Class 6 Imo 3 Year e Book Level 2 13

Level 2

SOLVED PAPERS 3 years (2012 -2014)

6

INSTANT

Copyright © 2014 Science Olympiad Foundation. Printed with the permision of Science Olympiad Foundation. No part of

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

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

Published by : MTG Learning Media (P) Ltd. Corporate Office : Plot 99, 2nd Floor, Sector 44 Institutional Area, Gurgaon, Haryana. Phone : 0124 - 4951200 Web: mtg.in Email: [email protected] Regd. Office : 406, Taj Apt., Ring Road, Near Safdarjung Hospital, New Delhi-110029

Visit

www.mtg.in for buying books online.

MTG Work-Books / olympiad books CLASS 1

International Mathematics Olympiad

National Science Olympiad

International English Olympiad

MTG CSS Series

CLASS 2



National Cyber Olympiad


MTG CSS Series


MTG CSS Series

CLASS 3









MTG CSS Series


MTG CSS Series


MTG CSS Series

CLASS 5




CLASS 6








Science IQ Challenge

Math IQ Challenge


MTG CSS Series

Master Mental Ability in 30 Days

CLASS 8





MTG CSS Series

Math IQ Challenge


Psychology of Success

The Secrets of SUCCESS




Math IQ Challenge








CLASS 10


Math IQ Challenge










Math IQ Challenge







CLASS 12


Math IQ Challenge







Class

1 to 10

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 6

Section I : Logical Reasoning 1. In the given arrangement some symbols are there each of which is preceded by a digit and some digits are there each of which is preceded by a symbol. What is total number of both these ? 9 V @ S 2 G R A

(A) 3

3 Q £ B Z 7 C Y D T 4 * P F 6 @ $ 5 E H B J d

(B) 1

(C) 2

(D) None of these

2. If city is called village, village is called forest, forest is called sofa, sofa is called freeze and freeze

is called bathroom, then where do deer live ? (A) Village (B) Sofa

(C) Freeze

(D) Forest

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

A D

4.

Find the wrong term in the given series : 2, 3, 8, 28, 112, 565 (A) 3 (B) 28 (C) 8

5.

With the help of given diagram, find how many persons take tea and wine but not coffee.

(A) 20

(B) 17

(C)

(D)

D

(A)

(B)

A

D A

(D) 112

(C) 25

(D) 15

6. Introducing Suchi, Naman says, ‘‘She is the wife of only nephew of only brother of my mother.’’

How is Suchi related to Naman ? (A) Wife (B) Sister

7.

Find the missing number in the adjoining table. (A) 94 (B) 76 (C) 16 (D) 73

8.

Choose the correct mirror-image of fig. (X), if the mirror is placed along MR.

(A)



(B)

(C) Sister-in-law



(C)



(D) Son-in-law

(D)



3 9.

5th IMO | Level-II | Class 6 |

Three out of these figures are similar in a certain way. Find the figure which is different from the rest.

(A)

(B)

(C)

(D)

10. How many pairs of letters are there in the word PURPOSEFUL which have as many letters between

them in the word as in the English alphabet ? (A) One (B) Two

(C) Three

(D) Four

11. The length and breadth of a room are 8 m and 6 m respectively. A cat runs along side all the four walls and finally along a diagonal in order to catch a rat. How much total distance is covered by the

cat ? (A) 10 m

(B) 14 m

(C) 38 m

(D) 48 m

12. At a party P, Q, R, S and T are sitting in a circle. The group comprises an officer, an industrialist and a businessman. The businessman is sitting in between the industrialist and his wife S. P is an officer married to T who is the sister of Q. The industrialist is seated to the right of R. Both

the ladies are unemployed. Who among them is a graduate ? (A) P (B) Q (C) R

(D) Data inadequate

13. Find the figure from the options which will continue the series established by the problem figures.

(A)

(B)

(C)

(D)

14. Six friends P, Q, R, S, T and U are sitting around a hexagonal table each at one corner. P is second to the left of U. Q is the neighbour of R and S. T is second to the left of S. Who among the following are the neighbours of P ?

