Class 9 IMO 5 Years Book level 2 (2014-2019)

Citation preview

INTERNATIONAL MATHEMATICS OLYMPIAD

Level 2 SOLVED PAPERS

CLASS

9

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 9

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-9 | Level 2

logical reasoning 1.

If the words in the sentence, “She showed several sample snaps to Shikha's maternal sister” are rearranged in the alphabetical order, which will be the middle word? A. B. C. D.

2.

3.

4.

NJNQMXAWGH ITOEKHLQST NJQNQXAWGF NJRMQXAGWF

(i)

M, P L, Q P, Q Can’t be determined

(ii)

There is a definite relationship between figures (1) and (3). Establish a similar relationship between figures (2) and (4) by selecting a suitable figure from the options that would replace the question mark (?) in fig. (4). Problem Set ? B.

(1)

(2)

(3)

(4)

C. D. 8.

Study the following arrangement carefully and answer the question given below . 1 H # U J 9 4 $ R 2 K • E L9 H PA% T 3 F M T @7 G O S = 6 X How many such symbols are there in the above arrangement, each of which is immediately followed by a vowel and not immediately preceded by a number?

Niece Uncle Nephew Brother

A. One

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

2 3 4 5

A.

Pointing to Mohit, Sana said, “His mother’s brother is the father of my son Nitin.” How is Mohit related to Sana? A. B. C. D.

5.

7.

Among six friends L, M, N, P, Q and S, each having a different height, N is taller than Q and P but shorter than M. P is taller than only Q while S is shorter than only L. Which of the following pairs represents the tallest and the shortest respectively among the five friends? A. B. C. D.

Two positions of a dice are shown below. If the face with 1 dot is at bottom, then the number of dots on the top is _______. A. B. C. D.

Snaps Sample Several Shikha's

In a certain code REFERENDUM is written as HZZRBUCHDS and SIMULATION is written as ITEXXOSOHT. How is EXECUTIVES written in that code language? A. B. C. D.

6.

B. Two C. Three D. Fig. (X)

B. C.

9.

Priya starts from point N and moves 25 metres south, then she turns left and moves 30 metres, then she turns right and moves 15 metres to reach point P. What is the distance of P from N and which direction is she facing with respect to point N? A. B. C. D.

D.

2019

Zero

50 50 45 40

metres metres metres metres

South-West South-East South-East South

7th IMO | Class-9 | Level 2

3

10. There are two rows of numbers. 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 operation of numbers progress from left to right. Rules : (i) (ii) (iii)

(iv)

(v)

A. B. C. D. 11.

If an odd number is followed by another composite odd number, they are to be multiplied. If an even number is followed by an odd number, they are to be added. If an even number is followed by a number which is the perfect square, the even number is to be subtracted from the perfect square. If an odd number is followed by a prime odd number, the first number is to be divided by the second number. If an odd number is followed by an even number, the second one is to be subtracted from the first one. If x is the resultant of the first row, what is the resultant of the second row? 36 27 7 x 15 126 125 11 9 15

Study the following information carefully and answer the question given below . (i) In a family of 6 persons, there are two couples. (ii) The Lawyer is the head of the family and has only two sons–Mrinal and Rakesh–both Teachers. (iii) Mrs. Reena and her mother-in-law both are Lawyers. (iv) Mrinal's wife is a Doctor and they have a son, Ajay. What is/was Ajay's Grandfather's occupation? A. B. C. D.

Teacher Lawyer Doctor Can't be determined

A. B. C. D.

26 25 10 Can't be determined

A. B.



C.



D. 15. Select a figure from amongst the options which shows similar characteristics/properties as shown by the Problem figures. A. B. C. D. 16. Which of the following is the correct mirror image of the given Fig. (X), if the mirror is placed vertically right ?

B. C. D.

2019

5 only 1, 4, 7 4, 7 4, 5, 6

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

A.

12. Rohit is sixteenth from the front in a column of boys. There are twice as many behind him as there are in front. How many boys are there between Rohit and fifth boy from the end of the column? A. B. C. D.

13. Study the given diagram and identify the region representing girls who are employed and educated.

4

7th IMO | Class-9 | Level 2

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

C. 241 D.

425

19. The question is based on the following six numbers .

A.

382 473 568

If 382 is written as 238, 473 as 347 and so on, then which of the following two numbers will have least difference between them ?

B. C.

728 847 629

A. B. C. D.



D. 18. Find the missing character, if the same rule is applied to (i), (ii) and (iii).

A. B.

& & & &

382 728 568 847

20. If 'A @ B' means 'A is added to B'; 'A * B' means 'A is multiplied by B'; 'A # B' means 'A is divided by B'; 'A $ B' means 'B is subtracted from A'; then number of boys (B) in a class is equal to one-fourth of three times the number of girls (G) in the class can be represented as ______. A. B. C. D.

184 210

473 629 629 728

B B B B

= = = =

(3 (3 (3 (3

# * * $

G) G) G) G)

*4 @4 #4 #4

MATHEMATICAL REASONING 21. The equations x – y = 1 and 2x + y = 8 are given. The area bounded by these two lines and y-axis is ______. A. B. C. D.

8 sq. units 13.5 sq. units 11 sq. units 9 sq. units

22. PS and QT are the medians of DPQR and QT||SU. If PR = 12 cm, find the value of RU. A. B. C. D.

6 cm 2.5 cm 4 cm 3 cm

23. In the given figure, O is the centre of the circle. If ∠AOB = 90°, find m ∠APB. A. B. C. D.

130° 150° 135° Can’t be determined

P T U

Q

24. In a class, teacher gave two identical cardboard pieces which are in the shape of a parallelogram to two groups. First group was asked to find area of parallelogram using AB as base. Then, another group was asked to find height h of the parallelogram with AD as base.

S

R

A. B. C. D.

P A

B 90° O

2019

What is the height of the parallelogram in group II? 4.8 cm 4 cm 5.6 cm 8.4 cm

25. In the adjoining figure, the value of x is A. B. C. D.

110° 130° 120° 125°

7th IMO | Class-9 | Level 2

5

26. Find the value of p, if the mean of the following distribution is 7.5.

A. B. C. D.

x

3

5

7

9

11

13

f

6

8

15

p

8

4

1 2 3 4

25° 30° 35° 115°

A

C

35° O

D 25°

E

B

28. In the given figure, the radius of each of the smallest 1 circles (C1, C 2, C3, C4, C5, C 6 and C7) is of the 12 radius of the biggest circle B1. The radius of each of the middle sized circles (P1, P2, P3 and P4) is three times the radius of the smallest circle. The area of the shaded portion is _____ times the area of the biggest circle. A. B. C.

23 48 53 48 14 23

B. C.



D.



A. B. C. D.

cm cm cm cm

1 2 3 4

sq. sq. sq. sq.

unit units units units

32. A bar code is formed using 25 black and certain white bars. White and black bars alternate. The first and the last are black bars. Some of the black bars are thin and others are wide.

The number of white bars is 15 more than the thin black bars. The A. B. C. D.

A. B. C. D.

29. A triangle has sides with lengths 13 cm, 14 cm and 15 cm. A circle whose centre lies on the longest side touches the other two sides. The radius of the circle is (in cm) ______ A.

12.5 16.5 18.5 14.5

number of thick black bars is _____. 14 15 16 17

33. In the given figure, PQRS is a cyclic quadrilateral. Find the value of x.

51 91

D.

A. B. C. D.

31. The area of the triangle formed by the 2x + 3y = 6 and the coordinate axes is

27. In the given figure, AB is a diameter of a circle with centre O. If ADE and CBE are straight lines, meeting at E such that ∠BAD = 35° and ∠BED = 25°, find ∠BDC. A. B. C. D.

Calculate the perimeter of trapezium MNRQ.

43 9 49 9

100° 180° 270° 120°

34. In the given figure, PQRS is a parallelogram, PO and QO are, respectively, the angle bisectors of ∠P and ∠Q. Line LOM is drawn parallel to PQ. Which of the following is true? A.

PL = QM

B.

LO = OM

C.

OM = QM

D.

All of these

35. OCDE is a rectangle inscribed in a quadrant of a circle

56 9

of radius 10 cm. If OE = 2 5 cm, find the area of the rectangle.

63 15

30. PQR is a triangle in which PQ = 5.6 cm, PR = 4.8 cm and QR = 6.2 cm. M is the midpoint of PQ and N is the midpoint of PR.

2019

A.

20 cm2

B.

