7th SOF International Mathematical Olympiad 2nd Level for Class 8

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JEE Main & Advanced | AIPMT | BOARDS | OLYMPIAD | NTSE

FOUNDATION COURSE For Classes 8, 9 & 10 Class 8

Class 9

Class 10

4th

LEVEL - 2 Year 2010-11

SECTION I : LOGICAL REASONING 1.

Find out the wrong term in the given series. 125, 126, 124, 127, 123, 129 (A) 126

2.

(C)

(D)

(B) Telephone

(C) Telegram

(D) Post

(B) Bag

(C) Book

(D) Watch

Which set of numbers is similar to the given set (48, 24, 12) ? (A) (44, 22, 10)

6.

(B)

If 'book' is called 'watch', 'watch' is called 'bag', 'bag' is called 'dictionary' and 'dictionary' is called 'window', which is used to carry the books ? (A) Dictionary

5.

(D) 129

Four words have been given, out of which three are alike in some manner and the fourth one is different. Choose the odd one out. (A) Electricity

4.

(C) 123

Choose the Venn diagram which best represents relationship among "Nose, Hand, Body" ?

(A)

3.

(B) 124

(B) (46, 22, 11)

(C) (40, 20, 10)

(D) (42, 20, 10)

A matrix of certain characters is given. These characters follow a certain trend, rowwise or column wise. Find out the missing character. (A) 15

28

20

7

(B) 18

84

35

12

(C) 20

45

?

9

(D) 25 7.

Which of the following most closely resembles the mirror image of the given combination ? WHITE (A)

8.

(B)

(C)

(D)

Find a suitable figure from the options which will continue the given series established by the four problem figures P, Q, R and S. Problem Figures

? P

(A) 9.

Q

R

(B)

S

(C)

(D)

Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence. (i) Protein (ii) Problem (iii) Proverb (iv) Property (v) Project (A) (i), (ii), (iii) (iv), (v)

4 th IMO | LevelII | Class 8

(B) (ii), (i), (iv), (iii), (v)

(C) (ii), (v), (iv), (i), (iii) 2

(D)

(iii), (iv), (v), (ii), (i)

10. Select a figure from amongst the four alternatives, which when placed in the blank space of figure (X) would complete the pattern. ?

Figure (X)

(A)

(B)

(C)

(D)

11. If '+' means '´', '´' means '–', '¸' means '+' and '–' means '¸', then find the value of 175 – 25 ¸ 5 + 20 ´ 3 + 10 ? (A) 77

(B) 160

(C) 240

(D) 2370

12. If in a certain language, ITNIETAM is the code for INTIMATE, which word has the code TREVNIETARBI? (A) INVRETIBRATE

(B) INVERTIBARTE

(C) INVERTIBRATE

(D) INVERITBARTE

13. The given question consists of five figures marked (i), (ii), (iii), (iv) and (v) called the Problem figures. Select a figure from amongst the alternatives which will continue the same series as established by the five Problem Figures. Problem Figures

? (i)

(A)

(ii)

(iii)

(iv)

(B)

(v)

(C)

(D)

14. Rohan ranks fifth from the top and twentysixth from the bottom in a class. How many students are there in the class ? (A) 30

(B) 32

(C) 33

(D) 34

15. Select the combination of numbers so that the letters arranged accordingly will form a meaningful word. T E L S C A 1 2 3 4 5 6 (A) 1, 2, 3, 4, 6, 5

(B) 4, 6, 5, 1, 2, 3

(C) 5, 6, 4, 1, 3, 2

(D) 6, 5, 3, 2, 4, 1

16. Anshuman is facing South. He turns 135° in the anti clockwise direction and then 180° in the clockwise direction. Which direction is he facing now ? (A) Northeast

(B) Northwest

(C) Southeast

(D) Southwest

17. Count the number of cubes in the given figure. (A) 14 (B) 15 (C) 16 (D) 17 3


18. The 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 you have to choose a figure which would most closely resemble the unfolded form of Fig. (Z)

