CLASS 10 IMO WORKBOOK

10

5

(2007-2011)

INSTANT

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IIT-JEE | AIEEE | NEET | BOARDS | OLYMPIAD | NTSE

FOUNDATION COURSE For Classes 8, 9 & 10 Class 8

Class 9

Class 10

1st

Year 2007

Class 10

1st IMOSETA - 2007

2

SECTION I : LOGICAL REASONING Direction (Q1 3): In each of the following three questions a series of numbers/alphabets is given which follows certain rules. One of the numbers/alphabets is missing. Choose the missing number/ alphabets from the alternatives given below. 1.

284, 140, 68, ? (A) 70

(B) 34

(C) 32

(D) 60

(B) 18

(C) 24

(D) 22

(B) ETK

(C) ERS

(D) ERJ

(E) None of these. 2.

17496, 1944, 216, ? (A) 20 (E) None of these.

3.

AXB, BWD, CVF, DUH, ? (A) ETJ (E) None of these. Direction (Q4 5): In each of the following questions there are five groups of letters four of them are alike in some manner, while one is different. Find out the different one.

4.

(A) NOPR

(B) SURT

(C) PROQ

(D) FHEG

(B) BDFH

(C) IKMO

(D) YACE


(A) ACEG (E) None of these.

6.

In a row of 40 children facing North, Satish is eighth to the right of Ajay. If Ajay is 18th from the right end of the row, how far is Satish from the left end of the row? (A) 32nd

(B) 10th

(C) 31st

(D) 29th


In the following figure, the represents educated, the represents urban and the the honest people. Study the figure carefully and answer the question which follow.

represents s

1 3 6 4

7 2 5

Which number represents who are honest but not educated and not urban? (A) 2

(B) 1

(C) 6

(D) 3


In a certain code ‘PURE’ is written as ‘QVQD’ and ‘COPE’ is written as ‘DPOD’. How is ‘WHEN’ written in that code? (A) XIFO (E) None of these.

(B) VGDM

(C) XIDM

(D) VGFO

SETA 9.

1st IMO - 2007 Class 10

3

Arrange the words in the sequence in which they occur in dictionary. 1.

Indorse

(A) 1 2 3 4

2.

Infant

3.

(B) 1 2 4 3

Infidel

(C) 4 3 2 1

4.

Inflect

(D) 3 4 2 1

(E) None of these. Direction (Q10 11): In the following questions select from the answer choices an appropriate number to replace the question mark 3

10.

6

45

(A) 117

9

11 1

85

?

(B) 122

2

(C) 123

(D) 141

(E) None of these.

9

6 99

11. ?

(A) 10

(B) 14

15

(C) 5

(D) 9

(E) None of these. 12. Seema and Rajat start together from a point. They walk 10 kms towards North. Seema turns to her left and walk 5 kms, while Rajat turns Right and walk only 3 kms. Now Seema turns towards her left and Rajat towards his right and both walk 15 kms forward. How far are they from each other (A) 2 kms

(B) 8 kms

(C) 13 kms

(D) 15 kms

(E) None of these. 13. How many right angled triangles are there in the given figure (A) 12

(B) 15

(C) 9

(D) 11

(E) None of these. 14. Assume A = 0, B = 2, C = 1, D = 3, E = 4, F = –2, M = 10 B × C + A + D × M = ? (A) 32

(B) 52

(C) 22

(D) 42

(E) None of these. 15. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group? (A) March

(B) January

(C) July

(D) June

(E) May. 16. If P denotes +, Q denotes –, R denotes × and S denotes ¸ , which of the following statements is correct. Select the appropriate number among the given choices. 36 R 4 S 8 Q 7 P 4 = ? (A) 58 (E) None of these.

(B) 55

(C) 63

(D) 15

Class 10

1st IMOSETA - 2007

4

17. The positions of how many digits in the number 7354612 will remain unchanged after the digits within the number are rearranged in descending order from left to right? (A) One

(B) Two

(C) Three

(D) More than three.

(E) None of these. 18. X and Y are sisters. Y is wife of Z, P is son of Q, M is daughter of Y. N is husband of X, Q is father of Y. O is daughter of L, K is wife of L. X is mother of L. Who is the brother of L? (A) M

(B) Z

(C) L

(D) Q

(E) P. Direction (Q19 20): Read carefully the information given below. In a group of five boys A, B, C, D and E. A and C are good in English and Maths, B and C are good in English and General knowledge, E and D are good in Science and Drawing. B and D are good in Drawing and General knowledge. While E is good in Drawing, Maths and Science. 19. Who is good in English, Drawing and General knowledge? (A) A

(B) B

(C) E

(D) C

(E) D. 20. Who is good in English and Maths but weak in General kowledge? (A) E

(B) C

(C) A

(D) D

(E) B.

SECTION II : MATHEMATICAL REASONING 21. The weighted median A w is equal to (A)

å wx å w

(B)

å xF å F

(C)

å

x n

(D)

å x

(E) None of these. 22. What will be the difference of the roots of quadratic equation 4y 2 – 4y + 1 = 0? (A) 0

(B) 1

(C) -

1 2

(D) 2

(E) None of these. 23. The area of sector is equal to (A) pr 2

(B)

pr 2 q 360 °

(C) p(R + r) (R – r)

(D) 2pr

(E) None of these. 24. The mode of data given below is 16. What is the value of x ? 13, 15, 16, 14, 16, 14, 13, 14, 13, x, 16, 17, 18, 17 (A) 15

(B) 16

(C) 17

(D) 18

(C) 6

(D) 8

(E) None of these. 25. The number of subsets of A = {0, 7, 8} will be (A) 3 (E) None of these.

