Level 2
SOLVED PAPERS 3 years (2012 -2014)
INSTANT
8
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 Ofce : Plot 99, 2nd Floor, Sector 44 Institutional Area, Gurgaon, Haryana. Phone : 0124 - 4951200 Web: mtg.in Email:
[email protected] Regd. Ofce : 406, Taj Apt., Ring Road, Near Safdarjung Hospital, New Delhi-110029
Visit
www.mtg.in for buying books online.
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 Ofce : Plot 99, 2nd Floor, Sector 44 Institutional Area, Gurgaon, Haryana. Phone : 0124 - 4951200 Web: mtg.in Email:
[email protected] Regd. Ofce : 406, Taj Apt., Ring Road, Near Safdarjung Hospital, New Delhi-110029
Visit
www.mtg.in for buying books online.
MTG MT G WORK WORK�BOO �BOOKS KS / OL OLYMPIA YMPIAD D BOOK BOOKS S CLASS 1
International Mathematics Olympiad
National Science Olympiad
International English Olympiad
MTG CSS Series
CLASS 2
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
CLASS 3
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
MTG WORK�BOOKS / OLYMPIAD BOOKS CLASS 4
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
CLASS 5
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
CLASS 6
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
MTG WORK�BOOKS / OLYMPIAD BOOKS CLASS 7
International Mathematics Olympiad
National Science Olympiad
Math IQ Challenge
National Cyber Olympiad
Science IQ Challenge
International English Olympiad
MTG CSS Series
Master Mental Ability in 30 Days
CLASS 8
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
Math IQ Challenge
Science IQ Challenge
Psychology of Success
The Secrets of SUCCESS
Master Mental Ability in 30 Days
MTG WORK�BOOKS / OLYMPIAD BOOKS CLASS 9
International Mathematics Olympiad
Math IQ Challenge
National Science Olympiad
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
The Secrets of SUCCESS
International English Olympiad
Master Mental Ability in 30 Days
CLASS 10
International Mathematics Olympiad
Math IQ Challenge
National Science Olympiad
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
The Secrets of SUCCESS
International English Olympiad
Master Mental Ability in 30 Days
MTG WORK�BOOKS / OLYMPIAD BOOKS CLASS 11
International Mathematics Olympiad
Math IQ Challenge
Science IQ Challenge
National Science Olympiad
Psychology of Success
National Cyber Olympiad
The Secrets of SUCCESS
Master Mental Ability in 30 Days
CLASS 12
International Mathematics Olympiad
Math IQ Challenge
Science IQ Challenge
National Science Olympiad
Psychology of Success
National Cyber Olympiad
The Secrets of SUCCESS
Master Mental Ability in 30 Days
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
Computers & IT Achievers Section Grand Total Computers & IT Achievers Section Grand Total
No. of Questions
Marks per Question
Total Marks
30 5 35 45 5 50
1 2
30 10 40 45 15 60
1 3
NATIONAL SCIENCE OLYMPIAD Class
3 to 4
5 to 10
11 and 12
Section
Science Achievers Section Grand Total Science Achievers Section Grand Total Physics & Chemistry Achievers Section Mathematics/Biology Grand Total
No. of Questions
Marks per Question
Total Marks
30 5 35 45 5 50 25 5 20 50
1 2
30 10 40 45 15 60 25 15 20 60
1 3 1 3 1
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
Total Marks
30 5 35 45 5 50
1 2
30 10 40 45 15 60
1 3
5th
LEVEL - 2 Year 2011-12
| 5th IMO | Level-II | Class 8
2
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 gure 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
6.
(B) G
(C) H
(D) None of these
Select a gure from amongst the given options which will continue the same series established by ve problem gures. Problem Figures
(A)
7.
(C)
(D)
Which one of the following when placed at the sign of interrogation shall complete the matrix ?
(A) E10 8.
