IMO class 9 5 years Question papers

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Class

1 to 10

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

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

Class 8

Class 9

Class 10

Class 9 4th

Year 2010

Copyright©2015. Science Olympiad Foundation (SOF)

4th IMO - 2010

SECTION  I  :  LOGICAL  REASONING  1. 

A rat runs 20 m towards East and turns to right, runs 10 m and turns to right, runs 9 m and again  turns to left, runs 5 m and turns to left, runs 12 m and finally turns to left and runs 6 m.  Now which  direction  is  the  rat  facing?  (A)  East 

2. 

(C)  North 

(D)  South 

Choose  the  odd  numeral  pair/group  in  the  given  question  :  (A)  2 – 8 

3. 

(B)  West 

(B)  3 – 27 

(C)  4 – 32 

(D)  5 – 125 

The given question contains four problem figures marked 1, 2, 3 and 4.  Select a figure from amongst  the  options  which  will  continue  the  same  series  as  given  in  the  Problem  figures.  Problem Figures 

?  1 

(A) 

4. 

2 

3 

(B) 

4 

(C) 

(D) 

What  comes  next  in  the  given  pattern  ?  10,  19,  40,  77,  158,  ___  ?__  (A)  311 

5. 

(B)  307 

(C)  301 

(D)  299 

Count  the  number  of  cubes  in  the  given  figure.  (A)  23  (B)  24  (C)  25  (D)  None of these 

6. 

Two positions of a dice are given.  When 2 is at the top, which of the following  numbers  could  be  at  the  bottom ? 

7. 

(A)  1 

(B)  2 

(C)  3 

(D)  4 

(B)  55 

(C)  66 

(D)  121 

20 friends meet at a marriage reception of their common friend. Everyone of 20 friends shook hands  with  each  other  only  once.  Find  the  number  of  handshakes.  (A)  400 

9. 

(ii) 

If  7 * 1  =  64;  3 * 9  =  144.  What  is  the  value  of  5 * 6  ?  (A)  22 

8. 

(i) 

(B)  380 

(C)  40 

(D)  190 

Which  of  the  given  options  will  come  next  in  the  given  series  ?  ZUA,  XOC, VIE,  TCG,  ____  ?___  (A)  RAI 

4 th  IMO  |  Level­I  |  Class 9 

(B)  SAG 

(C)  RAG  2 

Copyright©2015. Science Olympiad Foundation (SOF)

(D)  RWI

4th IMO - 2010

10.  The  given  question  consists  of  two  sets  of  figures.    Figures  1,  2,  3  and  4  constitute  the  Problem  set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between  figures  3  and  4  by  choosing  figure  4  from  the  alternatives.  Problem Set 

?  1 

(A) 

2 

3 

(B) 

4 

(C) 

(D) 

11.  One evening before sunset two friends Sumit and Mohit were talking to each other face to face.  If  Mohit's  shadow  was  exactly  to  his  right  side,  which  direction  was  Sumit  facing?  (A)  North 

(B)  South 

(C)  West 

(D)  None of these 

12.  Sarthak remembers that his brother's birthday is after 15 th  but before 18 th  of February whereas his  sister  Kashish remembers  that her  brother's birthday  is after  16 th  but  before 19 th  of February.    On  which  day  in  February  is  Sarthak's  brother's  birthday?  (A)  16 th 

(B)  17 th 

(C)  18 th 

(D)  19 th 

13.  Out of the four figures (A), (B), (C) and (D), three are similar in a certain way.  However, one figure  is  not  like  the  other  three.  Choose  the  figure  which  is  different  from  the  rest. 

(A) 

(B) 

(C) 

(D) 

14.  Find  the  missing  character  in  the  given  question.  (A)  18 

(B)  24 

(C)  36 

(D)  48 

7  9  21 27  4  2  36 18  9  4  54  ? 

15.  In the given number sequence, how many such even numbers are there which are exactly divisible  by  its  immediate  preceding  number  but  not  exactly  divisible  by  its  immediate  following  number?  3  8  4  1  5  7  2  8  3  4  8  9  3  9  4  2  1  5  8  2  (A)  One 

(B)  Two 

(C)  Three 

(D)  Four 

16.  If  'a'  means  'plus',  'b'  means  'minus',  'c'  means  'multiplied  by'  and  'd'  means  'divided  by'  then  18  c  14  a  6  b  16  d  4  =  ?  (A)  63 

(B)  254 

(C)  288 

(D)  1208 

17.  The  numbers  in  the  given  figures  are  arranged  according  to  a  particular  rule.  Select  the  correct  answer  which  is  to  be  written  at  the  place  of  sign  of  interrogation  for  third  figure.  (A)  31 

4 

9 

(B)  23 

25 

18 

16  81 

26 

25  64  64 

? 

144 

(C)  24  36 

(D)  25

49 

3 

Copyright©2015. Science Olympiad Foundation (SOF)

36 

4 th  IMO  |  Level­I  |  Class 9 

4th IMO - 2010

18.  How  many  squares  does the  following  figure  contain? 

(A)  27 

(B)  19 

(C)  30 

(D)  None of these 

19.  How  many  pairs  of  letters  are  there  in  the  word  'LANGUISH'  which  have  as  many  letters  between  them  in  the  word  as  in  the  alphabet?  (A)  Nil 

(B)  One 

(C)  Three 

(D)  Four 

20.  A  bus  starts  from  city  X.  The  number  of  women  in  the  bus  is  half  of  the  number  of  men.  In  city Y, 10 men leave the bus and five women enter.  Now, number of men and women is equal.  How  many  passengers  entered  the  bus  in  the  beginning?  (A)  15 

(B)  30 

(C)  36 

(D)  45 

SECTION  II  :    MATHEMATICAL  REASONING  21.  The  number (3 -

3) is  a/an  ____  . 

3)(3 +

(A)  Rational number 

(B)  Natural number 

(C)  Real number 

(D)  All of these 

22.  Which  of  the  following  polynomials  has  (x  +  1)  as  a  factor?  I.  x 3  +  x 2  +  x  +  1  II.  x 4  +  x 3  +  x 2  +  x  +  1  III.  x 4  +  3x 3  +  3x –2  +  x  +  1  IV.  x 3  +  x 2  –  (2  +  2  )x  +  2  (A)  Only I  (B)  Only III  (C)  II  and  IV  (D)  I  and  II  23.  Two  distinct  lines  _____  .  (A)  Always intersect 

(B)  Always either intersect or are parallel 

(C)  Always have two common points 

(D)  None of these 

24.  In  the  given  figure,  value  of  x  is  ____  .  C  30°  x 

A 

(A)  45° 

45° 

34°  B 

(B)  34° 

D 

(C)  64° 

(D)  109° 

25.  Which  of  the  following  statements  is  correct  ?  (A)  A triangle has two right angles.  (B)  All the angles of a triangle are more than 60°.  (C)  An exterior angle of a triangle is always greater than the opposite interior angles.  (D)  All the angles of a triangle are less than 60°.  26.  A  point  is  defined  as  _____  .  (A)  That which has no length no breadth no height.  (C)  Dimensionless, but represented by dot only.  4 th  IMO  |  Level­I  |  Class 9 

(B)  Small part of a line with no length.  (D)  Undefined term and represented by a dot.

4 

Copyright©2015. Science Olympiad Foundation (SOF)

4th IMO - 2010

27.  On  plotting the  points  O  (0,  0),  A  (3, 0),  B(3,  4),  C(0,  4) and  joining  OA,  AB,  BC  and  CO,  which  of  the  following  figure  is obtained  ?  (A)  Square 

(B)  Rectangle 

(C)  Trapezium 

(D)  Rhombus 

28.  A student is given three sticks of lengths 12 cm, 6 cm and 4 cm respectively.  He is asked to make  a  triangle  and  then  find  the  area  of  the  triangle  formed  by  the  3  sticks  ?  (A)  36 cm 2 

(B)  12 cm 2 

(C)  24 cm 2 

(D)  Providing area not possible 

29.  If  lines  l  ||  m  and Ða  : Ðb  =  3  :  2, ÐQ  =  90°  and Ðb  + Ðc  =  100°,  then  find ÐP  from  given  figure.  A 

l 

P 

a 

Q  b 

c 

m 

B 

(A)  26° 

(B)  32° 

(C)  12° 

(D)  62° 

30.  Which  of  the  following  is  a  factor  of  (x  +  y) 3  –  (x 3  +  y 3 )  ?  (A)  x 2  + y 2  + 2xy 

(B)  x 2  + y 2  – xy 

(C)  xy 2 

(D)  3xy 

31.  Through  how  many  maximum  number  of  quadrants  can  a  straight  line  pass  ?  (A)  2 

(B)  3 

(C)  1 

(D)  4 

32.  What  must  be  subtracted  from  4x 4  –  2x 3  –  6x 2  +  x  –  5,  so  that  the  result  is  exactly  divisible  by  2x 2  +  x  –  1  ?  (A)  5 

(B)  12 

(C)  – 4 

(D)  – 6 

33.  In  the  given  figure,  AB  ||  DE,  then  measure  of ÐACD  is  _____  .  A 

B  l 

40°  C 

D 

(A)  43° 

34.  If

7- 1 7+ 1

43° 

E 

(B)  40° 

-

7 + 1  7 - 1 

(A)  a = 0, b = 

3  2 

(C)  83° 

(D)  97° 

= a + b  7,  then  find  the  values  of  a  and  b.  (B)  a =

-3  , b = 1  2 

(C)  a = 0,  b =

-2  3 

(D)  a = 4, b = 2 

35.  If  a  +  b  +  c  =  9  and  a 2  +  b 2  +  c 2  =  35,  then  find  the  value  of  a 3  +  b 3  +  c 3  –  3abc.  (A)  52 

(B)  108 

(C)  216 

(D)  182 

36.  If  ordinate  of  a  point  is  zero,  then  this  point  always  lies  ____  .  (A)  On the x­axis 

(C)  In the III rd  quadrant 

(B)  On the y­axis 

5 

Copyright©2015. Science Olympiad Foundation (SOF)

(D)  In the IV th  quadrant 4 th  IMO  |  Level­I  |  Class 9 

4th IMO - 2010

37.  ABCD  is  a  given  field  whose  sides  are  indicated.    If ÐDAB  =  90°,  then  area  of  the  field  is  ___.  D 

28 m  C  15 m 

9 m  A  2 

40 m 

2 

(A)  180 m 

B 

(C)  306 m 2 

(B)  126 m 

(D)  300 m 2 

38.  Points  in  which  abscissa  and  ordinate  have  different  signs  will  lie  in  ____  .  (A)  I st  and III rd  quadrants  (B)  III rd  and IV th  quadrants  (C)  II nd  and III rd  quadrants  (D)  II nd  and IV th  quadrants  39.  ABC is an isosceles triangle with AB = AC.  Altitudes are drawn to the sides AB and AC from vertices  B  and  C.    One  altitude  CF  is  found  to  be  4  cm  and  BC  =  5  cm.    Find  EC,  where  BE  is  altitude  to  side  AC.  (A)  4 cm 

(B)  5 cm 

(C)  3 cm 

(D)  None of these 

40.  In  given  figure,  if  AB  ||  CD  ||  EF,  PQ  ||  RS, ÐRQD  =  25°  and ÐCQP  =  60°,  then ÐQRS  is  equal  to  ____  .  S  R  B 

A  C  Q 

25° 

D 

60°  E 

(A)  85° 

F 

P 

(B)  135° 

(C)  145° 

(D)  110° 

SECTION  III  :    EVERYDAY  MATHEMATICS  41.  The  M.P. of a camera is  (A)  25% profit 

3  9  of  the C.P. and S.P.  is  of M.P. Find the percentage  of profit  or loss.  2  10  (B)  35% profit 

(C)  33.33% loss 

(D)  None of these 

42.  P can do a job in 10 days, Q can do the same job in 12 days and R can do the same job in 15 days.  In  how  many  days  they  will  finish  the  work  together?  (A)  2 

(B)  4 

(C)  6 

(D)  12 

43.  Armaan  goes  10  km  distance  with  average  speed  of  6  km/hr  while  the  rest  20  km  he  travels  with  an  average  speed  of  15  km/hr.  What  is  the  average  speed  of Armaan  during  the  whole  journey?  (A)  10 km/hr 

(B)  12 km/hr 

(C)  13 km/hr 

(D)  14.5 km/hr 

44.  A  father  is  three  times as  old  as his  son. After twelve  years,  his age  will  be twice  that  of his  son.  Find  their present  ages.  (A)  10, 30 

(B)  12, 36 

(C)  6, 36 

(D)  124, 24 

45.  250  men  took  a  dip  in  a  water  tank  at  a  time,  which  is  80  m  ×  50  m.  What  is  the  rise  in  the  water  level  if  the  average  displacement  of  1  man  is  4  m 3 ?  (A)  22 cm  4 th  IMO  |  Level­I  |  Class 9 

(B)  25 cm 

(C)  18 cm 

6 

Copyright©2015. Science Olympiad Foundation (SOF)

(D)  30 cm

4th IMO - 2010

46.  Rahul went to purchase a Nokia mobile handset. The shopkeeper told him to pay 20% tax if he asked  for the bill. Rahul manages to get the discount of 5% on the actual sale price of the mobile and he  paid the shopkeeper ` 3325 without tax.  Besides he manages to avoid to pay 20% tax on the already  discounted  price.  What  is  the  amount  of  discount  that  he  has  got  ?  (A)  ` 750 

(B)  ` 375 

(C)  ` 875 

(D)  ` 525 

47.  ABC is a triangle. D, E and F are the mid­points of the sides BC, CA and AB respectively. The ratio  of  the  area  of D ABC  and D DEF  is  _____  (A)  4 : 1 

(B)  5 : 1 

(C)  3 : 1 

(D)  Can't be determined 

48.  P and  Q  can do  a piece of  work  in 12 days,  Q  and  R  in  15  days,  R  and  P  in 20  days.  In how many  days  can  R  alone  do  it?  (A)  60 

(B)  50 

(C)  25 

(D)  24 

49.  A  tent  is  in  the  form  of  right  circular  cone  10.5  m  high,  the  diameter  of  the  base  being  13  m.  If  8  men  are  in  the  tent,  find  the  average  number  of  cubic  metres  of  air  space  per  man.  3  m 3  (A)  32  28 

9  (C)  36  m 3  13 

(B)  59.75 m 3 

3  3  (D)  58  m  32 

50.  If  the  annual  increase  in  the  population  be  20%  and  the  present  population  be  10,000.    What  will  be  the  population  after  3  years ?  (A)  16,000 

(B)  17,280 

(C)  14,400 

(D)  1,728 

SPACE FOR ROUGH WORK

7 

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4 th  IMO  |  Level­I  |  Class 9 

Class 9 5th

Year 2011

Copyright©2015. Science Olympiad Foundation (SOF)

2

5th IMO - 2011

Section I : Logical Reasoning 1.

