Class 7 Imo 5 Years E Book 2019

INTERNATIONAL MATHEMATICS OLYMPIAD

Level 2 SOLVED PAPERS

CLASS

7

5 Years (2014, 2016-2019)

INSTANT 2019

Copyright © 2019 Science Olympiad Foundation. Printed with the permission 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 provided 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 previous years' papers of IMO exam.

Published by : MTG Learning Media (P) Ltd. Corporate Office : Plot 99, 2nd Floor, Sector 44 Institutional Area, Gurugram, Haryana-122003. Phone : 0124 - 6601200 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.

Do you want yourself to be updated about frequently asked questions (FAQs)

Subscribe to our YouTube Channel

https://www.facebook.com/pcmbtoday

BLOG

https://www.youtube.com/MTGBOOKS

Subscribe us on blog.pcmbtoday.com

2019

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 1 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

Maths Practice-cumWorkbook

Learning English

National Science Olympiad

National Cyber Olympiad

Science Practice-cumWorkbook

Learning Grammar

2019

International English Olympiad

International General Knowledge Olympiad

Know Your IQ Math

Learning Computers

Learning Mathematics

Learning & Knowing

Reasoning

Learning Science

EVS

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 2 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

Maths Practice-cumWorkbook

Learning English

National Science Olympiad

National Cyber Olympiad

Science Practice-cumWorkbook

Learning Grammar

2019

International English Olympiad

International General Knowledge Olympiad

Know Your IQ Math

Learning Computers

Learning Mathematics

Learning & Knowing

Reasoning

Learning Science

EVS

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 3 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

Maths Practice-cumWorkbook

Science Practice-cumWorkbook

Olympiad Prep-Guide Science

Know Your IQ Math

Learning English

Learning Grammar

Learning Mathematics

2019

International General Knowledge Olympiad

Learning Computers

Learning & Knowing

Reasoning

Learning Science

EVS

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 4 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

Maths Practice-cumWorkbook

Science Practice-cumWorkbook

Olympiad Prep-Guide Science

Know Your IQ Math

Learning English

Learning Grammar

Learning Mathematics

2019

International General Knowledge Olympiad

Reasoning

Learning Computers

Learning Science

Learning & Knowing

EVS

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 5 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

Maths Practice-cumWorkbook

Science Practice-cumWorkbook

Olympiad Prep-Guide Science

Know Your IQ Math

Learning English

Learning Mathematics

Learning Grammar

2019

International General Knowledge Olympiad

Reasoning

Learning Computers

Learning Science

Learning & Knowing

EVS

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 6 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

International General Knowledge Olympiad

Reasoning

Maths Practice-cumWorkbook

Science Practice-cumWorkbook

Olympiad Prep-Guide Science

Know Your IQ Math

Learning Computers

Learning Mathematics

2019

Learning & Knowing

NCERT at your Fingertips

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 7 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

International General Knowledge Olympiad

Reasoning

Maths Practice-cumWorkbook

Science Practice-cumWorkbook

Olympiad Prep-Guide Science

Know Your IQ Math

Math IQ Challenge

Science IQ Challenge

Master Mental Ability in 30 Days

Learning Computers

Learning Mathematics

2019

Learning & Knowing

NCERT at your Fingertips

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 8 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

Maths

National Science Olympiad

National Cyber Olympiad

International English Olympiad

International General Knowledge Olympiad

Reasoning

Science

Olympiad Prep-Guide Science

Know Your IQ Math

Math IQ Challenge

Science IQ Challenge

Practice-cum-Workbook

Practice-cum-Workbook

Master Mental Ability in 30 Days

Learning Computers

Learning Mathematics

2019

Learning & Knowing

NCERT at your Fingertips Science

NCERT at your Fingertips Mathematics

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 9 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

International General Knowledge Olympiad

Reasoning

Math IQ Challenge

Science IQ Challenge

Master Mental Ability in 30 Days

NTSE Chapterwise

2019

NTSE Explorer

NCERT at your Fingertips Science

NCERT at your Fingertips Mathematics

MTG WORKBOOKS / OLYMPIAD BOOKS Check complete details on www.mtg.in

CLASS 10 For latest releases and revised editions CLICK HERE

International Mathematics Olympiad

National Science Olympiad

National Cyber Olympiad

International English Olympiad

International General Knowledge Olympiad

Reasoning

Math IQ Challenge

Science IQ Challenge

NTSE Chapterwise

MAT for NTSE

2019

NTSE Explorer

NCERT at your Fingertips Science

NCERT at your Fingertips Mathematics

For Classes 6, 7, 8, 9, 10, 11 & 12 Class 6

Class 7

11

Class

12

Class 8

Class

Class 9

2019

Class 10

JEE (Main & Advanced) | NEET | BOARDS | OLYMPIAD | NTSE

FOUNDATION COURSE For Classes 6, 7, 8, 9 & 10

Class 6

Class 7

Class 8

Class 9

Class 10

2019

For Classes 10, 11 and 12 Class 12

Class 11

Class 10

2019

For Classes 10 & 12 Class 10

Class 12

2019

NEW LAUNCH

For Classes 3 to 8

For Classes 1 to 8

NEW LAUNCH

2019

IMPORTANT INSTRUCTIONS Exam Date : 9th February 2020 Center of exam : As assigned by SOF on your admit card. Kindly coordinate with your school coordinator for exact information about exam. Write to [email protected] for any enquiry. Mode of exam : IEO/NSO/IMO level 2 for academic year 2019-20 will be a paper-pen objective test. Pattern of the exams : 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

No. of Questions Marks per Question

Mathematics Achievers Section Grand Total Mathematics Achievers Section Grand Total

30 5 35 45 5 50

1 2 1 3

Total Marks 30 10 40 45 15 60

INTERNATIONAL ENGLISH OLYMPIAD Class 3 to 4

5 to 12

Section

No. of Questions Marks per Question

Word and Structure Knowledge, Reading Achievers Section Grand Total Word and Structure Knowledge, Reading Achievers Section Grand Total

2019

Total Marks

30

1

30

5 35

2

10 40

45

1

45

5 50

3

15 60

CLASS 7

Contents ÂÂ IMO - Level-2 (2014) ÂÂ IMO - Level-2 was an online exam. (2015) ÂÂ IMO - Level-2 (2016) ÂÂ IMO - Level-2 (2017) ÂÂ IMO - Level-2 (2018) ÂÂ IMO - Level-2 (2019)

2019

LEVEL - 2 Year 2013-14 2019

2

7th IMO | Class-7 | Level 2

logical reasoning logical reasoning 1.

If O = 16, FOR = 42, then what is FRONT equal to?



A. B. C. D.

2.

A girl introduced a boy as the son of the daughter of the father of her uncle. The boy is girl's



A. B. C. D.

3.

Seven people – A, B, C, D, E, F and G – are standing in a single line, facing a booth. E is somewhere ahead of F. There is exactly one person standing between C and G. D is immediately behind A. F is behind both B and D. If D and C are fourth and fifth in line respectively, then which of the following must be true?



A. B. C. D.

4.

Rakesh's school bus is facing North when it reaches his school. After starting from Rakesh's house, it turns right twice and then left before reaching the school. What direction was the bus facing when it left the bus stop in front of Rakesh's house?

61 65 73 78

Son Uncle Nephew None of these

F A F B

is is is is

seventh first sixth first



A. B. C. D.

Five Two Three Four

7.

Find the missing number in the given number pattern.



A. B. C. D.

8.

Select the figure from the options that will replace the question mark(?) to continue the series in Problem Figure.

68 27 19 58

A.

B.





C.



A. B. C. D.

5.

In a school, the following codes were used during physical exercise. '1' means 'start walking', '2' means 'keep standing', '3' means 'start running at the same spot', '4' means 'sit down'. How many times will a student who performs the following sequence without error from the beginning to the end have to sit down?

9.

West East South North

1 2 3 4 2 3 1 4 4 3 2 2 1 2 4 3 1 4 4 1 2

A. B. C. D.

3 2 5 4

6.

How many pairs of alternate numbers have a difference of 3 in the given series?

D.





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

A.

B.





C.

D.







10. Count number of straight lines required to make given figure.

6 4 1 2 2 8 7 4 2 1 5 3 8 6 2 1 7 1 4 1 3 2 8 6

2019



A. B. C. D.

14 13 11 12

3

7th IMO | Class-7 | Level 2

11. Unscramble the letters in the given words and find the odd one out.

A. B. C. D.

nrtiagle ubnmer getracnle irclce



2 6



B. D.

3 4

13. S e l e c t a n o p t i o n w h i c h w i l l m a k e u p t h e Figure (X).

A.

B.



D.



D.









16. Study the figure given below and answer the following question. What is the sum of the numbers which belong to one figure only?

