IMO (SOF) CLASS 8th LEVEL-2

Level 2

SOLVED PAPERS 3 years (2012 -2014)

INSTANT

8

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

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

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

7th


2

7th IMO | Class-8 | Level 2

logical reasoning logical reasoning 1.

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 of numbers progress from left to right.

Study the following information carefully and answer the question given below:

Rules

Four players P, Q, R and S are holding 4 cards each. Each of them has an Ace, a King, a Queen and a Jack. All of them have all the suits (spade, heart, club and diamond).

I.

I.

If an odd number is followed by a two-digit even number then they are to be added. II. If an odd number is followed by a two-digit odd number then the second number is to be subtracted from the first number. III. If an even number is followed by a number which is a perfect square of a number then the second number is to be divided by the first number. IV. If an even number is followed by a two-digit even number then the first number is to be multiplied by the second number. 8 16 16 14

13 11 12 144

What is the difference between the resultant of the first set of numbers and the second set of numbers?

A. B. C. D.

2.

A set of figures carrying certain characters, is given. Assuming that the characters in each set follow a similar pattern, find the character which would replace the question mark (?).

A. B. C. D.

3.

A square transparent sheet with a pattern is given. Select an option as to how the pattern would appear when the transparent sheet is folded along the dotted line.

106 118 210 222

III. R has Queen of club and King of spade. IV. S has jack of club. Ace of diamond is with

A. B. C. D.

5.

Count the minimum number of straight lines required to make the given figure.

A. B. C. D.

6.

Select the option which will exactly make up the key figure (X).

C.

D.

P R Q S

8 10 12 14

A.

B.

C.

D.

7.

The post office is to the east of the school while my house is to the south of the school. The market is to the north of the post office. If the distance of the market from the post office is equal to the distance of my house from the school, in which direction is the market with respect to my school?

A. B. C. D.

B.

P has Ace of spade and Queen of diamond.

II. Q has Ace of club and King of diamond.

262 226 136 206

A.

4.

North East North-east South-west

3


8.

A watch reads 4.30. If the minute hand points East, in what direction will the hour hand point?

A. B. C. D.

9.

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

North North-west South-east North-east

12. There is a certain relationship between the figures (i) and (ii) & (iii) and (iv). Identify the relationship and find the missing figure.

A.

B.

C. A.

B.

C.

D.

13. Three different positions X, Y and Z of a dice are shown in the figures given below. Answer the following question which is based upon these figures.

D.

10. Find the missing figure in the given figure matrix.

Sum of top and bottom faces in position Y. A. More than 5 B. 5 C. Less than 5 D. Cannot be determined

14. If > denotes +; < denotes –; + denotes ÷; – denotes =; = denotes 'less than'; and × denotes 'greater than'; then which of the following is incorrect statement ? A. 3 + 2 > 4 × 9 + 3 < 2 B. 3 > 2 > 4 × 18 + 3 < 1 C. 3 > 2 < 4 × 8 + 4 < 2 D. 3 + 2 < 4 × 9 + 3 < 3 A.

B.

C.

D.

11. 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 7, O by 1, L by 3, T by 6, V by 5, S by 8, A by 9 and C by 2.

A.

92156873

B.

92157683

C. D.

92516783 92156837

15. Deepanshu said to Naman, "That boy playing football is the younger of the two brothers of the daughter of my father's wife." How is the boy playing football related to Deepanshu? A. Son B. Brother C. Cousin D. Nephew 16. There is a series of seven figures. First and last unnumbered figures are the beginning and end of series. One of the five numbered figures does not fit into the series. Identify the figure need to be replaced.

A. B. C. D.

1 2 3 4

4


17. Read the following information carefully to answer the question given below: A person is asked to put in a basket one apple when ordered 'One', one guava when ordered 'Two', one orange when ordered 'Three' and is asked to take out from the basket one apple and one guava when ordered 'Four' and 'Five' respectively. 4 4 5 4 5 3 4 5 3 1 4 5 3 1 2 4 5 4 5 3 4 5 3 If 8 of each type of fruits are already in the basket then, how many apples will be there in the basket at the end of the above order sequence?

A. B. C. D.

1 2 3 4

same as A's income, B's income is _____.