(A) U and P

(B) T and R

(C) U and R

(D) None of these

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

(A)

(B)

(C)

(D)

16. In a row of students Rakesh is 12th from the left and Kartik is 17th from the right. When they interchange their positions Kartik becomes 27th from the right. How many students are there between

Kartik and Rakesh? (A) 9

(B) 12

(C) 7

(D) 10

4


17. In the following sequence how many 8’s are there each of which is preceded by an odd number, but not followed by an even number ? (A) 3

7 8 2 8 9 3 8 5 2 3 8 4 7 8 1 9 8 8 5 (B) 2 (C) 5 (D) 1

18. In the given sequence, how many unshaded circles will there be in pattern 99?

Pattern 1

(A) 98

Pattern 2

Pattern 3

(B) 100

Pattern 4

(C) 96

(D) 95

19. If ‘–’ stands for division, ‘+’ stands for multiplication, ‘÷’ stands for subtraction and ‘×’ for addition,

then which one of the following equations is correct ? (A) 6 ÷ 20 × 12 + 7 – 1 = 70 (B) 6 + 20 – 12 ÷ 7 + 1 = 62 (C) 6 – 20 ÷ 12 × 7 + 1 = 57 (D) 6 + 20 – 12 ÷ 7 – 1 = 38

20. The given question consists of two sets of figures. Figures (i), (ii), (iii) and (iv) constitute the problem set. There is a definite relationship between figures (i) and (ii). Establish a similar relationship

C (i)

C

(ii)

(iii)

(B)

S

(C)

? (iv)

T

S

C

T

(A)

C

T

T

T S

S

T

T





in figure (iv).

S

between figures (iii) and (iv) by selecting a suitable figure from the options that would replace (?)

S

(D)

S

Section II : Mathematical reasoning 21. Find the average of all the odd numbers from 1 to 16. (A) 4 (B) 9 (C) 8

(D) 17

22. What is the missing number that shall go in the box? 600.051 = 600 + (B) 0.05

+ 0.001

(A) 0.005

(C) 0.5

23.

Which one of the following statements is true? (A) If a number is divisible by 3, it must be divisible by 9. (B) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately. (C) A number is divisible by 18, if it is divisible by both 3 and 6. (D) None of these

24. Find the value of 50 – (– 48) – (– 2) – 110 + (– 80) – (– 100) (A) 10 (B) – 10 (C) 100

(D) 5

(D) – 100

5


DIRECTION (Q.No. 25-27) : Study the following graph carefully and answer the questions that follow. Three different products (in thousands) produced by a company in five different years

25. What was the total number of all the products produced by the company in the year 2006 and

2008 together ? (A) 10750

(B) 107.5 lacs

(C) 105700

(D) None of these

26. What is the difference between the total number of Pen Drives and CDs produced by the company

in the year 2008 and the number of Key Boards produced by the company in the year 2006 ? (A) 40000 (B) 4000 (C) 35000 (D) 3500

27. What was the ratio of the number of CDs produced by the company in the year 2009 to the number

of Key Boards produced by the company in the year 2005 ? (A) 9 : 10 (B) 11 : 10 (C) 10 : 9

(D) 10 : 11

28. How many unit cubes must be transferred from the solid on the left to the solid on the right so that both of them have the same number of unit cubes ?

(A) 5

(B) 3

(C) 4

(D) 2

29. What is the minimum number of shaded squares that must be added so that the line AB becomes a line of symmetry ?

(A) 1

(B) 2

(C) 3

(D) 4

6


30. Find the area of the shaded part of the given figure (not drawn to scale).

(A) 182 cm2

(B) 320 cm2

(C) 128 cm2

(D) 192 cm2

31. What fraction of the figure is shaded ?

(A)

4 12

(B)

5 12

(C)

32. Find the value of 6435.9 + 7546.4 + 1203.5. (A) 15188.5 (B) 15155.5

7 12

(D)

(C) 15185.8

9 12

(D) 15815.8

33. Select the INCORRECT match. Column I Column II

(A) Points are collinear

if they lie on same line.

