Class 9 Imo 3 Year e Book Level 2 13

Level 2

SOLVED PAPERS 3 years (2012 -2014)

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9

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FOUNDATION COURSE For Classes 8, 9 & 10 Class 8

Class 9

Class 10

IMPORTANT INSTRUCTIONS Changes in the Mode and Pattern in SOF Level 2 Exams for year 2014- 2015 Exam Date : 7th and 8th February 2015. Kindly coordinate with your school coordinator for exact date and center for exam. Write to [email protected] for any query related to it. Mode of exam : NCO/ NSO/ IMO Level 2 for the academic year 2014-15 will be an Online Test Pattern of the exams : National Cyber Olympiad Class 3 to 4

5 to 12

Section

No. of Questions Marks per Question

Computers & IT Achievers Section Grand Total Computers & IT Achievers Section Grand Total

30 5 35 45 5 50

1 2 1 3

Total Marks 30 10 40 45 15 60

NATIONAL SCIENCE OLYMPIAD Class 3 to 4

5 to 10

11 and 12

Section

No. of Questions Marks per Question

Science Achievers Section Grand Total Science Achievers Section Grand Total Physics & Chemistry Achievers Section Mathematics/Biology Grand Total

30 5 35 45 5 50 25 5 20 50

1 2 1 3 1 3 1

Total Marks 30 10 40 45 15 60 25 15 20 60

International Mathematics Olympiad Class 3 to 4

5 to 12

Section Mathematics Achievers Section Grand Total Mathematics Achievers Section Grand Total

No. of Questions Marks per Question 30 5 35 45 5 50

1 2 1 3

Total Marks 30 10 40 45 15 60

5th

LEVEL - 2 Year 2011-12

| 5th IMO | Level-II | Class 9

2

Section I : Logical Reasoning 1.

Six people – Rohit, Suneet, Deepak, Vikas, Kanak and Manish–were all born on the same day of the year, but each was born in a different year, during a single six-year period.

I.

Rohit is older than Deepak.

II.

Suneet is older than both Vikas and Kanak.

III. Manish is 2 years older than Vikas. IV. Rohit was born either in 1962 or in 1963.

V. The oldest member of the group was born in 1960.

If Manish is the oldest of the group, then which of the following must be true ?

(A) Deepak was born in 1960.

(B) Rohit was born in 1962.

(C) Vikas was born in 1961.

(D) Suneet was born in 1961.

2. Choose the correct option that will replace the question mark in the given number series. 1 1 2 2 11 , 12 , 14 , 16 , ___ ? 9 2 7 3 1 1 1 (A) 8 3 (B) 19 2 (C) 20 (D) 22 3 3. If Circle S stands for households having a scooter; Circle T stands for households having a TV set; Circle W stands for households having a washing machine; Circle C stands for households having a car; then households having all the four items are represented by the region ____.

(A) 7

(B) 8

(C) 9

(D) 12

4. If a meaningful word can be formed using the letters NWROD, each only once, then the fourth letter of that word is your answer. If more than one word can be formed, then 'Y' is your answer and if no such word can be formed, then 'Z' is your answer.

(A) Z

(B) R

(C) W

(D) Y

5. Ajay left home for the bus stop 15 minutes earlier than usual. It takes 10 minutes to reach the stop. He reached the stop at 8.40 a.m. What time does he usually leave home for the bus stop?

(A) 8.30 a.m.

(B) 8.45 a.m.

(C) 8.15 a.m.

(D) None of these

6. If '–' stands for 'division', '+' for 'multiplication', '÷' for 'subtraction' and '×' for 'addition', which one of the following equations is incorrect?

(A) 6 + 20 – 12 ÷ 7 – 1 = 3

(B) 6 – 20 ÷ 12 + 7 + 1 = 57

(C) 6 + 20 – 12 ÷ 7 × 1 = 4

(D) 6 ÷ 20 × 12 + 7 – 1 = 70

7.

Robin says, "If Jai gives me ` 40, he will have half as much as Atul, but if Atul gives me ` 40, then the three of us will all have the same amount." What is the total amount of money that Robin, Jai and Atul have between them?

(A) ` 240

(B) ` 320

(C) ` 360

(D) ` 420

(C) 7 (33) 4

(D) 11 (112) 3

8. Choose the odd numeral group.

(A) 1 (–80) 9

(B) 6 (12) 2

5th IMO | Level-II | Class 9 |

3 9.

Find the missing number in the given figure.

(A) 13

(B) 14

(C) 20

(D) 21

15 3

?

1 2

16

4 18 6 19

17 5

10. Select a figure from amongst the options which will continue the same series as established by the five figures.

(A)

(B)

(C)

(D)

11. Which of the following is the correct option to find the code for "books" ?

Statement-1 : '253' means 'books are old'.

Statement-2 : '546' means 'man is old'.