A. B. C. D.

` ` ` `

40,000 60,000 80, 000 1,20,000

19. In a class of 46 students, 18 played football, 17 played cricket including 6 who played football. 16 students played hockey including 4 who played cricket, but not football. Five students played carrom but no outdoor games. Which of the following figures represents these facts? A.

18. Read the following information carefully to answer the question given below: The sum of the incomes of A and B is more than that of C and D taken together. The sum of the incomes of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the incomes of B and D. If A's income be ` 80,000 per annum and the difference between the incomes of B and D be the

B.

C.

D.

20. Count the number of faces in the given solid.

A. B. C. D.

17 18 19 None of these

Mathematical reasoning  3 ⋅ 2n − 4 ⋅ 2n  a p − q −2 ( p − q )  21. Simplify + × a  q 2 2n − 2n −1  a q − pq 

A. B. C. D.

n

–1 1 –2 2

22. Find the area of the shaded region in the following figure.

A. B. C. D.

A.

B.

C.

D.

24. Find a + b + c + d + e + f in the given figure if, AOD, BOE and FOC are straight lines.

28. 45 sq. cm 113.6 sq. cm 59.8 sq. cm 103.5 sq. cm

23. Which of the following is a possible net for the solid?

A. B. C. D.

360° 540° 420° 120°

5


4 2 , then find the value of 2 +1 1 x+2 x+2 2 +  = 2 2 x−2 x−2 2

25. If x =

2

A.

B.

12 + 8 2 / 5

C.

12 − 8 2 / 5

D.

16 2 + 24 5

1° 2

A.

72

C.

105º

B.

135º

D.

67

1° 2

27. In the figure below, PQRS is a square, LSR is an equilateral triangle. Find the value of x + y + z.

A. B. C. D.

240° 90º 105º 60º

28. An unbiased dice is thrown two times having first six consecutive odd numbers on each six faces. Find the probability of getting even sum.

A. B.

C.

D.

1 0 1 36 4 36

2 th of a page with 5 dimensions 25 cm and 30 cm respectively. If the real area of the map is 10800 sq. m, the scale to which the map is drawn, is A. B. C. D.

1 1 1 1

cm cm cm cm

= = = =

36 m 26 m 33 m 6m

`40 `30 `40 `30

32. If a = (2–2 – 2–3), b = (2–3 – 2–4) and c = (2–4 – 2–2) then find the value of 3abc.

A.

−63 1024

B.

−63 2048

C.

−9 2048

D.

9 1024

3

1   3  3 x − 3  = 2, then  x

A.

B. 0 C. 1 D. –1

±

3

x+

1 = _______. x

3

10 3

34. The volume of a hemispherical ball is given by the 2 V = pr 3 , where V is the volume and r is the radius. 3 Find the diameter of the hemisphere whose volume is

29. In an Atlas, a map occupies

by by by by

then find ( P + Q − R) . 2 A. 175 B. 165 C. 185 D. 200

33. If

R paid more than Q R paid more than Q Q paid more than R Q paid more than R

A. B. C. D.

31. If P : Q : R = 6 : 5 : 4 and P2 + Q 2 + R 2 = 192500,

26. Three friends distributed their total property. The ratio of total property, share of first friend and share of second friend is 24 : 7 : 8. Find the central angle of sector, which represents the share of the third friend.

30. Q and R borrowed `26000 and `25000 respectively, for a period of 2 years. Q paid simple interest at the rate of 2% p.a., while R paid compound interest at the same rate, compounded annually. Who paid more interest and by how much?

A. B. C. D.

468512 3 m . 21 22 m 11 m 33 m 44 m

35. Factorise : (x – y)2 a 2 + 2(x – y) (x + y) ab + b 2 (x + y)2

A. B. C. D.

(ax (ax (ax (ax

– by) (ax + by) + by) (bx + ay) – ay + bx + by) (ax – ay + bx + by) + ay + bx + by) (ax – ay + bx + by)

6


EVERYDAY MATHeMATICS

36. Ravi borrowed `45000 from Sahil. A part of the sum is borrowed at 10% p.a. under simple interest for 4 years and the remaining part at 11% p.a. under simple 1 interest for 4 years. If the total interest earned by 2 Sahil is ` 19900, then find the sum borrowed at each rate.