(B) Diameter is a chord

passing through centre of the circle.

(C) Parallel lines

are lines which do not meet.

(D) Simple curve

is a curve which crosses itself.

34. If the diagonals of a quadrilateral bisect each other at right angles, then the quadrilateral is a

____. (A) Parallelogram

(B) Trapezium

35. If 5 : 4 : : 30 : x, then the value of x is ____. (A) 24 (B) 12

(C) Rhombus

(D) Rectangle

(C) 3/2

(D) 6

36. If the cost of 25 packets with 12 pencils in each packet is ` 750, then the cost with 30 packets of

8 pencils in each packet is _____. (A) ` 600 (B) ` 720

(C) ` 640

(D) ` 620

37. The figure is a solid cuboid. How many rectangular faces does it have ?

(A) 6

38. If

(A)

=

(B) 8 1 and 2 +

=

(C) 3

(D) 4

1 , then which one of the following has the greatest value? 4

(B)



(C)

×

(D)

–

7


39. If the length of each side of a unit square is 2 cm, find the perimeter of the given figure.

(A) 200 cm

40. The value of

4 (A) 11

(B) 124 cm 2 1 1 is _______. + + 5 4 2 3 (B) 20

(C) 100 cm

(D) 50 cm

3 (C) 1 20

7 (D) 2 20

Section III : Everyday Mathematics 41. Rahul had 68 marbles more than Rohit. After Rohit bought another 23 marbles, Rohit had

many marbles as Rahul had. How many marbles did Rahul have ? (A) 36 (B) 72 (C) 81

3 as 8

(D) 144

42. The ratio of Mohit’s age to Gaurav’s age is 6 : 5 now. If Mohit is 9 years older than Gaurav, Gaurav

is _____ years old. (A) 45

(B) 54

(C) 63

(D) 72

43. A machine makes 24 paper cups in 2 minutes. At this rate, how many paper cups will it make in

540 seconds ? (A) 108

(B) 216

(C) 432

(D) 864

44. 2 chairs and 1 table cost ` 54000. If 1 chair and 1 table cost ` 38000, what is the cost of 5

chairs ? (A) ` 60000

(B) ` 92000

(C) ` 80000

(D) ` 20000

45. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is _____.

(A) 1520 m2

(B) 2420 m2

(C) 2480 m2

(D) 2520 m2

46. Tanuj walked 8.96 km on Tuesday, 7.50 km on Wednesday and some distance on Thursday. If he walked 21010 metres in three days, how much distance did he walk on Thursday?

(A) 5.45 km

(B) 4.55 km

(C) 5.54 km

(D) 5.55 km

47. Ayush had a square cardboard of edge 40 cm. The cardboard was cut into 4 equal triangles. Find the area of each triangle.

(A) 10 cm2

(C) 80 cm2

(D) 800 cm2

1 3 hr. Pooja slept 1 hr more than Ashu. How long did Pooja sleep ? 2 5 (A) 7 hr 6 mins (B) 7 hr 12 mins (C) 7 hr 10 mins (D) 7 hr 24 mins

48. Ashu slept for 5

(B) 400 cm2


8

49. Ria bought 11 dresses and 12 shirts altogether. Each dress costs ` 250 and each shirt costs

` 100 less than the dress. How much did Ria spend ? (A) ` 5540 (B) ` 5405 (C) ` 4550

(D) ` 5450

50. The charges for parking a car are shown below :

For the first hour For every additional hour or part thereafter

` 50 ` 25.50

Mr. Samrat parked his car from 9:00 a.m. to 2:30 p.m. How much did he pay? (A) ` 165 (B) ` 175.5 (C) ` 187.5 (D) ` 177.5 SPACE FOR ROUGH WORK

6th


2


Section-I : Logical Reasoning 1. If every third letter from the English alphabets is dropped, which letter will be fourth to the right of fourteenth letter from your right?

(A) M

(B) N

(C) E

(D) A

2.