A. B. C. D.

20 16 21 27

17. If ÷ means +, – means ÷, × means – and + means ×, (36 × 4) − 8 × 4 then =? 4 + 8 × 2 + 16 ÷ 1 A. 0 B. 8 C. 12 D. 16 18. There is a certain relationship between the figures (i) & (ii) and (iii) & (iv). Identify the relationship and find the figure from the options which will replace the question mark in figure (iv).



C.





Which number lies at the bottom face in position X? A. C.

B.

C.

12. 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.



A.



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

A.

B.





C. A.

B.



C.



D.





19. Insert the missing character, if the same rule is followed in (i), (ii) and (iii).

D.







15. Select a figure from the options which will continue the series established by the Problem Figures.



A.

10



B.

15



C. D.

20 25

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

2019

A. B. C. D.

8 9 12 15



4

7th IMO | Class-7 | Level 2

Mathematical reasoning

21. The value of 1 +



A.

1 1+

1

1−

1 16

5 3 7 + 4 − 2 + 3 is ____. 2 8 8

1976 264

B.

16 11



C.

145 24



D.

294 31





Step 1 : Let the unit’s digit be x. Step 2 : Then, ten’s digit = (9 – x) \ number = 10 × (9 – x) + x ⇒ 90 – 10x + x = (90 – 9x) Step 3 : Adding 27 to the number 90 – 9x we get 117 – 9x Step 4 : Number with digits interchanged is 10x + (9 – x) = 9x + 9 Step 5 :127 – 9x = 9x + 9 Step 6 : Therefore unit’s digit = 6 and ten’s digit = 3 Step 7 : Hence the number = 36. A. Step 7 B. Step 5 C. Step 4 D. Step 3 and step 6

23. Which of the following shaded fraction represents



A. B. C. D.

` 125 ` 167.50 ` 150 None of these

26. PQRS is a rectangle. E and G is the mid-point of SR and PQ respectively, PF = FR. The ratio of total area of triangle PFQ and triangle FER to area of rectangle PQRS is ______.

22. A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Given below are the steps to find the number. Identify the wrong step.

25. A person borrows ` 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 1 6 % p.a. for 2 years. Find his gain in the transaction 4 per year.



A. B. C. D.

9: 4 3:8 5 : 8 None of these

27. The figure shows a trapezium PQRS whose lengths are in centimetres. If area of PQRS is 72 cm2 , find the value of x.

A. B. C. D.

2 4 6 8

28. The median of the given data is

98, 75, 96, 180, 270, 102, 94, 100, 610, 200, 75, 80 A. B. C. D.

100 98 97 99

 1   1   1  1   2  1 −  1 −  1 −  ....... 1 −   ?         2 3 4 10 

29. What percentage of numbers from 1 to 70 have squares that end in the digit 1?

A.



C.









B.



D.



A.

292°



B.

122°



C.

112°



D.

120°

1% 14% 20% 21%

30. The circumference of two circles are 44 m and 88 m. Find the difference in the areas of the circles.

24. Find x in the given figure.

A. B. C. D.



2019

A. B. C. D.

142 642 462 426

m2 m2 m2 m2

5

7th IMO | Class-7 | Level 2

31. Simplify : 2p3 A. B. C. D.





+ 8p2 – 7p + 15 – 6p3 – 5p2 – 8p + 7 + 16p – 9 4p3 + p – 3p2 + 4 –4p3 – 3p2 – p + 13 –4p3 + 3p2 + p + 13 4p3 + 3p2 – p + 13

32. Match the columns.

(a)



(b)



(c)



A. B. C. D.

Column I (Solid)



(a) (a) (a) (a)

→ → → →



34. ln the figure (not drawn to scale), ABCD is a parallelogram with AB = BD = CD and ADEF is a trapezium with AD parallel to FE. Find the value of y and z respectively.

(i)





Column II (Top view)

What fraction of the total number of apples were rotten? A. 6/175 B. 4/175 C. 3/139 D. 2/171

(ii)

(iii)

(i); (b) → (iii); (c) → (ii) (ii); (b) → (iii); (c) → (i) (ii); (b) → (i); (c) → (iii) (iii); (b) → (i); (c) → (ii)

33. The bar graph shows the number of rotten apples in 7 boxes. There are 100 apples in each box.



A. B. C. D.

35. The given figure is formed by two identical circles in a rectangle. E and F are the centres of the circles. 22 Find the area of the shaded part (Take π = ). 7







86°, 45° 104°, 30° 112°, 15° 104°, 12°

A. B. C. D.

330 336 236 300

cm2 cm2 cm2 cm2

EVERYDAY MATHeMATICS 36. Rohan has just finished reading 204 pages of a storybook. He plans to finish reading the rest of the book in the next 7 days by reading the same number of pages each day. If he reads 35% of the book in the next 5 days, how many pages does the book have?

A. B. C. D.

300 400 500 600



A.

48



B.

105



C.

112



D.

168

38. Niketan bought 8 shirts and 6 pairs of pants. Each shirt costs ` 126 and the 8 shirts cost twice as much as the 6 pairs of pants. How much did he pay for the 8 shirts and 6 pairs of pants ?

37. There are some sweets in a jar. The sweets can be put into boxes of 3 or 7 with no sweets left over. When the sweets are put into boxes of 20, there are 5 sweets left over. What is the smallest possible number of sweets in the jar?

2019



A.

` 1478



B.

` 2180



C.

` 840



D.

` 1512

6

7th IMO | Class-7 | Level 2

39. 0.6 of the pupils in a class like to play badminton. 1 of the remaining pupils like to play basketball, 6 2 pupils like soccer and 8 pupils like table tennis. How many pupils like to play badminton?



A. B. C. D.

10 18 30 40

A. B. C. D.

3.3 4.8 6.6 7.4 th

1 41. Sneh's age is   of her father's age. Sneh's father's 6 age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated two years before, then what is Sneh's present age?

A.



B. C. D.

A.



B.



C. D.

58% 2 % 3 60% 78% 62

43. Rihana took a loan of ` 1200 with simple interest for as many years as the rate of interest. If she paid ` 432 as interest at the end of the loan period, what was the time?

40. The marks scored in an examination are converted from 50 to 10 for the purpose of internal assessment. The highest marks were 47 and the lowest were 14. The difference between the new maximum and the minimum internal assessment scores is _______.



2 years 3 24 years 30 years 5 years 6

42. 1100 girls and 700 boys are examined in a test; 42% of the girls and 30% of the boys failed. The percentage of the total who pass is ______.



A. B. C. D.

3.6 years 6 years 18 years Cannot be determined

44. A park, square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road?

A. B. C. D.

576 metres 600 metres 670 metres None of these

45. A card is drawn from a pack of 52 cards. The probability of getting a queen is ________.

A.



B.



C.



D.

1 13 6 13 1 26 1 52

Achievers section 46. Study the figure carefully.

Find : (a) the perimeter (b) the area a A. 329 m B. 329 m C. 156 m D. 166 m

b 547 297 740 740

47. In the given question below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

In how many years will a sum of money put at simple interest treble itself?



I.



The rate of interest is 12 1 % . 2 III. The sum doubles itself in 8 years at simple interest. A. Any one of the three B. Any two of the three C. I and II only D. II and III only

2

m m m2 m2



2019

II.

The interest earned in 4 years is half the sum.

7

7th IMO | Class-7 | Level 2

48. Read the statements carefully and select the correct option. Statement-1 :

124 × 93 × 4 63 × 82 × 27

+

2 × 34 × 25 9 × 42

7

 x −1 y 2   x3 y − 5  Statement-2 : If  2 −4  ÷  −2 3  x y  x y 

then A. B. C. D.

= 198

A.

= x p ⋅ yq

p = 4 and q = 2 Statement-1 is true and statement 2 is false. Statement-1 and 2 are true . Statement-1 and 2 are false. Statement-1 is false and statement-2 is true.

=1

B.



C.



D.

=1 = 11 2

−5

49. Select the incorrect match of shaded fraction.



2 3

3 5

50. Fill the blank. The value of the product of two ____________ fractions is __________ each of the two fractions.

A. B. C. D.

SPACE FOR ROUGH WORK

2019

=1

Improper, more than Proper, more than Improper, less than Proper, equal to

LEVEL - 2 Year 2015-16 2019

Mathematics 1.

Which of the following sign will replace * in 2 × 6 – 12 ÷ 4 * 2 = 5 * 6? A. + B. – C. × D. ÷

2.

Which of the following options hold? Statement - 1 : 24 is divisible by 4 and the factors of 4, i.e. 0, 1, 2, 4, 8 also divide 24.



Statement - 2 : If a number is divisible by another number, then it is divisible by each of the multiple of that number.



A. B. C. D.

3.

In the given figure, ∠AOB = 2∠BOC, ∠AOE = 3∠BOC, ∠EOD = 4∠BOC, ∠DOC = 5∠BOC. Find 2∠AOB + 3∠BOC.