(B)
(B) E12
(C) S10
(D) S12
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
3
(D) Father-in-law
5th IMO | Level-II | Class 8 |
5th IMO | Level-II | Class 8 |
3 9.
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 nally? (A) North-east
(B) North-west
(C) South
(D) South-west
10. Select a gure from amongst the options, which when placed in the blank space of g. (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 denitions ? (A) 2 Z 2 A 4 O 1 A 4 M 8
8Y2A3A4Q2A4
(B)
(C) 10 X 2 O 2 A 4 O 1 M 2
(D) 12 X 4 O 2 Q 1 A 4 A 2
12. Group the given gures into three classes using each gure 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 'oor', 'oor' 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 gure.
(A) 34
| 5th IMO | Level-II | Class 8
(B) 35
4
| 5th IMO | Level-II | Class 8
4
15. The given question consists of a set of three gures 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 gure from the options which would most closely resemble the unfolded form of g. ( Z ).
X
(A)
Y
(B)
Z
(C)
(D)
16. Thirty six vehicles are parked in a parking lot in a single row. After the rst 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 gures 1, 2, 3 and 4. There is a denite relationship between gures 1 and 2. Establish a similar relationship between gures 3 and 4 by selecting a suitable gure from the options that would replace the question mark (?) in g. (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.
Hundred
5.
Million
(A) 1, 2, 4, 3, 5
3.
(B) 1, 5, 3, 2, 4
Billion
(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
(C)
12
−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
5
(D) 25
5th IMO | Level-II | Class 8 |
5th IMO | Level-II | Class 8 |
5 23. If ab + bc + ca = 0, then the value of (A) –1
1 a2
−
bc
+
1 b2
(B) a + b + c
24. Find the number of factors of 512. (A) 8 (B) 10
1
+
ca c2 − 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? (A)
25
1 2
(B)
24
3
(C)
4
21
1 3
(D)
1
23
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 : 4 x + 17 13 x − 2 x − + 18 32 3 (A)
418 117
(B) 6
=
7x 12
−
x + 16 36
(C) 1
8
(D)
−
3
29. Two-fth 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
| 5th IMO | Level-II | Class 8
(B) II only
(C) I and II both
6
(D) Data inadequate
| 5th IMO | Level-II | Class 8
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
(B) 41
32. Find the sum of
1 1 1 + + 2 6 12
+
7
(A)
(B)
8
1 20
+
(C) Data inadequate 1 1 1 1 1 + + + + 30 42 56 72 90
11
+
1 110
(C)
12
+
(D) None of these
1 . 132
15
17
(D)
16
18
33. In the given gure, AE = BC and AE || BC and the three sides AB, CD and ED are equal in length. If ∠ A = 102°, nd the measure of
(A) 138° 34.
If
x + y x − y
=
∠ BCD.
(B) 162° 5 x and 3 ( y + 2)
(A) (4, 1)
=
(C) 88°
(D) None of these
2, the value of ( x , y ) is _____. (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)(a16 + b 16 ) is ______. (A) a16 – b 16 (B) a16 + b 16 (C) a 31 – b 31 (D) a 32 – b 32 37. In the given gure, RISK and CLUE are parallelograms and
∠ R =
70° and
∠ L is
half of
∠ESI .
Find
the measure of x. K
S
E
U
x
R
(A) 75°
I
C
(B) 55°
L
(C) 65°
(D) 30°
38. Find the area of the following polygon, if AL = 10 cm, AM = 20 cm,
E
AN = 50 cm, AO = 60 cm and AD = 90 cm.