Statement-3 : '378' (A) Only Statement(B) Only Statement(C) Only Statement(D) None of these.

means 'buy 1 is sufficient 2 is sufficient 3 is sufficient

good books'. to answer the question. to answer the question. to answer the question.

12. A family has a man, his wife, their four sons and their wives. The family of every son also has 3 sons and one daughter. Find out the ratio of number of male members to female members in the

whole family. (A) 4 : 1

(B) 8 : 3

(C) 3 : 1

(D) 17 : 9

13. In the question there are seven figures, the first and last of which are unmarked and the remaining are marked as P, Q, R, S and T. These seven figures form a series. However, one of the five numbered figures does not fit into the series. Select that figure from the options.

(A) P

(B) R

(C) S

(D) Q

14. Choose the figure which is different from the rest.

(A)

(B)

(C)

15. What is the minimum number of line segments required to make the given figure?

(A) 10

(B) 12

(C) 14

(D) 16

(D)


4

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

(A)

(B)

(C)

(D)

17. A square transparent sheet with a pattern is given. Figure out from amongst the options as to how the pattern would appear when the transparent sheet is folded at the dotted line.

(A)

(B)

(C)

(D)

18. If the first and third letters in the word NECESSARY are interchanged, also the fourth and the sixth letters, and the seventh and the ninth letters are interchanged, then which of the following would

be the seventh letter from the left? (A) A (B) Y

(C) R

(D) E

19. Choose the correct option that will replace the question mark in the given letter-number series.

C4X, F9U, I16R, __ ?_ (A) K25P

(B) L25P

(C) L25O

(D) L27Poning

20. A child is looking for his father. He went 90 metres in the East before turning to his right. He went 20 metres before turning to his right again to look for his father at his uncle's place 30 metres from this point. His father was not there. From there he went 100 metres to the North before meeting his father in a street. How far from the starting point did the son meet his father?

(A) 80 metres

(B) 100 metres

(C) 140 metres

(D) 260 metres

Section II : Mathematical reasoning 21. When in a frequency distribution class widths are not same and we have to draw histogram

then, (A) We mark class size as width and the given frequency as length and draw the rectangle. (B) We reduce class size to minimum class size keeping the length same. (C) We find the proportionate lengths of the class corresponding to minimum width and draw the rectangle. (D) None of these

22. An experiment is performed 350 times and there are three possible events A, B and C in the experiment. Possible occurrences of the three events are recorded. Which one of the records is possible?

(A) A : 176, B : 80, C : 98

(B) A : 90, B : 0, C : 250

(C) A : 200, B : 100, C : 50

(D) A : 110, B : 110, C : 110


5

23. Which of the following is the correct match with respect to the given question? 'ABCD' is a rhombus such that ∠ACB = 40° then ∠ADB is ______. Column-I Column-II (a) 70° (i) As ∠ADB = 1/2 (180° – 40°) (b) 45° (ii) ∠C + ∠D = 900 (c) 50° (iii) ∠BCD = 80° ⇒ ∠ADC = 100° \ ∠ADB = (1/2) x 100° (d) 60° (iv) All sides are equal (A) (a) → (i) (B) (c) → (iii) (C) (d) → (iii) (D) (b) → (iv) 24. In a gym, in one exercise you have to continuously toss solid cylindrical dumbbells and catch them. Cylindrical dumbbells are of length 1 m and base diameter also 1 m. If density of the material used is 4 kg per m3, then the weight tossed is _____.

(A) 3.14 kg

(B)

p/2 kg

(C) 4p kg

(D) 12.56 kg

25. Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. The

median of the data is 24. The mean of the data is _____. (A) 20 (B) 23.9 (C) 25

 26. The value of   (A) 1

5 −2  − 3 − 2 2 is _____.  5 +1 (B) –1 (C) 2

(D) 27

5 +2+

(D) –2

27. If (3x – 1)7 = a 7x 7 + a 6x 6 + a 5x5 + .... + a 1x + a 0, then a 7 + a 6 + a 5 + ..... + a 1 + a 0 = ____.

(A) 0

(B) 1

(C) 128

(D) 64

28. In the given figure, AB = 14 cm, radius of incircle of DABC is 4 cm,

AF = 6 cm, AE = 6 cm and BD = 8 cm. Find AC and BC. (A) 14 cm, 16 cm (B) 11 cm, 13 cm (C) 12 cm, 14 cm (D) 13 cm, 15 cm

29. Which of the following statements is incorrect ? (A) All prime numbers greater than 2 are odd. (C) Two times a natural number is always even.