Both Statement-1 and Statement-2 are true. Statement-1 is true and Statement- 2 is false. Statement-1 is false but Statement- 2 is true. Both statement-1 and Statement- 2 are false.



A. B. C. D.

122° 124° 168° 180°

4.

Find the value of the expression.



–1152 + (–118) – (–32) – (13) – (–56) – (–2183) + 5



A. B. C. D.

5.

The H.C.F. and L.C.M of 23 × 32 × 5 × 11, 24 × 34 × 52 × 7 and 25 × 33 × 53 × 72 × 11 respectively are _______.



A. B. C. D.

–993 –3137 993 389

23 25 23 25

× × × ×

32 34 32 34

× × × ×

5; 22 × 33 × 52 × 7 53, 23 × 33 × 53 × 72 × 11 5, 25 × 34 × 53 × 72 × 11 53 × 72 × 11, 23 × 53 × 72 × 11

2

6.

Which of the following number sentence is represented on the number line shown below?



A. B. C. D.

7.

What percentage of the given figure is shaded?



A. B. C. D.

8.

 96.54 − 89.63 965.4 − 896.3  The value of 10 −3 ×  ÷ = __ ____  96.54 + 89.63 9.654 + 8.963  is equal to ______.



A. B. C. D.

9.

In the given figure, ABCD is a parallelogram, BFE is a right-angled triangle and GAD is a straight line. Find x.



A. B. C. D.

– 2 + (– 3) = 1 1 + (– 2) = – 2 1 – (+ 2) = – 1 None of these

38% 60% 40% 50%

10–4 10–1 10 10–5

30° 31° 32° 33°

m + 2 p m + 2q 4 pq + = , then the value of 10. If m = m − 2 p m − 2q p+q _____.

A. B.

2 4



C.

2mpq ( p + q)



D.

None of these | 9th IMO | Class-7 | Level 2

2019

11. The parking fee of a certain car park is as follows: For the 1st hour ` 2.50 For every additional half an hour or part ` 0.90 thereof

If Kartikay parks his car in the car park for 5 hrs 50 mins, how much must he pay?



A. B. C. D.

` ` ` `

8.75 9.90 11.50 17

12. Aman, Rahul, Raj and Nikhil each took the same spelling test. F Aman spelled 7/10 of the words correctly. F Rahul spelled 3/4 of the words correctly. F Raj spelled 4/5 of the words correctly. F Nikhil spelled 2/3 of the words correctly.

Who spelled the least number of words correctly and arrange their fraction in ascending order?



A.



B.



C.



D.

Aman, 7 < 3 < 4 < 2 10 4 5 3 3 2 4 7 Rahul, < < < 4 3 5 10 2 Raj, < 3 < 7 < 4 3 4 10 5 2 7 3 4 < < Nikhil, < 3 10 4 5

a+b+c 13. If a = b = c , then   c 3 4 7 A. 17 B. 16 1 C. 16 D. 2

4

is equal to ____ .

D.



A. B. C. D.

660 30 650 100

17. A b o y m u l t i p l i e d 9 8 7 b y a n i n t e g e r a n d obtained 559981 as his answer. If in the answer both 9’s are wrong and the other digits are correct, then the correct answer would be ______.

A. B. C. D.

553681 555181 555681 556581

 3 1 ÷ 1 1 of 5 1  2 2 3  2 is _______ . 18. The value of of   2  2 1 + 1 1 of 3 1  2 2 2 A. 56 99 56 B. 1023 28 C. 341 D. 182 31 19. Find the sum of ∠ a, ∠ b, ∠ c and ∠ d.

14. Latika has to type a 5-pages document. Each page contains an average of 840 words. How long will she take to type the whole document if she types at the rate of 30 words per minute? 1 A. 1 hrs 12 1 B. 2 hrs 3 1 C. 1 hrs 2

16. If RS || PQ and RT || UQ, then find the value of 8x – 2y.

3 2 hrs 4

15. Find the value of 2 x − 9 . 5 A. 92 B. 22 C. 112 D. 43



A. B. C. D.

280° 290° 360° 240°

20. Read the below statement carefully and complete it by selecting the correct option. Parth purchased a machine for ` 80,000 and spent ` 5000 on repairs and ` 1000 on transport and sold at ` 1,07,500. He earns _______ on this transaction.

A. B. C. D.

Profit Profit Profit Profit

of of of of

` ` ` `

32000 25900 21500 19500 3

9th IMO | Class-7 | Level 2 |

2019

21. Shalini borrowed ` 800 which amounts to ` 1164 in 1 3 yrs. What would be the amount in 5 1 yrs? 2 2 A. ` 1800 B. ` 364 C. ` 1372 D. ` 850 22. Two numbers are in the ratio 5 : 3. If 10 is subtracted from both the numbers, their ratio changes to 5 : 7. The sum of numbers initially was ______. A. 8 B. 15 C. 13 D. 12 23. Anshu started a business investing ` 2,25,000. After 6 months Divya joined her with ` 3,25,000. Out of a annual total profit of ` 19995, Divya's share is _____ .

A. B. C. D.

` 15400 ` 17200 ` 19600 None of these

28. A boy was asked to write the value of (3)5 × (9)2 . He wrote it as 3592. The difference between the obtained value and the actual value is _____.

A. B. C. D.

29. The value of 4 x − 3 , if 2 ______.

A.



B.



C.



D.

A. B. C. D.

48 24 56 72

() () () 8 5

3

×

8 5

−6

=

5 8

1− 2 x

is

0 5 2 −1 5 −7 2

30. The given figure shows a triangle and a circle enclosed in a square. Find the area of the shaded parts. (Take p = 3.14)

24. If three quarters kg of sugar costs 90 paise, then how many paise will 200 gm cost?

0 16091 3592 4560

paise paise paise paise

25. In the given figure, ABF is a straight line. If AB = AC, then ∠ACB – ∠DBF is _____.

32 cm



A. B. C. D.

16 cm

200.96 cm2 712.96 cm2 512 cm2 818.42 cm2

31. Which of the following is correct with respect to shaded part of a figure?

A. B. C. D.

30° 20° 10° 15°

26. If books bought at price ranging from ` 200 to ` 350 are sold at price ranging from ` 300 to ` 425, what is the greatest possible profit that might be made in selling eight books ?

A. B. C. D.

` ` ` `

400 600 1800 2000



A.



B.

=

4 9



C.

=

5 10



D.

=

7 10

=

3 12

27. Which of the following is true for the value of 4xy(x – y) – 6x2 (y – y 2) – 3y 2 (2x2 – x) + 2xy(x – y).

A. B. C. D.

–195 for x = 0 & y = 1 2535 for x = 1 & y = 0 –2535 for x = 5 & y = 13 7605 for x = 13 & y = 5

4

| 9th IMO | Class-7 | Level 2

2019

32. A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet ? (Take p = 3.14)

A. B. C. D.

78.5 cm2 23.44 cm2 87.92 cm2 26.54 cm2

33. The average cost of a shirt, skirt, blouse and a pair of pants is ` 73.50. If the average cost of the shirt, skirt and blouse is ` 72, find the cost of the pair of pants.

A. B. C. D.

` ` ` `

294 216 78 511

34. Mohit spent 45% of his salary on a laptop. If Mohit had ` 1980 left from his salary after buying the laptop, how much was his salary?

A. B. C. D.

` ` ` `

38. The given table shows the charges for parking a car in a mall. Time

Cost

8 a.m. - 5 p.m.

80 paise per half an hour

After 5 p.m.

` 2.15



Priya parked her car from 11.30 a.m. to 6.15 p.m. If she gave a ` 100 note to pay parking charges, then how much did she get back after payment?



A. B. C. D.

` ` ` `

80.30 80.95 85.85 89.05

39. In the given figure (not drawn to scale), ADE is an isosceles triangle, BCA is a right-angled triangle, FBA and ACD are equilateral triangles. If ∠ADE = 45° and ∠ABC = 52°, then find x.

2420 3069 2871 3600

35. Find the range, mean, median and mode respectively of the given data :

75, 200, 98, 75, 100, 98, 75, 96, 180, 270, 102, 94, 100, 610, 200, 75, 80



A. B. C. D.

355, 160, 100, 100 535, 148.70, 98, 75 535, 132.2, 97, 200 5, 150.29, 99, 75

36. Two unbiased dice are tossed. What is the probability of getting a product divisible by 3?

A.



B.



C.



D.

11 36 7 18 5 9 15 36

A.



B.



C.



D.

1 2 3 13 2 3

A. B. C. D.

38° 40° 60° 44°

40. If one angle is the average of the other two angles and the difference between the greatest and least angles is 60°, then the angles of the triangle are in the ratio_____ .

