D.

4,6,9 3,4,8 6,8,9 5,7,9

8.

Find the number of squares formed in the given figure.



A. 15 B. 11 C. 12 D. None of these

D.

Which of the following figures is exactly embedded in the given figure as one of its parts?

| IMO | Class-9 | Set-B | Level 1

9.

In a row of boys, Vishal is 16th from the left end and Ashish is 18th from the right end. Aryan is 11th from Vishal towards the right end and 3 rd from Ashish towards the right end. How many boys are there in the row?





A. 38 B. 36



C. 41

D.

Can't be determined



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

(ii) If a two digit even number is followed by a two digit odd number which is a perfect square, then the even number is to be subtracted from the odd number. (iii) If a three digit number is followed by a two digit number, then the first number is to be divided by the second number. (iv) If a prime number is followed by an even number, then the two numbers are to be added. (v) If an even number is followed by another even number, then the two numbers are to be multiplied. 255 17 11 X 4 13 If X is the resultant of the first row, then what will be the resultant of the second row?

A. 7 B. 8 (1) (2)

(3) (4)

C. 10 D. 12

A.

13. Three positions of a dice are shown below. Find the number on the face opposite to the face showing number 5.

B.

5 C.

2

× D.

2

48

3

3

51 1

7

8 ?

5

2

6

A. 120

D. 6 14. If 'P × Q' means 'P is the daughter of Q', 'P + Q' means 'P is the father of Q', 'P ÷ Q' means 'P is the mother of Q' and 'P – Q' means 'P is the brother of Q' , then in the expression 'M ÷ N + R – T × K', how is M related to K?

A.

Mother-in-law



C.

57



B.

Sister-in-law



D.

75

C. Aunt

12. 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)

1

C. 3

B. 60



6

B. 1

7

3

1

2 3

A. 4

11. Find the missing number, if same rule is followed in all the three figures. 5

2 3

If a two digit odd number is followed by another two digit odd number, then they are to be added.

IMO | Class-9 | Set-B | Level 1 |



D.

Mother

15. Find the missing term in the given series. CMP, ENN, HOK, LPG, ? A. PRC

B.

OQA

C. RPC

D.

QQB 3

MATHEMATICAL REASONING 16. Temperature of a body can be measured in Celsius unit as X°C or in Fahrenheit unit as Y°F. The relation between the two scales of temperature is given by the 9 linear equation Y = X + 32°. 5





A. x+y

(i)

Find the temperature of a body in Fahrenheit, if the temperature of the body is 60°C. (ii) If the temperature of a body is 77°F, then find the temperature in Celsius. (i) (ii) A. 140°F 35°C B. 80°F 60°C C. 140°F 25°C D. 70°F 75°C 17. A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the vessel, then what percent of the beverage can be poured from the bowl into the cylindrical vessel?

2 66 % A. 3 1 78 % B. 2

C.

100%



D. None of these

(

) (

) (

8+3 2 + 7 − 2 − 3−4 2

)

= a + b 2 , then 6−2 2 find the value of a and b respectively.

18. If

24 15 2 A. , 7 7 −24 −15 B. , 7 7 24 15 C. , 7 6 24 15 D. , 7 7 19. PQRS is a parallelogram. M and N are the mid-points of sides PQ and RS respectively. If XY is any line intersecting PS, MN and QR at X, O and Y respectively such that XY || PQ, then find the ratio in which O divides the line XY.

A. 1 : 3 B. 1 : 1 4

C. 1 : 4 D. 2 : 1

20. Find the quotient, when x 3/2 – xy1/2 + x1/2 y – y 3/2 is divided by (x1/2 – y1/2). B. x–y

C.

x1/2 + y1/2

D. x2 – y2 21. A money lender borrows money at 4% p.a. on simple interest and pays interest at the end of the year. He lends it at 6% p.a. compound interest compounded half-yearly and receives the interest at the end of the year. Thus, he gains `104.50 per year. Find the amount of money he borrows. A. ` 5500 B. ` 4500 C. ` 5000 D. ` 6000 22. In the given figure, if AB || CD, then the value of x is ______.

A.

25°



B.

30°



C.

45°



D.

50°

23. If the base radius and the height of a right circular cone are increased by 20%, then the percentage increase in volume is _________ (approximately).