(B) If x ≥ 0, then x3 ≥ 0 (D) For any x, 2x + 1 > 3

30. If the perpendicular distance of a point P from the x-axis is (7776)1/6 and the foot of the perpendicular

lies on the negative side of x-axis, the point P always has _____. (A) Negative y-coordinate (B) Positive y-coordinate (C) Negative x-coordinate (D) Positive x-coordinate

31. Sum of three altitudes of a triangle is _______ the sum of the three sides of the triangle. (A) Less than (B) Greater than (C) Equal to (D) Can't be determined 32. Match the columns : Column I Column II (a) A solid has (p) 0 dimension (b) A surface has (q) 1 dimension (c) A point has (r) 2 dimensions (s) 3 dimensions (A) (a) → r, (b) → q, (c) → p (B) (a) → r, (b) → p, (c) → q (C) (a) → s, (b) → p, (c) → q (D) (a) → s, (b) → r, (c) → p


6

33. Sixteen cylindrical cans, each with a radius of 1 unit, are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and the walls of the box, then which of the following could be the interior area of the bottom of the box in square units? (A) 16 (B) 32 (C) 64 (D) 128 34. ABCD is a parallelogram. The diagonals AC and BD intersect at a point O. If E, F, G, and H are the mid-points of AO, DO, CO and BO respectively, then the ratio of (EF + FG + GH + HE) to

(AD + DC + CB + BA) is ______. (A) 1 : 1 (B) 1 : 2

35. If a + b + c = 0, then

(A) 0

(C) 1 : 3

(D) 1 : 4

a 2 b2 c 2 is equal to _____. + + bc ca ab (B) 1 (C) 3

36. If x = 3 9 , y = 4 11, z = 6 17 then ______. (A) x > y > z (B) y > z > x

(D) 2

(C) z > y > x

(D) x < y = z

37. The string of length n is wound on the exterior four walls of a cube of side 'a' cm starting at point C and ending at point D exactly above C, making 4 turns equally spaced. The side of the cube is ______.

(A) a =

2n 255

(B) a =

(n )2 16

(C) a =

n 257

(D) a = 2 15n

38. If ABCD is a parallelogram, E is the mid-point of AB and CE bisects ∠BCD, then ∠DEC is _____. (A) 60° (B) 90° (C) 100° (D) 120° 39. Let U be the upper class boundary of a class in a frequency distribution and M be the mid-point

of the class. Which one of the following is the lower class boundary of the class? M +U M +U (A) M + (B) U + (C) 2M – U (D) M – 2U 2 2

40. Here the steps of construction of an equilateral triangle one of whose altitudes measures 5 cm are given. In these steps, one step is wrong. Which step does not fit in the steps of construction ?

STEPS OF CONSTRUCTION : (i) Draw a line XY. (iii) From P, draw PQ ^ XY.

(v) Construct ∠PAB = 60° and ∠PAC = 60°, meeting XY at B and C respectively. Then, DABC is the required equilateral triangle. (A) (i) only (B) (ii) only (C) (v) only (D) (iii) only

(ii) Mark any point P on it. (iv) From P, set off PA = 5 cm cutting PQ at A.

Section III : Everyday Mathematics 41. On Charvi's birthday, Tanya was asked to buy birthday caps. Caps were of different dimensions, so she was confused; she came back home and measured Charvi's head with her palm. Two of her palms totally covered the head with a little more space to be neglected. So she went to the shop again and measured with her palm and bought birthday caps. The width of her palm was 7 cm. Can you guess the plane area of head the cap will cover?

(A) 44 cm

(B) 88 cm

(C) 154 cm2

(D) 2156 cm22


7

42. 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 ? 4 2 3 5 (A) (B) (C) 7 (D) 7 7 7 43. The problem given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is / are necessary to answer the question.

How many marks did Tarun secure in English ? (i) The average marks obtained by Tarun in four subjects including English are 60. (ii) The total marks obtained by him in English and Mathematics together are 170. (iii) The total marks obtained by him in Mathematics and Science together are 180.

(A) I and II only

(B) II and III only

(C) I and III only

(D) None of these

44. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

(A) 2 : 3 : 4

(B) 6 : 7 : 8

(C) 6 : 8 : 9

(D) None of these

45. A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same was 38 cm when folded along the other set of sides. What is the area of the paper?

(A) 140 cm2

(B) 240 cm2

(C) 560 cm2

(D) None of these

46. The given bar-graph here shows the percentage distribution of the total production of a car manufacturing company into various models over two years. Study the graph carefully and answer the question. Percentage of six different types of cars manufactured by a company over two years

Difference between total number of cars of models P, Q and T manufactured in 2000 and 2001 is ____.

(A) 2,45,000

(B) 2,27,500

(C) 2,10,000

(D) 98,000


8

47. 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 cylinder, then how much beverage is contained in the vessel from the bowl ?

2 1 (A) 66 % (B) 78 % (C) 100% 3 2 (D) More than 100% (i.e., some liquid will be left in the bowl).