X

(A)

Y

(B)

Z

(C)

(D)

19. The given figure (X) is embedded in one of the options. Select the option figure which contains figure (X) as its part. (A)

(B)

(C)

(D)

Figure (X)

20. The given question consists of four figures marked (i), (ii), (iii) and (iv) called the Problem figures. Select a figure from amongst the alternatives which will continue the same series as established by the three problem figures. Problem Figures

? (i)

(A)

(ii)

(iii)

(B)

(iv)

(C)

(D)

SECTION II : MATHEMATICAL REASONING 21. How many of the following numbers are divisible by 3 but not by 9 ? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276 (A) 5

(B) 6

(C) 7

(D) 0

22. Onefifth of a number exceeds oneseventh of the same number by 10. The number is _____ . (A) 125

(B) 150

(C) 175

(D) 200

23. Mohit plants 15376 apple trees in his garden and arranges them so that there are as many rows as there are apples trees in each row. The number of rows is ____ . (A) 124

(B) 126

(C) 134

(D) 144

24. The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is _____ . (A) 25 4 th IMO | LevelII | Class 8

(B) 27

(C) 30 4

(D) 35

25. If the length and breadth of a rectangle are changed by + 20% and –10%. What is the percentage change in area of rectangle ? (A) 8%

(B) 10.8%

(C) 20%

(D) Data insufficient

th

æ 5 ö 26. The C.P. of an article is ç ÷ of the S.P. What is the percentage profit or loss ? è6ø (A) 20% loss

(B) 16.66% profit

(C) 16.66% loss

(D) 20% profit

27. A can do a piece of work in 8 days, B can do it in 16 days, while C can do it in 80 days. In how many days they can complete the whole work, working together ? (A) 5

2 (C) 8 3

(B) 6

2 (D) 20 5

28. By what least number 675 be multiplied to obtain a number which is a perfect cube ? (A) 5

(B) 6

(C) 7

(D) 8

29. The sum of two natural numbers is 64. Which of the following cannot be the ratio of these two numbers ? (A) 3 : 5

(B) 1 : 3

(C) 7 : 9

(D) 3 : 4

1 (C) 111 % 9

(D) 190%

30. If x is 90% of y, then what percent of x is y ? 1 (B) 101 % 9

(A) 90%

31. Which of the following statements is false for a rectangle ? (A) It has two pairs of equal sides.

(B) Its diagonals bisect each other.

(C) Its diagonals are perpendicular.

(D) Its diagonals are equal.

32. A dodecahedron has ___ faces. (A) 8 (B) 10 (C) 12 (D) 14 33. The radius of a wheel is 0.25 metres. The number of revolutions it will make to travel a distance of 11 km will be ____ . (A) 2800

(B) 4000

(C) 5500

34. Find the area of the field as shown in the figure.

(D) 7000

A

2

(A) 70 cm

(B) 128 cm 2

4 cm

G 4 cm F 4 cm E

12 cm

4 cm D

(C) 140 cm 2 (D) 96 cm 2

B 3 cm C

5


DIRECTION (3537) : The following piechart represents the total number of valid votes obtained by four students who contested for school elections. The total number of valid votes polled was 720.

35. Who has won the election ? (A) Veer

(B) Ranbir

(C) Siddharth

(D) Vipul

36. What is the minimum number of votes obtained by any candidate ? (A) 110

(B) 120

(C) 80

(D) 100

37. By how many votes did the winner defeat the nearest contestant ? (A) 20

(B) 30

(C) 50

(D) 40

38. Factorise : 4a 2 + 12ab + 9b 2 – 8a – 12b (A) (2a – 3b) (2a – 3b – 4)

(B) (2a + 3b) (2a + 3b – 4)

(C) (2a – 3b) (2a + 3b – 2)

(D) (2a + 3b) (3a + 2b – 4)