A. B. C. D.

60 68 73 78

% % % %

24. In the given figure (not drawn to scale), L, M and N are the mid-points of the sides QR, RP and PQ respectively of a DPQR. QM intersects the line LN at U and RN intersects the line LM at V, then UV = kQR. Find the value of k. P

A. 4 B. 1/4

N

C. 2 D. 1/2

M U

Q

V L

R

| IMO | Class-9 | Set-B | Level 1

25. In the given figure (not drawn to scale), AC = BD and if BC is subtracted from AC and BD, then AB = CD. A

B

C

D

Which of the following Euclid's axioms explains the above result?

A.

If equals are added to equals, the wholes are equal.



B.

If equals are subtracted from equals, the remainders are equal.



C.

Things which coincide with one another are equal to one another.



D.

Things which are equal to the same thing are equal to one another.

26. Study the given graph carefully.

A. 46 B. 44.9

C.

45.9



D.

43.5

29. Which of the following is incorrect?

A.

If three angles of a quadrilateral are equal, then it is always a parallelogram. B. The line segments joining the mid points of the sides of an equilateral triangle divides it into four congruent triangles. C. PQRS is a parallelogram in which diagonal SQ bisects ∠PQR. If ∠PQS = 42°, then ∠SPQ = 96°. D. None of these 30. In the given figure (not drawn to scale), MN is the diameter of circle with centre O. If ∠MNR = 55°, ∠RMT = 30° and ∠MNS = 60°, then find the value of ∠NMR and ∠MRT respectively. R

T

M

Sum of abscissae of points P and R is ______.

A. 5 B. 6 C. 9 D. –3

27. Simplify: (i) If

4

n+3

3− n

×8

( )

−n 2 64 2

= 29 n × 43n , then find the value

of 2n.

(ii) If

(i) (ii)

A.

3/2

4/5



B.

2

3/5



C.

3

16/25



D.

3

9/25

28. The mean of 150 observations was found to be 45. If at the time of calculation, two items were wrongly taken as 42 and 28 instead of 35 and 25, then find the correct mean. IMO | Class-9 | Set-B | Level 1 |

S



A.

35°, 25°



B.

25°, 15°



C.

45°, 65°



D.

30°, 20°

31. The three vertices of a square ABCD are A(4, 3), B(–3, 3) and C(–3, – 4). Find : (i) The coordinates of D. (ii) The area of square ABCD.

x + x − 1 − x = 1, then find the value of x.

N

O

(i)

(ii)



A.

(– 4, – 4)

49 sq. units



B.

(3, – 4)

25 sq. units



C.

(2, – 4)

36 sq. units



D.

(4, – 4)

49 sq. units

32. In DDEF and DPQR, DE = DF, ∠F = ∠P and ∠E = ∠Q. The two triangles are

A. Isosceles but not necessarily congruent.



B.

Isosceles and congruent.



C.

Congruent but not isosceles.



D. Neither congruent nor isosceles. 5

33. An open rectangular cistern when measured from outside is 1.15 m long, 0.94 m broad and 70 cm deep. It is made up of iron, which is 5 cm thick. Find (i) The capacity of cistern. (ii) Volume of iron used.   (i)  (ii) A. 756700 cm3 573300 B. 756700 cm3 529200 3 C. 529200 cm 227500 D. 573300 cm3 183400

3

cm cm3 cm3 cm3



A. 0.02 B. 0.77 C. 0.445 D. 0.325

35. In the given figure (not drawn to scale), ∠DAB and ∠BAC are in the ratio 2 : 3 respectively and AB = DB. Find the value of x.

34. A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table shows the results of 1000 cases. Distance < 4000 4000-9000 9000-14000 > 14000 (in km) Frequency 20 210 325 445

If you buy a tyre of this company, then what is the probability that it will last more than 9000 km?

E 100°

A

x D



A. B. C. D.

B

C

72° 68° 56° None of these

EVERYDAY MATHEMATICS 36. A piece of rectangular cardboard sheet measuring 40 inch × 25 inch is made into an open chocolate box by cutting out squares of side 'p' from each corner. Which of the following expressions is equivalent to the volume of the box? 3 2 A. 4p – 120p + 950p

B. 4p3 + 130p2 + 1000p

C. 4p3 – 130p2 + 1000p D. None of these



37. There are some marbles of two colours black and golden in a jar. If the ratio of the number of black marbles to the golden marbles is 5:3 and the total number of marbles in the jar is 120, then how many black marbles are there in the jar?

A.

45



B.