Study the following information and answer the question given below it. A blacksmith has five iron articles A, B, C, D and E, each having a different weight. (i) A weighs twice as much as B. (ii) B weighs four and a half times as much as C. (iii) C weighs half as much as D. (iv) D weighs half as much as E. (v) E weighs less than A but more than C.



Which of the following is the lightest? (A) A (B) B

(C) C

(D) D

2. Choose the odd numeral pair/group. (B)

1 1 − 2 8

(C)

1 1 − 3 12

(D) 24 – 6



(A) 9 – 3

3.

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



(A)

4.

Out of four figures marked (A), (B), (C) and (D) three are similar in a certain manner. However one



(B)



(C)



(D)

figure is not like the other three. Choose the figure which is different from the rest. (B)

(C)

(D)



(A)

5.

In the matrix there are eight designs and one space is left blank as shown by a question mark. Which answer figures will replace the question mark?







?

(A)

6.

The bank balance of Puran is more than that of Sushma but less than the bank balance of Singh.



(B)



(C)



(D)

If the bank balance of Puran, Sushma and Singh be x, y and z respectively then which of the

following is correct? (A) x < y < z

7.

Find the number of triangles in the given figure.



(A) 18



(B) 20



(C) 24



(D) None of these

(B) y < x < z

(C) z < x < y

Copyright©2015. Science Olympiad Foundation (SOF)

(D) x < z < y

3

5th IMO - 2011 8.

Which number will replace the question mark?

10



(A) 8

4

8

5

6 14 8

6 14 8

6? 4

18

14

22

(B) 4

11

15

(C) 10

(D) 6

9. There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance A climbs on X 5 cm but slips down 1 cm. B climbs on Y 6 cm but slips down 3 cm. C climbs on Z 7 cm but slips down 2 cm. If each requires 50 chances to reach the top of the pillar, what is the height of the shortest pillar?

(A) 144 cm

(B) 152 cm

(C) 153 cm

(D) 141 cm

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

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



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



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



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

1

2

3

4

5

6

7

8

9

11. If 324 × 150 = 54, 251 × 402 = 48 and 523 × 345 = 120, then 651 × 345 = ? (A) 120 (B) 85 (C) 144 (D) 60 12. Find the figure which contains the Fig. (X) as its embedded part.

Fig. (X)



(A)



(B)



(C)



(D)



13. In the number 5904627813 first and sixth digits are interchanged; and similarly the positions of second and seventh digits and so on are interchanged. Which of the following will be the 4 th digit

from the right after the new arrangement? (A) 1 (B) 9

(C) 4

(D) 0

14. In the given matrix the values of A, B and C respectively are ____.

(A) A = 13, B = 11, C = 9

(B) A = 13, B = 9, C = 11



(C) A = 9, B = 11, C = 13

(D) A = 9, B = 13, C = 11

9 A 12 B 10 7 8 C 11

15. Two cars start from opposite places on a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and runs for another 25 km and then takes the direction to reach the main road. In the mean time, due to a minor break down the other car has run only 35 km along the main road. What would be the distance between the two cars at this point?

(A) 65 km

(B) 75 km

(C) 80 km

Copyright©2015. Science Olympiad Foundation (SOF)

(D) 85 km

4

5th IMO - 2011

16. Neelam, who is Rohit's daughter, says to Indu, "Your mother Reeta is the younger sister of my

father, who is the third child of Sohanji." How is Sohanji related to Indu? (A) Maternal uncle (B) Father (C) Grandfather (D) Father-in-law

17. If Moon is called Star, Star is Sun, Sun is Earth, Earth is Jupiter, Jupiter is Mars and Mars is

Mercury, where does man live? (A) Mars (B) Jupiter

(C) Earth

(D) Sun

18. In the given figure, square represents doctors, triangle represents ladies and circle represents surgeons. Which letter represents the ladies who are both doctors and surgeons? P S T Q



(A) U

R U

(B) T

(C) S

(D) P

19. In the given question, which number will replace the question mark? 4 5 0 6 7



(A) 0

8 7 1 6 4

(B) 2

0 11 ? 2 2

(C) 11

(D) 12

20. If the positions of the third and tenth letters of the word DOCUMENTATION are interchanged, and likewise the positions of the fourth and seventh letters, the second and sixth letters, are also interchanged, then which of the following will be eleventh letter from the right end?

(A) C

(B) I

(C) T

(D) U

Section II : Mathematical reasoning 21. If x < –1, then which of the following expressions holds?

(A) x < x2 < x3

(B) x < x3 < x2

(C) x2 < x3 < x

(D) x3 < x < x2

22. If the perimeter of a rectangular garden plot is 80 metres, which of the following could be the length of one of its sides?

I. 30 metres

II.

40 metres



(A) I only

(B) II only

III. 50 metres (C) III only

(D) I and II

23. In the adjoining figure, circles with centres at L, M and N each have a radius of 2 units and are placed as shown here. If PQRS is the smallest rectangle that will enclose the 3 circles, what is the area of PQRS?

S

R L

P



(A) 8 sq.units

(B) 12 sq.units

M

N Q

(C) 16 sq.units

(D) 32 sq.units

24. If 3x + 2y = 17 and x and y are positive integers, then y could be which of the following?

(A) 2

(B) 3

(C) 4

Copyright©2015. Science Olympiad Foundation (SOF)

(D) 5

5

5th IMO - 2011 25. In the given figure l 1 || l 2. Which of the following must be true?

(A) f = b



(B) b = c



(C) c = e



(D) d = f

26. In the adjoining figure, point P the intersection of lines l 1 and l 2 has coordinates (a, b) as shown here. Which of the following could be the ordered pair (a, b)? Y l1

P (a,b)

X

O



(A)  5, − 

5  2

l2

5 (B)  −1,   8

(D)  2 , 1   3 3

(C) (0, 4)

27. In the given figure, three equilateral triangles have a common vertex then x + y + z =



(A) 90°

(B) 120°

(C) 150°

28. If a right triangle has sides of length 1 and

(D) 180°

2, which of the following could be the length of the

remaining side?

I.

1



(A) I only

II.

2

III.

(B) II only

3

(C) III only

(D) I and III only

29. The expression (a + b + c)2 + (a + b – c)2 + (a – b + c)2 + (b + c – a)2 equals ____.

(A) 4(ab + ac + bc)

(B) 2(a2 + b2 + c 2 + ab + bc + ac)



(C) 4(a2 + b2 + c 2)

(D) (a2 + b2 + c 2)

30. A die is rolled 10,500 times. The frequency of each outcome is shown in the table. What is the empirical probability of the outcomes of multiples of 3? Outcome Frequency



(A)

1153 3500

(B)

1675

1153 3459

1725

1642

1768

(C)

1873

1153 10500

1817

(D)

3459 105000

31. In D's ABC and PQR, AB = PQ, BC = QR are extended to X and Y respectively and ∠ABX = ∠PQY. Under which congruency criterion, the triangles are congruent ?

(A) SSS

(B) SAA

(C) SSA

(D) SAS

(C) 7/11

(D) 7/13

æ ö1/ 6 32. Find the value of çç 117649 ÷÷ . è 1771561÷ø

(A) 3/11

(B) 13/7

Copyright©2015. Science Olympiad Foundation (SOF)

6

5th IMO - 2011

33. ABCD is a trapezium, in which AB || DC, AD ^ AB and E & F are points on AD & BC respectively. BD is joined. If ∠EFC = 110°, ∠ABD = 60°, ∠BDC = x° and ∠DCF = y°, then values of x and y are ____.

(A) 60°, 70°

(B) 50°, 80°

(C) 90°, 40°

(D) 30°, 100°

34. Fill in the blank :

If a straight line meets two other straight lines so as to make the sum of the two interior angles on one side of the transversal less than two right angles, then the other straight lines extended



infinitely, will meet ____ the transversal. (A) On that side of (B) On another side of

(C) On

(D) Can't be determined

35. Which of the following options in Column I with reasons in Column II is correct with respect to the following question :

How many linear equations in x and y can be satisfied by x = 1 and y = 3?

Column I Column II

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

Only one Exactly two Infinitely many Exactly three

(i) (ii) (iii) (iv)

as only x = 1, y = 3 is given. one for x = 1, second for y = 3. one for x = 1, second for y = 3 and third for x + y = 3. as point (1, 3) lies on graph and through one point infinite lines can pass, so we get infinite graphs or infinite equations.

36. If the product of two surds is a rational number, then each one of them is called the _____ of the

other _____. (A) Negative

(B) Rationalising factor

(C) Conjugate surd

(D) Binomial surd

37. If one leg of an isosceles right-angled triangle is increased by 6 cm and the other leg is increased by 4 cm, then change in area of the triangles is 24 sq cm. Find the length of the leg of the original

triangle. 5 cm (A) 12

(B)

12 cm 5

(C)

1 cm 5

(D)

1 cm 12

38. Remainder when a 2 + b 2 + 2(ab + bc + ca) is divided by (a + b + 2c) is _______. (A) a + b (B) ab (C) a – b (D) 0 39. The value of

l+m

xl

2

xm

(A) x

2

⋅m+n

xm xn

2

2

⋅n+l

xn xl

2

= ______.

2

(B) –1

(C) 1

(D) 0

40. All the three quadrilaterals ADEC, ABIH and BCGF are squares and ∠ABC = 90°. If the area of ADEC = x 2 and area of AHIB = y 2(x 2 > y 2), then find the area of BCGF? D E

H A I

B

F



(A) x2 + y2

(B) 2y2

C

G

(C) 2x2

Copyright©2015. Science Olympiad Foundation (SOF)

(D) x2 – y2

7

5th IMO - 2011

Section III : Everyday Mathematics 41. A class starts at 10 a.m. and lasts till 1.27 p.m. Four periods are held during this interval. After every period, 5 minutes are given free to the students. The exact duration of each period is ____.

(A) 42 minutes

(B) 48 minutes

(C) 51 minutes

(D) 53 minutes

42. In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimations, what is the average of different probable weights of Arun?

(A) 67 kg

(B) 68 kg

(C) 69 kg

(D) None of these

43. A man walked diagonally across a square plot. Approximately, what was the percent saved by not walking along the edges?

(A) 20

(B) 24

(C) 30

(D) 33

44. A man purchases two clocks A and B at a total cost of ` 650. He sells A at 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?

(A) ` 225, ` 425

(B) ` 250, ` 400

(C) ` 275, ` 375

(D) ` 300, ` 350

45. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons is increased by ____ of the original share.

(A) 1/9

(B) 1/8

(C) 1/7

(D) 7/8

46. A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been ____.

(A) 122

(B) 118

(C) 114

(D) 124

47. Reema bought x pens at ` 2.60 each and y greeting cards at 80 paise each. If the pens cost ` 12 more than the cards, the equation involving x and y is _____.

(A) 13x – 4y = 6

(B) 13x – 4y = 60

(C) 260x – 8y = 100

(D) 260x – 8y = 12

48. To make a marriage tent, poles are planted along the perimeter of a square field at a distance of 5 metres from each other and the total number of poles used is 20. What is the area (in sq. metres) of the square field?

(A) 500

49. Hussain's weight is 1 weight?

(A) 90 kg

(B) 400

(C) 900

(D) None of these

1 times the weight of Rahim. Their total weight is 90 kg. What is Hussain's 4 (B) 50 kg

(C) 40 kg

(D) 20 kg

50. In a class, the number of boys is more than the number of girls by 12% of the total strength. The ratio of boys to girls is _____.