2

æ3ö æ 2 ö 39. If x = è ø ´ è ø 2 3 æ 2 ö (A) è ø 3

-4

10

, find the value of x –2 . æ 3 ö (B) è ø 2

-12

æ 2 ö (C) è ø 3

6

é ù ê 1 ö æ 1 ö ú æ 40. The value of ê 35.7 - 3 + is _____ . - 2 + 1÷ ç 1 ÷ ú ç 3+ ÷ ç 2 + ÷ ú ê çè 3ø è 2 øû ë (A) 30 (B) 34.8 (C) 36.6

(D) 1

(D) 41.4

SECTION III : EVERYDAY MATHEMATICS 41. A tank is

2 6 full. If 16 litres of water is added to the tank, it becomes full. The capacity of the 5 7

tank is (A) 28 litres

(B) 32 litres

(C) 35 litres

(D) 42 litres

42. Of the three numbers, the sum of the first and the second number is 45; the sum of the second and the third number is 55 and the sum of the third and thrice the first number is 90. The third number is ______ . (A) 20


(B) 25

(C) 30

6

(D) 35

43. The difference between the cost price and selling price of an article is ` 240. If the profit is 20%, the selling price is _____ . (A) ` 1240

(B) ` 1400

(C) ` 1600

(D) ` 1200

44. A train 280 metres long, running with a speed of 63 km/hr will pass a tree in (A) 15 secs

(B) 16 secs

(C) 18 secs

(D) 20 secs

45. The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is ____ . (A) ` 4800

(B) ` 6000

(C) ` 8000

(D) Data inadequate

46. If the diameter of the base of a closed right circular cylinder be equal to its height 'h' then its total surface area is ______ . (A)

2 2 ph 3

(B)

3 3 ph 2

(C)

3 2 ph 2

(D) ph3

47. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is _____ . (A) 14 years

(B) 18 years

(C) 20 years

(D) 22 years

48. Shikha cycles to her school at an average speed of 12 km/hr. It takes her 20 minutes to reach the school. If she wants to reach her school in 15 minutes, what should be her average speed ? (A) 16 km/hr

(B) 20 km/hr

(C) 25 km/hr

(D) 10 km/hr

49. Anusha has to pay 4% sales tax in addition to the price of a certain article. Find the price of her article, if she pays ` 2.6 in all. (A) ` 4

(B) ` 2.50

(C) ` 5

(D) ` 7.60

50. The outer dimensions of a closed box are 10 cm by 8 cm by 7 cm. Thickness of the wood is 1 cm. Find the total cost of wood required to make box, if 1 cm 3 of wood costs ` 2.00. (A) ` 320

(B) ` 1240

(C) ` 640

(D) ` 240

SPACE FOR ROUGH WORK

7


5th


2

| 5th IMO | Level-II | Class 8

Section I : Logical Reasoning 1. If FULFNHW is the code for CRICKET, then EULGH is the code for which word ? (A) PRIDE (B) BRIDE (C) BLADE (D) BLIND 2.

Which letter represents the artists who are neither doctors nor scientists nor dancers?

(A) A

(B) D

(C) F

(D) G

3. Choose one number which is similar to the numbers in the given set : 992, 733, 845, 632 (A) 114 (B) 326 (C) 425 (D) 947 4.

Choose the figure from the options which is different from the rest. (A)

5.

(B)

(C)

(D)

Which letter is tenth to the right of the letter which is exactly the middle letter between F and D?

F J M P O W R N B E Y C K A V L D G X U H Q I S Z T

(A) D

(B) G

(C) H

(D) None of these

6.

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

1

(A)

2

(B)

3

4

5

(C)

(D)

7.

Which one of the following when placed at the sign of interrogation shall complete the matrix ?

(A) E10

(B) E12

(C) S10

(D) S12

8. Arun said, "This girl is the wife of the grandson of my mother." Who is Arun to the girl ?

(A) Father

(B) Grandfather

(C) Husband

(D) Father-in-law

3 9.