F
(A) 337.5 cm2
20 cm
2
(B) 384 cm
A
N
L M 30 cm
(C) 5500 cm2
60 cm
O 40 cm
D
B C
2
(D) 5050 cm
39. Two dice are thrown simultaneously. Find the probability of getting a multiple of 3 as the sum. (A)
1 2
(B)
1
(C)
3
7
1 4
(D)
5 6
5th IMO | Level-II | Class 8 |
5th IMO | Level-II | Class 8 |
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
(C)
2
1
(D) 1
3
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
42. A man bought apples at the rate of 8 for
(C) `
(B) 100
560
(D)
`
560.75
34 and sold them at the rate of 12 for
apples should be sold to earn a net prot of (A) 90
`
`
`
57. How many
45 ? (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 nish 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 nish in a day? (A)
1
(B)
6
1
(C)
9
2
(D)
5
45. A sum of money invested at compound interest amounts to
`
2 7
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
(C) 42
4
(D) 54
1 1 1 of a pencil is black, of the remaining is white and the remaining 3 cm is blue, nd 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
50. A shopkeeper sold a T.V. set for
(C) 40 `
(D) 73
17,940 with a discount of 8% and earned a prot of 19.6%. What
would have been the percentage of prot earned if no discount was offered? (A) 24.8% (C) Cannot be determined
(B) 25% (D) None of these
6th
LEVEL - 2 Year 2012-13
| 6th IMO | Level-II | Class 8
2
SECTION I : LOGICAL REASONING 1.
2.
If AMRITSAR is coded as MAIRSTRA, then CALCUTTA will be coded as (A) ACLCTUAT (B) LACTUCAT (C) ACCLTUAT
(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.
(B) Beena
(C) Gauri
(D) Data inadequate
A boy rst goes in South direction, then he turns towards left and travels for some distance. After 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 the Members of Parliament. Different regions are being
Politicians
L
circle represents the graduates, and the square represents Teachers
represented by letters of English alphabets. Who among the following are graduate member of parliament and politicians
D
C
(B) G (D) E
H
F
Members of Parliament
G
B
also? (A) B (C) F 5.
E
A
Graduates
Five persons are standing in a queue. One of the two persons at the extreme ends is a Professor 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.
9.
(C) 5
(D) 0
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.
(D) Fourth
Ajay is positioned 8 th from the left and Amit is positioned 9 th from the right in a row of 15 students. How many students are between Ajay and Amit? (A) 2 (B) 1
7.
(C) Third
(C) Daughter
(D) Niece
Find the missing number. (A) 38
(B) 64
(C) 4
(D) 16
16
9
9
36
143
236
1
?
M and N are good at Hockey and Volleyball. O and M are good at Hockey and Baseball. P and N
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
3
(D) N
6th IMO | Level-II | Class 8 |
6th IMO | Level-II | Class 8 |
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 th to the right of the letter which is exactly the middle letter between F and D? (A) G (B) X (C) U (D) H 11. The given question contains Problem gures containing ve gures 1, 2, 3, 4, 5. Select one gure from the options which will continue the same series as given in the Problem gures. Problem Figures ? 1
(A)
2
3
5
4
(B)
(C)
(D)
12. Figures (1) and (2) bears a certain relationship. Similarly, Fig. (4) bears the same relationship to the Fig. (3). Select the gure 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 gure?
(A) 15
(B) 18
(C) 20
(D) 19
14. Select a gure from the options which will complete the Fig.(X)? (A)
(B)
(C)
(D)
15. Select a gure from the options which contains the same placement of dot as in the Fig.(X)
(A)
| 6th IMO | Level-II | Class 8
(B)
(C)
4
(D)
| 6th IMO | Level-II | Class 8
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)
R I V A H A M
(B)
MAHAVIR (C)
RMAHAVI
(D)
R IVAHAM
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
6
(D)
18. A series is established if one of the four options is placed in place of the sign '?' in the problem gures. Select the gure.
(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. 51 (A) + and
÷
(B) – and
×
÷ 3
+ 17 × 2 – 12 = 10 (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 gure, not drawn to scale, ABCD is a trapezium. BF is a straight line. Find (A) 72°, 152° (B) 80°, 152° (C) 70°, 142° (D) 82°, 150°
∠ DCE and ∠ ADE .