Select which of the following options will be the mirror image of the given word, if the mirror is placed vertically to the left. G a y A T R I s u t r A

(A)

(B)

(C)

(D)

3. Choose the odd-one out.

(A) 49

(B) 85

(C) 36

(D) 81

4.

How will you code ACCOMMODATE if S and V are coded as 8 and 5 respectively?

(A) 26-24-24-12-14-14-12-23-22-26-7

(B) 26-24-24-12-14-14-12-23-26-7-22

(C) 2-25-25-12-7-14-14-23-26-22-12

(D) 26-24-12-14-7-14-23-21-26-22-8

5.

Find out the wrong term in the given series. 196, 169, 144, 121, 80

(A) 80

(B) 121

(C) 169

(D) 196

6.

Select a figure from the options that forms a correct water image of the given figure. CCC (A)

CCC

(B)

CCC

(C)

CCC

(D)

CCC

7. 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.

Rules :

(i) If a two-digit odd number is followed by a two-digit odd number they are to be added.

(ii) If a two-digit even number is followed by a two-digit odd number which is a perfect square, the digit number is to be subtracted from the odd number.

(iii) If a three-digit number is followed by a two-digit number the first number is to be divided by the second number.

(iv) If a prime number is followed by an even number the two are to be added.

(v) If an even number is followed by another even number the two are to be multiplied. 16 8 32

132 11 X2 If X is the resultant of the first row, what is the resultant of the second row? (A) 192

(B) 128

(C) 132

(D) 144

3 8.


Select a figure from the options which will form a series established by the Problem figures. Problem Figures

?

(A)

(B)

(C)

(D)

9.

In the given figure, if the centres of all the circles are joined by horizontal and

vertical lines, then find the total number of squares that can be formed. (A) 6 (B) 7

(C) 8

(D) 10

10. If 'A + B' means A is the father of B, 'A – B' means A is the brother of B, 'A ÷ B' means A is the wife B and 'A × B' means A is the mother of B, then which of the following represents M is the

maternal grandmother of T? (A) M × N ÷ S + T (B) M × N – S ÷ T

(C) M × S – N ÷ T

(D) M × N × S ÷ T

11. Select a figure from the options which indicates the correct relationship between the three given

words.

"Triangle, Four-sided figure, Square"

(A)

(B)

(C)

(D)

12. Select a figure from the options which contains Fig. (X) as its part.

Fig. (X)

(A)

(B)

(C)

(D)

13. Five friends A, B, C, D and E are standing in a row facing north but not necessarily in the same order. Only B is between A and E, C is immediate right to E, and D is immediate left to A. On the

basis of above information, which of the following statements is definitely true? (A) B is to the right of E. (B) A is second to the left of C. (C) D is third to the left of E. (D) B is to the left of A.

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

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

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

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

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

1

2

3

4

5

6

7

8

9

4

| 6th IMO | Level-II | Class 6 15. In the given question,

means ≠ ÷ means ≥ means ≤

= means <

+ means >

× means =

If a + b and b + c then_____. (A) c ÷ a (B) a = c

(C) a

(D) c = a

c

16. A square transparent sheet with a pattern is given. Find from amongst the options as to how the pattern would appear when the transparent sheet is folded along the dotted line. Transparent Sheet

(A)

(B)

(C)

(D)

17. A man is facing west. He turns 45° in the clockwise direction and then another 180° in the same

direction and then 270° in the anticlockwise direction. Which direction is he facing now? (A) South (B) North-West (C) West (D) South-West

18. Consider the figures X, Y and Z showing a sheet of paper folded and punched on the sheet of paper. Select a figure from the options which will most closely resemble the pattern unfolded position of figure.