5th IMO | Level-II | Class 8 |

Deepa moved a distance of 75 metres towards the north. She then turned to the left and walked for about 25 metres, turned left again and walked 80 metres. Finally, she turned to the right at an angle of 45°. In which direction was she moving finally ?

(A) North-east

(B) North-west

(C) South

(D) South-west

10. 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)

11. Different alphabets stand for various symbols as indicated below. Addition : O

Subtraction : M

Multiplication : A

Division : Q Equal to : X Greater than : Y

Less than : Z

Which one of the following is correct according to above definitions ?

(A) 2 Z 2 A 4 O 1 A 4 M 8

(C) 10 X 2 O 2 A 4 O 1 M 2

(B)

8 Y 2 A 3 A 4 Q 2 A 4

(D) 12 X 4 O 2 Q 1 A 4 A 2

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

1

2

3

6

7

8

(A) 1, 4, 7 ; 3, 6, 9 ; 2, 5, 8 (C) 1, 4, 7 ; 2, 6, 9 ; 3, 5, 8

4

5

9

(B) 1, 6, 9 ; 2, 4, 7 ; 3, 5, 8 (D) 1, 5, 7 ; 2, 6, 9 ; 3, 4, 8

13. If 'wall' is called 'window', 'window' is called 'door', 'door' is called 'floor', 'floor' is called 'roof' and 'roof' is called 'ventilator', what will a person stand on ?

(A) Window

(B) Wall

(C) Floor

(D) Roof

(C) 36

(D) None of these

14. Find the number of triangles in the given figure.

(A) 34

(B) 35

4


15. The 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 which would most closely resemble the unfolded form of fig. (Z).

X

(A)

(B)

Y

Z

(C)

(D)

16. Thirty six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters

and so on. Find the number of scooters in the second half of the row. (A) 10 (B) 12 (C) 15

(D) 17

17. The given question consists of figures 1, 2, 3 and 4. 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 question mark (?) in fig. (4).

(A)

(C)

(B)

(D)

18. Letters of the word given below have been jumbled up. Choose the option which gives the correct order of the letters as indicated by the numbers to form a meaningful word. A C P E T S

(A) 1, 6, 3, 4, 2, 5

1 2 3 4 5 6 (B) 2, 3, 4, 1, 5, 6 (C) 5, 6, 3, 4, 1, 2

(D) 6, 5, 3, 4, 2, 1

19. Which of the following collections of letters will look the same in the mirror ? (A) OSMIHOM (B) VHRTRVH (C) HIMOSTA (D) AOVIVOA 20. Which would be the proper order of the following (in ascending order) ?

1. Trillion

2. Thousand

4.

5.

(A) 1, 2, 4, 3, 5

Hundred

3.

Billion

Million

(B) 1, 5, 3, 2, 4

(C) 4, 2, 3, 5, 1

(D) 4, 2, 5, 3, 1

Section II : Mathematical reasoning 21. If x 2 + y 2 = 25 and xy = 12, then the value of x –1 + y –1 is _____.

(A)

12 5

(B)

7 12

(C)

−7 12

(D) Both (B) and (C)

22. What is the least number which must be subtracted from 369 to make it a perfect cube ?

(A) 8

(B) 26

(C) 2

(D) 25

5 23. If ab + bc + ca = 0, then the value of

(A) –1

1 2

a − bc

(B) a + b + c

24. Find the number of factors of 512. (A) 8 (B) 10

+

5th IMO | Level-II | Class 8 | 1 2

+

1 2

b − ca c − ab (C) abc

will be _____.

(C) 4

(D) 0 (D) 14

DIRECTION (Q.No. 25-27) : Study the following graph carefully and answer the following questions.