23. Which one of the following numbers is completely divisible by 45? (A) 181560 (B) 331145 (C) 202860
5
(D) 2038550
6th IMO | Level-II | Class 8 |
6th IMO | Level-II | Class 8 |
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 25.
(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
8
(0.03)2 + (0.21)2 + (0.065) 2
26. The value of
(0.003)2 + (0.021)2 + (0.0065)2
(A) 0.1
(B) 10
is:
27. In the given gure 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 gure. 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 ve pupils for their Mathematics test. Study the graph and answer the questions.
29. What is the average marks obtained by the ve 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
| 6th IMO | Level-II | Class 8
6
(D) Tarun
| 6th IMO | Level-II | Class 8
6
31. In the gure, 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
(C)
8
1
(D)
16
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 .
A
14 cm 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
(D) 7
38. Which one of the following cannot be the square of a natural number? (A) 30976 (B) 75625 (C) 28561
(D) 143642
39. Three unbiased coins are tossed. What is the probability of getting at most two heads? (A)
3 4
(B)
1
(C)
4
7
3 8
(D)
7 8
6th IMO | Level-II | Class 8 |
6th IMO | Level-II | Class 8 |
7 40. If LO || MN , nd 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
42. A man purchased a box full of pencils at the rate of 7 for 8 for
` 11.
In this transaction, he gained
(A) 100
` 10.
(B) 112
` 9
(D) None of these and sold all of them at the rate of
How many pencils did the box contain? (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
46. A shopkeeper sold sarees at
` 266
(C)
` 15,000
(D) None of these
each after giving 5% discount on labelled price. Had he not
given the discount, he would have earned a prot 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
48. The price of a T.V. set worth
` 20,000
(C) 28 years is to be paid in 20 instalments of
(D) 30 years ` 1000
each. If the rate
of interest be 6% per annum and the rst instalment be paid at the time of purchase, then the value of the last instalment covering the interest as well will be _______. (A)
` 1050
| 6th IMO | Level-II | Class 8
(B)
` 2050
(C)
8
` 3000
(D) None of these
| 6th IMO | Level-II | Class 8
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
50. A certain number of tennis balls were purchased for
`
(D) 72 km/hr
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
LEVEL - 2 Year 2013-14
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.
4.
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.
P has Ace of spade and Queen of diamond.
II.
Q has Ace of club and King of diamond.
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 rst 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 rst number. IV. If an even number is followed by a two-digit even number then the rst number is to be multiplied by the second number. 8 16 16 14
III. R has Queen of club and King of spade. IV. A. B. C. D. 5.
What is the difference between the resultant of the rst set of numbers and the second set of numbers? A. B. C. D.
6.
262 226 136 206
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. 7.
A.
C.
7th IMO | Class-8 | Level 2
B.
D.
P R Q S
Count the minimum number of straight lines required to make the given gure. A. B. C. D.
A set of gures carrying certain characters, is given. Assuming that the characters in each set follow a similar pattern, nd the character which would replace the question mark (?). A. B. C. D.
3.
106 118 210 222
S has jack of club.
Ace of diamond is with
13 11 12 144
2.
Study the following information carefully and answer the question given below:
8 10 12 14
Select the option which will exactly make up the key gure (X).
A.
B.
C.
D.
The post ofce 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 ofce. If the distance of the market from the post ofce 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.
North East North-east South-west
3
3
7th IMO | Class-8 | Level 2 8.
9.
A watch reads 4.30. If the minute hand points East, in what direction will the hour hand point? A.
North
B.
North-west
C.
South-east
D.
North-east
12.
Select a gure which will continue the same series as established by the ve Problem Figures.
13.
1 0.
11.
4
There is a certain relationship between the gures (i) and (ii) & (iii) and (iv). Identify the relationship and nd the missing gure.
A.
B.
C.
D.
B.
C.
D.