75

C. 60 D. 80 38. The king, queen and jack of heart cards are removed from the deck of 52 cards and then the remaining cards are well shuffled. One card is selected at random from the remaining cards. What is the probability of getting an ace card? 4 3 A. B. 49 49 12 3 C. D. 52 52 6

39. Anya's piggy bank is full of ` 10 and ` 5 coins. It contains three times as many ` 5 coins as ` 10 coins. The total amount of money in piggy bank is ` 300. How many coins of ` 10 are there in the piggy bank? A. 12 B. 36 C. 18 D. 16 40. A tank can be filled by two taps P and Q in 15 hours and 20 hours respectively. The full tank can be emptied by a third tap R in 10 hours. If all the three taps are turned on at the same time, then in how much time will the empty tank be filled up completely?

A. 30 hours



B.

45 hours



C.

40 hours



D. 60 hours

41. A school provides milk to students daily in cylindrical glasses of diameter 7 cm each. If the glass is filled with milk up to a height of 12 cm, then how many litres of milk is needed to serve 1600 students?

A. 739.2 litres



B.

538 litres



C.

740 litres



D. 400 litres | IMO | Class-9 | Set-B | Level 1

42. One year ago, Sugandha was four times as old as her son Ritik. Six years hence, Sugandha's age will exceed her son's age by 9 years. What is the ratio of present ages of Sugandha and her son? A. 9 : 2 B. 11 : 3 C. 12 : 5 D. 13 : 4

44. A cycle was sold at a loss of 8%. If it was sold for ` 121 more, then there would have been a gain of 3%. What was the cost price and selling price of the cycle respectively? A. ` 1012, ` 1000 B. ` 1000, ` 1300 C. ` 1100, ` 1012 D. ` 1002, ` 1100

43. A company bought 45 laptops and 15 printers to modernize billing operations. If the price of each 5 times the price of each printer, then laptop was 3 what percent of the total cost of the purchase was the total cost of laptops?

45. A person has to completely put each of three types of juices, 210 litres of orange juice, 220 litres of guava juice and 260 litres of litchi juice in bottles of equal size without mixing any of the above three types of juices such that each bottle is completely filled. What is the least possible number of bottles required? A. 45 B. 69 C. 72 D. 55



A. B. C. D.

72.5 % 78 % 90 % None of these

ACHIEVERS SECTION 46. Match the linear equations given in Column-I with their solutions given in Column-II and select the correct option. Column-I



Column-II

(P) 5x = – 2y + 7

(a) (0, 0)

(Q) 4x – 6y = 0

(b) (2, 0)

(R) 3y = 5 x + 7 3 (S) 2x – y = 4

(c) (3, – 4) (d) (3, 4)

A. (P) → (b) ; (Q) → (c); (R) → (a); (S) → (d)

B. (P) → (c) ; (Q) → (b); (R) → (d); (S) → (a) C. (P) → (c) ; (Q) → (a); (R) → (d); (S) → (b) D. (P) → (d) ; (Q) → (b); (R) → (a); (S) → (c) 47. Read the statements carefully and select the correct option. Statement-I : If two circles with centres A and B intersect each other at points M and N, then the line joining the centres AB bisects the common chord MN at right angle. Statement-II : Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. Then the distance between their centres is 8 cm. A. Both Statement-I and Statement-II are true. B. Both Statement-I and Statement-II are false. C. Statement-I is false but Statement-II is true. D. Statement-I is true but Statement-II is false. IMO | Class-9 | Set-B | Level 1 |

48. Let ABC be a triangle in which AB = 5.8 cm, BC + CA = 8.4 cm and ∠B = 60°. Given below are the steps of constructing the triangle ABC. Which of the following options is correct while arranging the steps in correct order? (P) Join AD. (Q) From ray BX, cut off line segment BD = BC + CA = 8.4 cm. (R) Draw a line segment AB of length 5.8 cm. (S) Draw a perpendicular bisector of AD meeting BD at point C. Join AC, ABC is the required triangle. (T) Draw ∠ABX = 60° at point B of line segment AB.