4 5 cm 2 40 cm2 80 cm2

C. D.

6

7th IMO | Class-9 | Level 2

EVERYDAY MATHeMATICS 36. Karan tells his daughter Alia, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". If present ages of Alia and Karan are x and y years respectively, represent this situation algebraically. A. B. C. D.

7x – y = 42; y – 3x = 6 x – y = 42; y – 3x = 6 x – 7y = 6; y – x = 4 x – 7y = 42; 3y – x = 6

37. A cylindrical road roller made of iron is 1 m wide. Its inner diameter is 54 cm and thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the roller if 1 c.c. of iron weighs 8 gm. (p = 3.14) A. B. C. D.

1425.6 kg 1424.304 kg 1567.06 kg 1424.034 kg

B. C. D.

4 7 0.10 0.8 5 7

` ` ` `

litres litres litres litres

A. B. C. D.

202.25 m2 202.125 m2 200.25 m2 None of these

C.

3 8 1 2

B.

7 8

D.

1 4

44. There are only five people in Aman's family. Aman, his wife, a son and two daughters. The younger th

20,000 22,000 24,000 25,000

40. The largest possible length of a tape which can measure 525 cm, 1050 cm and 1155 cm length of clothes in a minimum number of attempts without measuring the length of a cloth in a fraction of the tape's length is ______. A B. C. D.

200 300 358 400

42. A heap of wheat is in the form of a cone, whose diameter is 10.5 m and height 7 m. Find the lateral surface area of wheat in the heap.

A.

39. Pratik invested an amount of ` 12,000 at the rate of 10 % p.a. simple interest and another amount at the rate of 20 % p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14 % p.a. Find the total amount invested. A. B. C. D.

A. B. C. D.

43. Three fair coins are tossed simultaneously. Find the probability of getting atleast two heads.

38. In a cricket match, a batsman hits a boundary 8 times out of 40 balls he plays. Find the probability that he didn't hit a boundary. A.

41. When a barrel is 40% empty it contains 80 litres more than when it is 20% full. The full capacity of the barrel (in litres) is _____.

25 cm 105 cm 75 cm 50 cm

2019

4 daughter’s age is   of the elder daughter’s age. 5 3 The age of eldest daughter is times that of her 8 th 1 father Aman and the age of the son is   that of 5 his father Aman. 4 years ago the age of his wife was 8 times that of his son and now the sum of the ages of the younger daughter and wife is same as the sum of the ages of Aman and his son. The average age of the family is A. B. C. D.

22.2 years 25.4 years 21.2 years 23 years

45. The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is A. B. C. D.

91 910 1001 1911

7th IMO | Class-9 | Level 2

7

Achievers Section 46. Rearrange the following steps of constructing a triangle when the base angles say ∠B and ∠C and its perimeter BC + CA + AB is given (1) Draw perpendicular bisectors PQ of AX and RS of AY. (2) D r a w a l i n e s e g m e n t , s a y X Y e q u a l t o BC + CA + AB. (3) Let PQ intersect X Y at B and RS intersect XY at C. Join AB and AC. (4) Make angles LXY equal to ∠B and MYX equal to ∠C. (5) Bisect ∠LXY and ∠MYX. Let these bisectors intersect at a point A. A. 1 → 3 → 5 → 4 → 2 B. 2 → 4 → 5 → 1 → 3 C. 5 → 4 → 3 → 2 → 1 D. 2 → 3 → 5 → 4 → 1 47. Which of the following statements is INCORRECT ? A. B. C. D.

A linear equation in two variables has infinitely many solutions. The graph of every linear equation in two variables is a straight line. The graph of x = a is a straight line parallel to the y-axis. Every point on the graph of a linear equation in two variables is a solution of the linear equation. Every solution of the linear equation may not be a point on the graph of the linear equation.

48. Fill in the blanks. A circle is the collection of all points in a plane which are P from a fixed point in the plane. The fixed point is called Q of the circle and fixed distance is called R of the circle. A circle divides the plane on which it lies into S parts.   P   Q   R A. Equal radius centre B. Equidistant centre radius C. Distance centre radius D. Normal radius centre

49. Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. The perimeter of the parallelogram is _______ than that of the rectangle. A. B. C. D.

Greater Lesser Equal Can't be determined

50. If a + b = 10 and ab = 21, a > 0 & b > 0 then Column-I Column-II (i) a3 – b 3 (p) 58 (ii) a 2 + b 2 (q) 40 (iii) a 2 – b 2 (r) 316 A. (i)–(r), (ii)–(q), (iii)–(p) B. (i)–(p), (ii)–(q), (iii)–(r) C. (i)–(r), (ii)–(p), (iii)–(q) D. (i)–(p), (ii)–(r), (iii)–(q)

SPACE FOR ROUGH WORK

2019

S two three two four

LEVEL - 2 Year 2015-16 2019

Mathematics 1.

Fill in the blanks. A non-terminating and non-recurring decimal expansion is a/an ________ number. The decimal expansion of

1 is in ______ form. 125



A. B. C. D.

Rational, terminating Irrational, terminating Rational, non-terminating recurring Rational, recurring

2.

A pair of dice is thrown. The probability of getting even number on first die & odd number on the second die is 1 5 1 2 1 4 1 3



A.



B.



C.



D.

3.

A point whose abscissa and ordinate are 2 and –5 respectively, lies in



A. B. C. D.

4.

Which of the following statements is INCORRECT?



A. B. C. D.

5.

The dimensions of a rectangular piece of paper are 22 cm × 14 cm. It is rolled once across the breadth and once across the length to form right circular cylinders of biggest possible surface areas. Find the difference in volumes of the two cylinders that will be formed.

First quadrant Second quadrant Third quadrant Fourth quadrant

7.

The mean of the data x1, x 2 , ...., x n is 102, then mean of the data 5x1, 5x 2 , ....., 5x n is



A. B. C. D.

8.

A triangle and a parallelogram have same base and same area. If the sides of the triangle are 20 cm, 25 cm and 35 cm, and the base side is 25 cm for the triangle as well as the parallelogram, find the vertical height of the parallelogram.



A.



B.

2 6 cm 4 6 cm



C. D.

6 cm None of these

9.

How many linear equations are satisfied by x = 2 and y = –3?



A. B. C. D.

102 204 606 510

Only one Two Three Infinitely many

10. In the figure given below, l || u and m || n. If ∠ACB = 55° and ∠AED = 30°, find x, y, z and q respectively.

A solid has 3 dimensions. A surface has 2 dimensions. A line has 0 dimension. None of these

A. B. C. D.

11. How many statements are INCORRECT?

(i)



(ii)



(iii)

It is not possible to construct a triangle whose sides are



(iv)

A. B. C. D.



A. B. C. D.



A. 196 cm3 B. 308 cm3 C. 49 cm3 D. 105 cm3

6.

3 cm, 3 cm and 6 cm 5 cm, 12 cm and 13 cm 15 cm, 8 cm and 17 cm 3 cm, 4 cm and 5 cm

2

95°, 125°, 150°, 55° 150°, 95°, 125°, 55° 125°, 150°, 95°, 55° 55°, 95°, 150°, 125° If a circle is divided into four equal arcs, each is a minor arc. A sector of a circle can have area more than the area of the whole circle. The area of each quadrant of a circle is one-third of the area of the whole circle. One and only one chord of a circle can be the diameter of the circle. 1 2 3 0 | 9th IMO | Class-9 | Level 2

2019

12. In the given figure, l || BC and D is mid-point of BC. If area (DABC) = x × area (DEDC), find the value of x.

evenly over the rest of the field. Find the rise in the level of the rest of the field.

A. B. C. D.

25 cm 15 cm 125 cm 200 cm

18. The abscissa of a point is positive in the



A.



B. C. D.



1 2 1 4 2

A. B. C. D.

and AC = 9 cm. (Take 110 = 10.5 approx.)

7.5 cm 8 cm 9 cm 4.5 cm

A.



B.



C.



D.