Rewrite the word VOCALIST in the numeric form by writ ing its rst four lett ers in the reve rse orde r 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.
92516783
D.
92156837
B.
C.
D.
Three different positions X , Y and Z of a dice are shown in the gures given b elow. Answer the following question which is based upon these gures.
Sum A. B. C. D.
Find the missing figure in the given figure matrix.
A.
A.
of top and bottom faces in position Y . More than 5 5 Less than 5 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
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 gures are the beginning and end of ser ies. One of the ve numbered gures does not t into the series. Identify the gure need to be replaced.
A. B. C. D.
1 2 3 4
7th IMO | Class-8 | Level 2
4 17.
7th IMO | Class-8 | Level 2 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.
same as A's income, B's income is _____. A. B. C. D. 19.
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. 18.
1 2 3 4
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.
20.
40,000 ` 60,000 ` 80, 000 ` 1,20,000
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 gures represents these facts? A.
B.
C.
D.
Count the number of faces in the given solid. A. B. C. D.
If A's income be ` 80,000 per annum and the difference between the incomes of B and D be the
`
17 18 19 None of these
MATHEMATICAL REASONING
21.
22.
23.
Simplify A.
–1
B.
1
C.
–2
D.
2
3 ⋅ 2n
− 4 ⋅ 2n 2 n − 2 n −1
a p − q + q 2 × a −2( p − q) a q − pq
n
Find the area of the shaded region in the following gure. A.
28. 45 sq. cm
B.
113.6 sq. cm
C.
59.8 sq. cm
D.
103.5 sq. cm
24.
A.
B.
C.
D.
Find a + b + c + d + e + f in the given gure if, AOD, BOE and FOC are straight lines.
Which of the following is a possible net for the solid?
7th IMO | Class-8 | Level 2
A.
360°
B.
540°
C.
420°
D.
120°
5
5
7th IMO | Class-8 | Level 2
25.
If x =
4 2 2 +1
30. , then nd the value of
x + 2 x + 2 2 + 2 x − 2 x − 2 2
1
2
A. B.
12 + 8 2 / 5
C.
12 − 8 2
D. 26.
31.
5
C.
72
1°
B.
2
105º
D.
135º 67
A.
R paid more than Q by ` 40
B.
R paid more than Q by ` 30
C.
Q paid more than R by ` 40
D.
Q paid more than R by ` 30
If P : Q : R = 6 : 5 : 4 and P 2 + Q 2 + R 2 = 192500, then nd ( P + Q − R ) . 2 A. 175
Three friends distribu ted their total property. The ratio of total property, share of rst friend and share of second friend is 24 : 7 : 8. Find the central angle of sector, which represents the share of the third friend. A.
27.
16 2 + 24
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?
32.
B.
165
C.
185
D.
200
If a = (2 –2 – 2 –3), b = (2 –3 – 2 –4) and c = (2 –4 – 2 –2) then nd the value of 3 abc.
1° 2
−63
A.
In the gure below, PQR S is a square, LSR is an equilateral triangle. Find the value of x + y + z .
1024
−9
C.
33.
A. B. C. D. 28.
An unbiased dice is thrown two times having rst six consecutive odd numbers on each six faces. Find the probability of getting even sum. A. B. C. D.
29.
34.
1 0 1 36 4
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 1 1 1 1
cm cm cm cm
= = = =
36 m 26 m 33 m 6m
35.
3
3
1 3 x − 3 x = 2, then
3
−63 2048 9 1024
x +
1 3
x
= _______.
10
±
B.
0
C.
1
D.
–1
3
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
A. B. C. D.
36
D.
2048
A.
is
In an Atlas, a map occupies
A. B. C. D.
6
240° 90º 105º 60º
If
B.
468512 21 22 11 33 44
m3 .
m m m m
Factorise : ( x – y)2 a 2 + 2( x – y) ( x + y) ab + b 2 ( x + y)2 A.