37. Find the probability of drawing a face card from a deck of 52 cards.



A. B. C. D.

1 1 1 5

: : : :

2 4 2 7

: : : :

3 13 5 11

41. If 6(3x + 2) –5(6x – 1) – 12x = 6(x – 3) –5(7x – 6), 2x − 3 . then find the value of 4x − 3 A. 2/7 B. –1 C. 5/7 D. –5/7 42. If 20% of b = a, then a% of 20 is the same as _____.

1 4

A. B. C. D.

4% of b 5% of b 20% of b None of these 5

9th IMO | Class-7 | Level 2 |

2019

43. Naman bake cakes in a microwave. The microwave takes 10 minutes to warm up before the first tray of cake is baked. Each cake takes 20 minutes to bake. Which of the following tables show the relationship between the number of cakes Naman bakes and the total microwave time?

A.



B.



C.



D.

44. If p : every fraction is a rational number and q : every rational number is a fraction, then which of the following options hold?

A. B. C. D.

p is true and q is false. p is false and q is true. Both p and q are true. Both p and q are false.

45. A cricket team won 3 matches more than they lost. If a team win gives them 2 points and loss (–1) point, how many matches, in all, they have played if their score is 23?

A. B. C. D.

17 20 37 40

Achievers section 46. Which of the following shaded fraction represents   1 1 1 4  1 −  1 −  1 −  ....... 1 − 1   ?  10    2   3   4 

A.



B.



D.

47. PQRS is a rectangle. E, F and G are the mid points of SR, PR and PQ respectively. The ratio of area (PSEF) to area of rectangle PQRS is ______.



A. C.



What is the principal sum?



I.

The sum amounts to ` 690 in 3 years at S.I.



II.

The sum amounts to ` 750 in 5 years at S.I.



III. The rate of interest is 5% p.a.

C.



48. Given below a question is followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

9:4 5 : 8

B. D.

3:8 None of these

6



A. B.

Only I and III Only II and III



C. D.

Only I and II Any two of the three

3 2 ) − (2 1 ) ( 3 2 49. Find the value of (4 34 ) − (3 13 )

A.

37 97



B.

74 97



C.

1



D.

None of these

2

2

2

2

32−21 2 . ÷ 3 3 1 4 −3 4 3

23 74

| 9th IMO | Class-7 | Level 2

2019

50. A scientist is comparing the weights of the four molecules listed in the given table.

Which one of these molecules is the lightest?



A. B. C. D.

Salt Pure water Hydrochloric acid Potassium hydroxide

SPACE FOR ROUGH WORK

7

9th IMO | Class-7 | Level 2 |

2019

LEVEL - 2 Year 2016-17 2019

MATHEMATICS 1.

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

A. –2.5



A. 1 and 3 only



B.

2 only



C.

4 only



D. 6 only

5.

In the given figure (not drawn to scale), PQRS is a rhombus, RST and PSV are isosceles triangles, STUV is a square and QRT is a straight line. Find ∠PSR + ∠SPV.

B. 2.2 C. –0.8 D. 1.4 2.

Which of the following rational numbers do not lie 4 11 ? between and 33 25

2 A. 25 14 B. 33

A. 72°

4 C. 13

C. 108°

B. 54° D. 36°

7 D. 25 3.

In the given figure, state whether the triangles are congruent, if yes find the correct order of vertices.



A.

Yes, DPQR @ DSRT 



B.

No, they are not congruent



C.

Yes, DRST @ DRPQ



D.

Yes, DSTR @ DRPQ

7.

A bottle is

How many more triangles in the given figure must be shaded to make the fraction of unshaded part equal 5 to ? 8

A. 3 B. 4 C. 2 D. 5 4.

6.

27 x + 5 = 6 x + 5 following steps are involved. 3 Which of the following step(s) is incorrect ? To solve

Step 1 : 27x + 5 = 3(6x + 5)

1 A. 4

Step 2 : 27x + 5 = 3 × 6x + 5

1 B. 3

Step 3 : 27x + 5 = 18x + 15 Step 4 : 27x – 18x = 15 – 5

1 C. 6

Step 5 : 9x = 10 Step 6 : x =

3 full of soft drink. The drink in the bottle 4 can fill 6 glasses. If the drink in the bottle is poured out to fill 4 glasses, find the fraction of drink left in the bottle.

10 9

1 D. 2

2

| 10th IMO | Class-7 | Level 2

2019

8.

The average of 5 numbers is 6x. If four of them are x, 7, 6, 4, then find the fifth number. Give your answer in terms of x.

17 + x A. 5

B.

A. ` 6000 B. ` 6500 C. ` 7500

29x – 17

D. ` 5500

C. 6x – 17 D. 5x – 17 9.

13. Sam sold a guitar at a profit percentage of 25%. If he earns the profit of ` 1500, then what was the selling price of the guitar?

The given figure shows a circle, centred at O, enclosed in a square. Find the total area of shaded parts.

14. If the hypotenuse of a right angled triangle is 5th multiple of remainder of (2379 ÷ 4) and one of its sides is the highest common factor of 18 and 27, then what is the length of the other side (in cm)? A. 12 B. 15 C. 18 D. 10



A. 121 cm2



B.

2

145 cm



C.

130 cm2



D. 119 cm2

15. The ages of 9 students are given as 18, 27, 18, 18, 19, 26, 26, 19 and 36. Find the mean, mode and median respectively.

37 1 = 2+ 10. If , then (b + c) (11a –13) 1 13 a+ b+c is equal to



A.

20, 18, 18



B.

23, 18, 19



C.

23, 18, 18



D.

19, 19, 18

16. A cube is rolled, if the numbers –1, –2, 0,1, –2, 3 are written on the faces of cube, then

A. –11 B. 5 C. 11



(i)

D. –4



(ii) Find the probability of getting 3.

11. A long metallic wire of length x 2y + 5xy + 6xy 2 is bent in the form of a triangle. If the two sides are 3xy + 4x 2y and 2x 2y + 2xy, then find the length of third side.

A.

6x2y + 5xy

B. 4xy2 – 3x2y 2

D. 4x2y – 3xy2 + 5xy 12. In a zoo, the ratio of the deers and elephants was 3 : 4. When two new deers are added to the group, the ratio of the deers to the elephants becomes 4 : 5. How many deers and elephants respectively are there in the zoo now?

A.

32, 40



B.

30, 40



C.

30, 42



D.

32, 42

(i)

(ii)

A. 1/6

1/3

B. 1/3

1/6

C. –2/6

3/6

D. –4/6

3/6

11  −1  17. Subtract   from and add the result in addition  9  12

C. 6xy – 5x y 2

Find the probability of getting –2.

5 1 of  and  . 8 2 1 A. 8 113 B. 72 9 C. 113 263 D. 72 3

10th IMO | Class-7 | Level 2 |

2019

18. When two parallel lines are cut by a transversal, which pair of angles will always be supplementary?

A. Corresponding angles



B.

Alternate angles



C.

Vertically opposite angles



D. Interior angles on the same side of the transversal

B. C.

19. Garima bakes a cake, she uses 250 g brown sugar in 1 kg of flour. Find the ratio of

(i)

Sugar to flour



(ii) Flour to sugar



(iii) Sugar to the amount of sugar and flour together (i) (ii) (iii)

D.

23. The teacher tells the class that the highest marks obtained by a student in her class is four times the lowest marks plus 5. The highest marks is absolute value of (–6 × 13), find the lowest marks. A. 18.25



A. 4 : 1

1 : 4

1:5

B. 40



B. 3 : 2

3 : 2

2:5

C. 36.5



C. 2 : 3

3 : 2

2:5

D. 25



D. 1 : 4

4 : 1

1:5

24. In a school, 10x 2 + 3xy + y 2 , 2x 2 + 9x + 2yx and 7x 3 + 8xy + 2y 3 students are enrolled for NCO, NSO and IMO respectively. Find the total number of students enrolled for all the three exams when x = 2 and y = 3.

20. Find the value of P, Q and R.

A. 321 B. 263 C. 261 D. 250 P

Q

a c and , if ad > bc, then b d _____ and if ad < bc, then ______.

R

25. In two rational numbers

A. 4 5 1 B. 5 8 1

a c a c A. < and < b d b d

C. 7 2 6 D. 8 2 4  1  1 1 1 1 21. Solve :  3 ÷ 1 −  2 − −  4  4 2 2 4

1     6  

A. 78

a c a c B. > and < b d b d a c a c C. > and > b d b d

B. 100



C. 128

26. Two towers 18 m and 28 m high stand upright on a ground. If their feet is 24 m apart, then the distance between their tops is _______.

D. 26 2x + 7 2x + 3 , then find the value of x and correct = 3 2 representation on the number line.

22. If

A.



4

D. None of these



A. 26 m



B.

24 m



C.