The difference of a rational number and an irrational number is an irrational number. The product of a non-zero rational number with an irrational number is an irrational number. The quotient of an irrational number with a nonzero rational number is an irrational number. None of these

15. If we multiply or divide both sides of a linear equation in two variables with a non-zero number, then the solution of the linear equation

A. B. C. D.



A. B. C. D.

57 45 75 72

cm2 cm2 cm2 cm2

20. Let l be the lower class limit of a class-interval in a frequency distribution and m be the mid-point of the class. Then, the upper class limit of the class is

14. Select the INCORRECT statement.

First and Second quadrant Second and Third quadrant Third and Fourth quadrant Fourth and First quadrant

19. Find the area of the quadrilateral ABCD in which AB = 7 cm, BC = 6 cm, CD = 12 cm, DA = 15 cm

13. It is not possible to construct a triangle ABC with BC = 5 cm, ∠B = 75° and AB + AC equal to

A. B. C. D.

Changes Changes in case of multiplication only Changes in case of division only Remains unaltered

16. If (2x + 1) is a factor of the polynomial p(x) = kx3 + ( k −1) . 23x 2 + 71x + 30, then find the value of 8 A. –2 5 B. 8 1 C. 8 D. 2 17. A field is 15 m long and 12 m broad. At one corner of this field a rectangular well of dimensions 8 m × 2.5 m × 2 m is dug, and the dug-out soil is spread



A.



B.



C. D.

m + l+m 2 l + m+l 2 2m – l m – 2l

21. If (2k – 1, k) is a solution of the equation 10x – 9y = 12, then k =

A. B. C. D.

1 2 3 4

22. In the given figure, E and F are mid-points of the sides AB and AC respectively of the DABC; G and H are mid-points of the sides AE and AF respectively of the DAEF. If GH = 1.8 cm, find BC.



A. B. C. D.

7.2 cm 10 cm 15 cm 72 cm 3

9th IMO | Class-9 | Level 2 |

2019

23. In Fig. (i), X is the centre of the circle and in Fig. (ii), O is the centre of the circle. Find a and f respectively.

28. The construction of a triangle ABC, given that BC = 3 cm, ∠C = 60°, is possible when the difference of AB and AC is equal to

A. B. C. D.

3.2 cm 3.1 cm 3 cm 2.8 cm

29. Which of the following polynomials has (x + 1) as a factor?

A. B. C. D.

78°, 38°, 48°, 76°,

76° 43° 76° 78°

24. In DABC, AB = 7.2 cm, BC = 4.8 cm, AM ^ BC and CL ^ AB. If CL = 4 cm, find AM.



(i) x 3 + x 2 + x + 1 (ii) x 4 + x 3 + x 2 + x + 1 (iii) x 4 + 3x 3 + 3x 2 + x + 2



(iv) A. B. C. D.

x3 – x2 – ( 2 + 2 ) x − 2 (i), (ii) (iii), (iv) (ii), (iii) (i), (iv)

30. A die is thrown 300 times and the outcomes 1, 2, 3, 4, 5, 6 have frequencies as below : Outcome Frequency

1 55

2 53

3 58

4 49

5 48

6 37

Find the probability of getting a prime number.

A. B. C. D.

4 cm 10 cm 5 cm 6 cm



25. If DABC @ DPQR and DABC is not congruent to DRPQ, then which of the following is not true?

A. B. C. D.

BC = PQ AC = PR QR = BC AB = PQ

26. W h i c h o f t h e f o l l o w i n g i s n o t t r u e f o r a parallelogram?

A. B. C. D.

Opposite sides are equal Opposite angles are equal Opposite angles are bisected by the diagonals Diagonals bisect each other

27. If bisectors of ∠A and ∠B of a parallelogram ABCD intersect each other at P, bisectors of ∠B and ∠C at Q, bisectors of ∠C and ∠D at R and bisectors of ∠D and ∠A at S, then PQRS is a

A.

Rectangle



B.

Rhombus



C. D.

Square None of these

4

A. B. C. D.

0.395 0.53 0.355 0.215

31. In figure, ABCD is a parallelogram and E is mid-point of the side CD, then area (ABED) = k × area (DBEC), then k =



A.



B.



C.



D.

2 1 2 3 1 3

32. If x =

4 , then 1  x + 2  = 2  8 + 60 x 



A.

5



B.

3



C.

2 5



D.

2 3 | 9th IMO | Class-9 | Level 2

2019

33. In the given figure, ABCD is a rhombus. Find y.

39. The distance of the point P(4, 3) from the origin is



A. B. C. D.

A. B. C. D.

(y+7 (y−7 (y−7 (y+7

3 )( y + 5 3 )( y + 5 3 )( y − 5 3 )( y − 5

3) 3) 3) 3)

35. In the given figure, AC = BC and ∠ACY = 140°.



Find A. B. C. D. A.



B. C. D.

x and y respectively. 110°, 100° 40°, 110° 110°, 110° 140°, 100° A straight line may be drawn from any one point to any other point. A terminated line can be produced indefinitely. All right angles are equal to one another. None of these

37. The weights (in kg) of 15 students are : 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.

A. B. C. D.

41 35 35 37

kg, kg, kg, kg,

35 41 35 36

kg kg kg kg

38. If l = 1+ 2 + 3 and m = 1 + 2 − 3 , then

units units units units



C.



D.

1 157 cm 2 7 8800 2 cm 7

41. If E is an event associated with an experiment, then

A. P (E) > 1 B. –1 < P (E) < 1 C. 0 ≤ P (E) < 1 D. None of these

42. A triangle and a parallelogram have a common side and are of equal areas. The triangle having sides 26 cm, 28 cm and 30 cm stands on the parallelogram. The common side of the triangle and the parallelogram is 28 cm. Find the vertical height of the triangle and that of the parallelogram respectively.

36. Euclid’s Postulate 1 is

4 3 5 7

40. A circular piece of paper of radius 20 cm is trimmed into the shape of the biggest possible square. Find the area of the paper cut off. (Use p = 22 . ) 7 A. 457 1 cm2 7 B. 800 cm2

56° 107° 33.5° None of these

34. Factorise : y 2 − 12 3 y + 105.

A. B. C. D.



A. B. C. D.

26 20 12 24

cm, cm, cm, cm,

24 24 24 12

cm cm cm cm

43. If l and m be two positive real numbers such that l > 3m, l2 + 9m2 = 369 and lm = 60, then find the l − 3m value of . 12

A.



B.



C.



D.

1 12 1 4 9 5 4

44. The distance between the graph of the equations x = –3 and x = 2 is

l 2 + m 2 − 2l − 2m = 8 A. 1 B. 0 C. –1 D. 5



A. B. C. D.

1 2 3 5

unit units units units 5

9th IMO | Class-9 | Level 2 |

2019

45. Which of the following is not possible in case of a triangle ABC?

A.

AB = 3 cm, BC = 4 cm and CA = 5 cm



B. C. D.

AB = 5 cm, BC = 8 cm and CA = 7 cm ∠A = 50°, ∠B = 60° and ∠C = 70° AB = 2 cm, BC = 4 cm and CA = 7 cm

Achievers Section 46. If (x 3 + ax 2 + bx + 6) has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), find the value of 2a + 3b.

A. B. C. D.

–9 9 –11 11

47. If O is centre of circle as shown in figure, ∠SOP = 102° and ∠ROP = ∠SOU = 72°, then find ∠OSU and ∠RTU respectively.



Difference between total number of cars of models P, Q and T manufactured in 2000 and 2001 is ______.



A. B. C. D.

54°, 45°, 54°, 45°,



93° 110° 96° 94°

48. If h, s, V be the height, curved surface area and volume of a cone respectively, then (3pVh3 + 9V2 – s2 h2) is equal to

A. B.



C.



D.

36 V

Percentage of six different types of cars manufactured by a company over two years

2,45,000 2,27,500 2,10,000 98,000

50. While constructing a triangle ABC, in which BC = 3.8 cm, ∠B = 45° and AB + AC = 6.8 cm we follow the following steps :

0 p V sh

49. The given bar-graph shows the percentage distribution of the total production of a car manufacturing company into various models over two years. Study the graph carefully and answer the question.

A. B. C. D.



Step 1 : D raw the perpendicular bisector of CD meeting BD at A. Step 2 : From ray BX, cut-off line segment BD equal to AB + AC i.e., 6.8 cm. Step 3 : J oin CA to obtain the required triangle ABC. Step 4 : Draw BC = 3.8 cm. Step 5 : Draw ∠CBX = 45° Step 6 : Join CD. Arrange the above steps in correct order. A. 4, 5, 6, 1, 2, 3 B. 5, 4, 6, 2, 3, 1 C. 4, 5, 2, 6, 1, 3 D. None of these

SPACE FOR ROUGH WORK

6

| 9th IMO | Class-9 | Level 2

2019

LEVEL - 2 Year 2016-17 2019

MATHEMATICS 1.

In the given figure, PQR is a right angled triangle, right angled at Q. If QRST is a square on side QR and PRUV is a square on PR, then PS = _______.

A. x= B. y= C. x= D. y=

50 50 50 50

+ + + +

16y, 16x, 16y, 16x,

` ` ` `

370 120 120 370

6.