48. A pineapple costs ` 7. A watermelon costs ` 5. X spends ` 38 on these fruits. The number of

pineapples purchased is _____. (A) 2 (B) 3

(C) 4

(D) Data inadequate

49. Due to an increase of 30% in the price of eggs, 3 less eggs are available for ` 7.80. The present

rate of eggs per dozen is _____. (A) ` 8.64 (B) ` 8.88

(C) ` 9.36

(D) ` 10.40

50. A housewife saved ` 2.50 in buying an item on sale. If she spent ` 25 for the item, approximately

how much percent did she save in the transaction ? (A) 8% (B) 9% (C) 10% SPACE FOR ROUGH WORK

(D) 11%

6th



2

Section I : Logical Reasoning 1.

Rahul told Anand, "Yesterday I defeated the only brother of the daughter of my grandmother." Whom did Rahul defeat?

(A) Son

(B) Father

(C) Brother

(D) Father-in-law

2. In a row of boys, if P who is tenth from the left and Q who is ninth from the right interchange their positions, P becomes fifteenth from the left. How many boys are there in the row?

(A) 23

(B) 27

(C) 28

3.

A, B, C, D, E, F, G, H and I are nine houses. C is 2 km east of B. A is 1 km north of B and H is 2 km south of A. G is 1 km west of H while D is 3 km east of G and F is 2 km north of G. I is situated just in middle of B and C while E is just in middle of H and D. Distance between A and F is _____.

(A) 1 km

(B) 1.41 km

(D) 31

(C) 2 km

(D) 3 km

4. The two expressions on either side of the sign (=) will have the same value if two terms on either side or on the same side are interchanged. The correct terms to be interchanged have been given as one of the four alternatives under the expressions. Find the correct alternative in the given case. 7 × 2 – 3 + 8 ÷ 4 = 5 + 6 × 2 – 24 ÷ 3

(A) 2, 6

(B) 6, 5

(C) 3, 24

(D) 7, 6

5. The given below input rearranges step-by-step in a particular order according to a set of rules. In this case the last step of arranged input is Step V. Input : 85 16 36 04 19 97 63 09 Step I : 97 85 16 36 04 19 63 09 Step II : 97 85 63 16 36 04 19 09 Step III : 97 85 63 36 16 04 19 09 Step IV : 97 85 63 36 19 16 04 09 Step V : 97 85 63 36 19 16 09 04 Study the above arrangement carefully and then answer the following question. Which of the following will be Step III for the input below ? Input : 09 25 16 30 32 18 17 06

(A) 32 30 25 09 16 18 17 06

(B) 32 30 09 25 16 18 17 06

(C) 32 09 25 16 30 18 17 06

(D) 32 30 09 25 16 19 17 06

6.

If a 1 mm thick paper is folded so that the area is halved at every fold, then what would be the thickness of the pile after 50 folds? 52 km (A) 25 × 106 km (B) (C) 50 × 2 × 10–6 km (D) 250 × 10–6 km 10−6

7.

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

(A)

(B)

(C)

(D)


3 8.

All surfaces of a cube are coloured. If a number of smaller cubes are taken out from it, each side

is 1/4 the size of the original cube's side, find the number of cubes with only one side painted. (A) 60 (B) 30 (C) 24 (D) 16

9. Each of the vowels in the word 'MAGNIFY is replaced by number '2' and each consonant is replaced by a number which is the serial number of that consonant in the word, i.e., M by 1, G by 3 and

so on. What is the total of all the numbers once the replacement is completed? (A) 22 (B) 24 (C) 25 (D) 26

10. Find out which of the following options replace the question mark in the figure matrix?

(A)

(B)

(C)

(D)

11. Choose the correct mirror-image of the Fig.(X).

(A)

12.

What is the number of straight lines and the number of triangles in the given figure? (A) 10 straight lines and 34 triangles (B) 9 straight lines and 34 triangles (C) 9 straight lines and 35 triangles (D) None of these

(B)

(C)

(D)

13. In the following diagram, the circle represents 'College Professors', the triangle represents 'Surgical Specialists', and rectangle represents 'Medical Specialists'.

What does B represent? (A) Professors who are neither Medical nor Surgical Specialists. (B) Professors who are not Surgical Specialists. (C) Medical Specialists who are neither Professors nor Surgical Specialists. (D) Professors who are not Medical Specialists.

14. There are seven figures, the first and last of which are unnumbered and the remaining 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. Find the figure.

(A) 4

(B) 5

(C) 3

(D) 2


4

15. Select the pair of figures from the given options, which does not have a similar relationship to that in the given pair of Problem Figures.

(A)

(B)

(C)

(D)

16. Study the information given below and answer the question that follow.

(i) A, B, C, D, E and F are six students in a class.

(ii) B and C are shorter than F but heavier than A.

(iii) D is heavier than B and taller than C.

(iv) E is shorter than D but taller than F.

(v) F is heavier than D.

(vi) A is shorter than E but taller than F.

Which of the following statements is true for F as regards height and weight? (A) He is lighter than E and taller than E. (B) He is heavier than B and taller than E. (C) He is heavier than B but shorter than D. (D) He is lighter than E and also shorter than E.