(ax – by) (ax + by)
B.
(ax + by) (bx + ay)
C.
(ax – ay + bx + by) (ax – ay + bx + by)
D.
(ax + ay + bx + by) (ax – ay + bx + by)
7th IMO | Class-8 | Level 2
6
7th IMO | Class-8 | Level 2 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 nd the sum borrowed at each rate. A. B. C. D.
37.
` 18625 ` 17650 ` 18750
5000 ` 4000 ` 4250 ` 5250
1 2 1 2
: : : :
44.
5:7 10 : 10 5:6 8:9
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.
43.
`
The age of Sarthak is one-fth 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.
40.
` 15600
In a Winter sale offer, a shopkeeper allows a discount of 15%. Even after giving the discount, he makes a pro t of 6.25%. Raghav bough t a sweat er wh ich w as marked at ` 5000. Find the cost price of this sweater for the shopkeeper. A. B. C. D.
39.
42.
In an ofce, the ratio of the salary of an ofcer to that of a clerk is 30 : 7. If the salary of the clerk is ` 14375 less than that of the ofcer, then what is the salary of the ofcer? A. B. C. D.
38.
10000, 35000 25000, 20000 15000, 30000 5000, 40000
41.
11 22 33 None of these
7th IMO | Class-8 | Level 2
45.
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
A test consists of questions each carrying 3 mark, 4 mark and 6 marks in the ratio 2 : 2 : 1. If t he maximum marks in the exam is 100, then nd the number of questions of each type. A.
20, 20, 10
B.
10, 10, 5
C.
15, 15, 30
D.
15, 15, 10
A fountain pen with a cylindrical barrel of diameter 3 cm and height 14 cm, lled 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
One day, the ratio of the number of rst class and second class passengers who travelled were in the ratio 1 : 30. The ratio of the rst and second class fares is 3 : 1. The total amount collected from the pas senger s tha t day was ` 66000. Find the amount collected from the rst class passengers (in ` ). A.
`
3000
B.
`
6000
C.
`
9000
D.
`
12000
A man purchased a plot which is in the shape of a square. The area of the plot is 12 hectares 3201m 2 . Find the length of each side of the plot (in cm). A.
34900
B.
35100
C.
35900
D.
36100
7
7
7th IMO | Class-8 | Level 2 ACHIEVERS SECTION
46.
Let s, m and f denote the respective time taken by son, mother and father to complete the work. If
1 s
+
1 m
then nd
A.
B.
C. D. 47.
1
=
1
,
24
1 s
1
+
m
1
1 s
+
+ 1 f
5
1
=
f
1 18
and
and
1 m
1
+
f
=
1 36
48.
Cubes of the numbers for which the digits in the units place are 2, 8 and 3, 7 end in _____ and _____ respectively.
,
1 1 1 , , respectively s m f
A. C. 49.
,
5
,
1
,
,
3
,
1
,
which of the following is necessarily true?
5
A. B. C. D.
None of these
Study the statements and select the correct option. x − 5
50. 2 = 3
p
Statement 2 :
In the given figure,
∠TUV = x, ∠QRS = y and ∠ QV W = z , then
16 144 144 144
Statement 1 :
2, 3 and 7, 3 5, 4 and 3, 7
If
3
2 5 9 3
B. D.
m | | l | | n and PT | | QR .
16 144 144 144 1
4, 6 and 2, 7 8, 2 and 7, 3
3
, , , 16 144 144 144 1
Fill in the blanks :
a m a n = b b
0
, then x = 5
mp n
x > y = z x < y = z x = y = z Cannot be determined
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.
Statement 1 is true and statement 2 is false
A.
132.68 cm2
B.
Statement 1 and 2 are true
B.
121.12 cm2
C.
Statement 1 and 2 are false
C.
108.56 cm2
D.
Statement 1 is false and statement 2 is true
D.
None of these
SPACE FOR ROUGH WORK