X

(A)

(B)

Y

Z (C)

(D) None of these

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

Fig. (X)

(A)

(B)

(C)

(D)

5


20. Two positions of a dice is given below. Look at them carefully assuming the pictures to be correct and answer the question. #1

#2

Which figure is on the face indicated by the arrow #1? (A) (B) (C)

(D)

Section-II : Mathematical reasoning 21. Find the largest 5-digit number which is completely divisible by 89. (A) 99947 (B) 99999 (C) 99936

(D) 99942

22. The minimum number of factors of a given number is _____ and a multiple of a given number is

divisible by the _____. (A) 1, given number (C) 2, multiples of given number

(B) 2, given number (D) 1, multiples of given number

23. The length, breadth and height of a room are 9 m 10 cm, 7 m 80 cm and 3 m 90 cm respectively. Find the greatest length of a tape which can be used to measure the dimensions of the room in

exact number of times. (A) 1m 16 cm (B) 1m 30 cm

(C) 1m 90 cm

(D) 1m 60 cm

24. The value of 63.7– 28.89 + 76.4 – 37.66 is _____. (A) 73.50 (B) 73.52 (C) 73.55

(D) 73.58

25. The descending order of XX, XXXVI, V is _____. (A) V, XXXVI, XX (B) XX, V, XXXVI

(D) XXXVI, XX, V

(C) V, XX, XXXVI

26. What least number should be added to 1410 to get a number exactly divisible by 43 ? (A) 9 (B) 1 (C) 3 (D) 7 P

27. If l ||m and PQ is a transversal, then which of the following is false?

a

(A) ∠b = ∠g

(B) ∠a = ∠h

(C) ∠a = ∠g

g

(D) ∠f + ∠h = 180°

Q

c e

f h

b d

I

m

28. The given solid is made up of identical blocks. How many such blocks are required to make the given solid?

(A) 14

(B) 20

(C) 17

29. The value of –297 – (–7) – 428 – (–18) + (–62) is _______. (A) –2152 (B) –228 (C) –258

(D) 15 (D) –762

6


30. If perimeter of the given figure is 68.3 cm, then the sum of x + y is ____.

(A) 8.6 cm

(B) 8.1 cm

(C) 8.4 cm

(D) 9.8 cm

31. The given picture is shaded to represent a fractional number.

How many of the stars in the group below must be shaded to represent a fraction with the same value of above unshaded fractional number ?

(A) 5

(B) 6

(C) 8

(D) 10

DIRECTION (32 - 33) : Read the following graph and answer the questions below.

32. Which month has maximum sale? (A) April (B) July

DEC

NOV

OCT

SEP

AUG

JULY

JUNE

MAY

APR

MAR

FEB

JAN

Sale (In thousands)

50 45 40 35 30 25 20 15 10 5

MONTHS

(C) August

(D) Data inadequate

33. If the total sale is 325000 then total sales in March and November is ______.

(A) 40000

(B) 50000

(C) 45000

(D) 55000

(C) 2

(D) 1

34. Find the value of (P + Q) × (R + S).

(A) 1

(B) 3

2 9

2 9

7


35. When Garima multiplies a certain number by 19 and adds 9 to the product, she gets 313. Find the

number. (A) 13

(B) 14

(C) 15

(D) 16

36. In a DABC, if 3∠A = 4 ∠B = 6∠C, then ∠A + ∠B – 3∠C =

(A) 70°

(B) 40°

(C) 20°

(D) 60°

37. The area of the unshaded region in the figure is ______. 16 m 7m

7m

16 m 7m

(A) 207 m2

38. If

(B) 158 m2

7m

(C) 256 m2

(D) 196 m2

km : 10 km = 9000 paise : ` 3, then box contains_____.

(A) 500

(B) 600

(C) 900

(D) 300

39. The sum of four girls is 57 years and their ages are in the proportion 3 : 4 : 5 : 7. The difference between the age of eldest and youngest girl is _____.

(A) 8 years

(B) 10 years

(C) 12 years

(D) 15 years

40. In DABC, AB = AC and AD ^ BC, BE ^ AC and CF ^ AB. Then, DABC is symmetrical about ______.

(A) AD

(B) BE

(C) CF

(D) None of these

Section-III : Everyday Mathematics 41. The maximum number of students among whom 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) 91

(B) 910

(C) 1001

(D) 1911

42. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was ` 4.20 and that of Y was ` 6.30, in which year commodity X will cost 40 paise more than the commodity Y?