17. In a shop, the items were arranged in a shelf consisting of six rows. Biscuits are arranged above the tins of chocolates but below the rows of packets of chips, cakes are at the bottom, and the bottles of peppermints are below the tins of chocolates. The topmost row had the display of jam

bottles. Where exactly are the bottles of peppermints? Mention the place from the top. (A) 2nd (B) 3rd (C) 4th (D) 5th

18. 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 answer set that would replace the question mark(?) in Fig.(S)

(A)

(B)

(C)

(D)

19. There is a set of four figures labelled P, Q, R and S called the Problem Figures. Select a suitable figure, so that a series is formed by figures P, Q, R and S.

(A)

(B)

(C)

(D)


5

20. Rewrite the word VOCALIST in the numeric form by writing its first four letters in the reverse order and then the next four letters in the reverse order by substituting I by 8, O by 1, L by 3, T by 2,

V by 5, S by 7, A by 9 and C by 6. (A) 96156873 (B) 96157683

(C) 96516783

(D) 96152783

Section II : Mathematical reasoning 21. A rationalizing factor of

(A)

3

4 + 1

3 16

- 3 4 + 1 is ________.

(B)

3

4 − 1

(C)

3

4 +2

(D)

3

4 −2

22. Consider the volumes of the following:

1. A parallelopiped of length 5 cm, breadth 3 cm and height 4 cm

2. A cube of each side 4 cm

3. A cylinder of radius 3 cm and length 3 cm

4. A sphere of radius 3 cm

The volumes of these in the decreasing order is ____.

(A) 1, 2, 3, 4

(B) 1, 3, 2, 4

(C) 4, 2, 3, 1

(D) 4, 3, 2, 1

23. If the polynomial 16x4 – 24x3 + 41x2 – mx + 16 be a perfect square, then the value of "m" is _____. (A) 12 (B) –12 (C) 24 (D) –24 24. If the roots of (p – q)2 x 2 + 2 (p 2 – q 2) x + k = 0 are equal, then k = ________. (A) (p + q)2 (B) (p – q)2 (C) p2 – q2 (D) 0 25. In the given figure, O is the centre of the circle and XOY is a diameter. If XZ is

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

other chord of the circle, then which of the following is correct ? XZ < OZ XY > XZ OX + OZ < XZ XZ + ZY < XY

26. P is the mid-point of side AB to a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. Then BR is equal to ________.

(A) BQ

(B)

(C) 2BQ

(D) None of these

1 BQ 2

27. In the given figure, AE = BC and AE || BC and CD = ED. If ∠A = 102°, then find the measure of ∠BDE.

(A) 138°

(B) 162°

(C) 24°

(D) None of these

28. The number of numbers from 1 to 200 which are divisible by neither 3 nor 7 is ______. (A) 115 (B) 106 (C) 103 (D) Less than 100


6

29. There is a cone of height 12 cm, out of which a smaller cone (which is the top portion of the original cone) with the same vertex and vertical axis is cut out. What is the ratio of the volume of the larger (actual) cone to the remaining part of the cone, if the height of the smaller cone is 9 cm and

AD DE ? = AB BC

(A) 3 : 1

(B) 9 : 1

(C) 64 : 37

(D) 16 : 7

30. In a triangle ABC, O is the centre of incircle PQR, ∠BAC = 65°,

∠BCA = 75°, find ∠ROQ. (A) 80° (B) 120° (C) 140° (D) Can't be determined

31. If

x y z = = , then the value of (x + y + z) is _______. (b - c )(b + c - 2a ) (c - a )(c + a - 2b ) (a - b)(a + b - 2c )

(A) a + b + c

(B) 0

(C) a2 + b2 + c 2

(D) Can't be determined

32. If a, b, g are such that a + b + g = 2, a2 + b2 + g2 = 6, a3 + b3 + g3 = 8, then a4 + b4 + g4 is

equal to ________. (A) 10

(B) 12

(C) 18

(D) None of these

33. In the given figure, ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ =

(A) RB

1 AC . Also, PQ when produced meets BC at R. Then CR = _______. 4

(B)

1 CB 3

(C)

1 CB 4

(D) None of these

34. 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 ar(DBOE) = ?

(A)

1 ar ( DABC ) 3

(B)

1 ar ( DABC ) 4

(C)

1 ar ( DABC ) 6

(D)

1 ar ( DABC ) 8

35. Four dice are thrown simultaneously. Find the probability that all of them show the same faces. 1 15 15 1 (A) (B) (C) (D) 216 16 36 2


7

36. The construction of a DABC in which BC = 6 cm and ∠B = 50° is not possible when (AB – AC) is

equal to ________. (A) 5.6 cm

(B) 5 cm

(C) 6 cm

(D) 4.8 cm

37. Which least number must be subtracted from 9999999 so that it will become the multiple

of 125? (A) 124

(B) 4

(C) 24

(D) None of these

38. When 5 is added to the numerator and denominator both of a (positive) fraction, then the new

ratio of numerator to denominator becomes 11 : 15. What is the original ratio? (A) 15 : 25 (B) 3 : 5 (C) 38 : 40 (D) Data inadequate

39. AB and CD are two parallel lines and a transversal PQ intersects AB and CD at M and N respectively. If the bisector of the interior angles form a quadrilateral, then formed quadrilateral is a ______.