A. B. C. D.

10000, 35000 25000, 20000 15000, 30000 5000, 40000

37. In an office, the ratio of the salary of an officer to that of a clerk is 30 : 7. If the salary of the clerk is `14375 less than that of the officer, then what is the salary of the officer?

A. B. C. D.

`15600 `18625 `17650 `18750

38. In a Winter sale offer, a shopkeeper allows a discount of 15%. Even after giving the discount, he makes a profit of 6.25%. Raghav bought a sweater which was marked at `5000. Find the cost price of this sweater for the shopkeeper.

A. B. C. D.

` ` ` `

5000 4000 4250 5250

39. The age of Sarthak is one-fifth of the age of his mother and the sum of the ages of the son and the mother is equal to the age of the father. After 15 years, the sum of the ages of the son and his mother will be four-third of his father's age. Find the ratio of the present ages of Sarthak, mother and father respectively.

A. B. C. D.

1 2 1 2

: : : :

5 : 7 10 : 10 5:6 8:9

40. Twenty two men can complete a piece of work in 17 days. They work for 2 days. How many more men should now be employed so as to complete the work in another 10 days.

A. B. C. D.

11 22 33 None of these

41. In a company, the average salary of male employees is ` 9200 and that of female employees is ` 8200. If the average salary per employees is ` 8900, the percentage of female employees of the total employees is_______.

A.

30

B.

40

C.

50

D.

25

42. A test consists of questions each carrying 3 mark, 4 mark and 6 marks in the ratio 2 : 2 : 1. If the maximum marks in the exam is 100, then find the number of questions of each type.

A.

20, 20, 10

B.

10, 10, 5

C.

15, 15, 30

D.

15, 15, 10

43. A fountain pen with a cylindrical barrel of diameter 3 cm and height 14 cm, filled with ink, can write 3600 words. How many words can be written with that pen using 220 ml of ink? (Take 1cc = 1 ml)

A.

6000

B.

5000

C.

7000

D.

8000

44. One day, the ratio of the number of first class and second class passengers who travelled were in the ratio 1 : 30. The ratio of the first and second class fares is 3 : 1. The total amount collected from the passengers that day was `66000. Find the amount collected from the first class passengers (in `).

A.

` 3000

B.

` 6000

C.

` 9000

D.

` 12000

45. A man purchased a plot which is in the shape of a square. The area of the plot is 12 hectares 3201m2 . Find the length of each side of the plot (in cm).

A.

34900

B.

35100

C.

35900

D.

36100

7


Achievers section

46. Let s, m and f denote the respective time taken by son, mother and father to complete the work. 1 1 1 1 1 1 1 1 1 + = , + = and + = , s m 24 s f 18 m f 36

If

1 1 1 1 1 1 and , , . respectively then find + + s m f s m f

A.

1 1 5 3 , , , 16 144 144 144

B.

1 5 1 3 , , , 16 144 144 144

C.

1 3 1 5 , , , 16 144 144 144

D.

None of these

47. Study the statements and select the correct option.

x −5

 Statement 1 :  9 

5  2     3 

 Statement 2 :  n 

m  a   =  a      b  b

A. B. C. D.

Statement Statement Statement Statement

1 1 1 1

p

0

2 =   , then x = 5 3 mp n

is true and statement 2 is false and 2 are true and 2 are false is false and statement 2 is true

48. Fill in the blanks : Cubes of the numbers for which the digits in the units place are 2, 8 and 3, 7 end in _____ and _____ respectively.

A. C.

4, 6 and 2, 7 8, 2 and 7, 3

B. D.

2, 3 and 7, 3 5, 4 and 3, 7

49. In the given figure,   m | | l | | n and PT | | QR . If ∠TUV = x, ∠QRS = y and ∠QVW = z, then which of the following is necessarily true?

A. B. C. D.

x > y = z x
50. In the figure given below, O is the centre of the circle and OPQR is a rectangle. A is a point on PO 1 such that AO = PO and B is the mid point of OR. 3 Find the area of the shaded region if PA = 8 cm and BR = 4 cm (Use p = 3.14)

A. B. C. D.

132.68 cm2 121.12 cm2 108.56 cm2 None of these

Space for Rough Work

ANSWER KEYS 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)

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)

5.

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

6.

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

7.

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)

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

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

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

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

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

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

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

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

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

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

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

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

IMO (SOF) CLASS 8th LEVEL-2

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