25. In the year 2006, the people who prefer playing Tennis is what percent of the people who prefer

playing Cricket, Football and Tennis together in that year ? 1 3 1 (A) 25 (B) 24 (C) 21 2 4 3

(D) 23

1 3

26. The number of people who prefer playing Tennis in 2006, is how many millions less than the

number of people who prefer playing Tennis in 2005 ? (A) 110 (B) 105 (C) 100

(D) 95

27. What is the ratio of the number of people who prefer playing Cricket in 2001 to the number of

people who prefer playing Tennis in the year 2003 ? (A) 14 : 17 (B) 16 : 13 (C) 15 : 11

(D) 13 : 15

28. Solve for x : Solve for x :

(A)

418 117

4 x + 17 13 x − 2 x 7 x x + 16 − + = − 18 32 3 12 36

(B) 6

(C) 1

(D) −

8 3

29. Two-fifth of one-third of three-seventh of a number is 15. What is 40 percent of that number ?

(A) 72

(B) 84

(C) 136

(D) 105

30. The question given below is followed by two statements. You have to study the question and the two statements given to decide which of the statement(s) is/are required to answer the question.

What is the area of the right-angled triangle ?

I. II.

Length of the hypotenuse is 5 cm. Perimeter of the triangle is four times its base.

(A) I only

(B) II only

(C) I and II both

(D) Data inadequate

6


31. In a two-digit number, the digit in the unit's place is four times the digit in ten's place and sum of the digits is equal to 10. What is the number ?

(A) 14

32. Find the sum of

(B) 41

(C) Data inadequate

(D) None of these

1 1 1 1 1 1 1 1 1 1 1 + + + + + + + + + + . 2 6 12 20 30 42 56 72 90 110 132

7 (A) 8

(B)

11 12

(C)

15 16

(D)

17 18

33. In the given figure, AE = BC and AE || BC and the three sides AB, CD and ED are equal in length. If ∠ A = 102°, find the measure of ∠ BCD.

(A) 138°

(B) 162°

(C) 88°

(D) None of these

x+y 5 x 34. If = and = 2, the value of (x, y) is _____. x−y 3 ( y + 2) (A) (4, 1) (B) (2, 8) (C) (1, 4)

(D) (8, 2)

35. If m, n are the positive integers (n > 1) such that mn = 121, then value of (m – 1)n (A) 12321 (B) 1 (C) 1000 (D) 11

+ 1

is ______.

36. The greatest divisor of (a – b)(a + b)(a 2 + b 2)(a 4 + b 4)(a 8 + b 8)(a 16 + b 16) is ______. (A) a16 – b16 (B) a16 + b16 (C) a 31 – b 31 (D) a 32 – b 32 37. In the given figure, RISK and CLUE are parallelograms and ∠R = 70° and ∠L is half of ∠ESI. Find the measure of x. K

R

(A) 75°

(B) 55°

E

I

x

U

S

C

L

(C) 65°

(D) 30°

38. Find the area of the following polygon, if AL = 10 cm, AM = 20 cm, AN = 50 cm, AO = 60 cm and AD = 90 cm.

E

F

(A) 337.5 cm2

(B) 384 cm2

(C) 5500 cm2

(D) 5050 cm2

20 cm A

L

M 30 cm

B

N

60 cm

O 40 cm

D

C

39. Two dice are thrown simultaneously. Find the probability of getting a multiple of 3 as the sum.

(A)

1 2

(B)

1 3

(C)

1 4

(D)

5 6

7 40. The value of


( x − y )3 + ( y − z )3 + (z − x )3 is equal to _____. 9( x − y )( y − z )(z − x )

(A) 0

(B)

1 2

(C)

1 3

(D) 1

Section III : Everyday Mathematics 41. What annual payment will discharge a debt of ` 1025 due in 2 years at the rate of 5% compound

interest ? (A) ` 550

(B) ` 551.25

(C) ` 560

(D) ` 560.75

42. A man bought apples at the rate of 8 for ` 34 and sold them at the rate of 12 for ` 57. How many apples should be sold to earn a net profit of ` 45 ?

(A) 90

(B) 100

(C) 135

(D) 150

43. The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. The age of the youngest boy is _____.

(A) 21 years

(B) 18 years

(C) 15 years

(D) 9 years

44. A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work can they finish in a day ?

(A)

1 6

(B)

1 9

(C)

2 5

(D)

2 7

45. A sum of money invested at compound interest amounts to ` 4624 in 2 years and to ` 4913 in 3 years. The sum of money is _____.

