Download IMO LEVEL-2 Booklet For Class-X PDF

TitleIMO LEVEL-2 Booklet For Class-X
Tags Elementary Mathematics Circle Geometric Shapes Elementary Geometry
File Size5.0 MB
Total Pages31
Document Text Contents
Page 1

LEVEL - 2

Year 2011-12

5th

Page 2



SECTION I  : LOGICAL REASONING 

1.  There are six persons A, B, C, D, E and F. C  is  the sister of F. B  is the brother of E's husband. D 
is the  father of A and grandfather of F. There are  two fathers,  three brothers and a mother  in the 
group. Which of  the  following is a group of brothers? 
(A)   (B)   (C)   (D)  

2.  Anita, Mahima, Rajan, Lata and Deepti are five cousins. Anita  is twice as old as Mahima. Rajan is 
half  the age of Mahima. Anita  is half  the age of Deepti and Rajan  is  twice  the age of Lata. 
If Mahima  is 16  years  old,  then what  is  the age of Lata? 
(A)   (B)   (C)   (D)  

3.  If second Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then 
how many working days are  there  in  that month? 
(A)   (B)   (C)   (D)  

4.  If the same function is applied to reach the results in each of the three sets of numbers given then 
which number will  replace the question mark  in  the third set of numbers? 
(A)  
(B)   21  5 

17  7 
24 

28  16 13  2 

25  10 7  8 
30  ? (C)  

(D)  

5.  If the first and the second letters of the word UNPRECEDENTED are interchanged with the last and 
the second last letters and similarly the third and the fourth letters are interchanged with the third 
and the fourth  letters from the last respectively and so on, then what will be the seventh  letter to 
the  right  of  the third  letter  from  the  left end? 
(A)   (B)   (C)   (D)  

6.  Ravi wants  to go  to the university. He  starts  from his home which  is  in the East and comes  to a 
crossing. The road to the left ends in a theatre, and straight ahead is the hospital. In which direction 
is the university  if all  the  four places are  in different directions ? 
(A)   (B)   (C)   (D)  

7.  Find out the wrong  term  in the number series. 
105, 85,  60, 30,  0, –  45, –  90 

(A)   (B)   (C)   (D)  

8.  Choose the number­letter group which  is different from  the others. 
(A)   (B)   (C)   (D)  

9.  Select  a  figure  from  amongst  the  options which will  continue  the  series  established by  the  five 
problem figures. 

Problem Figures 



(A)  (B)  (C)  (D)

Page 15

7 6th IMO | Level-II | Class 10 |

38. a person of height 2 m wants to get a fruit which is on the top of a pole of height 10
3

m if he

stands at distance of 4
3

m from the foot of the pole, then the angle at which he should throw

the stone, so that it hits the fruit is _____.
(a) 15° (B) 30° (c) 45° (D) 60°

39. The point (–4, –2) lies on a circle. What is the length of the radius of this circle, if the centre is
located at (–8, –10)?

(a) 48 (B) 80 (c) 108 (D) 288

40. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the
boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park
(in sq. m) is ______.

(a) 15360 (B) 153600 (c) 30720 (D) 307200

Section-iii : eVeRYDaY MatHeMaticS

41. In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees
is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. the
length of the garden is ______.

(a) 20 m (B) 22 m (c) 24 m (D) 26 m

42. 3 years ago, the average age of a family of 5 members was 17 years. a baby having been born,
the average age of the family is the same today. the present age of the baby is _____.

(a) 1 year (B) 1
1
2

years (c) 2 years (D) 3 years

43. Rajan got married 8 years ago. His present age is
6
5 times his age at the time of his marriage.

Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's
sister is ______.

(a) 32 years (B) 36 years (c) 38 years (D) 40 years

44. In a History examination, the average for the entire class was 80 marks. If 10% of the students
scored 95 marks and 20% scored 90 marks, what was the average marks of the remaining students
of the class?

(a) 65.5 (B) 72.5 (c) 75 (D) 85

45. Padma purchased 30 kg of rice at the rate of ` 17.50 per kg and another 30 kg rice at a certain
rate. She mixed the two and sold the entire quantity at the rate of ` 18.60 per kg and made 20%
overall profit. At what price per kg did she purchase the lot of another 30 kg rice?

(a) ` 12.50 (B) ` 13.50 (c) ` 14.50 (D) ` 15.50

46. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for
14 months, 8 months and 7 months respectively. What was the ratio of their investments?