(A) 15 : 11

(B) 11 : 14

(C) 14 : 11

Copyright©2015. Science Olympiad Foundation (SOF)

(B) 8 : 11

Class 9 6th

SET A Year 2012

Copyright©2015. Science Olympiad Foundation (SOF)

2

6th IMO - SET A Section I : Logical Reasoning

1. In the following question, the symbols @, © , $ and % are used with the following meanings as illustrated below : 'A $ B' means 'A is not smaller than B'; 'A @ B' means 'A is neither smaller than nor equal to B'; 'A © B' means 'A is neither smaller than nor greater than B'; 'A % B' means 'A is neither greater than nor equal to B'. Now in the following question, assuming the given statements to be true, find which of the three conclusions, I, II and III given below them is/are definitely true and give your answer accordingly. Statements : K © P, P @ Q, Q $ R Conclusions : I K @ R II. R % P III. Q % K (A) Only I and II are true (B) Only II and III are true (C) Only III is true (D) All I, II and III are true 2.

Select a figure from amongst the options which will continue the same series as established by the five Problem Figures P, Q, R, S and T.



+

S

C

C S +

(A)

3.



Study the following information carefully and answer the question given below. P, Q, R, S, T, V and W are seven passengers and I, II, III are three different vehicles. There are atleast two passengers in each vehicle I, II and III and one of them is a lady. There are two engineers, two doctors and three teachers among them. R is lady doctor and she does not travel with the pair of sisters P and V. Q, a male engineer travels with only W, a teacher in vehicle I. S is a male doctor. Two persons belong to same profession do not travel in the same vehicle. P is not an engineer and travels in vehicle II. How many lady members are there amongst them?



(A) Three

4.

Inspector Jatin travelled from his police station for 400 metres. He then turned left and travelled 500 metres straight after which he turned left again and travelled for 400 metres straight. He then turned right and walked for another 600 metres straight. How far is he from the Police station?



(A) 1.0 km

C

S

(B)

+



C



(B) Four

(B) 1.1 km

(C)



+ S

(C) Three or Four

(C) 1.4 km

(D)

+

(D) Data inadequate

(D) 1.8 km

5. Read the following information carefully and answer the question given below it.

(i) There is a group of six persons A, B, C, D, E and F in a family. They are Psychologist, Manager, Lawyer, Jeweller, Doctor and Engineer.



(ii) The doctor is the grandfather of F who is a Psychologist.



(iii) The Manager D is married to A.



(iv) C, the Jeweller, is married to the Lawyer.



(v) B is the mother of F and E.



(vi) There are two married couples in the family.



How is A related to E? (A) Brother (B) Uncle

(C) Father

Copyright©2015. Science Olympiad Foundation (SOF)

(D) Grandfather

3

6th IMO - SET A 6.

Vijay is fifteenth from the front in a column of boys. There were thrice as many behind him as there were in front. How many boys are there between Vijay and the seventh boy from the end of



the column? (A) 33

7.

Which of the options will come next in the series?



(A) QUR

8.

If the code of SENSITIVE is QHLVGWGYC then what will be the code of M ICROSOFT? (A) KGAPMQMDT (B) QKETQUQHV (C) KLAUMVMIR (D) LKBTNUNHS

9.

RUST = 9-6-8-7 and BOARD = 25-12-26-9-23, how will you code ‘BEAT’? (A) 25-23-24-7 (B) 25-21-26-7 (C) 25-22-25-7

(B) 34

(C) 35

(D) Data inadequate

JAZ, LEX, NIV, POT, __ ?_ (C) RUR

(B) RUS

(D) RSR

(D) 25-22-26-7

10. If 12% people in a village are suffering from cancer and 13% from blood pressure, which of the following diagram best represents the sick population of the village ? (A)

(B)



(C)





(D)





11. Look at the symbol-letter-number sequence given below.

2 P J @ 8 $ L B 1 V # Q 6 d G W 9 K C D 3  • £ 5 F R 7 A Y 4



Thre e of the following four are similar in relation to their positions in the above sequence and



hence form a group. Which one does not belong to that group? (A) Q K 5 (B) L 6 D (C) P L d

(D) 1 G 

12. A child went 90 m in the East to look for his father, then he turned right and went 20 m. After this he turned right and after going 30 m, he reached to his uncle's house. His father was not there. From there he went 100 m to his North and met his father in the shop. How far did he meet his

father from the starting point? (A) 80 m (B) 100 m

(C) 140 m

13. Match the given net with the correct picture.

(A)

(B)







(D) 260 m



(C)



(D)



14. Find out which of the options completes the figure matrix? (A)

(B)

(C)







(D)



Copyright©2015. Science Olympiad Foundation (SOF)



4

6th IMO - SET A

15. A goldsmith has five gold rings, each having a different weight :

Statement 1 : Ring D is weighing twice as much as ring E.



Statement 2 : Ring E is weighing four times as much as ring F.



Statement 3 : Ring F is weighing half as much as ring G.



Statement 4 : Ring G is weighing half as much as ring H.



Statement 5 : Ring H is weighing less than ring D but more than ring F.



Which of the following represents the descending order of weights of the rings ? (A) D, E, G, H, F (B) E, G, H, D, F (C) D, E, F, G, H (D) Data inadequate

16. In the following question from amongst the options, select the one which satisfies the same conditions of placement of the dot as in Fig. (X).

(A)

(B)

(C)



(D)









17. In the given question, which number will replace the question mark? 5 3 6 7 4 4 5 5 8 572

492



7

(A) 115

(B) 130

4

9

6

8

? 9

7

(C) 135

2

5

(D) 140

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

19.

(A)





(B)



(C)



(D)



Find the number of quadrilaterals in the given figure. (A) 10 (B) 6 (C) 9 (D) None of these



20. Rita drives to the north of her place of stay at A and after travelling 25 km, finds that she has driven in the wrong direction. She then turns to her right and travels 2 km, and then she again turns to the right and drives straight another 25 km. How much distance has she now to cover to go back to the starting point ?

(A) 25 km

(B) 2 km

(C) 4 km

Copyright©2015. Science Olympiad Foundation (SOF)

(D) 40 km

5

6th IMO - SET A Section II : Mathematical reasoning

21. The expression 2x3 + ax 2 + bx + 3, where a and b are constants, has a factor of x – 1 and leaves a remainder of 15 when divided by x + 2. Find the value of a and b respectively.

(A) –3, 8

(B) 3, –8

(C) –3, –8

(D) 3, 8

22. If 'l', 'b' and 'h' of a cuboid are increased, decreased and increased by 1%, 3% and 2% respectively,

then the volume of the cuboid ______. (A) Increases (B) Decreases (C) Increases or decreases depending on original dimensions (D) Can't be calculated with given data

23. A box of chocolates contain 5 chocolates with hard centres and 4 with soft centres.

Amit takes a chocolate, selected at random, from the box and eats it.



Ajay then takes a chocolate, selected at random, from the box.



Find the probability that Amit and Ajay both choose a chocolate with a hard centre. (B) 4 (C) 3 (D) 5 (A) 5 9 18 18 9



24. In given figure, ABCD and ABEF are two cyclic quadrilaterals. If ∠BCD = 110°, then ∠BEF = ? (A) 55°



(B) 70°



(C) 90°



(D) 110°

A

D F

110°



B

E

C

 (a 2 − b2 )3 + (b2 − c 2 )3 + (c 2 − a 2 )3  25. The value of 3  =? (a − b )3 + (b − c )3 + (c − a )3  

(A) 3(a + b)(b + c)(c + a)

(B) 3(a – b)(b – c)(c – a)



(C) (a – b)(b – c)(c – a)

(D) 1

26. How many planes can be made to pass through three distinct points? (A) One if they are collinear (B) Infinite if they are collinear (C) Only one if they are non collinear (D) Both (B) and (C) 27. The line BE is a diameter of the given circle. If ∠BAC = 33° and ∠EBC = 57°. Then ∠CAE =

(A) 57°



(B) 33°



(C) 48°



(D) 90°

28. The term containing the highest power of x in the polynomial f(x) is 2x4. Two of the roots of the equation f(x) = 0 are – 1 and 2. Given that x 2 – 3x + 1 is a quadratic factor of f(x), find the

remainder when f(x) is divided by 2x – 1. 1 (B) 2 (A) 1 8

(C) 0

Copyright©2015. Science Olympiad Foundation (SOF)

(D) –1/3

6

6th IMO - SET A

29. The sum of a number and its reciprocal is thrice the difference of the number and its reciprocal. The number is _________.

(A) ± 2

1 (B) ± 2

(C) ± 3

x −3 32 30. Solve for x : 2 = (1/ 2) x . −x 8 4 1 1 (B) 1 (A) 2 5 5

31. 2.6 − 0.82 = _________ . 182 (A) 99

(C) 3

180 (B) 999

(C)



1 5

175 99

(D) Both (A) and (B)

(D) 1

3 5

184 999

(D)

32. The base of an isosceles triangle is 4 cm and its area is 16 cm2. If one of the two equal sides of

the triangle is k cm, the approximate value of k – 1.24 is ___________. (A) 9 cm (B) 7 cm (C) 10 cm

(D) 8 cm

33. ABCD is a rectangle. If ABP and BCQ are equilateral triangles, ∠PBQ = ____.

(A) 65°



(B) 75°



(C) 60°



(D) 90°

A

B Q P

D

C

34. A certain distance is covered at a certain speed (s1). If half of this distance is covered in double the time at speed (s2). Find the ratio of the two speeds.

Also, if s1 is 60 km/hr, find s2.

(A) 1 : 16, 3.75 km/hr

(B) 4 : 1, 15 km/hr

(C) 2 : 1, 30 km/hr

(D) 2 : 8, 240 km/hr

35. If product of abscissa and ordinate of a point is positive, then the point lies in

(A) I quadrant

(B) III quadrant

(C) IV quadrant

(D) Both (A) and (B)

36. The two circles have radii x and 3x. A point is chosen, at random, inside the larger circle. Find, in its simplest fractional form, the probability

x

that this point is in the shaded area.

(A) 7/8

(B) 8/9



(C) 1/9

(D) 1/8

37. Find the missing value.

(A) 6

(13)3 + 73 (13)2 + 72 − ?

= 20

(B) 20

(C) 91

3x



(D) 19

number of students who took part in the survey.

at

Physics

em th

Mathematics obtained 25 more votes than Chemistry. Calculate the

Ma

subject. The pie chart represents the number of votes for each subject.

ics

38. The students in a college were asked to vote for their favourite

120°

45° 105°



(A) 250

(B) 500



(C) 450

(D) 600

Copyright©2015. Science Olympiad Foundation (SOF)

Ge

Chemistry

og

ra

ph

y

7

6th IMO - SET A

39. A cuboidal metal block of dimensions 20 cm × 16 cm × 12 cm weighs 6 kg. Find the weight of

block of the same metal of size 10 cm × 8 cm × 8 cm. (A) 3 kg (B) 8 kg (C) 7 kg

(D) 1 kg

40. What percentage of a day is six hours and 45 minutes?

(A) 7.218%

(B) 8.3%

(C) 28.125%

(D) None of these

Section III : Everyday Mathematics 41. The population of a town was 160000 three years ago. If it had increased by 3%, 2.5% and 5% in the last three years, find its present population.

(A) 167366

(B) 177466

(C) 177366

(D) 177365

42. The taxi charges in a city comprise of a fixed charge, together with the charge of the distance covered. For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charge paid are Rs. 204. What will a person have to pay for travelling a distance of 30 km?

(A) Rs. 236

(B) Rs. 240

(C) Rs. 248

(D) Rs. 252

43. Savita has Rs. 27 in the form of fifty paise and twenty-five paise coins. She has twice as many twenty-five paise coins as she has 50 paise coins. How many coins of each kind does she have?

(A) 27, 54

(B) 30, 60

(C) 25, 50

(D) 40, 80

44. A trader purchases 70 kg of tea at Rs. 15 per kg and 30 kg of tea at Rs. 18.50 per kg. If the packing charges are 2 percent, then at what price he must sell the mixture of two to gain 15%?

(A) Rs 18.82 per kg

(B) Rs. 18 per kg

(C) Rs. 18.50 per kg

(D) Rs.17.80 per kg

45. The average age of a family of 6 members 4 years ago was 25 years. Meanwhile a child was born in this family and still the average age of the whole family is same today. The present age of child is _______.

(A) 2 years

(B) 1

1 years 2

(C) 1 year

(D) Data insufficient

46. 2 men and 3 women finish 25% of the work in 1 day, while 6 men and 14 women can finish the whole work in 5 days. In how many days will 20 women finish it?

(A) 20

(B) 25

(C) 24

(D) None of these

47. Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes?

(A) 6 mins

(B) 8 mins

(C) 10 mins

(D) None of these

48. Suresh travelled 1200 km by air which formed (2/5) of his trip. One third of the whole trip, he travelled by car and the rest of the journey he performed by train. Find the distance travelled by train. Also, find the speed of the train if the time taken for the train to travel the whole distance is 8 hrs.

(A) 1600 km, 350 km/hr (C) 1800 km, 300 km/hr

(B) 800 km, 375 km/hr (D) 480 km, 380 km/hr

Copyright©2015. Science Olympiad Foundation (SOF)

8

6th IMO - SET A

49. Three lightships flash simultaneously at 6:00 a.m. The first lightship flashes every 12 seconds, the second lightship every 30 seconds and the third lightship every 66 seconds. At what time will the three lightships next flash together?

(A) 6:09 a.m.