(A) Rectangle

(B) Square

(C) Trapezium

(D) None of these

40. A large solid sphere of diameter 15 m is melted and recast into several small spheres of diameter 3 m. What is the percentage increase in the surface area of the smaller spheres over that of the

large sphere? (A) 200%

(B) 400%

(C) 500%

(D) Can't be determined

Section III : Everyday Mathematics 41. A bonus of ` 1000 is to be divided among three people so that Rohit receives twice as much as

Sachin, who receives one-fifth as much as Gagan. How much money should Gagan receive? (A) ` 100 (B) ` 250 (C) ` 375 (D) ` 625

42. Samant bought a microwave oven and paid 10% less than the original price. He sold it with 30%

profit on the price he had paid. What percentage of profit did Samant earn on the original price? (A) 17% (B) 20% (C) 27% (D) 32%

43. Shekhar started a business investing ` 25,000 in 1999. In 2000, he invested an additional amount of ` 10,000 and Rajeev joined him with an amount of ` 35,000. In 2001, Shekhar invested another additional amount of ` 10,000 and Jatin joined them with an amount of ` 35,000. What will be Rajeev's share in the profit of ` 1,50,000 earned at the end of 3 years from the start of the business

in 1999? (A) ` 45,000

(B) ` 50,000

(C) ` 70,000

(D) ` 75,000

44. A does half as much work as B in three-fourth of the time. If together they take 18 days to complete

the work, how much time shall B take to do it? (A) 30 days (B) 35 days

(C) 40 days

(D) None of these

45. Sixteen years ago, Tanya's grandfather was 8 times older to her. He would be 3 times of her age

8 years from now. Eight years ago, what was the ratio of Tanya's age to that of her grandfather? (A) 1 : 2 (B) 1 : 5 (C) 3 : 8 (D) None of these


8

46. David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was ` 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240%

of the amount invested in Scheme B, what was the amount invested in Scheme B? (A) ` 5000 (B) ` 6500 (C) ` 8000 (D) None of these

47. In a bullet the gun powder is to be filled up inside the metallic enclosure. The metallic enclosure is made up of a cylindrical base and conical top with the base of radius 5 cm. The ratio of height of cylinder and cone is 3 : 2. A cylindrical hole is drilled through the metal solid with height twothird the height of metal solid. What would be the radius of the hole, so that the volume of the hole (in which gun powder is to be filled up) is one-third the volume of metal solid after drilling?

(A)

88 cm 5

(B)

55 cm 8

(C)

55 cm 8

(D) None of these

48. Aman gave 40% of the amount he had, to Rohan. Rohan in turn gave one-fourth of what he received from Aman to Sahil. After paying ` 200 to the taxi driver out of the amount he got from Rohan,

Sahil now has ` 600 left with him. How much amount did Aman have? (A) ` 4000 (B) ` 8000 (C) ` 12000

(D) Data inadequate

49. A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month

over the whole? (A) 4500

(B) 4600

(C) 4680

(D) 4710

50. Kamla has a triangular field with sides 240 m, 200 m, 360 m, where she grew wheat. In another triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions?(1 hectare = 10,000 m 2).

(A) 6.10

(B) 5.32

(C) 8.27 SPACE FOR ROUGH WORK

(D) None of these

7th


2

7th IMO | Class-9 | Level 2

logical reasoning 1.

If the words in the sentence, “She showed several sample snaps to Shikha's maternal sister” are rearranged in the alphabetical order, which will be the middle word?

6.

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

A. B. C. D.

A. B. C. D.

2.

In a certain code REFERENDUM is written as HZZRBUCHDS and SIMULATION is written as ITEXXOSOHT. How is EXECUTIVES written in that code language?

7.

A. B. C. D.

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

A.

3.

Among six friends L, M, N, P, Q and S, each having a different height, N is taller than Q and P but shorter than M. P is taller than only Q while S is shorter than only L. Which of the following pairs represents the tallest and the shortest respectively among the five friends?

Snaps Sample Several Shikha's

NJNQMXAWGH ITOEKHLQST NJQNQXAWGF NJRMQXAGWF

A. B. C. D.

M, P L, Q P, Q Can’t be determined

4.

Pointing to Mohit, Sana said, “His mother’s brother is the father of my son Nitin.” How is Mohit related to Sana?

A. B. C. D.

5.

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

B.