(a) 5 : 7 : 8 (B) 28 : 49 : 64 (c) 38 : 28 : 21 (D) None of these

47. Simi can do a work in 3 days, while Meeta can do the same work in 2 days. Both of them finish
the work together and get ` 150. What is the share of Simi?

(a) ` 30 (B) ` 60 (c) ` 70 (D) ` 75

Page 16

8 | 6th IMO | Level-II | Class 10

48. A bicycle can be purchased on cash payment of ` 1500. The same bicycle can also be purchased
at the down payment (initial payment, at the time of purchasing) of ` 350 and rest can be paid in
3 equal installments of ` 400 for next 3 months. The rate of SI per annum charged by the dealer
is _____.

(A) 23
9

17
% (B) 17

9
23

% (C) 13
9

17
% (D) None of these

49. The question given 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.

A solid metallic cone is melted and recast into a sphere. What is the radius of the sphere?
I. The radius of the base of the cone is 2.1 cm.
II. The height of the cone is four times the radius of its base.
III. The height of cone is 8.4 cm.
(A) Only I and II (B) Only II and III (C) Only I and III (D) Any two of three

50. Yash invested a certain sum of money at 8% p.a. simple interest for ‘n’ years. At the end of ‘n’
years, Yash got back 4 times his original investment. What is the value of n?

(A) 50 years (B) 25 years (C) 12 years 6 months (D) 37 years 6 months

SPACE FOR ROUGH WORK

Page 30

79th IMO | Class-10 | Level 2 |

47. Rakesh has to buy a TV. He can buy TV either making
cash down payment of ` 14000 at once or by making
12 monthly instalments as below :

` 1500 (1st month), ` 1450 (2nd month), ` 1400
(3rd month), ` 1350 (4th month), ........
Each instalment except the first is ` 50 less than the
previous one.

Find (i) Amount of the instalment paid in the 9th
month.

(ii) Total amount paid in 12 instalments.
(iii) How much extra he has to pay in addition

to the amount of cash down payment ?
(i) (ii) (iii)
A. ` 1100 ` 16700 ` 900
B. ` 1200 ` 14700 ` 600
C. ` 1100 ` 14700 ` 700
D. ` 1100 ` 14700 ` 900

48. Find the mode of the distribution from the following
table :

Marks
Less

than 20
Less

than 40
Less

than 60
Less

than 80
Less

than 100
No. of

students
4 10 28 36 50

A. 48.904
B. 50.909
C. 62.804
D. 64.324

49. Arrange the given steps in correct order while
constructing a triangle similar to a given triangle ABC

with its sides equal to
3
4

of the corresponding sides

of the triangle ABC (i.e., of scale factor
3
4

).

1. Locate 4 points B1, B2, B3 and B4 on BX so that
BB1 = B1B2 = B2B3 = B3B4.

2. Draw a line through C ′ parallel to the line CA
to intersect BA at A′.

3. Draw any ray BX making an acute angle with
BC on the side opposite to the vertex A.

4. Join B4C and draw a line through B3 parallel to
B4C to intersect BC at C ′.

Then, DA′BC ′ is the required triangle.

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

50. Match the columns :
Column - I Column - II

(i) In figure, a circle touches
all four sides of quadrilateral
ABCD with AB = 18 cm, BC =
21 cm and CD = 12 cm, AD =
..........

A

BC

D

(a) 10 cm

(ii) In figure, value of x is ........

P
Q

x

T

S

R
5 cm 3 cm

2 cm

(b) 9 cm

(iii) Perimeter of DPST with PQ =
10 cm is ......

P

S T

Q R
U

(c) 3 cm

(iv) In figure, PQ = 6 cm, QR = 7 cm,
RS = 4 cm, PS = ...........

A

B

C

D

S R

P Q

(d) 20 cm


A. (i) → (b), (ii) → (a), (iii) → (c), (iv) → (d)
B. (i) → (a), (ii) → (b), (iii) → (d), (iv) → (c)
C. (i) → (b), (ii) → (d), (iii) → (a), (iv) → (c)
D. (i) → (b), (ii) → (a), (iii) → (d), (iv) → (c)

SPACE For roUGH WorK

Page 31

Answer Keys

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

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

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

8th IMo-Level 2 was an online exam. Hence, paper cannot be included in the booklet.

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

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