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. If AB = 12 cm, DE = 4 cm, PB = 8 cm, find RS.



A. B. C. D.

7.

In the given figure, ∠AFD = 25° and DBCF is a parallelogram. Find ∠EFC + ∠FDB + ∠FCB.



A. 85° B. 75° C. 100° D. 60°

8.

2.2 dm3 of lead is to be drawn into a cylindrical wire of diameter 0.50 cm. The length of the wire is



A. B. C. D.

9.

Find the mode of the following data.

A. PT B. RU C. QU D. PV 2.

Find the value of a 2 + 2ab + b 2 if the polynomial (x 3 – 10x 2 + ax + b) is exactly divisible by (x – 1) and (x – 2).



A. 81 B. 144 C. 225 D. 169 2 = 1.414 and 3 = 1.732 , then find the value of

3. If

( 2 − 1) + ( 2 + 1)

6 cm 8 cm 10 cm Can't be determined

( 3 + 1) . ( 3 − 1)



A. 2.346 B. 2.738 C. 4.237 D. 3.131

4.

Select the incorrect statement.



A.



B.



C.



D.

5.

The taxi fare in a city is such that ` 50 is the fixed amount, ` 16 per km is charged. Taking the distance covered as x km and total fare as ` y, write a linear equation in x and y. What is the total fare for 20 km?

A straight line can be drawn from one point to any other point. A terminated line can be produced indefinitely. A circle can be drawn with any radius and any centre. For every line L and for every point P not lying on L, there exists two lines passing through P and parallel to L.

2

110 m 112 m 98 m 124 m

Marks

10

15

20

25

30

35

40

Number of students

8

12

36

35

28

18

9

| 10th IMO | Class-9 | Level 2

2019



A. 25 B. 30 C. 20 D. 35



C. D.

240 cm2 280 cm2

14. Simplify : (x + y)3 – (x – y)3 – 6y(x 2 – y 2)

10. A coin is tossed 1000 times, if the probability of getting 3 a tail is , how many times head is obtained? 8 A. 525 B. 375 C. 625 D. 725 11. A cone, a hemisphere and a cylinder stand on equal bases and have the same height, the height being equal to the radius of the circular base. Their total surfaces area in the ratio A. ( 2 + 1) : 3 : 4 B. ( 3 + 1) : 3 : 4 C. 2 : 3 : 4 D. 2 : 7 : 8 12. With the vertices of DPQR as centres, three circles are described, each touching the other two externally. If the sides of the triangle are 26 cm, 10 cm and 24 cm. Find the radii of the circles.



A. 6 B. 8 C. 8 D. 2

y 2x x 2y y 3 xy

15. What must be subtracted from x 3 – 6x 2 – 15x + 80, so that the result is exactly divisible by x 2 + x – 12.

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

– – – –

6 2 4 5

16. ABCD is quadrilateral. If AC and BD are its diagonals, then the A. Sum of the squares of the sides of the quadrilateral is equal to the sum of the squares of its diagonals. B. Perimeter of the quadrilateral is equal to the sum of the diagonals. C. Perimeter of the quadrilateral is less than the sum of the diagonals. D. Perimeter of the quadrilateral is greater than the sum of the diagonals. 17. It is given that ∠XYZ = 64° and XY is produced to point P. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.



A. B. C. D.



4 cm, 6 cm, 20 cm 5 cm, 4 cm, 3 cm 3 cm, 5 cm, 6 cm None of these

3718 cm 2 and DA = 10 cm, find the area of the 7 rectangle.

is

A. B.

102°, 122°, 142°, 260°,

364° 302° 241° 120°

18. The perimeter of a triangle is

13. In the given figure, ABCD is a rectangle inscribed in a quadrant of a circle. If area of the quadrant



A. B. C. D.

220 cm2 300 cm2



A. B. C. D.

Greater than the sum of its altitudes. Less than the sum of its altitudes. Equal to twice the sum of its altitudes. Equal to the sum of its altitudes.

19. Which of the following statements is incorrect?

A. B.



C.



D.

If the mean of 4, 6, x, 8, 10, 13 is 8, then x = 7. If the median of 59, 62, 65, x, x + 2, 72, 85, 99 is 67, then x = 66. If the mode of 1, 3, 5, 7, 5, 2, 7, 5, 9, 3, p, 11 is 5, then the value of p is 7. If the mean of 10 observations is 15 and that of other 15 observations is 18, then the mean of all the 25 observations is 16.8. 3

10th IMO | Class-9 | Level 2 |

2019

20. In the given figure, O is centre of the circle and ∠BCO = 30°. Find x and y respectively.



A.

30°, 15°



B.

15°, 20°



C.

30°, 60°



D.

45°, 30°

21. If x =

x2 B.

1 x

+1

1 x D. x–1

22. If x 2 – 1 and x 2 – 4 are factors of ax6 + bx5 + cx 4 + dx 3 + ex 2 + fx + g, then find the value of (i) 21a + 5c + e (ii) a+c+e+g (i)



A. 0

(ii) 0

B. 1

0

C. 0

1



1

D. 1

23. If x100 + 100 is divisible by x + 1, then remainder is ______.

C. 99 D. 98

24. If (3x – y)7 = A0 x 7 – A1x6 · y + A2 x5 · y 2 – A3x 4 · y 3 + A4 x 3 · y4 – A5x 2 · y5 + A6 x · y6 – A7y 7, find the value of A0 – A1 + A2 – A3 + A4 – A5 + A6 – A7.

A. 512

B. 128 C. 256 D. 32 25. Difference between 'postulate' and 'axiom' is

A.

C.



D.

Axioms are taken for granted without proof whereas postulates are to be proved. 'Postulates' are the assumptions used specially for geometry and 'axioms' are the assumptions used throughout mathematics. None of these

A. ∠x > ∠y. B. ∠x = ∠y. C. ∠x < ∠y. D. None of these 27. In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are

There is no difference.

4

A. B. C. D.

Isosceles but not congruent. Isosceles and congruent. Congruent but not isosceles. Neither congruent nor isosceles.

28. If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has _______. A. x coordinate B. y coordinate C. y coordinate D. y coordinate

= = = =

–5 5 only – 5 only 5 or –5

29. A rhombus shaped field has green grass for 36 cows to graze. If each side of the field is 30 m and longer diagonal is 48 m, then how much area of grass each cow will get, if 216 m2 of area is not to be grazed.

A. 100

B. 101





x− C.



B.

26. ∠x and ∠y are exterior angles of a DABC, at the points B and C respectively. Also ∠B > ∠C, then relation between ∠x and ∠y is

a+2 + a−2 , then a = _____. a+2 − a−2

x+ A.



A. B. C. D.

6 m 2 12 m2 18 m2 29 m2

30. Any solution of the linear equation 2x + 0y = 9 in two variables, is of the form _______. 9  A.  , 0  2 9  B.  , n  , n is a real number 2  9 C.  n,  , n is a real number 2  9 D.  0,  2 | 10th IMO | Class-9 | Level 2

2019

31. In the given figure, ABCD is a parallelogram. If AP, BP, CR, DR are the angle bisectors of ∠A, ∠B, ∠C, ∠D respectively, then the quadrilateral PQRS is exactly a ________.



A. 4

B. 3 C. 5

D. 2

36. While working out a question on probability it was formed that there were 286 letters of English alphabet. The following was observation of occurrence of each letter a = 70, b = 14, e = 26, r = 40, i = 36;

A. B. C. D.

others (not including vowels) = 100

Square Parallelogram Rectangle Rhombus

Then probability of a vowel is 70 A. 286

32. O is any point in the interior of DABC, then (OA + OB + OC) is ________ 1 (AB + BC + CA). 2 A. Equal to B. Less than C. Greater than D. None of these

A. B. C. D.

105°, 105°, 115°, 105°,

15°, 13°, 13°, 13°,

60° 62° 62° 60°

A. B. C. D.

132 D. 286



A.

4 cm



B.

8 cm



C.

6 cm



D.

5 cm

38. Find two rational numbers between

34. The diameter of a sphere is decreased by 25%. By what percentage its volume decreases?

100 C. 286

37. In the given figure, chord AB and CD are equidistant chords from centre of the circle. If AB is 8 cm, then length of the chord CD is equal to _______.

33. In the given figure, find a, b and c respectively.



36 B. 286

25% 43.75% 43.50% 57.81%

35. Find the value of p, if the mean of the following distribution is 7.5. Number of students

3

5

7

9

11

13

Frequency

6

8

15

p

8

4

0.222332333233332... and 0.252552555255552... .