(A) 2010

(B) 2011

(C) 2012

(D) 2013

43. Water boils at 212°F or 100°C and melts at 32°F or 0°C. If the temperature of a particular day is 35°C, it is equivalent to_____.

(A) 85°F

(B) 90°F

(C) 95°F

(D) 99°F

44. The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is _____.

(A) 35.2

(B) 36.1

(C) 36.5

(D) 39.1

45. The total ages of A and B is 12 years more than the total ages of B and C. C is how many years

younger than A? (A) 12 years

(B) 24

(C) C is elder than A

(D) Data inadequate

8


46. The boys and girls in a college are in the ratio 3 : 2. If 20% of the boys and 25% of the girls are adults, the percentage of students who are not adults is _____.

(A) 58%

(B) 67.5%

(C) 78%

(D) 82.5%

47. A man bought a number of clips at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%?

(A) ` 4

(B) ` 5

(C) ` 6

(D) ` 7

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

(A) 20 litres

(B) 30 litres

(C) 40 litres

(D) 60 litres

49. A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is _____.

(A) 10%

(B) 10.08%

(C) 20%

(D) 28%

50. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 15 seconds, B in 30 seconds and C in 18 seconds, all starting at the same

point. After what time will they meet again at the starting point? (A) 26 minutes (B) 140 seconds (C) 90 minutes SPACE FOR ROUGH WORK

(D) 1 minute 30 seconds

7th


7th IMO | Class-6 | Level 2

2

logical reasoning logical reasoning 1.

The given question consists of five figures marked 1, 2, 3, 4 and 5 called the Problem Figures. Select a figure from amongst the options which will continue the same series as established by the five Problem Figures.

A.

B.

C.

D.

2.

There are certain common characteristics between the two Problem Figures. Select a figure from amongst the options which shows similar characteristics as shown by the Problem Figures.

A.

B.

C.

D.

3.

Select the figure from the options in which the given Fig. (X) is exactly embedded as one of its part.

A.

B.

C.

D.

4.

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

A.

1,4,7; 3,6,9; 2,5,8

B.

1,6,9; 2,4,7; 3,5,8

C.

1,4,7; 2,6,9; 3,5,8

D.

1,5,7; 2,6,9; 3,4,8

5.

From his house, Mohit went 15 kms to the North. Then he turned West and covered 10 kms. Then, he turned South and covered 5 kms. Finally, turning to East, he covered 10 kms. In which direction is he from his house?

A. B. C. D.

6.

Pointing to a woman in a photograph a man says, "She is the only daughter of my wife's mother-inlaw". How is the woman related to the man?

A. B. C. D.

Fig. (X)

East West North South

Daughter Wife Sister Mother-in-law

3


7.

8.

Which of the following Venn diagram correctly depicts the relationship amongst "Boys, Athletes, Dancers"? A. B. C.

Find the missing character in the question given below. 6

11

25

8

6

16

12

5

?

A. B. C. D.

9.

Which of the following will be the middle digit of the second highest number among the following five numbers if the positions of the first and the third digits in each number are interchanged?

18 16 12 10

432 851 719 643 287 8 3 5 1

10. In a class of students, Aarush rank is 23rd from top in Mathematics, whereas his rank is 27th from below in Physics. How many students are there in the class?

A. B. C. D.

50 40 48 Data inadequate

11. The positions of the first and the ninth letters in the word PRESBYTERIANISMS are interchanged. Similarly, the positions of the second and the tenth letters are interchanged, and so on. Which of the following will be the sixth letter from the right end after rearrangement?

I E

A. B. C. D.

da ja na None of these

13. Study the following arrangement carefully and answer the question given below.

D.

A. B. C. D.

C. D.

12. In a certain code language 'pik da pa' means 'where are you'; 'da na ja' means 'you may come'; and 'na ka sa' means 'he may go'. Which of the following means come in that code language?

A. A B. B

M % R 4 AT# J @ 7 D 5 I F N I E$ 3 6 W U 2 H 8 * K 9 B Q

Which of the following is the eighth to the left of the seventeenth from the left end of the above arrangement?