8m



D. 18 m | 10th IMO | Class-7 | Level 2

2019

27. Select the correct option.

32. If the average of first 50 natural numbers is 25.5, then sum of numbers is _______.



A. Orthocentre is the point of intersection of the perpendicular bisectors of the sides of a triangle.



B. Incentre is the point at which the three angle bisectors of a triangle meet.

B. 2550



C. Circumcentre is the point at which the medians of triangle meet.

D. 1470



D. Centroid is the point at which the altitudes of a triangle meet.

A. 1275 C. 1500

(Direction 33-35) : Study the given graph and answer the following questions.

28. The number of diagonals drawn from one vertex of a polygon of 17 sides is _______. A. 16 B. 15 C. 14 D. 17 4

 32   16  29. If  ×   243   81 

x+2

16

4 =  9

, then find the value

2

 x2 + x + 1  of  .  x 2 + x − 1  9 A. 4 3 B. 2

33. What fraction of students like Science to the students like English? 3 A. 5

C. 9 1 D. 3

2 B. 1 5

30. If two third of a number, half of the same number and one seventh of the same number and the number itself are added, the result is 3 less than 4th multiple of 10. The number is _______. 2 97 2 B. 16 97 2 C. 18 97 2 D. 17 97

A. 14

A. A right angled triangle



B.

An isosceles triangle



C.

An equilateral triangle



D. A scalene triangle

2 D. 5 34. Ratio of students who like Social Science and Hindi together to the students who like English, Mathematics and Science together is _______.

31. In ______ the incentre of triangle coincides with its circumcentre, orthocentre and centroid.

5 C. 3



A. 25 : 34



B.

33 : 22



C.

5:3



D. 3 : 5

35. What percent of students like Hindi?

A.

18.64%



B.

19.35%



C.

10.50%



D.

20.12% 5

10th IMO | Class-7 | Level 2 |

2019

36. 35% of the total population of a town are men and 25% are children. If 7,00,000 are men, then what is the total population of the town?

A. 1683



A.

20,00,000

D. 1263



B.

25,00,000



C.

11,00,000



D.

2,00,000

37. In the given figure (not drawn to scale), ABCD is a rhombus, FHI is an equilateral triangle and CEFG is a trapezium with EC parallel to FG. DCFI, BCG and GFH are straight lines. Find ∠CGF and ∠ECF.

B. 423 C. 1983

41. In a two digit number, ten's digit is twice the unit digit. The number formed by interchanging the digits is 27 less than the original number. The original number is ______. A. 36 B. 63 C. 84 D. 42 42. In a DABC, which of the following conditions holds? A. AB – BC > CA B. AB + BC < CA C. AB – BC < CA



A.

100°, 46°



B.

48°, 60°



C.

48°, 58°



D.

72°, 120°

D. AB + CA < BC 43. The marked price of an article is 12% higher than cost price. A discount of 10% is given on the marked price. In this kind of sales, the seller _______.

38. The value of x such that 2x + 3 = [(–4) × (–9) × (–25)] × [(–8) × (–1) × (–2) × (–5) × (0)] is _____. A. 0 −3 B. 2



A. Loses



B.

Bears no gain, no loss



C.

Gains



D. Data inadequate 1

 x a  ab 44.  b  x 

2 C. 3

1

 x b  bc  c  x

1

 x c  ca  a  = _______ . x

A. 1

3 D. 2 39. The price of an object A is ` 100 less than 6 times the price of an object B. A similar set of one object A and 4 object B is priced at ` 1400. Find the price of object A. A. ` 750

1 B. abc x 1 C. ab + bc + ca x ab D. ab + bc x 45. Solve : 999 1 + 999 2 + 999 3 + 999 4 + 999 5 + 999 6 7 7 7 7 7 7

B. ` 600 C. ` 850 D. ` 800

A. 5997

40. Find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder. 6

B. 5994 C. 5979 D. 2997 | 10th IMO | Class-7 | Level 2

2019

ACHIEVERS SECTION Statement-1 : Mode is most frequently occurring value in a given data. It is always less than the median of the data.

46. In the given figure (not drawn to scale), PQRS is a square with QT = QU. If SR = (7x – 6) cm and SP = (2x + 9)cm, then find

Statement-2 : Median of the data (1, 2, 2, 3, 2, 3, 4, 2, 3, 2, 2, 3, 2, 1, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3) is less than the mode.

The value of x



(i)



(ii) Area of DTRQ

(iii) ∠QTU and ∠UTR

A. Statement-1 is true and Statement-2 is false.



B.

Statement-1 is false and Statement-2 is true.



C.

Both Statement-1 and Statement-2 are false.



D. Both Statement-1 and Statement-2 are true.

49. Find the values of P, Q, R and S.

(i)



(ii) 56.25 cm2

A. 3

2

(iii) 60°, 30°



B.

3

56.25 cm

67.5°, 22.5°



C.

5

65.75 cm2

67.5°, 25.5°



D. 5

65.75 cm2

80°, 20°

Principal

Rate p.a.

Time

Simple Interest

Amount

` 6000

P

4 years

Q

` 7200

R

12%

3 years 4 months

S

` 17584

P

Q

R

S

47. Match the following:



A.

5%

` 1000

` 15,024

` 4250

Expression

Value of x



B.

5%

` 1200

` 12,560

` 5024

5 9 x × 35 × ( 27)3 (P) 2 = 27 (i) 4 3 (3) × (81)



C.

4%

` 1800

` 12,560

` 5024



D.

4%

` 1100

` 14,231

` 4250



(Q) 25(x + 3) = (5)3x – 5

9 (R)   4

2x

50. Find the value of x + y in the given figures.

(ii) 11

6  256  2 7 ÷ = 10 (iii)   81  3 2

(S) 2x = (32)1/3

(iv)

−7 2

A. P → (ii) ; Q → (i) ; (R) → (iv) ; (S) → (iii) B. P → (i) ; Q → (ii) ; (R) → (iii) ; (S) → (iv) C. P → (iv) ; Q → (iii) ; (R) → (ii) ; (S) → (i)

(a)

(b)

D. P → (iii) ; Q → (ii) ; (R) → (iv) ; (S) → (i)

A. 128°

114°

B. 130°

90°

C. 80°

66°

D. 114°

128°

48. Read the statements carefully and select the correct option.

SPACE FOR ROUGH WORK

7

10th IMO | Class-7 | Level 2 |

2019

LEVEL - 2 Year 2017-18 2019

MATHEMATICS 1.

Which of the following statements is false ?

6.

−5 8

A. lies to the left of 0 on the number line.

3 lies to the right of 0. 7 1 1 C. The rational numbers and − are on opposite 2 2 sides of 0 on the number line.



B.





D.

5 5 and − is not zero. 3 3

2. If X is the smallest five digit number formed by all the digits 0, 3, 5, 7, 2 (using each digit only once) and Y is the greatest five digit number formed by all the digits 0, 5, 7, 9, 1 (using each digit only once). Then find Y – X. A. 64741 B. 77144 C. 66938 D. 77153 3.

b The statement form of the equation –3 = 0 is given 5 by



A. B. C. D.

4.

In a class of 56 students, if 3 of the total students 8 1 like Tennis, of the total students like Chess and the 8 remaining like Basketball, then



4, 3, 5, 2, 1, 1, 3, 4, 6, 1, 3, 5, 6, 5, 5 Find the mean, median and mode respectively of the given data.

On the number line,

Sum of rational numbers

Taking away 5 from three times a number b gives 0. Taking away 3 from one-fifth of a number b gives 0. Five times of a number b is 3. Sum of one-fifth of a number b and 3 is 0.

(i)

How many less students like Tennis than Basketball? (ii) What is the ratio of the students who like Chess to the students who like Basketball? (i) (ii) A. 8 2:3 B. 7 4:1 C. 10 3:2 D. 7 1:4 5.

Subtract (4a – 2b + 3c) from the sum of (a – 2b), (3a – 4b + c) and (5a – 2b + 3c).



A. 4a B. 5a C. 3a D. 3a

+ 6b – – 6b + – 2b + + 2b –

c c 4c 4c



A. B. C. D.

7.

In the given figure, if ∠ABC = 60°, then find x.

3.6, 4, 5 3, 4, 5 3.6, 5, 4 4, 6, 5 A x 90°

140° 30°

C

B



A. 50° B. 60° C. 40° D. 30°

8.

The following are the steps involved in finding the positive value of x from the equation x2 = 23.04. Arrange the steps in a sequential order.



(i)



(ii) x = 4.8



(iii) x2 = 23.04 =



(iv) x =



A. B. C. D.

9.

Which of the following statements is INCORRECT?



A.