A.

0.2, 0.25



B.

0.2, 0.2525



C.

0.25, 0.2525



D.

0.25, 0.2552

39. In twelve hours beginning from past mid-night, the minute hand and hour hand will overlap _______.

A.

10 times



B.

11 times



C.

14 times



D.

None of these 5

10th IMO | Class-9 | Level 2 |

2019

40. Following are the steps of construction of a triangle ABC, in which BC = 3.8 cm, ∠B = 45° and AB + AC = 6.8 cm. Select the correct order of arrangement of steps. Step-1 : Draw the perpendicular bisector of CD meeting BD at A. Step-2 : Draw BC = 3.8 cm Step-3 : Join CD. Step-4 : From ray BX, cut-off line segment BD equal to AB + AC i.e., 6.8 cm. Step-5 : Draw ∠CBX = 45° Step-6 : Join CA to obtain the required triangle ABC.

A. 2, B. 2, C. 2, D. 2,

4, 5, 5, 5,

5, 3, 4, 4,

3, 1, 1, 3,

1, 4, 3, 1,

6 6 6 6



A.

65%



B.

40%



C.

60%



D.

None of these

43. Which of the following statements is incorrect?

A.

Product of two irrational numbers is always irrational.



B.

Sum of two irrational numbers can never be irrational.



C.

Sum of an integer and a rational number can never be an integer.



D.

All of these

44. If

9n × 32 × (3− n / 2 )−2 − (27)n 3m

3

3 ×2 value of m – n.

41. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m. The advertisements yield an earning of ` 5000 per m 2 per year. A company hired one of its walls for 3 months. How much rent did it pay? A. ` 3300000 B. ` 1650000 C. ` 1600000 D. ` 19800000



=

1 , then find the 27

A. –1

B. 1 C. 2

D. 0

45. Simplify :

( a 2 − b2 )3 + ( b2 − c 2 )3 + ( c 2 − a 2 )3 ( a − b)3 + ( b − c )3 + ( c − a )3

A. (a – b) (b – c) (c – a)

a2 + b2 + c 2 B.

42. In a middle school 3 out of 5 students make honor roll. What percent of students does not make honor roll?

C. (a + b) (b + c) (c + a)

D. 3abc

ACHIEVERS SECTION The internal and external diameters of a hollow

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

hemispherical vessel are 20 cm and 28 cm respectively.

Statement-I : In a quadrilateral ABCD,

Then, 4400 cm 2 . 7 (ii) Its outer curved surface area is 1232 cm2.



(AB + BC + CD + DA) > 2AC Statement-II : The sum of any two sides of a triangle is greater than the third side.

(i)

Its inner curved surface area is

15437 cm 3 . 21 (ii) (iii)



A.

Statement-I is true and Statement-II is false

(iii) Its volume is



B.

Both Statement-I and Statement-II are false

(i)



C.

Both Statement-I and Statement-II are true



A. T

T

F



D.

Statement-I is false and Statement-II is true.

B. T

T

T

C. F

F

F



T

F

47. Read the statements carefully and state 'T' for true and 'F' for false. 6

D. F

| 10th IMO | Class-9 | Level 2

2019

(i) (ii) 13 1 1 4 31 1 2 1 1 2 the value of x x x x + = 194 , find + , + and + x x x = , find + , + and + 194 A. DPQM DPQR x x x2 x4 x4 x3 x2 x3 B. DPMR DPQM 1 1 1 + 3 , x 2 + 2 and x + . x C. DPQR DPQM x x 1 1 1 3 2 D. DPQR DPMR x + 2 x+ x + 3 x x x A. 52 14 4 50. Two steel sheets each of length a1 and breadth a 2 B. 56 16 8 are used to prepare the surfaces of two right circular C. 56 16 4 cylinders – one having volume v1 and height a2 and other having volume v 2 and height a1. Then, D. 52 14 8 48. If x 4 +

1

49. If two sides AB and BC and the median AD of DABC are equal respectively to the two sides PQ and QR and the median PM of the other triangle PQR, then

A. v 1 = v 2 B. a1v1 = a2v 2 C. a2v1 = a1v 2 v1 v2 D. 2 = 2 a1 a2

(i) DABD ≅ (ii) DABC ≅

SPACE FOR ROUGH WORK

7

10th IMO | Class-9 | Level 2 |

2019

LEVEL - 2 Year 2017-18 2019

MATHEMATICS In the given figure, if DE || AF, AD || FG, then find the value of x and y respectively. G

30° x E

y

45°, 45° 120°, 45°

C



A. C.

B. D.

2.

Find the value of 'a', if 2x 4 – ax 3 + 4x 2 – x + 2 is divisible by 2x + 1.



A. C.

3.

The mean of the following distribution is 50.

28 –25

x f(x)

B. D.

10 17

30 5p + 3



(a) Volume of water.



(b) A metal sphere of radius 2 cm is totally submerged in the water. Find rise in the water level. A.

565.71 cm3

0.29 cm



B. C. D.

cm3

2.56 cm 3.23 cm

7.

In the given figure, find the value of y.

A

60°

A cylindrical container of base radius 6 cm, has water upto a height of 5 cm. Find :

 (a)  (b)

F

D 95°

B

6.

125°, 35° 125°, 30°

N

20° L

30

M

70 7p – 11

90 19



A. C.

8.

Which of the following statements is INCORRECT?



A.



B.



C.



D.

9.

Two identical circles with same inside design as shown in the figure are to be made at the entrance. The identical triangular leaves in a circle are to be painted red and the remaining area to be painted green. Find the total area to be painted red.

Find the value of p.

A. C.

B. D.

4.

A die thrown 100 times and the outcomes are recorded as follows: Outcome Frequency

2 20

3 12

4 18

5 15

6 10

Find the probability of getting:

(i) An even number. (ii) A prime number.   (i)  (ii) A. 13/25 71/100 B. 18/100 67/100 C. 12/25 47/100 D. 12/25 71/100 Simplify:



A.

0

B.

2 5



C.

5

D.

3 2

45° 90°

Pyramid is a solid figure, the base of which is a triangle or square or some other polygon and its side faces are equilateral triangles that converges to a point at the top. In geometry, we take a point, a line and a plane as undefined terms. If the area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square, then the area of the triangle also equals the area of the square. Euclid's fourth axiom says that things which coincide with one another are equal to one another.

cm

15 cm

1 1 1 − + (3 − 8 ) ( 8 − 7 ) ( 7 − 6 ) 1 1 − + ( 6 − 5 ) ( 5 − 2)

5.

B. D.

28



1 25

4 5

20° 30°

41

10 12

y

40°

°

0 –29

50 32

565.71 675.23 cm3 None of these



2

cm

1.

A. C.

126 cm2 1512 cm2

B. D.

756 cm2 None of these | IMO | Class-9 | Level 2

2019

10. Find a and b, if

A.

2 5+ 3 2 5− 3 + = a + 15 b . 2 5− 3 2 5+ 3

0, 5

46 C. , 0 17

B.

23 25 , 12 13

D.

1 2 , 17 17



11. P is the point (–5, 3) and Q is the point (–5, m). If sum of abscissas and ordinates of both points is equal, then the possible value of m is

A. C.

–5 – 10

B. D.

15. The construction of a DPQR in which QR = 6.4 cm and ∠Q = 60° is not possible when (PQ + PR) is equal to ______.

– 13 3

A. C.

6 cm 8 cm

B. D.

6.5 cm 7 cm

16. A rhombus shaped field has green grass for 12 cows to graze. If each side of the rhombus is 30 m and its diagonal is 48 m, then the area of the grass field which each cow can graze is ______.

A. C.

72 m2 48 m2

70 m2 864 m2

B. D.

x y z = = , then find the values 3 4 5 of x, y and z respectively.

17. In the given figure, if

12. Find the area enclosed between lines p, q, r and s.

A

B

D C

x

z Q

y P



A. C.

20 sq. units 25 sq. units

B. D.

24 sq. units 30 sq. units

13. ABCD is parallelogram as shown in the figure. O is any point on AC. PQ || AB and ML || AD. Then ar(DLOP) = L

D

O

P A

C

Q

M

B

A. ar(ABCD)

B.

C. ar(DLMA)

D.

ar(BMOQ) 1 ar(BMOQ) 2

14. For an integer n, a student states the following :



III. If n is even, (n − 1) is irrational. Which of the above statements would be definitely true ? Both I and III Both II and III

B D.