(B) 6:10 a.m.

(C) 6:11 a.m.

(D) 6:12 a.m.

50. A fruit seller has 24 kg of apples. He sells a part of these at a gain of 20% and the balance at a

loss of 5%. If on the whole he earns a profit of 10%, the amount of apples sold at a loss is ___. (D) 11.4 kg (A) 4.6 kg (B) 6 kg (C) 9.6 kg SPACE FOR ROUGH WORK

Copyright©2015. Science Olympiad Foundation (SOF)

Class 9 6th

SET B Year 2012

Copyright©2015. Science Olympiad Foundation (SOF)

2

6th IMO - SET B Section I : Logical Reasoning

1. Observe the given diagrams formed by unit squares. Not including the middle square hole, the number of unit squares needed to build the tenth pattern is _____.

(A) 90



(B) 91



(C) 92



(D) 93

2. Going 50 m to the south of my house, I turn left and go another 20 m. Then turning to the north,

I go 30 m and then start walking towards my house. In which direction am I walking now ? (A) North (B) East (C) North-West (D) South-East

3. If OLYMPICS is coded as PMZNOHBR, and JUMP is coded as KVLO, then COMPUTER will be coded

as _______. (A) DPNQVUFS

4.

Find out the correct option such that Fig. (X ) is embedded in one of them.

(B) DPNQTSFQ

(C) DPNQTSDQ

(D) BNLOTSDQ

Fig. (X)



(C)

(B)

(A)





(D)





5.

The given question consists of two sets of figures. Figures 1, 2, 3



and 4 constitute the problem set while option figures A, B, C and D constitute the answer set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the answer set that would replace the question mark (?)



in fig. (4).

(B)



(C)





(A)

6.

In the adjoining matrix, group the given figures into three classes using

(D)

each figure only once.



1

2

3

4

5

6

7

8

9



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



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



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



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

7.

Out of the given five figures, four are similar in a certain way. Find the odd one out.

(A)





(B)

(C)





Copyright©2015. Science Olympiad Foundation (SOF)

(D)



3

6th IMO - SET B 8. In the adjoining Venn diagram, the square represents women, the

triangle represents persons who are in government services, the circle represents educated persons and the rectangle represents persons working in private sector. Each section of the diagram is numbered then which number represents the uneducated women, who have government service as well as jobs in private sectors ?



(A) 6

(B) 4

9.

Which of the following letters/numbers in the given letter-number sequence below is exactly in the middle of the 9th letter/number from the left end and 7th letter/number from the right end ? B 3 K G 5 P D 7 9 E R J I M T 6 Z H Q 3 W 2 A



(A) I

(B) R

(C) 12

(C) J

(D) 9

(D) M

10. The given set of figures carry certain characters. Assuming that the characters in set follow a similar pattern, find the missing character.



(A) 2

(B) 9

(C) 17

(D) 18

11. Three positions of the same dice has been shown in the figure. What digit will be on the top if digit 2 is on the bottom?



(A) 1

(B) 4

(C) 5

(D) 6

12. If it is possible to make only one meaningful word with the first, the second, the sixth and the tenth letters of the word DISCLAIMER which of the following will be the third letter from the left end? If no such word can be made, give X as your answer and if more than one such word can be made, give Y as the answer.

(A) I

(B) R

(C) Y

(D) X

13. Rohit, Kunal, Ashish and John are students of a school. Three of them stay far from the school and one near it. Two study in class IV, one in class V and one in class VI. They study Hindi, Mathematics, Social Science and Science. One is good at all the four subjects while another is weak in all of these. Rohit stays far from the school and is good at Mathematics only while Kunal is weak in Mathematics only and stays close to the school. Neither Kunal, Rohit nor Ashish studies in class VI. One who is good at all the subjects studies in class V. Name the boy who is good at all the subjects.

(A) Rohit

(B) Kunal

(C) Ashish

(D) John

14. Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence. 1. Wrinkle 2. Wriggle 3. Writhe 4. Wretch 5. Wrath

(A) 4, 5, 1, 2, 3

(B) 5, 4, 2, 1, 3

(C) 4, 2, 5, 1, 3

(D) 5, 2, 1, 3, 4

15. If A * B means 'A multiplied by B'; A @ B means 'A minus B' ; A $ B means 'A plus B'; A # B means 'A divided by B', then what will be the total area of 21 circles, each with the same radius of r cm?

(A) 22 * r * 7 * r # 21

(B) 22 # 21 * r * r

(C) 66 * r2 # 7

Copyright©2015. Science Olympiad Foundation (SOF)

(D) 66 * r * r

4

6th IMO - SET B

16. The given question consists of five figures marked P, Q, R, S and T called the Problem Figures followed by four options. Select a figure from amongst options which will continue the same series as established by the five Problem Figures.

(A)

(B)







(D)

(C)







17. Find the mirror image of the given word, if the mirror is placed vertically to the left. ADMINISTRATION

(B) NOITARTSINIMDA

(C) NOT IARTSINIMDA

(D)

ADMINITSRATION

ADMINISTRATION

(A)



18. Find the number of triangles in the given figure.

(A) 26



(B) 27



(C) 28



(D) None of these

19. Pointing towards a photograph, Mohit said, 'His sister is the mother of Vinay, the son of my brother'. How Mohit is related to Vinay?

(A) Brother

(B) Uncle

(C) Nephew

(D) Brother-in-law

20. If 1 is subtracted from the last digit of each of the given below three digit numbers, the sum of the digits of how many of them are prime numbers? 972 526 487 359 251 (A) None (B) Two (C) One (D) Three

Section II : Mathematical reasoning 21.

In the adjacent figure AE = AF, then which of the following is true? (A) a + b + c = 180° (B) a + c = b (C) 2c + a = b (D) 2a + c = b

A

D

a

F x b B

x

y E c

C

22. The value of 1+ 2008 1+ 2009 1+ 2010 1+ 2011 ⋅ 2013 is _____.

(A) 2009

23. Simplify :

(A) 0

(B) 2010 6 + 2 3 − 6

6 − 3 + 2 (B) 1

(C) 2011

(D) 2013

(C) 2

(D) 3

4 3 6 − 2

24. If (x – 2y)6 = A 0x 6 – A1x 5 . y 1 + A 2x4 . y 2 – A 3x 3 . y 3 + A 4x 2 . y4 – A 5x . y 5 + A 6y 6, find the value of

A 0 – A 1 + A 2 – A 3 + A 4 – A 5 + A 6. (A) 0 (B) 2

(C) 1

Copyright©2015. Science Olympiad Foundation (SOF)

(D) –3

5

6th IMO - SET B 25. Abscissa of all the points on x-axis is _____. (A) 0 (B) 1

(C) 2

(D) Any number

26. 1500 families with 2 children were selected randomly, and the following data was recorded: Number of girls in a family Number of families



2 1 0 475 814 211

The probability of a family, chosen at random, having 1 girl is ____. 814 814 814 (B) (A) (C) 211 475 686

814 (D) 1500 V

27. In the given figure (not drawn to scale), TU || SR and TR || SV, then find ∠a and ∠b.

(A) a = 115°, b = 40°



(B) a = 120°, b = 65°



(C) a = 145°, b = 55°



(D) a = 105°, b = 35°

25° a U S

T 90° R P

50°

b

Q

Direction (28 & 29) : The line graph shows the sectorwise break-up of venture capital funding in India for the year 20XX.

28. Funding in the consumer-related sector exceeds that in the energy-related sector approx

by _____. (A) 400%

(B) 600%

(C) 500%

(D) 450%

29. The ratio of funding in the computer software service and the bio-technology sectors (taken

together) to that in the industrial products and machinery sector is _______. (A) 10 : 1 (B) 1 : 1 (C) 2 : 3 (D) 3 : 2 Copyright©2015. Science Olympiad Foundation (SOF)

6

6th IMO - SET B A

30. In the given figure, mark the relation between AB and AD.

(A) AB = AD



(B) AB < AD



(C) AB > AD (D) Data inadequate

B

C

1

2

D

31. Given a line l and a point P on it. How many lines can be drawn passing through the point P ? (A) Infinite (B) One (C) Two (D) Three 32. The positive solutions of the equation ax + by + c = 0 always lie in the ______. (B) 2nd quadrant (C) 3rd quadrant (D) 4th quadrant (A) 1st quadrant 33. Find the value of

52

(A) 10

3−3 62 98 3 − 1 / 25 (15) 4 / 3

31/ 3

.

(B) 28 2

(C)

3 2

(D)

125 27

34. A hand fan is made by stitching 10 equal size triangular strips of two different types of paper as shown in figure. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.

(A) 280 cm2



(B) 420 cm2



(C) 840 cm2



(D) 384 cm2

35. Which of the following statements is true ?

(A) A line segment has no end point.



(B) A ray has definite length.   (C) A ray PQ is the same as ray QP. (D) Three or more lines are concurrent if they have a common point.



36. In the given figure, ∠x and ∠y are _____.

(A) x = 70°, y = 37°



(B) x = 37°, y = 70°



(C) x = 50°, y = 57°



(D) x = 57°, y = 50°

37. Express 15.712 in the form of

(A)

5185 300

(B)

p , q ≠ 0. q

5185 100

(C)

5188 3

(D)

5185 330

38. What must be added to x4 + 2x3 – 2x 2 + x – 1 so that result is exactly divisible by x 2 + 2x – 3? (A) – x + 2 (B) 3 (C) x – 2 (D) 4x – 3 39. The radius of the cylinder is half its height and area of the inner part is 616 sq. cms. How many

litres of milk approximately, can it contain? (A) 1.4 L (B) 1.5 L

(C) 1.7 L

Copyright©2015. Science Olympiad Foundation (SOF)

(D) 1.9 L

7

6th IMO - SET B

40. In the given figure, T is a point on side QR of PQR and S is the point such that RT = ST. Then PQ + PR > _____.

(A) QR



(B) QT



(C) QS



(D) ST

Section III : Everyday Mathematics 41. The probabilities of a student getting A, B, C and D grade are 0.35, 0.25, 0.35 and 0.05, then the probability that a student gets at most grade C is ______.

(A) 0.35

(B) 0.40

(C) 0.95

(D) 0.65

42. A person lent out a certain sum on simple interest and the same sum on compound interest at certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is ______.

(A) 10%

(B) 11%

(C) 12%

(D) 12 1 % 2

43. A closed metallic cylindrical box is 1.25 m high and its base radius is 35 cm. If the metal sheet costs ` 80 per m2, the cost of the material used in the box is ______.

(A) ` 281.60

(B) ` 290

(C) ` 340.50

(D) ` 500

44. Latika bought a radio set and spent ` 110 on its repairs. She then sold it to Garima at 20% profit, Garima sold it to Megha at a loss of 10% and Megha sold it for ` 1188 at a profit of 10%. What is the amount for which Latika bought the radio set ?

(A) ` 850

(B) ` 890

(C) ` 930

(D) ` 950

45. In the month of January, the Railway Police caught 4000 ticketless travellers. In February, the number rose by 5%. However, due to constant vigil by the Police and the Railway staff, the number reduced by 5% and in April it further reduced by 10%. The total number of ticketless travellers caught in the month of April was ______.

(A) 3125

(B) 3255

(C) 3575

(D) 3591

46. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years ?

(A) 24 years

(B) 27 years

(C) 40 years

(D) 30 years

47. Four equal sized maximum circular plates are cut off from a square paper sheet of area 784 cm 2. The circumference of each plate is ______.

(A) 22 cm

(B) 44 cm

(C) 66 cm

(D) 88 cm

48. Priya plants 33124 mango trees in her garden and arranges them so that there are as many rows as there are mango trees in each row. The number of rows are ______.

(A) 128

(B) 182

(C) 281

Copyright©2015. Science Olympiad Foundation (SOF)

(D) 218

8

6th IMO - SET B

49. In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If she attempts in all 50 questions and scores 120 marks, the number of questions she attempts correct is _____.

(A) 62

(B) 44

(C) 42

(D) 34

50. A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby

decreases his average by 0.4. The number of wickets taken by him till the last match was _____. (A) 64 (B) 72 (C) 80 (D) 85 SPACE FOR ROUGH WORK

Copyright©2015. Science Olympiad Foundation (SOF)

Class 9 7th

SET A Year 2013

Copyright©2015. Science Olympiad Foundation (SOF)

2

7th IMO - Set A

logical reasoning 1.

2.



3.

Choose the correct option so that a series can be established. 17, 19, 23, 29, (.....), 37 A. 31 B. 33 C. 35 D. 36 In the given question, two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows is to be answered. The operations of numbers progress from left to right. Rules : (i) If an even number is followed by another even number they are to be added. (ii) If an even number is followed by a prime number they are to be multiplied. (iii) If an odd number is followed by an even number, the even number is to be subtracted from the odd number. (iv) If an odd number is followed by another odd number, the first number is to be added to the square of the second number. (v) If an even number is followed by a composite odd number, the even number is to be divided by the odd number. 65 11 12 15 3 11 What is the sum of the resultants of the rows? A. 366 B. 66 C. 264 D. 462

4.

Rita stands third in a row of twenty students, arranged in ascending order of height. Five new students join the group, all taller than Rita. What will be Rita's position if the students are now arranged in descending order of their heights?



A. B. C. D.

5.