2

A dice was thrown 15 times and following outcomes were noted:

x = 2

(iii) (iii) (iii) (iii)

( 48)2 (10)2 2304 100

48 10 → (iv) → (i) → (ii) → (i) → (ii) → (iv) → (i) → (iv) → (ii) → (iv) → (ii) → (i)

Two triangles are congruent if the two sides and one angle of first triangle are equal to the corresponding two sides and one angle of the other triangle. B. Two right triangles are congruent if the hypotenuse and one side of the first triangle are equal to the corresponding hypotenuse and one side of the other triangle. C. Two triangles are congruent, if the three sides of one triangle are equal to the corresponding three sides of the other triangle. D. None of these | IMO | Class-7 | Level 2

2019

10. Which of the following letters have both line of symmetry and rotational symmetry? A.

C.



D.

(i) The chosen letter is a vowel. (ii) The chosen letter is not a vowel. (i) (ii) A. 5/9 4/9 B. 4/9 5/9 C. 3/9 6/9 D. 6/9 3/9  3n+ 4 − 3 × 3n 1  12. The value of  + 3  is equal to 3   3 × 3n+3  1 3 A. 0 B. 3n+1  +   2 8 n+ 4  5  3 C.   D. 1 8 13. Calculate the area of the given figures and arrange them in ascending order.

4 cm 2.5 cm

8 cm 7 cm

2.8 cm

(i)

A. B. C. D.

4 cm (ii)

14 cm (iii)

(i), (ii), (iii) (iii), (i), (ii) (iii), (ii), (i) (ii), (i), (iii)

A. 95190 B. 71810 C. 82650 D. 72820

2 3 3 3 + 62 − 4 × 32 ÷ 1 5 7 5

A. <

B. > C. = D. Can't be determined 17. How many more squares must be shaded so that the 2 unshaded fraction of given figure is ? 5



A. 1 B. 2 C. 3 D. 5

18. The ratio between the present ages of M and N is 5 : 3. The ratio between M's age 4 years ago and N's age after 4 years is 1 : 1. What is the ratio between M's age after 4 years and N's age 4 years ago?

A. B. C. D.

2 1 4 3

: : : :

1 3 1 1



A. 3 B. 11 C. 17 D. None of these

20. Find the area of unshaded region (in cm2) for the given figure (not drawn to scale). x cm

a cm

x cm

y cm

15. How many times should a wheel of diameter 7 m rotate to go around the perimeter of a rectangular field of length 70 m and breadth 40 m?

in the given below

19. (461 + 462 + 463 + 464) is divisible by

14. Out of 167000 people in a constituency, 57% are included in the electoral rolls. Find the number of people that are not included in the electoral rolls.

5 3 4 1 × 2 + 51 − 75 ÷ 1 7 8 11

B.

11. A letter is chosen at random from the word ‘EDUCATION’. Find the probability that



16. What should come in place of expression?

A. 5 B. 10 C. 12 D. 8

a cm y cm

A. 4ax + 4ay + a2

B. 2ax + 4ay + a2



C. 2ax + 2ay + a2 D. 2ax + 4ay – a2 3

IMO | Class-7 | Level 2 |

2019

21. Simplify: [(a + b) (a + b)2] ÷ [a2 + 2ab + b2] A. a +b 2

2

26. In the given figure, if QP || TS and ∠QRS = 36°, then find ∠PQR. Q

B. a + 2b C. 2a + b 2

T

2

D. a+b

22.

1 2+ 4 3 5 If x = , then find the value of 3x – 5. 1 2+ 1 3+ 1 1+ 4

A. – 4 B. 5 D. –2 23. A borrows ` 800 at the rate of 12% per annum at simple interest and B borrows ` 910 at the rate of 10% per annum at simple interest. In how many years will their amounts of debts be equal? A.

18 years



B.

20 years



C.

22 years



D.

24 years

x

P

36° R

A. 75° B. 72° C. 45° D. 36°

27. The length and breadth of a rectangular flower bed are 24 m and 5 m respectively. How many squares can be cut from it if each square has side of 2 m?

C. 8





S 2x

A. 30 B. 20 C. 35 D. None of these

28. Two line segments are congruent if __________.

A. B. C. D.

They They They They

are parallel have same length are perpendicular have same initial point

29. Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of same length. What is the greatest possible length of plank?

24. Which of the following is CORRECT? 8 −5 A. and are equivalent rational numbers. 32 25

B.

 −20   −5   2 The value of   ÷    is .  8   3   3



C.

All integers are rational numbers.



D E

C

A

7m 14 m 42 m 63 m

30. Simplify :

  −3 4   9 −10   1 3    −  ×  ×   ×  +  × 5 3   2 4   2 5

1 D. is a rational number. 0 25. In the given figure, ABC is a triangle in which BC is produced to D. If ∠A : ∠B : ∠C = 3 : 2 : 1, and AC ⊥ CE, then find ∠ECD.

A. B. C. D.



A. –1 B. 1 C. Not defined D. 0

  21 3   7 16     ×  −  ×   8 14   9 7

31. Anubhav gets 4 marks for each correctly done question but loses 1 mark for each wrongly done question. He attempts 20 questions and gets 50 marks. How many questions he has attempted correctly?

B

A. 30°



B. 45° C. 60° D. 72° 4

A. 20 B. 18 C. 14 D. 16 | IMO | Class-7 | Level 2

2019

32. The perimeter of the given figure is 18 m and the area 1 of rectangular part ACEF is 8 m 2 . Find the length 2 and breadth of the rectangular part respectively.

A. 2.6 B. –2.4 C. 5.2 D. 3.6 36. If DPQR and DMQR are on the same base QR, PQ = MR and PR = MQ in the given figure, then which of the following gives a congruence relationship? P

M

Q

2 1 2 1 A. 1 m, 5 m B. 5 m, 1 m 2 3 3 2

A. DPQR ≅ DMQR

2 1 1 2 C. 5 m, 7 m 7 m, 5 m D. 3 2 2 3

C. DPQR ≅ DMRQ D. DPQR ≅ DQRM

B. DPQR ≅ DRQM

Direction (33-34) : The given bar graph shows the number of students (in thousands) who opted for three different specializations during the given five years in a university. Study the graph carefully and answer the questions that follows. Hindi

40

English

R

37. If the shaded cubes are removed, which solid will be obtained?

Mathematics

35 Number of students (in thousands)

30 25

20 15 10 5 0

2005

2006

2007 Years

2008

A. 1322 B. 1332 C. 27900 D. Cannot be determined

–4



A. 1 B. 2 C. 3 D. 4

 1  rd

B –5

D.

is   of Manu's expenditure and the sum of their 3 expenditures is ` 3000, then find the salaries of Ram and Manu respectively.

A + D 35. Find the value of  +B.  C 

–6

C.

39. The ratio of Ram's savings to his expenditure is 5 : 2 and that of Manu is 4 : 3. If Ram's expenditure

A. 20000 B. 18000 C. 15000 D. 80000

A

B.

38. Solve for x: (ab–1)2x–1 = (ba–1)x–2

34. What is the average number of students who opted for Mathematics in all the given years together?



2009

33. Out of the total number of students who opted for the given three subjects in the year 2009, 38% were girls. How many boys opted for Mathematics in the same year?

A.

C –3

D –2

–1

0

1

2

3

A. ` 725, ` 6000 B. ` 2625, ` 5250 C. ` 3600, ` 5255 D. ` 800, ` 5250 5

IMO | Class-7 | Level 2 |

2019

40. The given figure shows a circle in the square. Find the total area of shaded part in the given figure.



A. B. C. D.

144 432 576 288

41. Miara starts her journey from Delhi at 10 a.m. to Gurgaon. If her car is running at the speed of x km/hr and at 12 noon she observes that she is 5 km away from Gurgaon. Find the distance between Delhi and Gurgaon.

A. (3x B. (2x C. (5x D. (5x

+ + + +

5) 5) 2) 3)

A. B. C. D.

90 passengers 99 passengers 85 passengers 105 passengers

43. Find the least number which when divided by 35 leaves a remainder 25, when divided by 45 leaves a remainder 35, and when divided by 55 leaves a remainder 45.

12 cm 12 cm

cm2 cm2 cm2 cm2



km km km km

42. A bus starts from a depot filled to capacity. It stops at 1 a station A, where of the passengers alight and 30 3 board the bus. At station B, 1 of the passengers alight 4 and 12 board the bus. At station C which was the last stop, all the 84 passengers alight. What is the capacity of the bus?



A. 3465 B. 4575 C. 3455 D. 3670

44. What must be added to the sum of 2a 2 – 3a + 7, –5a2 – 2a – 11 and 3a2 + 5a – 8 to get 0? A. – 12 B. 12 C. a2 + a D. a–1 45. The selling price of a certain TV is `1700 more than the price the store paid. If the selling price is ` 24000, then price the store paid, is A. ` 22500 B. ` 21300 C. ` 25700 D. ` 22300

ACHIEVERS SECTION 46. The length and breadth of a playground are 100 m and 45 m respectively.