(A) ` 4360

(B) ` 4260

(C) ` 4335

(D) ` 4096

46. Three equal cubes are placed in a row touching each other. Find the ratio of the total surface area of the resulting cuboid to that of the sum of surface areas of the three cubes.

(A) 5 : 7

(B) 7 : 9

(C) 9 : 7

(D) None of these

47. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is _____.

(A) 29

1 5

(B) 37

1 4

(C) 42

(D) 54

1 1 1 of a pencil is black, of the remaining is white and the remaining 3 cm is blue, find the total 8 2 2 length of the pencil.

48. If

(A) 8 cm

(B) 10 cm

(C) 7 cm

(D) 6 cm

49. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is _____.

(A) 10

(B) 20

(C) 40

(D) 73

50. A shopkeeper sold a T.V. set for ` 17,940 with a discount of 8% and earned a profit of 19.6%. What would have been the percentage of profit earned if no discount was offered ?

(A) 24.8% (C) Cannot be determined

(B) 25% (D) None of these

6th


2


Section I : Logical Reasoning 1. If AMRITSAR is coded as MAIRSTRA, then CALCUTTA will be coded as (A) ACLCTUAT (B) LACTUCAT (C) ACCLTUAT 2.

(D) ACCLUTAT

Sunita is taller than Seema and Renu, Renu is shorter than Radha and Gauri. Beena is taller than Radha and shorter than Sunita. Sunita is not the tallest and Renu is not the shortest. Who is the

tallest? (A) Sunita

3.

A boy first goes in South direction, then he turns towards left and travels for some distance. After

(B) Beena

(C) Gauri

(D) Data inadequate

that he turns right and moves certain distance. At last he turns left and travels again for some

distance. Now, in which direction is he moving? (A) South (B) West

4.

In the given diagram, the smaller triangle represents the

(C) East

(D) North

teachers, the big triangle represents the politicians, the circle represents the graduates, and the square represents the Members of Parliament. Different regions are being

Politicians

L Teachers

represented by letters of English alphabets. Who among the following are graduate member of parliament and politicians

E D

C F H G B

Members of Parliament

also? (A) B (C) F

5.

Five persons are standing in a queue. One of the two persons at the extreme ends is a Professor

(B) G (D) E

A

Graduates

and the other is a Businessman. An Advocate is standing to the right of a Student. An Author is to the left of the Businessman. The Student is between the Professor and the Advocate. Counting

from the left end the Author is at which place? (A) First (B) Second

6.

Ajay is positioned 8th from the left and Amit is positioned 9th from the right in a row of 15 students.

How many students are between Ajay and Amit? (A) 2 (B) 1 (C) 5

7.

Pointing to Raman in the photograph, Aditi said, "The only son of his mother is my father". How

is Aditi related to Raman? (A) Mother's sister (B) Bua (Father's sister)

8.

Find the missing number.

(A) 38

(B) 64

(C) 4

(D) 16

9.

M and N are good at Hockey and Volleyball. O and M are good at Hockey and Baseball. P and N

(C) Third

(C) Daughter

(D) Fourth

(D) 0

(D) Niece 16

143 1

9

9

236

36

?

are good at Cricket and Volleyball. O, P and Q are good at Football and Baseball. Who among the

following is good at four games? (A) Q (B) P

(C) O

(D) N

3


10. Study the following arrangement of English alphabets and answer the question below: F J M P O W R N B E Y C K A V L D G X U H Q I S Z T

Which letter is 10 (A) G

th

to the right of the letter which is exactly the middle letter between F and D? (B) X (C) U (D) H

11. The given question contains Problem figures containing five figures 1, 2, 3, 4, 5. Select one figure from the options which will continue the same series as given in the Problem figures. Problem Figures ? 1

(A)

(B)

2

3

5

4

(C)

(D)

12. Figures (1) and (2) bears a certain relationship. Similarly, Fig. (4) bears the same relationship to the Fig. (3). Select the figure from the option which would replace the sign of question mark (?) in Fig. (4)?