A. (T) → (R) → (S) → (P) → (Q) B. (R) → (P) → (T) → (S) → (Q) C. (R) → (T) → (Q) → (P) → (S) D. (P) → (R) → (S) → (T) → (Q)

49. Fill in the blanks and select the correct option.



(i)

The sum of any two sides of a triangle is greater the median drawn to the third side. than P (ii) The perimeter of a triangle is Q than the sum of its three medians. (iii) If the altitude from the vertex of a triangle bisects the base, the triangle is R . P Q R A. Twice less isosceles B. Twice greater isosceles C. Half less equilateral D. Half greater equilateral 7

50. Read the statements carefully and state 'T' for true and 'F' for false.



(iii) Mode of the data 17, 21, 11, 48, 35, 11, 19, 17, 12, 13, 11, 15 is 11.





prime natural numbers is

(i)

If the number of observations is odd, then the n median is  + 1 2 

th

observation.

(ii) The mean of 25 observations is 18. Out of these observations, the mean of first 13 observations is 16 and that of the last 13 observations is 20. Then, th the 13 observation is 18.



(iv) The mean of first 15 27.5. (i) (ii) A. T F B. F T C. F F D. T T

(iii) (iv) F T T F F T F F

SPACE FOR ROUGH WORK

8

| IMO | Class-9 | Set-B | Level 1

ANSWER KEYS IMO 2014 1. (C) 11. (D) 21. (C) 31. (A) 41. (C)

2. (D) 12. (C) 22. (C) 32. (B) 42. (C)

3. (A) 13. (D) 23. (B) 33. (B) 43. (D)

4. (D) 14. (D) 24. (C) 34. (B) 44. (A)

5. (D) 15. (B) 25. (C) 35. (B) 45. (B)

SET A 6. (C) 16. (D) 26. (B) 36. (D) 46. (D)

7. (A) 17. (B) 27. (C) 37. (C) 47. (C)

8. (A) 18. (A) 28. (B) 38. (B) 48. (B)

9. 19. 29. 39. 49.

(B) (B) (C) (B) (C)

10. 20. 30. 40. 50.

(D) (D) (C) (A) (C)

1. (C) 11. (B) 21. (D) 31. (B) 41. (C)

2. (B) 12. (C) 22. (A) 32. (C) 42. (B)

3. (A) 13. (C) 23. (A) 33. (D) 43. (D)

4. (C) 14. (D) 24. (A) 34. (A) 44. (C)

5. (B) 15. (C) 25. (C) 35. (C) 45. (C)

SET B 6. (C) 16. (D) 26. (C) 36. (B) 46. (D)

7. (D) 17. (C) 27. (C) 37. (D) 47. (A)

8. (C) 18. (C) 28. (D) 38. (C) 48. (B)

9. 19. 29. 39. 49.

(C) (D) (A) (D) (C)

10. 20. 30. 40. 50.

(B) (A) (D) (B) (D)

IMO 2015 1. (C) 11. (D) 21. (A) 31. (B) 41. (B)

2. (D) 12. (B) 22. (D) 32. (C) 42. (B)

3. (D) 13. (B) 23. (B) 33. (C) 43. (D)

4. (C) 14. (A) 24. (C) 34. (D) 44. (A)

SET A 5. (C) 6. (D) 15. (D) 16. (A) 25. (D) 26. (A) 35. (A) 36. (C) 45. (D) 46. (B)

7. (A) 17. (C) 27. (C) 37. (B) 47. (A)

8. (B) 18. (A) 28. (C) 38. (A) 48. (A)

9. (B) 19. (D) 29. (B) 39. (A) 49. (C)

10. ( C ) 20. ( B ) 30. ( A ) 40. ( A ) 50. (D)

1. (B) 11. (D) 21. (A) 31. (A) 41. (D)

2. (A) 12. (D) 22. (D) 32. (C) 42. (B)

3. (D) 13. (B) 23. (C) 33. (C) 43. (C)

4. (B) 14. (B) 24. (D) 34. (C) 44. (B)

SET B 5. (C) 6. (D) 15. (B) 16. (D) 25. (A) 26. (B) 35. (B) 36. (C) 45. (C) 46. (A)

7. (B) 17. (C) 27. (A) 37. (A) 47. (A)

8. (A) 18. (B) 28. (B) 38. (B) 48. (C)

9. (C) 19. (A) 29. (C) 39. (B) 49. (B)

10. ( C ) 20. ( B ) 30. ( A ) 40. ( C ) 50. (D)

7. (D) 17. (B) 27. (B) 37. (C) 47. (B)

8. (D) 18. (C) 28. (C) 38. (D) 48. (D)

9. 19. 29. 39. 49.

(B) (C) (D) (C) (B)

10. 20. 30. 40. 50.