Both I and II All I, II and III

B. D.

36°, 48°, 60° 30°, 45°, 60°

18. The percentage of marks obtained by a student in the monthly unit tests are given below: Unit test I II III IV V Percentage of marks obtained 58 74 76 62 85 Find the probability that the student gets: (i) A distinction i.e. 75% or above. (ii) Less than 65% marks. (i) (ii) A. 1/5 2/5 B. 2/5 1/5 C. 2/5 2/5 D. 1/5 3/5 19. ABCD is a parallelogram in which ∠A = 60°. If the bisectors of ∠A and ∠B meet at P, then D

I. II.

A. C.

45°, 30°, 45° 30°, 45°, 30°

If n is odd, (n + 1)2 is even. If n is even, (n – 1)2 is odd.





A. C.

B

A

A. AD = DP C. DC = 2 AD

C

P

B. D.

PC = BC All of these 3

IMO | Class-9 | Level 2 |

2019

16

cm

20. A kite is in the shape of a square with side 16 cm and an isosceles triangle of base 4 cm and equal side of 6 cm each. Find the area of shaded part.

24. The mean of monthly salary of 12 employees of a firm is ` 14,500. If one more person joins the firm who gets ` 18,400 per month, then what will be the mean monthly salary now? A. ` 17,200

B.

` 14,500

C. ` 12,500

D.

` 14,800

6

cm

25. How many of the following statements is INCORRECT?

4 cm



A. C.

142.35 cm2 133.65 cm2

B. D.

25  256  +  3 64  625 

21. Simplify : 3

−1/ 4

+

125.64 cm2 216.38 cm2 1  64    125 

2/3

27 − 7 3 216 + 10 6 64 + 121

61 A. 729 1 C. 768

B. D.

−65 128 76 437



(i)

A binomial can have atmost two terms.



(ii) Every polynomial is a binomial.



(iii) A binomial may have degree 6.



(iv) Zero of a polynomial is always 1.



(v) A polynomial cannot have more than two zeroes.



A.

3

B.

2



C.

4

D.

5

26. PQRS is a square. N and M are the mid-points of sides SR and QR respectively. O is a point on diagonal PR such that OP = OR. Then (i) ONRM is a

P .

(ii) The ratio of ar(DORM) and ar(PQRS) is S

22. In the given figure, DABC and DABD are equilateral triangles. Find the coordinates of points C and D respectively.

N

Q .

R

M

O

Y C

P

X′

(–a, 0) A

(a, 0) B

O

X

D Y′



A. (a, 0), (–a, 0)



B. C. D.

B. C. D.

Q



A.

Square

1:2



B.

Rectangle

1:2



C.

Square

1:8



D.

Rectangle

1:4

27. Which of the following statements is true?

(–a, 0), (0, –a) (0, a), (0, –a) None of these

23. A dome of a building is in the form of a hemisphere. From inside, it was white washed at the cost of ` 997.92. If the cost of white washing is 400 paise per square metre, then find the volume of air inside 22   the dome.  Take π =   7  3 A. 83.16 m

Q

P

m3

523.90 425.20 m3 None of these

4



(i)

A major arc of a circle is the set of points of the circle that lie on or outside a central angle.



(ii) Equal chords of a circle are equidistant from the centre.



(iii) The opposite angles of a cyclic quadrilateral are supplementary.



A.

Only (i)

B.

Only (ii)



C.

Only (ii) and (iii)

D.

All (i), (ii) and (iii)

28. Factorise : p3(q – r)3 + q3(r – p)3 + r3(p – q)3

A.

2pq(p + q)(q + r)(r – p)



B.

3pqr(p – q)(r – q)(r – p)



C.

2pqr(p – q)(q – r)(p – r)



D.

3pqr(p – q)(q – r)(r – p) | IMO | Class-9 | Level 2

2019

29. Arrange the following steps of construction, while constructing triangle ABC, in which BC = 3.8 cm, ∠B = 45° and AB + AC = 6.8 cm.

 (i)  (ii)

A.

–153/65

18/127



B. C. D.

18/65 1/153 –153/65

18/127 3/65 5/127



Step-1 : From ray BX, cut-off line segment BD equal to AB + AC i.e., 6.8 cm.



Step-2 : Draw BC = 3.8 cm.



Step-3 : Draw the perpendicular bisector of CD meeting BD at A.



Step-4 : Join CD.



Step-5 : Join CA to obtain the required triangle ABC.

A



Step-6 : Draw ∠CBX = 45°.

a



A.

2, 6, 3, 1, 4, 5



B. C. D.

2, 6, 1, 4, 3, 5 2, 6, 3, 4, 5, 1 1, 2, 4, 5, 3, 6

33. In the given figure, O is the centre of a circle, BC is its chord and A is any point on the circle. If ∠BAC = a and ∠OBC = b, then find a + b.

O

B

30. Which of the following equations has graph as shown in figure?



A. 45°



B. C. D.

b

C

90° 180° 60°

34. In the figure, ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects CD at F. Then ar(DBDF) = k ar(ABCD). A B Find k. 1 A. 3 1 B. 2

A. x+y=0 B. y = 2x C. y = 2x + 4 D. y = x – 4 31. In the given figure, which of the following statements must be true? (ii) a + c + e = 180° (iii) b+f=c+e A.

(i) only



B. C. D.

(ii) only (iii) only (ii) and (iii) only ax 3

3x 2

2x 3

32. The polynomials + – 3 and – 5x + a when divided by (x – 4) leave the remainders R1 and R 2 respectively. Find the values of a in each of the following cases, if (i) R1 + R 2 = 0

C.



D.

2 1 4

C

F

E

35. To construct a wall 25 m long, 0.3 m thick and 6 m high, bricks of dimensions 50 cm × 15 cm × 10 cm, each are used. If the mortar occupies 1/10th of the volume of the wall, then find the number of bricks used.

(i) a+b=d+c





D

(ii) 2R1 – R 2 = 0



A.

5400



B. C. D.

5000 6000 6400

36. If one 24 is replaced by 26 in the given data, then find the median and mode respectively. 24, 17, 13, 24, 26, 20, 26, 30, 8, 41, 24

A.

24, 24



B. C. D.

26, 26 24, 26 24, 30 5

IMO | Class-9 | Level 2 |

2019

37. When numerator of a fraction is increased by 2, the fraction reduces to 1/3. Let numerator and denominator be x and y, respectively. Write the given data in form of a linear equation in two variables. A. x + 3y + 6 = 0 B. y – 3x + 6 = 0 C. 3x – y + 6 = 0 D. 3x + y – 6 = 0

A. B. C. D.

A line A point Infinitely many lines Two lines

39. Which one of the following statements is CORRECT?

A.



B.



C.



D.

If two angles forming a linear pair, then each of these angles is of measure 90°. Angles forming a linear pair can both be acute angles. Both of the angles forming a linear pair can be obtuse angles. Bisectors of the adjacent angles forming a linear pair form a right angle.

40. If the given figure, OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter, then CA = ______. A

A. a> B. a < C. a> D. a
>

0 0 0 0

43. Match the following.

38. The equation x – 2 = 0 on number line is represented by ________.

42. For which value, point A (a, b) lies in the quadrant III?

D

Column I Column II P. Postulate 1 1. A terminated line can be produced indefinitely. Q. Postulate 2 2. All right angles are equal to one another. R. Postulate 3 3. A straight line may be drawn from any one point to any other point. S. Postulate 4 4. A circle can be drawn with any centre and any radius. P Q R S A. 1 3 2 4 B. 4 3 2 1 C. 3 1 4 2 D. 3 4 1 2 Direction (44-45): The pie-chart shown below gives the distribution of land in a village under various food crops. Study the pie-chart carefully and answer the questions that follow: Distribution of areas (in acres) under various food crops

B Wheat Rice

O

Barley 36° 18°

72°

72°

Jowar 18° 99° 45° jra Ba Others Maize

C

A. 2OD B. OD C. AB D. AD 41. In the given figure, AB || CD. Diagonals AC and BD intersect at point O. If AO : OC = 1 : 3, then area of (∆AOB) = area of (∆ABD)

44. If the production of wheat is 6 times that of barley, then what is the ratio between the yield per acre of wheat and barley?

A. B. C. D.

3:2 3:1 12 : 1 2:3

45. If the total area goes up by 5%, and the area under wheat production goes up by 12%, then what will be the angle for wheat in the new pie-chart? 1 A. 4 C. 16

B. D.



1 9 116

6

A. B. C. D.

62.4° 76.8° 80.6° 84.2° | IMO | Class-9 | Level 2

2019

ACHIEVERS SECTION 46. Which of the following statements is true? Statement 1: A cylinder is within the cube touching all the vertical faces. A cone is inside the cylinder. If their heights are same with the same base, then the ratio of their volumes is 40 : 31 : 11.