C.

D.

(ii)

Problem Set

B.

C.

D.

8.

(1)

(2)

(3)

(4)

Study the following arrangement carefully and answer the question given below . 1 H # U J 9 4 $ R 2 K • E L9 H PA% T 3 F M T @7 G O S = 6 X How many such symbols are there in the above arrangement, each of which is immediately followed by a vowel and not immediately preceded by a number? A. One B. Two C. Three

Fig. (X)

D.

9.

Priya starts from point N and moves 25 metres south, then she turns left and moves 30 metres, then she turns right and moves 15 metres to reach point P. What is the distance of P from N and which direction is she facing with respect to point N?

A. B. C. D.

(i)

?

Niece Uncle Nephew Brother

A.

2 3 4 5

Zero

50 50 45 40

metres metres metres metres

South-West South-East South-East South


10. There are two rows of numbers. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operation of numbers progress from left to right.

Rules :

(i)

If an odd number is followed by another composite odd number, they are to be multiplied. (ii) If an even number is followed by an odd number, they are to be added. (iii) If an even number is followed by a number which is the perfect square, the even number is to be subtracted from the perfect square. (iv) If an odd number is followed by a prime odd number, the first number is to be divided by the second number. (v) If an odd number is followed by an even number, the second one is to be subtracted from the first one. If x is the resultant of the first row, what is the resultant of the second row? 36 27 7 x 15 126 A. 125 B. 11 C. 9 D. 15

11. Study the following information carefully and answer the question given below .

(i) In a family of 6 persons, there are two couples. (ii) The Lawyer is the head of the family and has only two sons–Mrinal and Rakesh–both Teachers. (iii) Mrs. Reena and her mother-in-law both are Lawyers. (iv) Mrinal's wife is a Doctor and they have a son, Ajay. What is/was Ajay's Grandfather's occupation? A. B. C. D.

Teacher Lawyer Doctor Can't be determined

12. Rohit is sixteenth from the front in a column of boys. There are twice as many behind him as there are in front. How many boys are there between Rohit and fifth boy from the end of the column?

A. B. C. D.

26 25 10 Can't be determined

3

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

A. B. C. D.

5 only 1, 4, 7 4, 7 4, 5, 6

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

A. B.

C.

D.

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

A. B.

C.

D.

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

A.

B.

C.

D.

4


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

C. 241

382 473 568

D.

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

A. B.

728 847 629

If 382 is written as 238, 473 as 347 and so on, then which of the following two numbers will have least difference between them ?

425

19. The question is based on the following six numbers .

B. C.

D.

473 629 629 728

& & & &

382 728 568 847

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

184 210

A. B. C. D.

A. B. C. D.

B B B B

= = = =

(3 (3 (3 (3

# * * $

G) G) G) G)

*4 @4 # 4 #4

MATHEMATICAL REASONING 21. The equations x – y = 1 and 2x + y = 8 are given. The area bounded by these two lines and y-axis is ______.

A. B. C. D.

8 sq. units 13.5 sq. units 11 sq. units 9 sq. units

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

A. B. C. D.

6 cm 2.5 cm 4 cm 3 cm

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

A. B. C. D.

130° 150° 135° Can’t be determined

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

P T U

Q

S

P A

B 90° O

What is the height of the parallelogram in group II?

R

A. B. C. D.

4.8 cm 4 cm 5.6 cm 8.4 cm

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

A. B. C. D.

110° 130° 120° 125°


5

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

A. B. C. D.

x

3

5

7

9

11

13

f

6

8

15

p

8

4

1 2 3 4

A. B. C. D.

25° 30° 35° 115°

A

C

35° O

D 25°

E

B

28. In the given figure, the radius of each of the smallest 1 circles (C1, C 2, C3, C4, C5, C 6 and C7) is of the 12 radius of the biggest circle B1. The radius of each of the middle sized circles (P1, P2, P3 and P4) is three times the radius of the smallest circle. The area of the shaded portion is _____ times the area of the biggest circle.

A. B.

C.

D.

23 48 53 48 14 23 51 91

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

A.

B. C.

D.

A. B. C. D.

12.5 16.5 18.5 14.5

cm cm cm cm

31. The area of the triangle formed by the 2x + 3y = 6 and the coordinate axes is

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

Calculate the perimeter of trapezium MNRQ.

43 9 49 9 56 9 63 15

30. PQR is a triangle in which PQ = 5.6 cm, PR = 4.8 cm and QR = 6.2 cm. M is the midpoint of PQ and N is the midpoint of PR.

A. B. C. D.

1 2 3 4

sq. sq. sq. sq.

unit units units units

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

The number of white bars is 15 more than the thin black bars.

The A. B. C. D.

number of thick black bars is _____. 14 15 16 17

33. In the given figure, PQRS is a cyclic quadrilateral. Find the value of x.

A. B. C. D.

100° 180° 270° 120°

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

A.