A. B. C. D.

@ U 8 T

14. Starting from a point P, Sachin walked 20 metres towards South. He turned left and walked 30 metres. He then turned left and walked 20 metres. He again turned left and walked 40 metres and reached a point Q. How far and in which direction is the point Q from the point P?

A. B. C. D.

20 10 10 10

metres metres metres metres

West East West North

15. A, B, C, D, E, F, G and H are sitting around a circle facing at the centre, C is third to the left of A and second to the right of E, B is second to the right of C. D is second to the right of F who is second to the right of A. G is not an immediate neighbour of C. Who is to the immediate right of C ?

A. B. C. D.

H G D Data inadequate

16. Find the least number of unit cubes to be added to the solid to form complete a cuboid.

A. 21

B.

20

C.

22

D. 18


4

17. There is a definite relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that will replace the question mark (?) in fig. (iii).

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

A.

A.

B.

B.

C.

C.

D.

D.

18. Which of the following options most closely resembles the mirror image of the given word if mirror is placed vertically left?

20. Count the number of squares in the given figure.

SUPERVISOR

A.

B.

C.

D.

A. B. C. D.

8 12 15 18

MATHEMATICAL REASONING 21. The given figure is made up of two identical rectangles. Find the area of the shaded part.

22. Find the weight of a cone in terms of w.

A. B. C. D.

8 cm2 40 cm2 12 cm2 20 cm2

A. B. C. D.

w kg 2 w kg 3 w kg 4 w kg

5


23. The length of pencil B is exactly half way between the lengths of pencil A and pencil C. What is the length of pencil B? (Give your answer as a mixed number in the simplest form.)

28. Which of the following statements are true?

A.

B.

C.

D.

2 cm 7 9 9 cm 14 4 9 cm 7 3 9 cm 7

19

24. Find the value of

(–17.5) + 152.82 ÷ 9 + 19.8 – (– 0.7) × 8.06 A. B. C. D.

24.90 22.612 24.854 24.922

Direction (25-26): The bar graph shows the number of students in 4 sections of a class.

(i)

The subtraction of an integer is the same as the addition of its additive inverse. (ii) One more than the given number gives the predecessor. (iii) When two negative numbers are added, we get a negative number. A. Only (i) B. Both (i) and (iii) C. Both (ii) and (iii) D. Only (iii)

29. The ratio of Mohit’s savings in account A to his 2 savings in account B was 8 : 7. He spent of his 5 total savings. He then transferred some money from one account to another so that both accounts had ` 765 each. How much money did he have at first?

A. B. C. D.

` ` ` `

2450 2500 2550 1460

30. Which of the following solids has the greatest number of faces?

A.

B.

C.

D.

25. How many students are there in class 6B?

A. B. C. D.

33 34 35 36

26. How many boys are there in the 4 sections altogether?

A. B. C. D.

66 56 68 58

27. Fill in the blank:

One A. B. C. D.

full turn of the hand is _______. 3 right angles 1 revolution 1 right angle 1 straight angle

31. Amit and Priya had an equal amount of money. After Priya bought a dress that cost ` 79.90 and Amit bought a watch that cost ` 193.40, Priya had 3 times as much money as Amit. How much money did Priya have at first? A. ` 56.75 B. ` 113.50 C. ` 170.25 D. ` 250.15 32. Find the smallest number of shaded squares to be added so that the figure has a line of symmetry.

A. B. C. D.

1 2 3 4


6

33. The given figure is made up of small squares. The length of one side of a small square is 2 cm. Find the area of the shaded region of the figure.

A.

174 cm2

B.

176 cm2

C.

177 cm2

35. Find the value of CLXXXVII – CX – LXXIV.

D.

178 cm

2

34. Find the least number, which when divided by 36, 24 and 48, leaves remainders 33, 21 and 45, respectively.

A. B. C. D. A. B. C. D.

141 140 142 144 IV III C XI

EVERYDAY MATHeMATICS 36. M a r y, C h a r u a n d J o h n h a v e ` 2 5 0 0 0 . 7 5 , ` 18000.79 and ` 8000.45, respectively in their personal bank accounts. How much money do they have altogether?