49. Fill in the blanks.

(i)



Statement 2: A conical tent is accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breath. Then the height of the cone is 15 metres.

(ii) The triangle formed by joining the mid-points of the sides of a right triangle is Q .



(iii) The figure formed by joining the mid-points of consecutive sides of a quadrilateral is R .



A.

Only statement 1



A.

Isosceles

Scalene



B.

Only statement 2



C.

Both statement 1 and statement 2



B. C. D.

Equilateral Isosceles Equilateral

Equilateral Trapezium Right triangle Parallelogram Right triangle Trapezium



D.

Neither statement 1 nor statement 2

47. In the given figure, if O is the centre of the given circle and chords AB and CD intersect at a point E inside the circle, then ∠AOC + ∠BOD is equal to



A.

  P   Q   R

Number of families 400 600 300 500 200

Girl 1 1 2 0 2

Column-I Column-II

48. State T for True or F for False. −2

Boy 1 2 1 2 0

If one family is chosen at random, then match Column-I with their corresponding probabilities in Column-II.

B.

1 (i)  4 

Parallelogram

50. A NGO selected 2000 families at random and surveyed them to determine number of children in a family. The data is given below :

3∠AEC

1 ∠AEC 2 C. ∠AEC D. 2∠AEC

The triangle formed by joining the mid-points of the sides of an isosceles triangle is P .

9 − 3 × 82 / 3 × 4 0 +    16 

−1/ 2

=

16 3

−3 1 (ii) + (0.01) −1/ 2 − (27) 2/3 = 4 2 1 (iii) 93/ 2 − 3 × 50 −    81

−1/ 2

= 15

3−3 × 62 × 98 = 25 2 (iv) 1 2 −4 / 3 1/ 3 3 5 × × (15) ×3 25 (i) (ii) (iii) (iv)

A.

T

F

T

F



B.

T

T

T

F



C. D.

F F

T F

T T

F T

The probability that the family chosen has 1 boy and 2 girls is

1.

1 10

Q. The probability that the family chosen has no boy is

2.

3 10



R. The probability that the family chosen has 1 boy and 1 girl is

3.

3 20



S. The probability that the family chosen has 2 boys

4.

1 5



P.

and 1 girl is P Q R S A. 2 4 3 1 B. 4 3 2 1 C. 1 2 3 4 D. 3 1 4 2 7

IMO | Class-9 | Level 2 |

2019

SPACE FOR ROUGH WORK

8

| IMO | Class-9 | Level 2

2019

LEVEL - 2 Year 2018-19 2019

MATHEMATICS 1.

The mean age of combined group of men and women is 35 years. If the mean age of men is 36 years and that of women is 32 years. Find the percentage of women in the group.



A. 25% B. 75% C. 27% D. 23%

2. If

Q

R

O

P

S

A. 16 2 cm

2

32 2 cm2 B. 28 2 cm2 C.

−3 3 2 4 3 = a 2 + b 3 , then − + 3+ 2 6+ 3 6+ 2



find the value of a + b. A. 0 B. 1 C. 2 D. –1

3.

Which of the following is correct?



A.



B.



C.



D.

4.

There is a cone of height 18 cm, out of which a smaller cone (which is the top portion of the original cone) with the same vertex and vertical axis is cut out. What is the ratio of the volume of the larger (actual) cone to the smaller cone, if the height of the smaller cone PS ST = ? is 12 cm and PQ QR

The sum of the three altitudes of a triangle is less than the sum of three sides of the triangle. The perimeter of a triangle is greater than the sum of its three medians. Any two sides of a triangle are together greater than twice the median drawn to the third side. All of these

P

S

Q

T

2 D. 64 2 cm

6.

I n q u a d r i l a t e r a l A B C D, i f ∠ D = 7 4 ° a n d ∠A : ∠B : ∠C = 4 : 2 : 5, then ∠C =



A. 175° B. 135° C. 150° D. None of these

7.

A pair of dice is thrown. The probability of getting prime number on first die and composite number on the second die is

1 A. 6

A. B. C. D.

3 : 1 9:1 27 : 8 16 : 7

5.

In the given figure, the semi-circle centered at O has a diameter 12 cm. The chord QR is parallel to PS and 1 QR = PS. The area of the trapezium PQRS is 3

2

1 2

1 C. 4 1 D. 3 8.

What must be subtracted from 4x 4 – 2x3 – 6x2 + x – 5 so that the result is exactly divisible by 2x2 + x – 1?



A. 6 B. – 6 C. 5 D. –1

9.

The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?



A. 75% B. 67% C. 43.75% D. 25%

R



B.

10. In the given figure (not drawn to scale), AB is diameter of a circle centred at O. Chord CD is equal to radius OC. If AC and BD (when produced) intersect at P, then find ∠APB. | IMO | Class-9 | Level 2

2019

15. Given below parallelograms are of same area. Find the value of h. O

A

S

B

R

h

C

D

E



P



A. 30° B. 60° C. 75° D. 50°

11. If a, b, c are such that a + b + c = 3, a 2 + b 2 + c 2 = 9, a 3 + b 3 + c 3 = 12, then a 4 + b 4 + c 4 is equal to ________.

A. 10 B. 12 C. 18 D. None of these

12. In the given figure (not drawn to scale), O is the centre of the circle. Find the value of x. x

51 72°



A. B. C. D.

A. 30° B. 44° C. 42° D. 50°



A. 45 B. 44 C. 21 D. 46

17. A point whose abscissa and ordinate are of same sign, lies in

A. B. C. D.

First or fourth quadrant. Second or third quadrant. First or third quadrant. Second or fourth quadrant.

P A

P : There are infinite number of lines which are passing through the point (2, 4).

A. B. C. D.

Both P and Q Only P Only Q Neither P nor Q

11 − 10

C

B

R

Q



A. B. C. D.

132 m2 77.06 m2 60.05 m2 216 m2

19. In the given figure, ABCD is a parallelogram and E is the mid-point of BC. Also, DE and AB produced such that they intersect at F. Then, D

12 − 11

A. < B. > C. = D. Can’t be determined

C E

14. Which of the following options make given expression true?

Q

4.8 cm 3 cm 5.6 cm 8.4 cm

18. In the given figure, the sides of DPQR are 22 m, 36 m and 16 m and sides of DABC are 12 m, 14 m and 8 m. Find the area of the shaded region.

Q : A linear equation in two variables has infinitely many solutions.

T

P

16. The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 are arranged in ascending order. If the median is 45, then find the mode of the given data.

13. Which of the following statements are true?

4.8

A

B

F

3 AB 2 AF = 2 AB B. C. AF = 3AB D. AF2 = 2AB2 AF = A.

3

IMO | Class-9 | Level 2 |

2019

20. When 6 is subtracted from the numerator and denominator both of a fraction, then the new ratio of numerator to denominator becomes 17 : 19. What is the original ratio?

A. B. C. D.

15 : 25 3:5 38 : 40 Data inadequate

21. In the given figure, the sides AB and AC of DABC are produced to points D and E respectively. If bisectors BP and CP of ∠CBD and ∠BCE respectively meet at point P, then find ∠BPC. A 62° B

C

D

E

24. For an integer n, a student states I. If n is odd, then (n + 1)2 is even. II. If n is even, then (n – 1)2 is odd.

25. The area of the triangle formed by 6x + 8y = 2 and the coordinate axes is

A. B. C. D.

1 sq. unit 2 sq. units 3 sq. units 0.04 sq. unit

26. Let R1 and R 2 are the remainders when the polynomials f(x) = 4x3 + 3x2 – 12ax – 5 and g(x) = 2x3 + ax2 – 6x + 2 are divided by (x – 1) and (x + 2) respectively. If 3R1 + R 2 + 28 = 0, then find the value of a.

P



III. If n is even, then ( n − 1) is irrational. Which of the above statements would be correct? A. Only I and III B. Only I and II C. I, II and III D. Only II and III

A. 59° B. 62° C. 61° D. 118°

22. There is a visit in a school by Directorate of Education. Girls are asked to prepare a rangoli in triangular shape. Dimensions of DABC are 26 cm, 28 cm and 25 cm. Garland is to be placed along the sides of DPQR, which is formed by joining mid-points of sides of DABC. Find the length of garland.