If 'Book' is called 'Pen', 'Pen' is called 'Paper', 'Paper' is called 'Eraser', 'Eraser' is called 'Scale' and 'Scale' is called 'Calculator', then with which does a student write?



A. B. C. D.

6.

Select a number which will replace the question mark in the number pattern given below.



A. B. C. D.

7.

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

22nd 23rd 18th Data inadequate

Book Paper Pen Calculator

16 15 28 21

Select the correct mirror image of the given Fig.(X), if the mirror is placed along MN.



A.



B. A.





C.



B.

C.

D.







D.





Copyright©2015. Science Olympiad Foundation (SOF)

3

7th IMO - Set A 8.

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

and moves 75 metres. In which direction is she now from her starting point?

9.

A.







B.



C.





D.





How many triangles are there in the given figure? A. B. C. D.

8 10 12 14

A.





B.



C.





D.

A. B. C. D.



A.



B.





C.



D.



14. If two is subtracted from each odd digit and three is added to each even digit in the number 3675249, how many digits will appear twice in the new number thus formed? A. 1 B. 2 C. 3 D. 4

11. P is the mother of Q and daughter of R. S is the daughter of Q and sister of T. How is P related to T?

South North South-West North-East

13. A sheet of paper as shown in Fig. (X) has to be folded to form a box. Choose a box from amongst the options that is similar to the box formed.

10. Pair of first two figures on left side of ': :' have a certain relationship between them. Establish the same relationship between the pair of figures on right side of ': :', which will replace the "?" mark.



A. B. C. D.

Paternal grandmother Maternal grandmother Data inadequate None of these

12. Priya starts her trip from a fixed point. She moves towards east and walks 25 metres. She then turns to her left and walks 30 metres. Next she moves 25 metres to her right. She then turns to her right again and walks 55 metres. Finally she turns to her right

15. Which letter/number in the given letter-number sequence is exactly in the middle of the 9th letter/ number from the left end and 10th letter/number from the right end? H 2 5 x A 3 bc z t 4 2 1 s 6 p 9 d o w u 7 nm A. O B. T C. 2 D. P 16. If the letters in the word rhombus are arranged as they appear in the english alphabets, the position of how many letters will remain unchanged? A. 1 B. 2 C. 3 D. 4

Copyright©2015. Science Olympiad Foundation (SOF)

4

7th IMO - Set A

17. Select from the options which forms the correct water image of the given word. CARING A. B. C. D. 18. Select a Venn diagram from the options which best represents the relationship amongst "Dog, Parrot, Pet animals"?



A.



C.







D.

B.



(i)



(ii)



(iii) (iv) (v) (vi) Who A. B. C. D.

C.

D.

A.



20. Read the following information and answer the question that follow.



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



B.



Four persons A, B, C and D eat mango, banana, orange or peach from Monday to Thursday. No two persons eat the same fruit on same day. Each of them eats only one fruit on a day and does not repeat it on any other day. Neither C nor D eats orange or peach on Tuesday. B eats banana on Wednesday. A eats peach on Monday. C does not eat mango on Thursday. D eats banana on Monday. eats orange on Tuesday? A B C Either A or B

MATHEMATICAL REASONING 21. In the given figure, AOB is a straight line and ∠AOX 3 = 57°, ∠X1OX4 = 97°, ∠X 3OB = 123° and ∠X4 OB = 68°. Find ∠AOX1.



A. B. C. D.

23. Find the remainder when 2x3 – 9x2 + x + 12 is divided by 2 + 3x.

A. B. C. D.

0 116/9 –2 182/27

24. PQRS is a rhombus and SRT is an equilateral triangle. If ∠QRS = 80°, then ∠QTR =

40° 30° 25° 15°

Q

A. B. C. D.

3 2 6 5

sq. sq. sq. sq.

units units units units

R

T

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

80°

P



A. B. C. D.

40° 20° 30° 50°

Copyright©2015. Science Olympiad Foundation (SOF)

S

5

7th IMO - Set A 25. In which quadrant does the point P(x, y) lie if xy < 0?

A. B. C. D.

I or II II or IV I or III III or IV

(

3 x 2 + 12 − A. 1 B. 2 C. 4 D. 0

3 x + 12

C. D.

20 15

31. Simplify :

26. The degree of the polynomial



)

2

+ 12 x + 4 is



27. In the given figure, ∠B < ∠A and ∠C < ∠D.

1 7+ 6

−

5 1− 6

− 7

A. 0 1 B. 2 1 C. 4 D. 1

32. What is the area of the shaded part in the given figure 22    π =  ? 7

18 cm

Then which of the following statements is true regarding the relationship between AD and BC?

A. B. C. D.

AD = BC AD < BC AD > BC Nothing can be said



A. B. C. D.

72 cm2 108 cm2 324 cm2 648 cm2

33. The given figure is not drawn to scale. Find the values of ∠QPS and ∠TRQ respectively. P

28. ABCD is a field in the form of a quadrilateral whose sides are AB = 40 m, BC = 15 m, CD = 28 m and AD = 9 m. If ∠DAB = 90°, the area of the field is

A. B. C. D.

306 312 126 218

m2 m2 m2 m2

X

P



A. B. C. D.

1 2 1 1

: : : :

Y

Q

A. B.

18 19

A. B. C. D.

78°, 88°, 62°, 82°,

135° S

R

140° 110° 150° 110°

34. The pie chart shows the grades attained by a group of students for a common test. 5% 10% E D

20% A

25% C B



30. The probability of selecting a boy in a class is 0.6 and there are 45 students in a class. Find the number of girls in the class.



R

4 1 2 1

T U 65°

Q

29. PQRS is a parallelogram. If X and Y are mid-points of PQ and SR respectively and diagonal SQ is joined. The ratio ar(||gm XQRY ) : ar(DQSR) =

S

23°



If 240 students sat for the common test and those who obtained Grade D and E failed the test, how many students passed the test? A. 42 B. 182 C. 215 D. 204

Copyright©2015. Science Olympiad Foundation (SOF)

6

7th IMO - Set A

35. Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted to form a cube whose diagonal is 12 3 cm. Find the edges (in cm) of the three cubes.



A. B. C. D.

6, 9, 8, 3,

8, 10 12, 15 9, 11 4, 5

EVERYDAY MATHeMATICS 36. The sides of a quadrangular field, taken in order are 26 m, 27 m, 7 m and 24 m respectively. The angle contained by the last two sides is a right angle. Find its area.

A. B. C. D.

324 m2 238.59 m2 375.84 m2 384.69 m2



37. The taxi fare in a city is ` 25 for first kilometre and ` 10.5 for next each subsequent kilometre. A traveller is charged ` 109 as the fare. How many kilometres did he travel?

A. B. C. D.

8 km 9 km 10 km None of these

38. Four runners started running the race in the same direction around a circular path of 7 km. Their speeds are 4 km/hr, 3 km/hr, 9 km/hr and 3.5 km/hr individually. If they have started their race at 6 o' clock in the morning, then at what time they will be at the starting point?.

A. B. C. D.

14 13 10 15

hours hours hours hours

39. A bookseller procures 40 books for ` 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

A. B. C. D.

` ` ` `

720 960 1200 1440

40. The population of a city had increased successively at the rate of 6%, 4% and 2% per annum during last three years. If its present population is 1124448, then what was its population three years ago?

A. B. C. D.

1000000 1050000 1080000 1100000

41. The length of longest pole that can be placed on the floor of a room is 12 m and the length of longest pole that can be placed in the room is 15 m. The height of the room is A. B. C. D.

3 6 9 4

m m m m

42. A and B can do a piece of work in 10 days; B and C in 12 days; A, B and C in 8 days. In how many days A and C together can do the same work?

A. B. C. D.

8 15 20 Can't be determined

43. There are four bells. They ring after every one minute, two and half minutes, 50 seconds and 5 seconds respectively. If all the four bells rang last time together at 8 : 20 p.m., then at what time will they all next ring simultaneously?

A. B. C. D.

8 8 8 8

: : : :

23 24 25 26

p.m. p.m. p.m. p.m.

44. The dimensions of a photograph are 4 cm and 1.8 cms. If the breadth of the enlarged photo is 4.5 cm and it was enlarged proportionally then what is the new length of new photograph?

A. B. C. D.

6 cm 5.4 cm 10 cm 9 cm

45. The price of a car depreciates in the first year by 25%, in the second year by 20%, in the third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is ` 10,00,000 is

A. B. C. D.

` ` ` `

7,80,000 5,10,000 6,90,000 1,70,000

Copyright©2015. Science Olympiad Foundation (SOF)

7

7th IMO - Set A

Achievers Section 46. Consider the figure below. I

48. Which of the following statements is correct? III

II



The ratio of the area of I to II is 8 : 1. The area of 2 III is 1 as much as the area of II. If the difference 3 between the area of I and II is 252 cm2 , then

(P) Area of I (Q) Area of II + III P A. 96 cm2 B. 288 cm2 C. 188 cm2 D. 86 cm2

A. B. C.



D.

Q 288 cm2 96 cm2 86 cm2 188 cm2



Statement 1 : If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is not isosceles. Statement 2 : If the bisector of the vertical angle of a triangle bisects the base, then the triangle is not isosceles. A. Statement 1 is true but statement 2 is false. B. Statement 1 is false but statement 2 is true. C. Both the statements are true. D. Both the statements are false.

50.

a, b, c are three sets of values of x : a : 2, 3, 7, 1, 3, 2, 3 b : 7, 5, 9, 12, 5, 3, 8 c : 4, 4, 11, 7, 2, 3, 4 Which one of the following statements is correct? A. Mean of a = Mode of c B. Mean of c = Median of c C. Median of b = Mode of a D. Mean, Median and Mode of a are equal



Statement 1 : (x + y) 3 = x 3 + y 3 + 3xy(x + y) and (x2 + y2) = (x + y)2 + 2xy 1 1 Statement 2 : If x 2 + 2 = 7, then the value of x3 + 3 = 19 x x 1 en the value of x3 + 3 = 19 x A. Statement 1 is true but statement 2 is false. B. Statement 1 is false but statement 2 is true. C. Both the statements are true. D. Both the statements are false.

All the angles of a triangle can be less than 60°. A triangle can have more than one obtuse angle. An exterior angle of a triangle is less than either of its interior opposite angles. An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

49. Select the correct option.

47. Select the correct option.



SPACE FOR ROUGH WORK

Copyright©2015. Science Olympiad Foundation (SOF)

Class 9 7th

SET B Year 2013

Copyright©2015. Science Olympiad Foundation (SOF)

2

7th IMO - Set B

logical reasoning 1.

Find out how will the key Fig. (X) look like after rotation?



A.



B.



C.



D.

2.

There is a set of figures carrying certain numbers. Assuming that the numbers in each set follow a similar pattern, find the missing number.





5.

If each of the odd digits in the number 54638 is decreased by 1 and each of the even digits is increased by 1, then which of the following will be the sum of the digits of the new number?



A. B. C. D.

6.

The given question is based on the diagram given below showing four persons at the four corners of a square region as shown.

25 26 28 27

From the positions in given figure, C and A move diagonally to opposite corners and then one side each clockwise and anti-clockwise respectively. B and D move two sides each clockwise and anti-clockwise respectively. Where is A now?



A. B. C. D.

2 6 8 64

3.

When the given figure is folded to form a cube, how many dots would lie opposite the face bearing five dots?



A.

1



B.

2



C.

3



D.

4

4.

Select the pair from options that has a relationship similar to the figure (X).



A.





A. B. C. D.

At At At At

the the the the

north-west corner north-east corner south-east corner south-west corner

7.

Some of the cricket players are tennis players, some tennis players are hockey players, no cricket player is a hockey player. Which of the following diagrams correctly represents the above statements?



A.



B.



C.



D.



Figure (X)

B.



C.



D.



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3

7th IMO - Set B 8.

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

out the alternative figure which contains Figure (X) as its part.

Figure (X)

A.



A.



B.



B.



C.



D.



C.

9.

In a coding language, the letters of the English alphabet are arranged in such a manner that all the vowels are put in the end and the remaining letters are arranged from the first letter onwards. The rearranged alphabets are used to denote the position occupied by letters in the original alphabets. What is the code of META?



D.



A. B. C. D.

TEAM PWLV LWPV QGYB

10. There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?

A. B. C. D.

20 30 50 60

0.16 : 0.0016 : : 1.02 : ? A. B. C. D.



13. Study the following information carefully and answer the question given below it: 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. Who is the mother? A. A B. B C. D D. E 14. Complete the pattern given in figure (X).

11. There is a certain relationship between pair of numbers given on either side of : :. Identify the relationship between the pair of numbers and select the option which will replace the question mark?



0.0102 0.102 1.020 10.20

12. In the following question, Figure (X) is followed by four alternative figures (A), (B), (C) and (D) such that Figure (X) is embedded in one of them. Trace



A.



B.



C.



D.





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4

7th IMO - Set B

15. In the given question, there is set of five figures called the problem set. Select a suitable figure which will replace the question mark in figure (3) so that a series is formed by the figures 1, 2, 3, 4 and 5 taken in order. Problem Set



A.



B.



C.



D.