A. B. C. D.

` ` ` `

51002.00 51001.88 51002.08 51001.99

37. The ratio of the marks scored by a student in English, Mathematics and Science is 1 : 2 : 1. If the total marks of three subjects is 800, then find the marks in each subject respectively.

A. B. C. D.

100, 300, 140, 200,

200, 600, 280, 400,

100 300 140 200

38. Vipul earns ` 15000 in 3 months. In how many months will he earn ` 95000?

A. B. C. D.

14 16 18 19

39. Five square flower beds each with sides 2 m are dugout from a piece of land, 10 m long and 5 m wide. What is the area of the remaining part of the land?

A. B. C. D.

30 40 50 60

sq. sq. sq. sq.

m m m m

40. Latika had 240 beads. She gave her friend and

1 of the beads to 6

3 of the remainder to her sister. How 4

many beads did her sister receive?

A. C.

40 150

B. D.

50 200

41. A story book costs ` m and a bag costs ` 5 more than a storybook. Find the cost of 1 bag and 3 storybooks in terms of m in the simplest form.

A. B. C. D.

` ` ` `

4 m (3 + 4m) (5 + 4m) (4m + 1)

42. Trees were planted at equal distances along a straight road. The distance between the first and the fifth tree is 40 m. Find the distance between the second and the ninth tree.

A. B. C. D.

30 50 80 70

m m m m

43. Three children walk together while going to school. Their steps measure 85 cm, 90 cm and 80 cm, respectively. At what distance from the starting point will they again start walking together?

A. B. C. D.

13698 cm 12040 cm 12240 cm 10 cm

44. Ashmit buys 638 chairs and 132 tables for his office. If a chair costs ` 1540 and a table costs ` 2465, find the total money spent by him.

A. B. C. D.

` ` ` `

1037900 1307900 1307090 1307009

45. The temperature at a place rises from –20 °C to 20 °C. What is the rise in temperature?

A. B. C. D.

20°C 40°C – 40°C 80°C

7


Achievers section 46. Which of the following is the INCORRECT step for constructing a perpendicular to a line through a point not on it?

Step 1 : Given a line l and a point M not on it. Step 2 : With M as centre, draw an arc which intersects line l at two points P and Q. Step 3 : Using the same radius and with P and Q as centres, construct two arcs that intersects at a point say N on the other side. Step 4 : Join MN. Thus MN is perpendicular to l. A. Only Step 1 B. Both Step 3 and Step 4 C. Only Step 3 D. All steps are correct.

47. Which of the following statements is incorrect?

A. B. C.

D.

Each angle of a rectangle is a right angle. All the sides of a rhombus are of equal length. All the sides of a parallelogram are of equal length. The diagonals of a square are perpendicular to one another.

48. Fill in the blanks: A region in the interior of a circle enclosed by an ___ P__ on one side and a pair of ___ Q__ on the other two sides is called a ___ R__.

A. B. C. D.

P arc radii arc chord

Q radii arc radii arc

49. Match the following: Lines of symmetry (i) 0 (ii) Only 1 (iii) 2 (iv) 3

A. B. C. D.

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

→ → → →

p. q. r. s.

R sector segment segment sector Example Isosceles triangle Equilateral triangle Scalene triangle Rectangle

s; (ii) → r; (iii) → p; (iv) → q q; (ii) → r; (iii) → p; (iv) → s r; (ii) → p; (iii) → q; (iv) → s r; (ii) → p; (iii) → s; (iv) → q

50. Select the correct option. Statement-1 : A number for which sum of all its factors is equal to twice the number, is called a perfect number. Statement-2 : 6 and 28 are perfect numbers.

A. B. C. D.

SPACE FOR ROUGH WORK

Statement-1 is true but Statement-2 is false. Statement-1 is false but Statement-2 is true. Both the Statements are true. Both the Statements are false.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

5.

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

6.

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

7.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Class 6 Imo 3 Year e Book Level 2 13

Recommend Documents