(a) Find the cost (in `) of levelling it at ` 5.50 per sq. m. (b) How much time will a boy take to go four times around the playground, if he walks at the rate of 5.8 m per minute? (a) (b) A. 28320 200 mins B. 24750 200 mins C. 29250 250 mins D. 24750 250 mins 47. When a die is rolled, then match the following. Column-I Column-II P. Probability of getting an even (i) 0 prime number is 1 Q. Probability of getting a factor (ii) 6 of 5 is 1 R. Probability of getting an odd (iii) 2 number less than 1 is 1 S. Probability of getting an odd (iv) 3 number is 6



A. P → B. P → C. P → D. P →

(ii), Q → (iii), R → (iv), S → (i) (i), Q → (iii), R → (ii), S → (iv) (ii), Q → (iv), R → (i), S → (iii) (iv), Q → (ii), R → (i), S → (iii)

48. Read the statements carefully and state 'T' for true and 'F' for false. (a) If

2x − 1 x−2 1 1 + = x− , then x = . 3 4 3 6

(b) If one-fifth of a number is 5 more than one-tenth of the same number, then the number is –10. (c) An equation remains same when the expression on the left and right side are interchanged. (d) If the total of four consecutive odd integers is 40, then the smallest number of them is 7. (a) (b) (c) (d)

A. F

T

F

T

B. T F F T C. F F T T D. F T F F | IMO | Class-7 | Level 2

2019

49. In the given figure, if AB || CD || XY and OC || EB, ∠ABE = 46° and ∠EDC = 33°, then O

B e

Y

E

D

A. e= B. e= C. e= D. e=

50. Read the statements carefully and select the correct option. Statement-I : While dividing a whole number by a fraction, we divide the whole number with the reciprocal of that fraction.

A F

X

Statement-II : The product of a proper and an improper fraction is greater than both the improper fraction and the proper fraction.

C

79°, ∠OCD = 46° 101°, ∠OCD = 33° 89°, ∠OCD = 46° 79°, ∠OCD = 33°



A. B. C. D.

Both Statement-I and Statement-II are true. Both Statement-I and Statement-II are false. Statement-I is true but Statement-II is false. Statement -I is false but Statement-II is true.

SPACE FOR ROUGH WORK

7

IMO | Class-7 | Level 2 |

2019

LEVEL - 2 Year 2018-19 2019

MATHEMATICS 1.

Two unbiased coins are tossed. What is the probability of getting at least 1 tail?

1 A. 4 1 B. 2 1 C. 3 3 D. 4 2.

C. 36 D. 40 6.

In the given figure (not drawn to scale), if ABCE is a parallelogram and BCD is a straight line, then find the value of x. E A

x

2 of 10 Which of the following options represent 5 parts shaded?



B A. 71° B. 109° C. 80° D. 90°

D

A person lent a certain sum of money at 8% simple interest and in 5 years, the interest amounted to ` 300 less than the sum lent. The sum lent was

A.

7.

B.

A. ` 600 B. ` 500 C. ` 350 D. ` 450

C.

8.



C

38°

Which of the following shows the net of the solid given below?

D. All of these 1− x

 27  3. If    8  A. 2 B. 1 C. 3 D. 4 4.

4 ×  9

−x

=

3 , then the value of x is 2

A.

Vinit, Naveen and Puneet begin to jog around a circular stadium. They complete their revolutions in 48 seconds, 60 seconds and 72 seconds respectively. After how many seconds will they be together at the starting point? 740 720 360 400





A. B. C. D.

secs secs secs secs

5.

The sum of three numbers is 116. If the ratio of the second to the third number is 9 : 16 and the first to the third number is 1 : 4, then the second number is

B.

C.

D.

A. 28 B. 30 2

9.

Abhishek bought 5 chocolates and 8 packet of cookies. Each chocolate costs ` 75 and the cost of each packet of cookies is twice the cost of chocolate. How much money did he pay? | IMO | Class-7 | Level 2

2019



10. During a cricket match, 4800 people showed their spirit by wearing home team’s colour. If 12000 people attended the game, then what percent of crowd wear same colour ?

15. In the given figure, if l || m and t is a transversal, then which of the following are true?



t

A. 80% B. 40% C. 20% D. 60%

4 3

11. The mean of 6 numbers is 50. If the mean of first four is 40 and that of last three is 70, then the fourth number is

A. B. C. D.

770 m2 240 m2 620 m2 None of these

A. ` 1210 B. ` 1575 ` 975 C. ` 1350 D.

A. 60 B. 70 C. 80 D. 50

12. Which of the following figures has order of rotation 3? A.

5 6

1

l

2

8

m

7

(i) (iii) A. B. C. D.



∠4 = ∠5 (ii) ∠2 = ∠3 ∠2 = ∠7 (iv) ∠6 = ∠8 Only (i) and (iii) are true Only (ii) and (iv) are true (i), (iii) and (iv) are true All (i), (ii), (iii) and (iv) are true

Direction (16-17) : The given bar graph shows the number of goals made by a football player during five years. Study the graph carefully and answer the following questions.

B.

Number of goals

C.

D. 13. Which condition of congruency is satisfied, if the two triangles made by the diagonal in the figure below are congruent?

400 350 300 250 200 150 100 50 0

2000

2001

2002 Years

2003

2004

16. Find the ratio of number of goals made by him during the year 2002 and 2003 together to the five years.



A. ASA B. SAS C. RHS D. SSS

14. The radius of a circular sheet of metal is 21 m. A circular piece of sheet is cut out from its centre. This piece has a radius of 14 m. What is the area of the 22 sheet left?  Take π =   7 

A. B. C. D.

11 27 12 25

: : : :

27 11 25 12

17. What is the average number of goals made by the player during all the five years?

A. 250 B. 320 C. 270 D. 135 3

IMO | Class-7 | Level 2 |

2019

18. A die is rolled once. Find the probability of getting

(i) an even prime number. (ii) a multiple of 2. (i) (ii) A. 1/6 1/6 B. 1/6 1/2 C. 2/3 1/6 D. 1/6 1/3

C. 320 D. 480 24. Puneet has a box of beads. 45% of the beads in the box are blue, 60% of the remaining beads are green and the rest are violet. If there are 33 more green beads than violet beads, then how many beads are blue?

19. Find the value of 3 1 1   ( p + q) −  q + p −  q + p − ( p + q)   .   4 3 4 

A. p+q B. 3p C. – 4q D. 0



25. Which of the following is correct?

20. Deepak purchased a car for ` 3,25,000. He spent ` 15,000 on repairing, ` 2,000 on transport and sold it with 20% profit. At what price did he sell the car? A. ` 3,75,200 B. ` 2,25,300 C. ` 4,10,400 D. ` 3,20,050 21. How many minimum number of squares must be shaded so that PQ becomes a line of symmetry? P

A. 50 B. 120 C. 95 D. 135



A.

Multiplication of two integers with unlike signs is always positive. B. When a positive integer is divided by a negative integer, the quotient obtained is a negative integer. C. Product of odd number of negative integers is positive. D. None of these

26. The product of the 9 fractions 1  1  1  1  1 −  1 −  1 −  ..... 1 −  = 2 3 4 10 10 A. 11 1 B. 9 1 C. 10 1 D. 2 1 ( p4q4 ) 2



Q A. 2 B. 3 C. 4 D. 5

22. The measure of an angle which is 34° more than its complement is

A. 90° B. 34° C. 62° D. 36°

23. A number is 68% of the other number. If the sum of these two numbers is 84% of 500, then what is the bigger number? A. 120 B. 250 4

1 24 24 6 ×(p q )

27. If the value of k.

1 12 12 3 ×(p q )

= ( pq )k , then find

A. 10 B. 8 C. 5 D. 6

28. In an equilateral D LMN, points A and B trisect side LM, points C and D trisect side LN and points E and F trisect side MN. Then perimeter of regular hexagon ABCDEF is how many times of the perimeter of D LMN? 1 A. times 2 1 B. times 3 2 C. times 3 1 D. times 6 | IMO | Class-7 | Level 2

2019

29. In the given figure (not drawn to scale), find the value of ∠m + ∠n + ∠p + ∠s. m

55°

n



p



34. If

C. 125° D. 215°

30. A man gains 10 % by selling a certain article for a certain price. If he sells it at double the previous price then the profit made is

A. 120 %



B. 60 %



C. 100 %



D. 80 %

D

30°

C

B A. 30°

B. 60° C. 45°

35. Consider the weights (in kg) of 9 students of a particular class given below:

D. 65°



A. 6.42 cm2



B. 3.44 cm2

3 7 1 1  5 3 3 36. Simplify : 4 ÷ ×  +  + ÷ of 5 8 3 4 7 4 7 1 6 56 A. 77 49 B. 80 2 C. 3 9

32. The given figure is formed by two identical semicircles in a rectangle. Find the area of shaded parts. (Take p = 3.14)

2 cm



2 cm

34, 35, 36, 40, 35, 35, 40, 45, 39 Which of the following is in the order from the least to the greatest? A. Mean, Mode, Median B. Mean, Median, Mode C. Mode, Median, Mean D. Mode, Mean, Median 2

E



A. ` 40 B. ` 20 C. `6 D. `8



31. In the given figure, AB ⊥ BC, BD ⊥ AC and CE bisects ∠C. If ∠A = 30°, then what is the measure of ∠CED? A



A. 7 B. 5 C. 6 D. 8 3 kg of wheat costs ` 45, then how much will 4 100 g cost?

A. 201°

B. 180°

C. 2.88 cm2 D. 4.04 cm2

33. The present ages of Kamal and Kalyan are in the ratio of 4 : 5. The product of their ages numerically is equal to 980. Find the difference between their ages (in years).