18. If ÷ means + , – means ÷, × means – and + means ×, (36´ 4) - 8´ 4 =? then 4 + 8´ 2 +16 ¸ 1 A. 0 B. 8 C. 12 D. 16 19. In the given question, three figures X, Y and Z are showing a sequence of folding a circular sheet of paper. The third figure Z depicts the cuts made in the folded paper. Select a figure which would most closely resemble the paper in fig. (Z) when unfolded.







A.



B.



C.



D.



16. Select the correct mirror image of Figure (X).

Figure (X)

A.



B.



C.





20. The given question consist of two sets of figures. Figures 1, 2, 3 and 4 constitute the problem set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the options that would replace the question mark (?) in figure (4).





A.



B.



C.



D.

D.

17. How many parallelograms are there in the following figure?



A. B. C. D.

16 14 10 None of these



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5

7th IMO - Set B

Mathematical reasoning 21. Find the numerical value of A : B where m öm+n-l

æ A = ççç x ÷÷÷ çè x n ÷ø

n ön+l- m

æx ç ´ çç çè xl

1/ a-c

÷÷ ÷÷ ø

A. B. C. D.

1 2 1 3

: : : :

A.



B. C. D.

26. Each edge of an equilateral triangle is ‘a’ cm. A cone is formed by joining any two sides of the triangle. What is the volume (in cm3) of the cone?

and 1/ c-b

´( x1/ c-a )

; a,

1 1 2 1

22. If x = 3- 5 , then

æx ÷ ç ´ çç ÷÷÷ çè x m ø

1/ b-a

B = ( x1/ a-b ) ´( x1/ b-c ) b, c being all different.

l öl+m- n

1/ 5 5

x 2 + 3x - 2

= ________

A.



B.



C.



D.

3 1/ 3

1 6 5 12 1 2 7 9

A. B. C. D.

A.

1 2 3 4



B.



C.



D.

7p cm2 3π cm 2 2 5π cm 2 2 10p cm2

B.



C.



D.





25. PQRS is the diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Find the area of the shaded portion. O is the centre of outer circle and R is the centre of inner circle.





a2

4 − π2

24 π3 a3 24 π

4π2 − 1

2

a3

1 − 4π2

8π 2 a3

 2 π 2 1 −   π 3

A. B. C. D.

21 cm 13 cm 17 cm 15 cm

1 1 28. If x = 7 + 4 3 and xy = 1, then the value of 2 + 2 x y is

24. If (x – 1), (x + 1) and (x – 2) are factors of x 4 + (p – 3) x3 – (3p – 5) x2 + (2p – 9) x + 6 then the value of p is

A.

27. Altitude and base of a right angle triangle are (x + 2) and (2x + 3) (in cm). If the area of the triangle be 60 cm2 , the length of the hypotenuse is

23. Two dice are tossed. The probability that the total score is a prime number is



A. B. C. D.

64 128 184 194

29. For which set of numbers do the mean, median and mode all have the same value?

A. B. C. D.

2, 1, 1, 1,

2, 3, 1, 1,

2, 3, 2, 1,

2, 3, 5, 2,

4, 5, 6, 5,

6 3 5 2

30. The remainder of the polynomial 5 + bx – 2x2 + ax3 when divided by x – 2 is twice the remainder when it is divided by x + 1, then 4b − a 4b B. a = A. a = −9 10 10 9 − 4b 4b C. a = D. a = 9 − 10 10 31. 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred’s and ten’s places are respectively ______.

A. B. C. D.

7 and 4 7 and 5 8 and 5 None of these

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6

7th IMO - Set B

32. How many bricks (number near to next hundred) will be required to build a wall 30 m long, 30 cm thick and 5 m high with a provision of 2 doors, each 4 m × 2.5 m and each brick being 20 cm × 16 cm × 8 cm when one-ninth of the wall is filled with lime?

A. B. C. D.

13500 13600 20050 18500

33. In given figure, P and Q are centres of two circles intersecting at B and C. ACD is a straight line. Then, ratio of ∠BQD and ∠ACB is



C. D.

1:2 1: 2

34. In given figure, ABCD is a rectangle in which CD = 6 cm, AD = 8 cm. Find the area of parallelogram CDEF.



A. B. C. D.

36 24 48 60

cm2 cm2 cm2 cm2

35. 40% of ? + 962 = 35% of 980 + 150% of 850

A. B.



1:1 2:1

A. B. C. D.

372 842 1640 1052

everyday Mathematics 36. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of the remaining persons increased by

A.



B.



C.



D.

1 7 1 8 1 9 7 8

37. A certain factory employed 600 men and 400 women and the average wage was ` 25.50 per day. If a woman got ` 5 less than a man, then what are their daily wages?

A. B. C. D.

Man Man Man Man

: : : :

` ` ` `

25; Woman : ` 20 27.50; Woman : ` 22.50 30; Woman : ` 25 32.50; Woman : ` 27.50

38. A cylinder with height and radius 2 : 1 is filled with soft drink and then it is tilted so as to allow some soft drink to flow off to an extent where the level of soft drink just touches the lowest point of the upper mouth. If 2.1 L of soft drink is retained in the cylinder, what is the capacity of the cylinder?



A. B. C. D.

3.6 L 4L 4.2 L None of these

39. In a lottery of 100 tickets numbered 1 to 100, two tickets are drawn simultaneously. Find the probability that both the tickets drawn have prime numbers. 2 A. 33 7 B. 50 7 C. 20 5 D. 66 40. The price of a Maruti car rises by 30%, while the sales of the car goes down by 20%. What is the percentage change in the total revenue?

A. B. C. D.

5 4 6 8

% % % %

41. Ramesh bought x apples at ` 0.50 each and y kiwi fruit at ` 0.80 each. He sold the apples at ` 0.85 each and the kiwi fruit at ` 1.00 each. Which of the following algebraic expressions correctly shows the profit earned by Ramesh?

Copyright©2015. Science Olympiad Foundation (SOF)

7

7th IMO - Set B

A. B. C. D.

35x + 20y 35xy 20xy 30x + 15y



42. A rectangular courtyard 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. Then the largest size of the tile which could be used for the purpose is (n × 3)cm. Find n.

A. B. C. D.

14 21 42 7

43. A typist uses a sheet measuring 20 cm by 30 cm lengthwise. If a margin of 2 cm is left on each side and a 3 cm margin on top and bottom, then percent of the pages used for typing is

A. B.

40 60

C. D.

64 72

44. A man borrows ` 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly installments. How much will each installment be?

A. B. C. D.

` ` ` `

1275 1283 1352 1377

45. The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is:

A.

460



B.

500



C. D.

600 640

ACHIEVERS SECTION 46. Which of the following is true?

P:

æ 2 1 ö÷ p æ öq- p çç p - ÷ çç p - 1 ÷÷ çè q ÷ø q 2 ÷÷ø çè ö p-q æ 2 öq æ ççq - 1 ÷÷ ççq + 1 ÷÷ çè p ÷ø p 2 ÷÷ø çè

æ p ö p-q = çç ÷÷÷ çè q ø

Q : If pqr = 1, then 1 1 1 + + = -1 -1 -1 1+ p + q 1+ q + r 1 + r + p- 1

A. B. C. D.

48. Find the product of (4x 2 – 9) and (2x 2 – 3x + 1) and divide the product by (4x3 – 7x + 3). Then the quotient will be ____. Is (4x3 – 7x + 3) a factor of the product?

A. B. C. D.

49. Match the columns.



6+2 3 = a + b 3; a, b > 0 then 33 -19 3 Column I Column II



(i)

a + b



(ii) (a + b)2 – 4ab



2 2 æ 1ö æ 1ö (iii) ççça + ÷÷÷ çççb + ÷÷÷ è aø è bø



(iv) ((a)3(b)–3) –1



A. B. C. D.

If

Both P and Q are correct. Both P and Q are wrong. P is correct Q is wrong. P is wrong Q is correct.

47. Let S1 be a square of side ‘a’. Another square S 2 is formed by joining the mid-points of the sides of S1. The same process is applied to S 2 to form yet another square S 3, and so on. If A1, A2, A3, … be the areas and P1, P2, P3, ..... be the perimeters of S1, S 2, S 3, …, P + P2 + P3 + ... respectively, then the ratio 1 = A1 + A2 + A3 + ... A. 2(1 + 2 ) a 2(2 - 2 ) B. a 2(2 + 2 ) C. a 2 ( 1 + 2 2) D. a

Does not exist, No 2x, No 2x – 3, Yes 2x – 1, Yes

 52    3 (b) 8

(a)

(c) 4

3   5 (i)→a; (ii)→c; (iii)→d; (iv)→d (i)→c; (ii)→b; (iii)→a; (iv)→d (i)→d; (ii)→a; (iii)→b; (iv)→d (i)→b; (ii)→c; (iii)→a; (iv)→d (d)

50. The value of 53.0853 ÷ 6 =

A. B. C. D.

8.747558532 7.847558922 6.874558922 8.847558922

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3

2

Class 9 8th

Set A Year 2014

Copyright©2015. Science Olympiad Foundation (SOF)

8th IMO - Set A

1

Logical Reasoning Two rows of numbers are given. The resultant of each row is to be worked out separately based on the following rules, and the question below the rows of numbers is to be answered. The operations of numbers in each row progress from left to right. Rules: (i) If an odd number is followed by another odd number, they are to be multiplied. (ii) If an even number is followed by another even number, the first number is to be divided by the second even number. (iii) If an even number is followed by the perfect square of an odd number, the first number is to be subtracted from the second number. (iv) If an odd number is followed by an even number, the two are to be added. (v) If an even number is followed by an odd number which is not a perfect square, the square of the odd number is to be added to the even number. 9 15 50 12 25 24 If the resultant of first row is x and that of second row is y, then find the value of x ÷ y. A. 18 B. 8 C. 5 D. 6

5.

2.

1.

3.

4.



A cube of side 10 cm is coloured red with a 2 cm wide green strip along all the sides on all the faces. Now, the cube is cut into 125 smaller cubes of equal size. How many cubes have three green faces each? A. 0 B. 4 C. 6 D. 8 Pointing to a woman in a photograph, a man says "She is the grandmother of the son of my daughterin-law's mother-in-law." How is the woman related to the man? A. Mother B. Mother-in-law C. Sister D. Wife P, Q and R are three points on the ground. Point P is North of point Q and ∠PQR is 135° in anticlockwise direction. In what direction is point R from point Q? A. North-East B. North-West C. South-East D. South-West



If all the consonants starting from B are given sequentially the value of even numbers such as B = 2, C = 4 and so on, and all the vowels are given double the value of the preceding vowel and the value of A is 5, then what is the value of REASONING? A. 162 B. 177 C. 185 D. 187

6.

A set of three figures X, Y and Z shows a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Select the figure from the options which would resemble the unfolded form of paper.



A.



B.



C.



D.

7.

Select the figure in which Figure (X) is exactly embedded as one of its part.

Figure (X)



A.



B.



C.



D.

8.

Two positions of a dice are shown below. What number will be opposite to the number 4? A. 5 6 1 B. 6 3 2 C. 3 4 4 D. 1



Copyright©2015. Science Olympiad Foundation (SOF)

2

9.

8th IMO - Set A

Select a figure from the options which will replace the question mark to complete the given series.

?

A.



B.



C.



D.

10. A set of figures carrying certain characters, is given. Assuming that the characters in each set follow a similar pattern, then find the missing character. 7

3 6

315

6

4

A.



B.



C.



D.

14. Count the number of straight lines and squares in the given figure.

1

11 2402 8

2



4 1190

5

?





A. B. C. D.

1 2 6 10

11.

Find A. B. C. D.

the odd one out. 18 : 108 42 : 132 22 : 112 26 : 156

A. B. C. D.

21 18 17 19

straight straight straight straight

lines, lines, lines, lines,



A.

C.





squares squares squares squares

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

12. Which of the following Venn diagrams best represents the relationship amongst, "Honesty, Intelligence, Aptitude"?

7 8 8 8

Figure (X)

B.

A.



C.



B.

D.

13. There is a definite relationship between figures P and Q. Establish a similar relationship between figures R and S by selecting a suitable figure from the options that would replace (?) in figure R.

Copyright©2015. Science Olympiad Foundation (SOF)



D.

8th IMO - Set A

3

MATHEMATICAL REASONING −1/ 2

1 9 −3×5 −    81 16. Find the value of −2 / 3  25  1  64  + +3    / 1 4 125  64   256    625 3/ 2

0



A.

15 13

B.

0



C.

16 5

D.

48 13

 1 1 1  24 22. If 2x = 4y = 8z and  + +  = , then the  2x 4 y 6z  7 value of z is

17. Evaluate: (2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) A. 8x3 – y3 + 27z3 – 18xyz B. 8x3 – y3 + 27z3 + 18xyz C. 8x3 + y3 + 27z3 + 18xyz D. 8x3 + y3 – 27z3 + 18xyz 18. In the given figure, DABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On the base BC a parallelogram DBCE of area same as that of DABC is constructed. Find the height DF of the parallelogram.

6.5

7.5

cm

cm

A

D

B

3 5 6 7

cm cm cm cm

19. If x 2 +

1



A. B. C. D.

A. B. C. D.

x

2

A. B. C. D.

E C

7 cm

= 98, then find the value of x3 +

890 970 990 1110

20. Simplify :

F

3 2 4 0

2 1 3 + − 5+ 3 3+ 2 5+ 2

21. Euclid stated that all right angles are equal to each other in the form of a/an . A. Axiom B. Definition C. Postulate D. Proof

1

x3

.