(A) (A) (D) (A) (B)

7. (C) 17. (C) 27. (A) 37. (D) 47. (C)

8. (B) 18. (C) 28. (C) 38. (C) 48. (A)

9. 19. 29. 39. 49.

(D) (C) (B) (A) (D)

10. 20. 30. 40. 50.

(C) (C) (D) (D) (D)

7. (D) 17. (B) 27. (A) 37. (A) 47. (C)

8. (C) 18. (B) 28. (B) 38. (A) 48. (B)

9. 19. 29. 39. 49.

(A) (B) (B) (B) (C)

10. 20. 30. 40. 50.

(A) (C) (A) (A) (D)

IMO 2016 SET A 1. (D) 2. (D) 3. (B) 4. (C) 5. (D) 6. (A) 11. (C) 12. (B) 13. (A) 14. (D) 15. (B) 16. (C) 21. (C) 22. (B) 23. (A) 24. (C) 25. (B) 26. (B) 31. (C) 32. (A) 33. (D) 34. (D) 35. (C) 36. (C) 41. (C) 42. (D) 43. (B) 44. (B) 45. (C) 46. (D) 1. (C) 11. (D) 21. (D) 31. (B) 41. (C)

2. (A) 12. (A) 22. (D) 32. (A) 42. (D)

3. (C) 13. (B) 23. (A) 33. (B) 43. (B)

4. (C) 14. (A) 24. (D) 34. (C) 44. (A)

5. (B) 15. (A) 25. (D) 35. (B) 45. (D)

SET B 6. (A) 16. (A) 26. (A) 36. (C) 46. (A)

IMO 2017 1. (B) 11. (D) 21. (D) 31. (B) 41. (B)

2. (B) 12. (B) 22. (B) 32. (D) 42. (C)

3. (C) 13. (D) 23. (C) 33. (C) 43. (D)

4. (A) 14. (C) 24. (D) 34. (A) 44. (C)

5. (B) 15. (C) 25. (C) 35. (C) 45. (B)

SET A 6. (C) 16. (C) 26. (A) 36. (B) 46. (C)

SET B 1. (C) 2. (C) 3. (C) 4. (A) 5. (A) 6. (A) 11. (D) 12. (C) 13. (A) 14. (D) 15. (D) 16. (D) 21. (A) 22. (B) 23. (C) 24. (A) 25. (D) 26. (B) 31. (C) 32. (A) 33. (C) 34. (B) 35. (D) 36. (B) 41. (C) 42. (B) 43. (B) 44. (D) 45. (D) 46. (C)

7. (B) 17. (A) 27. (C) 37. (C) 47. (C)

8. (A) 18. (A) 28. (B) 38. (D) 48. (A)

9. 19. 29. 39. 49.

(D) (C) (B) (A) (B)

10. 20. 30. 40. 50.

(D) (B) (A) (A) (D)

IMO 2018 1. (C) 11. (D) 21. (C) 31. (A) 41. (D)

2. (A) 12. (A) 22. (B) 32. (D) 42. (C)

3. (C) 13. (B) 23. (B) 33. (B) 43. (D)

4. (C) 14. (B) 24. (D) 34. (D) 44. (B)

SET A 5. (C) 6. (C) 15. (A) 16. (C) 25. (D) 26. (B) 35. (D) 36. (B) 45. (A) 46. (D)

7. (C) 17. (C) 27. (B) 37. (B) 47. (C)

8. (B) 18. (C) 28. (D) 38. (D) 48. (C)

9. 19. 29. 39. 49.

(C) (C) (D) (B) (A)

10. 20. 30. 40. 50.

(A) (B) (B) (C) (D)

1. (C) 11. (C) 21. (C) 31. (D) 41. (A)

2. (D) 12. (B) 22. (D) 32. (A) 42. (D)

3. (C) 13. (B) 23. (C) 33. (D) 43. (D)

4. (B) 14. (A) 24. (B) 34. (B) 44. (C)

SET B 5. (B) 6. (A) 15. (D) 16. (C) 25. (B) 26. (D) 35. (B) 36. (C) 45. (B) 46. (C)

7. (B) 17. (C) 27. (C) 37. (B) 47. (D)

8. (A) 18. (D) 28. (B) 38. (B) 48. (C)

9. 19. 29. 39. 49.

(C) (B) (A) (A) (B)

10. 20. 30. 40. 50.

(D) (A) (A) (D) (B)