40° 32° s



2 cm

2 cm

D. None of these

3 37. Sukriti spends   5

th

of her income on household

th

1 articles and   of her income on her personal 7 expenses. If her monthly income is ` 70000, then her monthly savings is A. ` 9000 B. ` 12000 C. ` 18000 D. ` 7000 5

IMO | Class-7 | Level 2 |

2019

38. Mr Sharma is three times as old as his daughter. After five years, the sum of their ages will be 62 years. Find the present age of his daughter.

A. B. C. D.

15 12 13 14

years years years years

A. B. C. D.

40. ABCD is a square park divided into 4 squares as shown in the figure. Semi circular flower beds are made as shown by the shaded portion. Find the area 22 of the shaded region  Take π =  .  7  14 m 7m

C



A. B. C. D.







D. 1

43. In the given figure (not drawn to scale), DAE, CBH and ACG are straight lines, DE || CH || FG. Find x and y respectively. F

70°

B y

C

D

x

H

35°

A



A. B. C. D.

E

70°, 35° 110°, 145° 110°, 35° 140°, 20°

B

75 m2 76 m2 77 m2 119 m2

45. In the given figure, if PR = QR, ∠SRP = ∠TRQ and ∠SQP = ∠TPQ, then S

41. A candidate must get 33% marks to pass. He gets 220 marks and fails by 11 marks. What is the maximum number of marks?

G

44. The L.C.M. of two numbers is (x + y) and their H.C.F. is A(x – y). If one of the number is A, then the other number is A. x–y B. x2 – y2 C. 2x – 2y D. x2 + y2

7m

A

A. 0

9 C. 2

The angles of the triangle are 90°, 45° and 45°. The triangle is right angled triangle. The triangle is isosceles. None of these

D



B. 5

39. If the angles of a triangle are in the ratio 1 : 1 : 2, then which of the following statements is incorrect?

42. If 0.5x – (0.8 – 0.2x) = 0.2 – 0.3x, then the value of x is

R

P

A. DSQR B. DSQR C. DRQS D. DQRS

A. 500 B. 689 C. 711 D. 700

T

@ @ @ @

DPTR DTPR DTPR DPRT

& & & &

SR SR SR SR

Q

= = = =

TR TR TR PT

ACHIEVERS SECTION 46. State ‘T’ for true and ‘F’ for false and select the correct option. (i) If a dealer sells two photo frame for ` 2400 each, gaining 20% on one and losing 20% on other, then his overall loss is ` 200. (ii) The price of a T.V. is reduced from ` 5400 to ` 5000. The percentage decrease in price is 5%. 6





(iii) If Alisha borrowed ` 10000 for 2 years at 5% p.a., then she has to pay interest after 2 years is ` 1000. (i) (ii) (iii) A. F T  F B. T T  F C. T F  T D. F F  T | IMO | Class-7 | Level 2

2019

47. Read the statements carefully and select the correct option.

Statement-I : A saree 5.5 m long and 1.25 m wide has a zari border 2.5 cm broad along its length on either side. Along the width, on one edge the zari border was 5 cm wide and on the other side the zari border was 25 cm wide. The area of the zari border is 5855 cm2.



Statement-II : If the diameter of the wheel of a car is 70 cm, then to travel 99 km it will make 45000 revolutions.



A. B. C. D.

Both Statement-I and Statement-II are true. Statement-I is true but Statement-II is false. Statement-I is false but Statement-II is true. Both Statement-I and Statement-II are false.

49. Simplify : 2 x +3 × 32 x − y × 5 x + y +3 × 6 y +1



(i)



8 (ii) If   3

6 x +1 × 10 y +3 × 15 x

(P)

(Q)

(R)

(S)



Column-II 62°

The complement angle of (2) 2 of 70° is 5

32°

Two complementary (3) angles are in the ratio 7 : 8. The largest angle is

48°

The supplement angle of (4) 3 of 160° is 4

60°

(P) A. (2) B. (3) C. (2) D. (4)

5

8 8 ×  =   3 3

x+2

, then find the value

of x. (i) (ii) A. 0 0 B. 1 –4 C. 1 2 D. 2 4 50. Find the unknown angle x in the given figures. C

48. Match the following and select the correct option. Column-I If the measure of two (1) supplementary angles are (3x + 15)° and (2x + 5)°, then the value of x is

2 x +1

B



(i) A

x

104° x

78°

D

E F

A 64°



(Q) (R) (S) (1) (3) (4) (1) (4) (2) (3) (4) (1) (2) (1) (3)

(ii) D B

32°

x C

(i) (ii) A. 104° 30° B. 122° 26° C. 122° 52° D. 120° 32° SPACE FOR ROUGH WORK

7

IMO | Class-7 | Level 2 |

2019

ANSWER KEYS IMO 2014 1. (D) 2. (D) 8. (A) 9. (C) 15. (D) 16. (A) 22. (B) 23. (B) 29. (C) 30. (C) 36. (B) 37. (B) 43. (B) 44. (A) 50. (A)

3. (C) 4. (A) 5. (D) 6. (A) 7. 10. (B) 11. (B) 12. (B) 13. (A) 14. 17. (A) 18. (A) 19. (C) 20. (D) 21. 24. (C) 25. (D) 26. (B) 27. (A) 28. 31. (C) 32. (A) 33. (A) 34. (B) 35. 38. (D) 39. (B) 40. (C) 41. (D) 42. 45. (A) 46. (C) 47. (A) 48. (B) 49.

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

2015 IMO-Level 2 was an online exam. Hence, paper cannot be included in the booklet.

IMO 2016 1. 2. 3. 4. 5. 6. 7. 8.

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

9. (B) 10. (A) 11. (C) 12. (D) 13. (B) 14. (B) 15. (D) 16. (A)

17. (C) 25. (D) 33. (C) 41. (C) 49. (B) 18. (C) 26. (C) 34. (D) 42. (A) 50. (A) 19. (B) 27. (C) 35. (B) 43. (C) 20. (C) 28. (B) 36. (C) 44. (A) 21. (C) 29. (D) 37. (B) 45. (C) 22. (A) 30. (B) 38. (D) 46. (D) 23. (D) 31. (A) 39. (C) 47. (B) 24. (B) 32. (B) 40. (A) 48. (D)

IMO 2017 1. (C) 2. (A) 3. (A) 4. (B) 5. (A) 6. (D) 7. 8. (B) 9. (D) 10. (A) 11. (C) 12. (A) 13. (C) 14. 15. (B) 16. (B) 17. (D) 18. (D) 19. (D) 20. (B) 21. 22. (A) 23. (A) 24. (B) 25. (B) 26. (A) 27. (B) 28. 29. (C) 30. (B) 31. (C) 32. (A) 33. (A) 34. (A) 35. 36. (A) 37. (B) 38. (B) 39. (D) 40. (A) 41. (B) 42. 43. (C) 44. (A) 45. (A) 46. (B) 47. (D) 48. (C) 49. 50. (A)

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

IMO 2018 1. 2. 3. 4. 5. 6. 7. 8.

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

9. (A) 10. (B) 11. (A) 12. (D) 13. (D) 14. (B) 15. (B) 16. (B)

17. (C) 25. (C) 33. (D) 41. (B) 49. (A) 18. (D) 26. (B) 34. (A) 42. (B) 50. (B) 19. (C) 27. (A) 35. (B) 43. (C) 20. (C) 28. (B) 36. (C) 44. (B) 21. (D) 29. (A) 37. (B) 45. (D) 22. (D) 30. (D) 38. (A) 46. (B) 23. (C) 31. (C) 39. (B) 47. (C) 24. (C) 32. (B) 40. (D) 48. (C)

2019

IMO 2019 1. 2. 3. 4. 5. 6. 7. 8.

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

9. 10. 11. 12. 13. 14. 15. 16.

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

17. 18. 19. 20. 21. 22. 23. 24.

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

2019

25. 26. 27. 28. 29. 30. 31. 32.

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

33. 34. 35. 36. 37. 38. 39. 40.

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

41. 42. 43. 44. 45. 46. 47. 48.

(D) 49. (D) 50. (B) (B) (B) (C) (C) (A)

(B) (B)