(A)

(B)

(C)

(D)

13. How many triangles are there in the following figure?

(A) 15

(B) 18

(C) 20

(D) 19

14. Select a figure from the options which will complete the Fig.(X)?

(A)

(B)

(C)

(D)

15. Select a figure from the options which contains the same placement of dot as in the Fig.(X)

(A)

(B)

(C)

(D)

4


16. Which of the following options is the correct mirror image of the given word, if the mirror is placed vertically to the left?

(A) RIVAHAM

(B) RMAHAVI

MAHAVIR (C) RIVAHAM

(D) HAMAVIR

17. Two positions of a dice are shown here.

When 1 is at the top, which number will be at the bottom? (A) 5 (B) 2 (C) 3 (D)

6

18. A series is established if one of the four options is placed in place of the sign '?' in the problem figures. Select the figure.

(A)

(B)

(C)

(D)

19. In a code language 'mu kay cit' means 'very lucky person' and 'dis hu mu' means 'fortunate and

lucky'. Which is the word in that language for 'lucky'? (A) mu (B) kay (C) cit

(D) dis

20. Two sign in the equation have been interchanged. Find out these two signs to make the equation correct.

(A) + and ÷

51 ÷ 3 + 17 × 2 – 12 = 10 (B) – and × (C) ÷ and ×

(D) × and +

Section II : Mathematical reasoning 21. Find the area of the shaded regions.

(A) 67 cm2

(B) 64 cm2

(C) 65 cm2

(D) 66 cm2

22. In the figure, not drawn to scale, ABCD is a trapezium.

BF is a straight line. Find ∠DCE and ∠ADE. (A) 72°, 152° (B) 80°, 152° (C) 70°, 142° (D) 82°, 150°

23. Which one of the following numbers is completely divisible by 45? (A) 181560 (B) 331145 (C) 202860

(D) 2038550

5


24. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in

each case. (A) 4

(B) 7

2 of 1568 + 265.75 = ? + 2455.60 7 (A) 10354.15 (B) 10578.15

(C) 9

(D) 13

(C) 10802.15

(D) 11250.15

(C) 102

(D) 103

25. 8

26. The value of

(0.03)2 + (0.21)2 + (0.065)2 is: (0.003)2 + (0.021)2 + (0.0065)2

(A) 0.1

(B) 10

27. In the given figure NQ || PO. Find the value of a.

(A) 26°

(B) 14°

(C) 10°

(D) 13°

28. Two identical metal bars were put into a container of water as shown in the given figure. When the two metal bars were removed, the water level fell to a height of 7 cm. What was the volume of each metal bar?

(A) 900 cm3

(B) 1800 cm3

(C) 4200 cm3

(D) 18000 cm3

DIRECTION (29-30) : The graph below shows the marks obtained by five pupils for their Mathematics test. Study the graph and answer the questions.

29. What is the average marks obtained by the five pupils? (A) 72 (B) 75 (C) 80 3 of Prateek's marks. 4 (B) Sohan (C) Rohit

(D) 65

30. Name the pupil whose marks are

(A) Mohit

(D) Tarun

6


31. In the figure, ABCD is a rectangle and line MN cuts the rectangle into half. Triangle MNO and triangle MNP are identical triangles. The area of shaded region is ______. A

E

F

D 8 cm

O M

N

5 cm P B

G

H

C

20 cm

(A) More than 180 cm2

(B) Equal to 120 cm2

(C) More than 120 cm2

(D) Less than 120 cm2

32. By what least number 4320 be multiplied to obtain a number which is a perfect cube? (A) 40 (B) 45 (C) 50 (D) 55 33. (64)

(A)

−

1 2

− (−32)

−

4 5

=?