A. –1 B. 2 C. 1 D. 3

27. In the given figure PCD and BCQ are straight lines. x y z If = = , then calculate the values of x, y and z. 3 4 5 A

A R



A. B. C. D.

36 cm 39.5 cm 26.3 cm 46 cm

B

Q P

B y° P

C



23. Mayank and Sujata, two students of class 9th together contributed `1000 to PPM relief fund. (i) Find the linear equation satisfying the data. (ii) If Sujata contributed `475, then how much Mayank contributed (in `)?     (i) (ii) A. 2x + y = 1000 575 B. x + y = 1000 525 C. 0⋅x + 1⋅y = 100 575 D. 2x + 2y = 500 525



4

A. B. C. D.

36°, 48°, 32°, 36°,

48°, 38°, 50°, 50°,

C

x°z°

D Q

60° 62° 55° 60°

28. In the given figure, AD is the median of DABC, BL and CM are perpendiculars drawn from B and C respectively. Which of the following is correct? A L B

C

D M

| IMO | Class-9 | Level 2

2019

A. DOAB ≅ DPQS B. DOAB ≅ DRQS C. DOAB ≅ DPQS D. None of these

A. BL || CM

B. DBLD @ DCMD C. LD = MD D. All of these 29. The maximum number of children among them 847 candies and 385 chocolates can be distributed in such a way that each child gets the same number of candies and same number of chocolates is

A. 77 B. 462 C. 85 D. 191

30. Consider point P(4, 3) and Q(3, 4). Which point is farthest from the origin? A. P B. Q C. Both are at equal distance D. Can't be determined

33. Avantika tells her son Kartik, "Eight years ago, I was 5 times as old as you were then. Also, four years from now, I shall be four times as old as you will be". If present ages of Avantika and Kartik are x and y years respectively, then represent this situation algebraically. A. 7x – y = 42; y – 3x = 6 B. x – y = 42; y – 3x = 6 C. x – 7y = 6; y – x = 4 D. x – 4y = 12; 5y – x = 32 34. The bar graph shows the export/import for 5 consecutive years for any goods. Answer the following question based on the graph.

31. In the given figure, LMNO and PMNQ are two parallelograms. R is any point on side MP such that ar (DNRQ) = k ar (||gm LMNO). Find the value of k. L M

R P O

N Q

1 A. 3 1 B. 2 1 C. 4 2 D. 3 32. In the given figures, PQRS is a square and DOAB is right angled triangle, then which of the following is not correct? P

B 5 A

5 O

C

S

5 Q

R



In which year the difference of the values of export and import is maximum?



A. B. C. D.

2007-08 2009-10 2010-11 2006-07

35. Select the correct statement. A. The sum of a rational number and an irrational number is a rational number. B. The product of a non-zero rational number with an irrational number is an irrational number. C. The quotient of an irrational number with a nonzero rational number is a rational number. D. None of these 36. The height of a cylinder is 14 cm and its volume is 396 cm3, then the curved surface area is ________.

A. B. C. D.

264 269 226 369

cm2 cm2 cm2 cm2 5

IMO | Class-9 | Level 2 |

2019

37. In the given figure, AB || DG, AC || DE, ∠EDH = 25° and ∠BAC = 20°. Find the values of x and y. B C

A



A. B. C. D.

G y 25°

x

20° D

E H

115°, 20° 95°, 20° 115°, 30° 90°, 25°

38. In the given figure, if C is the centre of circle, AB = 8 cm, DE = 8 cm and CD = 5 cm, then CF is equal to



C.



D.

If equals are subtracted from equals, the remainders are equal. Things which coincide with one another are equal to one another.

41. Sneha has a triangular field with sides 240 m, 280 m, 320 m, where she grew rice. Karan also have a triangular field with sides 270 m, 290 m, 300 m to grow rice. Who has more area to grow rice and how much more?

A. B. C. D.

Sneha, 2852.81 m2 Karan, 2852.81 m2 Karan, 5228.81 m2 None of these

42. In a triangle ABC, P, Q and R are the midpoints of side BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, then perimeter of the quadrilateral ARPQ is b cm. The value of



A. B. C. D.

3 2 5 4



cm cm cm cm

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

43. ABCD is a cyclic quadrilateral. If ∠BCX = 70° and ∠ADY = 80°, then find the values of x and y respectively.

39. Three fair coins are tossed simultaneously. Find the probability of getting at most two tails.

A x

3 A. 8

1 D. 8 40. In the given figure, if ∠ABC = ∠ACB, ∠3 = ∠4, then ∠1 = ∠2. A

D 4 B

1

3 2

C

Which of the following Euclid's axiom best illustrates the above? A.



B.

y

80° Y

7 B. 8 1 C. 2



b + 1 is 17

Things which are halves of the same things are equal to one another. If equals are added to equals, the wholes are equal.

6

A. B. C. D.

B 70°

D

C

X

70°, 80° 70°, 70° 80°, 70° None of these

44. Four cows are tethered at four corners of a square plot of side 74 metres, having length of rope half of the side of square. The area left ungrazed is

A. B. C. D.

675.5 m2 1280 m2 1173.43 m2 850.5 m2

45. If a + b = 12 and ab = 25, a > 0 and b > 0, then a3 – b3 is ± 338 11 A. ± 38 11 B. ± 2 11 C. ± 238 11 D. | IMO | Class-9 | Level 2

2019

ACHIEVERS SECTION 46. If x, y and z are consecutive positive integers such that x < y < z, then which of the following must be true?

I.

xyz is divisible by 6.

II. (z – x) (y – x + 1) = 4 III. xy is odd. A. Only I B. Only II C. Only III D. Only I and II 47. Consider the volumes of the following:

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

A cuboid of length 8 cm, breadth 6 cm and height 3 cm. A cube of each side 6 cm. A cylinder of radius 4 cm and height 8 cm. A sphere of radius 6 cm. volumes of these in the increasing order is 1, 2, 3, 4 1, 3, 2, 4 4, 2, 3, 1 4, 3, 2, 1

49. Following are the steps of construction of a DABC in which BC = 6 cm, ∠B = 60° and the sum of other two sides is 9 cm. I. Along BX, cut BP = 9 cm. II. Draw the perpendicular bisector of CP to intersect BP at A. III. Construct ∠CBX = 60°. IV. Draw BC = 6 cm. V. Join AC. VI. Join CP. Then, DABC is the required triangle.

Arrange them in proper order and select the correct option.



A. B. C. D.

50. Over the past 150 working days, the number of defective parts produced by a machine is given in the following table. Number of defective parts Days

48. Fill in the blanks and select the correct option. •

I f a, b, c are sides of a triangle and a2 + b2 + c2 = bc + ca + ab, then the triangle is P .

•

T  wo triangles are said to be congruent, if the ratio Q of corresponding sides is one.

•

I n DABC, if ∠B = 90°, AC = 6 cm and D is the mid-point of AC, then length of BD is R . P Q R Isosceles equal to 4 cm Equilateral equal to 3 cm Isosceles greater than 4 cm Equilateral greater than 3 cm

A. B. C. D.

III, I, VI, II, V, IV IV, III, I, II, VI, V IV, III, I, VI, II, V None of these

0

1

15 32

2

3

22 24

4

5

6

28 12 17



Determine the probability that tomorrow’s output will have



(i)



(ii) at least 2 defective parts.



(iii) not more than 4 defective parts.

no defective parts.

(i) (ii) A. 0.1 0.806

(iii) 0.686

B. 0.1 0.686 0.806 C. 0.2 0.686 0.806 D. 0.2 0.806 0.686

SPACE FOR ROUGH WORK

7

IMO | Class-9 | Level 2 |

2019

ANSWER KEYS IMO 2014 1. (D) 2. (D) 3. (B) 4. (C) 5. (C) 6. (B) 7. 8. (B) 9. (B) 10. (C) 11. (D) 12. (B) 13. (A) 14. 15. (C) 16. (B) 17. (B) 18. (A) 19. (D) 20. (C) 21. 22. (D) 23. (C) 24. (A) 25. (C) 26. (C) 27. (B) 28. 29. (C) 30. (D) 31. (C) 32. (C) 33. (A) 34. (D) 35. 36. (A) 37. (B) 38. (C) 39. (A) 40. (B) 41. (A) 42. 43. (C) 44. (A) 45. (A) 46. (B) 47. (D) 48. (B) 49. 50. (C)

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

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.

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

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

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

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

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

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

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

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

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

2019

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

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

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

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

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

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

2019

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

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

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

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

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

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

(C) (B)