PL = QM

B.

LO = OM

C.

OM = QM

D.

All of these

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

A.

20 cm2

B.

C. D.

4 5 cm 2 40 cm2 80 cm2

6


EVERYDAY MATHeMATICS 36. Karan tells his daughter Alia, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". If present ages of Alia and Karan are x and y years respectively, represent this situation algebraically.

A. B. C. D.

7x – y = 42; y – 3x = 6 x – y = 42; y – 3x = 6 x – 7y = 6; y – x = 4 x – 7y = 42; 3y – x = 6

41. When a barrel is 40% empty it contains 80 litres more than when it is 20% full. The full capacity of the barrel (in litres) is _____.

A. B. C. D.

200 300 358 400

litres litres litres litres

42. A heap of wheat is in the form of a cone, whose diameter is 10.5 m and height 7 m. Find the lateral surface area of wheat in the heap.

37. A cylindrical road roller made of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the roller if 1 c.c. of iron weighs 8 gm. (p = 3.14)

43. Three fair coins are tossed simultaneously. Find the probability of getting atleast two heads.

A. B. C. D.

1425.6 kg 1424.304 kg 1567.06 kg 1424.034 kg

38. In a cricket match, a batsman hits a boundary 8 times out of 40 balls he plays. Find the probability that he didn't hit a boundary.

A.

B. C.

D.

4 7 0.10 0.8 5 7

A.

C.

A. B. C. D.

` ` ` `

20,000 22,000 24,000 25,000

40. The largest possible length of a tape which can measure 525 cm, 1050 cm and 1155 cm length of clothes in a minimum number of attempts without measuring the length of a cloth in a fraction of the tape's length is ______.

A B. C. D.

25 cm 105 cm 75 cm 50 cm

202.25 m2 202.125 m2 200.25 m2 None of these

3 8 1 2

B.

7 8

D.

1 4

44. There are only five people in Aman's family. Aman, his wife, a son and two daughters. The younger th

4 daughter’s age is   of the elder daughter’s age. 5 3 The age of eldest daughter is times that of her 8 th 1 father Aman and the age of the son is   that of 5

39. Pratik invested an amount of ` 12,000 at the rate of 10 % p.a. simple interest and another amount at the rate of 20 % p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14 % p.a. Find the total amount invested.

A. B. C. D.

his father Aman. 4 years ago the age of his wife was 8 times that of his son and now the sum of the ages of the younger daughter and wife is same as the sum of the ages of Aman and his son. The average age of the family is

A. B. C. D.

22.2 years 25.4 years 21.2 years 23 years

45. The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is

A. B. C. D.

91 910 1001 1911


7

Achievers Section 46. Rearrange the following steps of constructing a triangle when the base angles say ∠B and ∠C and its perimeter BC + CA + AB is given

(1) Draw perpendicular bisectors PQ of AX and RS of AY. (2) D r a w a l i n e s e g m e n t , s a y X Y e q u a l t o BC + CA + AB. (3) Let PQ intersect X Y at B and RS intersect XY at C. Join AB and AC. (4) Make angles LXY equal to ∠B and MYX equal to ∠C. (5) Bisect ∠LXY and ∠MYX. Let these bisectors intersect at a point A. A. 1 → 3 → 5 → 4 → 2 B. 2 → 4 → 5 → 1 → 3 C. 5 → 4 → 3 → 2 → 1 D. 2 → 3 → 5 → 4 → 1

47. Which of the following statements is INCORRECT ?

A.

B.

C.

D.

A linear equation in two variables has infinitely many solutions. The graph of every linear equation in two variables is a straight line. The graph of x = a is a straight line parallel to the y-axis. Every point on the graph of a linear equation in two variables is a solution of the linear equation. Every solution of the linear equation may not be a point on the graph of the linear equation.

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

S two three two four

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

A. B. C. D.

Greater Lesser Equal Can't be determined

50. If a + b = 10 and ab = 21, a > 0 & b > 0 then Column-I Column-II

(i) a3 – b 3 (p) 58 (ii) a 2 + b 2 (q) 40 (iii) a 2 – b 2 (r) 316 A. (i)–(r), (ii)–(q), (iii)–(p) B. (i)–(p), (ii)–(q), (iii)–(r) C. (i)–(r), (ii)–(p), (iii)–(q) D. (i)–(p), (ii)–(r), (iii)–(q)

SPACE FOR ROUGH WORK

ANSWER KEYS 5 th IMO 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 32. 39. 46.

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

5. 12. 19. 26. 33. 40. 47.

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

5. 12. 19. 26. 33. 40. 47.

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

(A) (A) (A) (A) (A) (A) (A)

5. 12. 19. 26. 33. 40. 47.

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

6 th IMO 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 32. 39. 46.

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

7 th IMO 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 32. 39. 46.

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

Class 9 Imo 3 Year e Book Level 2 13

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