A.



C.

7 16 7 48

B. D.

7 32 7 64

23. In the given figure, ABCD is a rectangle. BD = BE, ∠BED = 40° and ∠EDA = 260°. Find ∠CDB. B A

260°



A. C.

D

25° 40°

C

B. D.

E

30° 45°

24. Fill in the blanks: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than right angles. A. Less, three B. More, two C. Less, two D. More, one 25. The weight, in kg, of 50 students are given below. 40 45 55 62 50 51 56 69 61 36 60 56 69 38 35 63 57 50 57 48 40 63 53 64 47 42 56 51 42 60 55 39 64 57 64 44 66 35 59 59 73 62 49 63 37 63 54 72 44 60 Find the mean, median and mode respectively for the given data. A. 55 kg, 57 kg, 64 kg B. 55 kg, 57 kg, 62 kg C. 53.92 kg, 56 kg, 63 kg D. None of these

Copyright©2015. Science Olympiad Foundation (SOF)

4

8th IMO - Set A

26. Select the correct match. A. When x = 5, y = 2.5 and when y = 5, x = 10, then x and y are inversely proportional. B. When x = 10, y = 5 and when x = 20, y = 2.5, then xy = constant. C. If x and y vary inversely, then on decreasing x, y will decrease in proportion. D. If x and y vary directly, then on decreasing x , y will increase in proportion.



27. Study the given graph and answer the following question. y

31. John is of the same age as Mohan. Ram is also of the same age as Mohan. State the Euclid's axiom that illustrates the relative ages of John and Ram. A. First Axiom B. Second Axiom C. Third Axiom D. Fourth Axiom

4 3

l

2 1 –1 O –1

–4 –3 –2

1

3

2

x

4

–2



Calculate the area enclosed by the lines l, x = –3, y = –2 and y = –x + 2. A. 16 sq. units B. 19 sq. units C. 20 sq. units D. 22 sq. units

28. In the given figure, the shape of a solid copper piece (made up of two pieces with dimensions as shown in the figure) is shown. The face ABCDEFA is the uniform cross-section. Assume that the angles at A, B, C, D, E and F are right angles. Calculate the volume of the piece. A F

22 cm

2 cm

B

5 cm

C

8 cm

D



A. 528 cm3 C. 580 cm3

3 cm

E

B. D.

I

58°

H

B

C

115°

F E

B. D.

120°, 225° 110°, 215°

32. The given question is followed by three statements. You have to study the question and all the three statements to decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the given question. What is the marked price of the suitcase? I. When a discount of 15% is offered, the profit earned is 10.5%. II. The cost price of the suitcase is ` 1500. III. The marked price is 30% above the cost price. A. I only B. Either I or III C. Any one of the three D. All I, II and III are required 33. The A(2, A. C.

area of the triangle formed by the points 0), B(6, 0) and C(4, 6) is . 24 sq. units B. 12 sq. units 10 sq. units D. None of these

34. In the given figure, AB || CD || EF. CE is joined and produced to G. If ∠BAC = 130°, ∠ACE = 140°, then find ∠DCE and ∠FEG respectively. A B



A. C.

C

D

E G

F

50°, 130° 140°, 40°

B. D.

90°, 90° 45°, 135°

35. Find the value of a and b respectively, if

45°

G

D

110°, 220° 120°, 235°

30. The value of p upto 35 decimal places is given below: 3.14159265358979323846264338327950288 Find the probability of occurring 8 in it. A. 1/3 B. 1/5 C. 5/36 D. 1/7

880 cm3 940 cm3

29. Study the figure shown here (not drawn to scale), If ABG is a straight line, then find ∠ABH and reflex ∠ABC respectively. A 60°

A. C.



A. B. C. D.

5+ 3 = 47 a + 3b 7−4 3 2, 1 1, 27 11, 28 2, 38

Copyright©2015. Science Olympiad Foundation (SOF)

8th IMO - Set A

5

EVERYDAY MATHeMATICS 36. A alone can complete a work in 16 days and B alone in 12 days. Starting with A, they work on alternate days. The total work will be completed in . A. 12 days B. 13 days

C.



D.

5 days 7 3 13 days 4 13

37. A sum of ` 1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is ` 106, then find the money lent at each rate. A. ` 750, ` 800 B. ` 600, ` 950 C. ` 650, ` 900 D. ` 850, ` 750 38. If 6 years are subtracted from the present age of Gagan and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Madan whose age is 5 years, then what is Gagan's present age? A. 48 years B. 60 years  C. 84 years D. 96 years 39. A certain factory employed 600 men and 400 women and the average wage was ` 25.50 per day. If a woman got ` 5 less than a man, then what is the daily wage of a man and woman respectively? A. ` 25; ` 20 B. ` 27.50; ` 22.50 C. ` 30; ` 25 D. ` 32.50; ` 27.50 40. A man earns ` 20 on the first day and spends ` 15 on the next day. He again earns ` 20 on the third day and spends ` 15 on the fourth day. If he continues to save like this, then how soon will he have ` 60 in hand? A. On 17th day B. On 27th day C. On 30th day D. On 24th day

41. The price of rice is reduced by 2% per kg. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier? A. 48 kg B. 49 kg C. 50 kg D. 51 kg 42. In a bag, there are coins of 25 paise, 10 paise and 5 paise in the ratio of 1 : 2 : 3. If there are ` 30 in all, then how many 5 paise coins are there? A. 50 B. 100 C. 150 D. 200 43. A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in of a day?

A. B. C. D.

1 4

1 4 19 41

44. The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is . A. 11 years B. 14 years

C.

15 years



D.

15

2 years 7

45. Village X has a population of 68000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year. In how many years will the population of the two villages be equal? A. 12 B. 13 C. 14 D. 15

Copyright©2015. Science Olympiad Foundation (SOF)

6

8th IMO - Set A

Achievers Section 46. Which of the following statements is INCORRECT? A. If the altitudes of a triangle are equal, then it is equilateral. B. If in a triangle, two sides are unequal, then the angle opposite to the longer side is greater than the angle opposite to the shorter side. C. In a triangle, side opposite to the larger angle is longer than the side opposite to the smaller angle. D. In a triangle, altitude from the vertex bisects the base. 47. The polynomial p(x) = x 4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find (a) the value of a. (b) the remainder when p(x) is divided by x + 2. (a) (b) A. 1 13 B. –3 48 C. 5 62 D. 8 43 48. Fill in the blanks. In coordinate geometry, the coordinate axes divide the plane into four parts called ___ P__. The point of intersection of the axes is called ___ Q__. The sign

of abscissa and ordinate will be same in ___ R__ and ___ S__ quadrants.   P   Q R S A. Quadrant x-axis II III B. Quadrant origin I III C. Quadrant origin I IV D. Quadrant origin I II 49. Which of the following options hold? Statement-1 : If any two angles and non-included side of one triangle are equal to the corresponding angles and side of another triangle, then the triangles are congruent (AAS congruence criterion). Statement-2 : If in two right triangles, hypotenuse and one side of a triangle, are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent (RHS congruence criterion). A. Statement-1 is true but statement-2 is false. B. Statement-1 is false but statement-2 is true. C. Both the statements are true. D. Both the statements are false. 50. Which of the following statements is INCORRECT for a parallelogram? A. Opposite sides are equal. B. Opposite angles are equal. C. Opposite angles are bisected by the diagonals. D. Diagonals bisect each other.

SPACE FOR ROUGH WORK

Copyright©2015. Science Olympiad Foundation (SOF)

Class 9 8th

Set B Year 2014

Copyright©2015. Science Olympiad Foundation (SOF)

8th IMO - Set B

1

Logical Reasoning 1.

2.

3.



What should come next in the letter series given below? AABAB CAB C DAB C D EAB C D E FA B C D E F G A B C D E F G _?__ A. A B. I C. H D. B How many pairs of letters are there in the word NURSING which have as many letters between them as in the English alphabet? A. One B. Three C. Five D. Six Study the following arrangement carefully and answer the question given below : M J % 4TE K I 9 # PA$ Q 3 8 N 5 U 7W* B @DF1Z6H What should come in place of question mark in the following series based on the above arrangement? J 4 E  I # A  Q 8 5  7 * @  ? A. F16 B. DG C. F6 D. F1Z

4.

Ravi starts from his house and moves towards South. He walks 100 m, then turns left and walks 200 m, turns right and walks 500 m. How far is he from his house?



A. B.

400 5 m 800 m



C.

200 10 m



D.

200 2 m

5.

Four brothers go to a dance party. As they leave, each of the brothers accidentally takes a hat belonging to another brother and a coat belonging to a third brother. M takes the coat belonging to the brother whose hat is taken by P, while P's coat is taken by the brother who takes M's hat. S takes J's hat. Whose hat was taken by P? A. Can't say B. S C. M D. Either S or J



6.

7.



In a certain code 'ring a bell' is written as '5 8 2', 'did not ring' is written as '3 5 9' and 'not a reason' is written as '7 2 9'. What is the code for 'ring? A. 8 B. 2 C. 5 D. 3 P, Q, R, S, T, U and W are sitting around a circle facing at the centre. S is third to the left of P who is second to the left of U. T is not a neighbour of either U or S. R is third to left of Q. Which of the following information represents the first person sitting to the immediate right of the second person? A. PQ B. UW C. RT D. PT

8.

A pile of cubes of equal size is arranged as shown in the figure. Now the block is dipped into a bucket full of red paint so that only the surfaces of the block get coloured. How many cubes are coloured on four faces only?



A. B. C. D.

9.

Find the missing character if the given matrix follows a certain rule row-wise or column-wise.

0 1 2 4

18

24

32

12

16

16

3

?

4

72



A. B. C. D.

2 3 4 5

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96 128

2

8th IMO - Set B

10. In the given Venn diagram, triangle represents the healthy, square represents the old and circle represents the men. Which of the following regions represents the men who are healthy but not old? 7 12 4 3 5



A.



B.



C.



D.

6



A. B. C. D.

1 2 3 7

11. Select the mirror image of Figure (X) from the given options, if the mirror is placed vertically to the right. F

E

14. There is a certain relationship between figures (i) and (ii). Establish the similar relationship between figures (iii) and (iv) by selecting a figure from the options which will replace the (?) in figure (iv).

?





G

E

D. G

G

E

12. Given below are the three figures (X), (Y) and (Z) showing a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Identify the unfolded form of piece of paper.

X

Y

Z



A.



B.



C.



D.



A.



B.



C.



D.

(ii)

(iii)

(iv)

J

C.

B.

J

E

F

F G

(i)

F

E

J



A.

F



J

J

G Figure (X)

13. The given question consists of Problem Figures followed by option figures. Select a figure which will continue the series. Problem Figures

15. Select the figure from the options which can be formed from the pieces given in Figure (X).

Figure (X)



A.



C.





Copyright©2015. Science Olympiad Foundation (SOF)

B.

D.

8th IMO - Set B

3

MATHEMATICAL REASONING 16. In figure, ∠L = 62°, ∠LMN = 54°. If MO and NO are bisectors of ∠LMN and ∠LNM respectively of L DLMN, find ∠ONM and ∠MON. A. 27°, 121° B. 64°, 32° O C. 64°, 121° D. 32°, 121° M N 17. In the figure, it is given that A K B



35°

D

C 25° Z

x

E F

19. The value of

A. B. C. D.

2 –1 3+ 2 1

A R

Q

B

6+2 3+2 2 +2 6 −

A. B. C. D.

85.5 92.5 90.5 87.5

22. A bag contains 8 red and 4 green balls. Find the probability that the ball drawn is red when one ball is selected at random.

A.

2 3

B.

1 3



C.

1 6

D.

5 6

23. In the given figure, ABCDEF is a regular hexagon and ∠AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF?

(i) AB ^ BF and EF ^ BF (ii) AC = BC (iii) KD is perpendicular to BC and DE. Find the measure of x. A. 75° B. 30° C. 60° D. 45°

18. In a DABC, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm. The perimeter of the quad. ARPQ is A. 91 cm B. 60 cm C. 51 cm D. 70 cm



C

P

1 5−2 6

is

20. If a + b + c = 15 and a2 + b 2 + c 2 = 83, find the value of a3 + b3 + c 3 – 3abc. A. 180 B. 71 C. 128 D. 95 21. Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be K% lower than the volume of B. The value of K must be



A.

1 12



B.

1 6



C.

1 24



D.

1 8

24. The value of expression

B

A F

C

O D

E

(0.6)0 − (0.1) −1  3  3  2

−1

3

 3  1 ⋅  +  −   2  3



A.

3 − 2

B.

2 3



C.

3 2

D.

9 4

−1

is

25. In the given figure, square 2 is formed by joining the mid-points of square 1, square 3 is formed by joining the mid-points of square 2 and so on. In this way total five squares are drawn. The side of the square 1 is 'a' cm. What is the sum of perimeters of all the five squares ? A.

(4 2 + 1)a cm ( 2 + 1)



B.

5 a cm 6



C.

(7 + 3 2 )a cm



D.