1 8

(B)

3 8

(C)

1 16

(D)

3 16

DIRECTION (34-35) : In the given diagram (not drawn to scale), the ratio of the area of circle A to the area of its hidden part is 5 : 2. The area of triangle B is twice as much as the area of circle A.

14 cm

A B 12 cm

34. What is the area of triangle B? (A) 80 cm2 (B) 76 cm2

(C) 84 cm2

(D) 82 cm2

35. What is the area of the hidden part of circle A? (A) 10 cm2 (B) 12 cm2

(C) 14 cm2

(D) 16 cm2

(C) 45

(D) 40

36. 45% of 1500 + 35% of 1700 = ?% of 3175

(A) 30

(B) 35

37. On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will

be the remainder? (A) 4

(B) 5

(C) 6

38. Which one of the following cannot be the square of a natural number? (A) 30976 (B) 75625 (C) 28561

(D) 7 (D) 143642

39. Three unbiased coins are tossed. What is the probability of getting at most two heads? 3 1 3 7 (A) (B) (C) (D) 4 4 8 8

7


40. If LO || MN, find the value of p.

(A) 50°

(B) 46°

(C) 56°

(D) 52°

Section III : Everyday Mathematics 41. In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?

(A) 30,000

(B) 35,000

(C) 37,000

(D) None of these

42. A man purchased a box full of pencils at the rate of 7 for ` 9 and sold all of them at the rate of 8 for ` 11. In this transaction, he gained ` 10. How many pencils did the box contain?

(A) 100

(B) 112

(C) 114

(D) 115

43. 85 kg of a mixture contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3 : 1?

(A) 5 kg

(B) 6.5 kg

(C) 7.25 kg

(D) 8 kg

44. If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day then in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day?

(A) 6

(B) 7

(C) 8

(D) 9

45. Mr. Dua invested money in two schemes P and Q offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a. respectively. If the total amount of interest accrued through two schemes together in two years was ` 4818.30 and the total amount invested was ` 27,000, what was the amount invested in Scheme P?

(A) ` 12,000

(B) ` 13,500

(C) ` 15,000

(D) None of these

46. A shopkeeper sold sarees at ` 266 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?

(A) ` 240

(B) ` 260

(C) ` 280

(D) None of these

47. The average age of 8 men is increased by 2 years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is ________.

(A) 22 years

(B) 24 years

(C) 28 years

(D) 30 years

48. The price of a T.V. set worth ` 20,000 is to be paid in 20 instalments of ` 1000 each. If the rate of interest be 6% per annum and the first instalment be paid at the time of purchase, then the value of the last instalment covering the interest as well will be _______.

(A) ` 1050

(B) ` 2050

(C) ` 3000

(D) None of these

8


49. A train 110 m long passes a man, running at 6 kmph in the direction opposite to that of the train, in 6 seconds. The speed of the train is ________.

(A) 54 km/hr

(B) 60 km/hr

(C) 66 km/hr

(D) 72 km/hr

50. A certain number of tennis balls were purchased for ` 450. Five more balls could have been purchased in the same amount if each ball was cheaper by ` 15. The number of balls purchased was _______.

(A) 10

(B) 15

(C) 20 SPACE FOR ROUGH WORK

(D) 25

ANSWER KEYS 4 th IMO 1. 8. 15. 22. 29. 36. 43. 49.

(D) 2. (D) 9. (C) 16. (C) 23. (D) 30. (B) 37. (A, B, C, D) (B) 50.

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

3. 10. 17. 24. 31. 38. 44.

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

4. 11. 18. 25. 32. 39. 45.

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

5. 12. 19. 26. 33. 40. 46.

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

6. 13. 20. 27. 34. 41. 47.

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

7. 14. 21. 28. 35. 42. 48.

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

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

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

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

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

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

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

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

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

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

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

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

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

(C) 5 th IMO

1. 8. 15. 22. 29. 36. 43. 50.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

7th SOF International Mathematical Olympiad 2nd Level for Class 8

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