None of these



Copyright©2015. Science Olympiad Foundation (SOF)

1

2 4 5

3

4

8th IMO - Set B

26. In the given figure, O is the centre of the circle. The distance between P and Q is 4 cm. Find the ∠ROQ. A. 50° B. 60° C. 70° D. 35°

31. ABCD is a trapezium in which AB | | CD. Then AC2 + BD 2 is equal to

R

°

35

P

O 2 cm

Q

27. In the given figure, CD || AE and CY || BA. Then ar(BCZY ) = C

D

X

B

Z Y E

A



A. B. C. D.

ar(DZDC) ar(DCBY) ar(DEDZ) All of these

28. The given diagram shows a cylinder with a diameter of 10 cm 10 cm and height 15 cm. The 15 cm shaded portion in the form of a cone, with base diameter 10 cm and height 6 cm, is hollowed out. Find the volume of the remaining solid, in cm3. A. 300 p B. 345 p C. 295 p D. 325 p

P(–3, –2)



AD2 AD2 AD2 AD2

L

B

+ BC2 – 2AB⋅CD + BC2 + 2AB⋅CD – BC2 + 2AB⋅CD – BC2 – 2AB⋅CD

32. PQRS is the diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles are drawn with PQ and QS as diameters P S as shown in figure. Find the R Q ratio of the area of the shaded region to that of the unshaded region. A. 3 : 15 B. 15 : 13 C. 5 : 13 D. 13 : 5 33. Each side of DABC is 12 units. D is the foot of the perpendicular dropped from A on BC, E is the midpoint of AD. The length of BE is 36 3 units



B.

6 7 units



C.

3 3 units

R



D.

3 7 units

Q(2, –2)

34. Divide the product of (4x 2 – 9) and (2x 2 – 3x + 1) by (4x 3 – 7x + 3). A. 2x – 3 B. 2x + 3 C. 2x D. 3x – 2

X

PQRS is a square. The coordinates of S are A. (–3, 3) B. (3, – 3) C. (–3, –3) D. (–3, 2)

30. If a (a – A. B. C. D.

A. B. C. D.

M

A.

Y

O



C



29. The given diagram is drawn on a cartesian plane. S

A

D

– b = 3, a + b + x = 2, then the value of b) [x 3 + 3(a + b)x 2 + 3x(a + b)2 + (a + b)3] is 84 48 32 24

35. In the figure below, two straight lines PQ and RS intersect each other at O. If ∠POT = 75°, find the values of a, b and c respectively. A. 21°, 84°, 48° B. 48°, 84°, 21° C. 84°, 21°, 48° D. 57°, 21°, 48°

Copyright©2015. Science Olympiad Foundation (SOF)

R 4b

P

Q

2c

O

75°

a b

T

S

8th IMO - Set B

5

EVERYDAY MATHeMATICS 36. 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B?

A.

77

1 3



B.

77

2 3



C.

78

1 3



D.

78

2 3

37. One year ago, Sheela was four times as old as her daughter Sakshi. Six years hence, Sheela's age will exceed her daughter's age by 9 years. The ratio of the present ages of Sheela and her daughter is _____. A. 9 : 2 B. 11 : 3 C. 12 : 5 D. 13 : 4 38. A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. In the total transaction, his gain or loss will be _____. A. Neither loss nor gain B. 5% loss C. 5% gain D. 10% gain 39. If 18 binders bind 900 books in 10 days, how many binders will be required to bind 660 books in 12 days? A. 22 B. 14 C. 13 D. 11 40. The population of a town is increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is _____. A. 4.37% B. 5% C. 6% D. 50%

41. A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay ` 5400 interest only for the period. The principal amount borrowed by him was . A. ` 2000 B. ` 10,000 C. ` 15,000 D. ` 20,000 42. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits ` 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is A. ` 120 B. ` 121 C. ` 122 D. ` 123 43. A man bought goods worth ` 6000 and sold half of them at a gain of 10%. At what gain percent must he sell the remainder so as to get a gain of 25% on the whole? A. 25% B. 30% C. 35% D. 40% 44. Gauri went to the stationers and bought things worth ` 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? A. ` 15 B. ` 15.70 C. ` 19.70 D. ` 20 45. Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in _____. A. 6 hrs

B.

2 6 hrs 3



C.

7 hrs



D.

1 7 hrs 2

Copyright©2015. Science Olympiad Foundation (SOF)

6

8th IMO - Set B

Achievers Section 46. Select the correct match. ( x − 2)( x − 4) Let f ( x) = x





Column I

Column II



A.



B.



C.



D.

f(x) is a polynomial As (x – 2), (x – 4), x are polynomials f(x) is an equation As it can be written as ax2 + bx + c p f(x) is a rational number As it is of the form , q q≠0 f(x) is not a polynomial As the exponents of x are not whole numbers.

A. B. C. D.

48° 42° 56° 58°

49. The given figure, not drawn to scale, is made up of 3 circles and 3 squares. Find the total area of the 22 shaded parts. (Take p = ) 7

56 cm

13 cm

47. The marks scored by some students for a question in the Science test are shown in the table below.



Marks

0

1

2

3

4

5

Number of students

3

2

3

5

x

1

(a) If the mode is 4, write down the smallest possible value of x. 1 (b) If the mean is 2 , find the value of x. 4

A. B. C. D.

(a) 6 5 6 6

(b) 2 2 4 3

28 cm



A. B. C. D.

1500 cm2 1680 cm2 1749 cm2 1149 cm2

50. The given pie chart shows the distance covered by Mohit from Monday to Thursday. The distance he covered on Tuesday was thrice the distance he covered on Wednesday. Mohit covered a distance of 201 km on Wednesday. Monday Thursday

48. In the given figure, ABCD is a parallelogram and CEFD is a rhombus. ∠ADF = 90° and ∠CFD = 24°. Find ∠DAB.

Tuesday

C B

D

A

24°

F

E

42 cm

(i)

Wednesday 1 12

What was the total distance he covered on the four days? (ii) What was the distance covered on Monday?   (i)   (ii) A. 2142 km 1005 km B. 2214 km 1008 km C. 2124 km 1102 km D. 2412 km 1005 km

SPACE FOR ROUGH WORK

Copyright©2015. Science Olympiad Foundation (SOF)

ANSWER KEYS 4 th  IMO (2010)  1.  (C)  11.  (B)  21.  (D)  31.  (B)  41.  (B) 

2.  (C)  12.  (B)  22.  (A)  32.  (D)  42.  (B) 

3.  (B)  13.  (D)  23.  (B)  33.  (C)  43.  (A) 

4.  (A)  14.  (B)  24.  (D)  34.  (C)  44.  (B) 

5.  (A)  15.  (B)  25.  (C)  35.  (B)  45.  (B) 

6.  (D)  16.  (B)  26.  (D)  36.  (A)  46.  (C) 

7.  (D)  17.  (A)  27.  (B)  37.  (C)  47.  (A) 

8.  (D)  18.  (A)  28.  (D)  38.  (D)  48.  (A) 

9.  19.  29.  39.  49. 

(D)  (C)  (A)  (C)  (D) 

10.  20.  30.  40.  50. 

(C)  (D)  (D)  (C)  (B) 

7. 17. 27. 37. 47.

(C)  (B)  (D)  (B)  (B) 

8. 18. 28. 38. 48.

(C)  (B)  (D)  (D)  (D) 

9. 19. 29. 39. 49.

(C)  (C)  (C)  (C)  (B) 

10. 20. 30. 40. 50.

(D)  (C)  (A)  (D)  (C) 

7. 17. 27. 37. 47.

(C)  (B)  (A)  (C)  (B) 

8. 18. 28. 38. 48.

(C)  (D)  (A)  (D)  (B) 

9. 19. 29. 39. 49.

(D)  (D)  (D)  (D)  (C) 

10. 20. 30. 40. 50.

(D)  (B)  (D)  (C)  (C) 

7.  (D)  17.  (B)  27.  (A)  37.  (D)  47.  (B) 

8.  (D)  18.  (C)  28.  (C)  38.  (C)  48.  (B) 

9.  19.  29.  39.  49. 

(A)  (B)  (B)  (B)  (D) 

10.  (D)  20.  (B)  30.  (C)  40. (A,C)  50.  (D) 

5 th  IMO (2011)  1. 11. 21. 31. 41.

(C)  (C)  (D)  (D)  (B) 

2. 12. 22. 32. 42.

(A)  (B)  (A)  (C)  (A) 

3. 13. 23. 33. 43.

(D)  (B)  (D)  (A)  (C) 

4. 14. 24. 34. 44.

(D)  (D)  (C)  (A)  (B) 

5. 15. 25. 35. 45.

(D)  (A)  (A)  (B)  (C) 

6. 16. 26. 36. 46.

(B)  (C)  (B)  (B)  (A) 

6 th  IMO (2012)  SET A  1. 11. 21. 31. 41.

(D)  (C)  (B)  (A)  (C) 

1.  (C)  11.  (C)  21.  (D)  31.  (A)  41.  (C) 

2. 12. 22. 32. 42.

(C)  (B)  (B)  (B)  (B) 

2.  (C)  12.  (C)  22.  (A)  32.  (A)  42.  (D) 

3. 13. 23. 33. 43.

(B)  (B)  (D)  (D)  (A) 

3.  (C)  13.  (C)  23.  (A)  33.  (B)  43.  (A) 

4. 14. 24. 34. 44.

(B)  (B)  (D)  (B)  (A) 

4.  (D)  14.  (B)  24.  (C)  34.  (C)  44.  (B) 

5. 15. 25. 35. 45.

(D)  (D)  (A)  (D)  (C) 

6. 16. 26. 36. 46.

(C)  (C)  (D)  (B)  (D) 

SET B  5.  (C)  6.  (A)  15.  (D)  16.  (D)  25.  (D)  26.  (D)  35.  (D)  36.  (B)  45.  (D)  46.  (A)  7 th  IMO (2013) 

1.  (A)  11.  (C)  21.  (D)  31.  (D)  41.  (C) 

2.  (D)  12.  (C)  22.  (A)  32.  (D)  42.  (B) 

3.  (B)  13.  (B)  23.  (D)  33.  (B)  43.  (C) 

4.  (B)  14.  (B)  24.  (B)  34.  (D)  44.  (C) 

SET A  5.  (B)  6.  (C)  15.  (C)  16.  (A)  25.  (B)  26.  (D)  35.  (A)  36.  (C)  45.  (B)  46.  (B) 

7.  (C)  17.  (B)  27.  (B)  37.  (B)  47.  (D) 

8.  (B)  18.  (C)  28.  (A)  38.  (A)  48.  (D) 

9.  19.  29.  39.  49. 

(B)  (A)  (D)  (C)  (D) 

10.  20.  30.  40.  50. 

(B)  (D)  (A)  (A)  (D) 

1.  (B)  11.  (A)  21.  (A)  31.  (C)  41.  (A) 

2.  (C)  12.  (D)  22.  (A)  32.  (B)  42.  (D) 

3.  (C)  13.  (D)  23.  (B)  33.  (B)  43.  (C) 

4.  (D)  14.  (D)  24.  (D)  34.  (C)  44.  (C) 

SET B  5.  (D)  6.  (D)  15.  (D)  16.  (C)  25.  (D)  26.  (B)  35.  (C)  36.  (A)  45.  (D)  46.  (B) 

7.  (C)  17.  (D)  27.  (C)  37.  (B)  47.  (C) 

8.  (D)  18.  (A)  28.  (D)  38.  (C)  48.  (C) 

9.  19.  29.  39.  49. 

(D)  (D)  (B)  (A)  (D) 

10.  20.  30.  40.  50. 

(D)  (D)  (C)  (B)  (D) 

8 th  IMO (2014) 

1.  (C)  11.  (D)  21.  (C)  31.  (A)  41.  (C) 

2.  (D)  12.  (C)  22.  (C)  32.  (B)  42.  (C) 

3.  (A)  13.  (D)  23.  (B)  33.  (B)  43.  (D) 

4.  (D)  14.  (D)  24.  (C)  34.  (B)  44.  (A) 

SET A  5.  (D)  6.  (C)  15.  (B)  16.  (D)  25.  (C)  26.  (B)  35.  (B)  36.  (D)  45.  (B)  46.  (D) 

7.  (A)  17.  (B)  27.  (C)  37.  (C)  47.  (C) 

8.  (A)  18.  (A)  28.  (B)  38.  (B)  48.  (B) 

9.  19.  29.  39.  49. 

(B)  (B)  (C)  (B)  (C) 

10.  20.  30.  40.  50. 

(D)  (D)  (C)  (A)  (C) 

1.  (C)  11.  (B)  21.  (D)  31.  (B)  41.  (C) 

2.  (B)  12.  (C)  22.  (A)  32.  (C)  42.  (B) 

3.  (A)  13.  (C)  23.  (A)  33.  (D)  43.  (D) 

4.  (C)  14.  (D)  24.  (A)  34.  (A)  44.  (C) 

SET B  5.  (B)  6.  (C)  15.  (C)  16.  (D)  25.  (C)  26.  (C)  35.  (C)  36.  (B)  45.  (C)  46.  (D) 

7.  (D)  17.  (C)  27.  (C)  37.  (D)  47.  (A) 

8.  (C)  18.  (C)  28.  (D)  38.  (C)  48.  (B) 

9.  19.  29.  39.  49. 

(C)  (D)  (A)  (D)  (C) 

10.  20.  30.  40.  50. 

(B)  (A)  (D)  (B)  (D)

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