(B) 5

SETA


5

26. If a, b be the roots of equation 4x 2 – 7x + 3 = 0 then the value of 25 12 (E) None of these. (A)

(B)

23 8

(C)

a b + will be b a

24 25

(D)

24 23

27. If the price of a material is increased by 10% and again increased price is decreased by 10%, then what will be the loss percentage? (A) 1%

(B) 1.5%

(C) 2%

(D) 5%

(E) None of these. 28. Which of the statements given below is correct, if discriminant for equation 5x 2 – 4x + 2 = 0 is D ? (A) D > 0

(B) D = 0

(C) D < 0

(D) D is not defined

(E) None of these. 29. If p is 25% less than q, then q is x% more than p, where x = ? 1 (A) 33 % 3

(B) 25

2 (D) 16 % 3

1 (C) 33 3

(E) None of these. 30. The selling price of two materials is Rs. 500. If there is loss of 20% on the first material and profit of 20% on the other material, then what will be the total percentage loss? (A) 4%

(B) 2.5%

(C) 3%

(D) 3.5%

(E) None of these. 31. The curved surface area of cone is equal to (A) prl square unit

(B)

1 2 pr h cubic unit 3

(C) pr(l + r) square unit (D) pr 2 l cubic unit

(E) None of these. 32. The volume of spherical shell is equal to 4 p(R 3 - r 3 ) 3 (E) None of these. (A)

(B) 4pr 2

(C) p(R + r) (R – r)

(D)

4 3 pr 3

33. The legs of a right angled triangle are 8 cm and 15 cm. The radius of the circle inscribed in the triangle is (in cm) 15 cm

(A) 1

(B) 2

(C) 3

(D) 4 8 cm

(E) None of these. 34. If x – k divides x 3 – 6x 2 + 11x – 6 =0, then k can't be equal to (A) 1

(B) 2

(C) 3

(D) 4

(E) None of these. 35. The system of equations tx + ty + t = 0 and x + (2 – t)y = 2 has no solution, if t = (A) 2 (E) None of these.

(B) 1

(C) – 6

(D) 4

Class 10

1st IMOSETA - 2007

6

36. In the given diagram shown below, if PB = 8 cm, AB = 4 cm, PD = 6 cm, then CD = ?

A

4 cm

C 16 cm 3 (E) None of these. (A)

x 2 - 2 4 x + 1 = 0

?

(B) 10 cm

37. If one root of a quadratic equation is (A)

B

(B)

D

8 cm

P

6 cm

(C) 6 cm

(D) 7 cm

1 , then the quadratic equation can be 4 - 3

x 2 - 4 x + 1 = 0

(C)

(D)

x 2 + 2 4 x + 1 = 0

x 2 - 2 3 x + 1 = 0

(E) None of these. 38. If base of a right angled triangle is twice the base of another right angletriangle and height of first right angle triangle is 1/4 th of other's height then what will be ratio of area of triangle one to triangle two. (A) 1 : 1

(B) 2 : 1

(C) 1 : 2

(D) 3 : 2

(E) None of these. 39. The measure of each exterior angle of a regular pentagon is (A)

p radian 6

(B)

2 p radian 5

(C)

p radian 3

(D)

3 p radian 5

(E) None of these. 40. a 2 – b 2 will be a perfect square if the ratio of a and b is (A) 1 : 2

(B) 3 : 4

(C) 5 : 4

(D) 4 : 5

(E) None of these.

SECTION III : EVERYDAY MATHEMATICS 41. There are three circles each of radius 7 cm. A triangle is formed by joining their centres. The angles at the centre made by the triangle are shown in the given figure, [42°,58°, 80°]. The area of the shaded portion is (A) 11 cm 2 11 2 cm 7 (E) None of these.

(C)

58°

22 2 cm (B) 7 (D)

80°

4 2 cm 7

42. ABCD is a square, inscribed in a circle of radius 14 cm. E, F, G, H are the middle points of the sides DA, AB,BC and CD respectively. The area of the square EFGH will be (A) 89 cm 2

(B) 196 cm 2

(C) 98 cm 2

(D) 392 cm 2

(E) None of these.

42°

A

F

E D

B G

H

C

SETA


7

43. Two circular wheels of the same radius r have their central hubs at a distance of a from one another. The minimum length of a fan belt which will pass around both the wheels, is (A) 2(a + pr ) (D)

a - pr 2

(B)

a + pr 2

r

(C) 2a + pr

(E) None of these.

44. In the figure, ABCD is a square with side 10. BAD is an arc of a circle with centre C. BCD is an arc of a circle with centre A. What is the area of the shaded region? (A) 100 50p

(B) 100 25p

(C) 50p 100

(D) 25p 100

(E) None of these.

A

B

D

C

45. Three men, four women and six children can complete a work in 7 days. A women does double the work a man does and a child does half the work a man does. How many women can complete this work in 7 days? (A) 8

(B) 7

(C) 12

(D) Cannot be determined

(E) None of these. 46. A and B run a kilometre and A wins by 25 sec. A and C run a kilometre and A wins by 275 m. B and C run the same distance and B wins by 30 sec. The time taken by A to run a kilometre is (A) 2 min 25 sec

(B) 2 min 50 sec

(C) 3 min 20 sec

(D) 3 min 30 sec

(E) None of these. 47. Plane A takes off at 4 pm and flies at a constant speed of X mphr. Plane B takes off at 5. 30 pm and flies the same route as that of A at a constant speed of Y mphr. Assuming Y is greater than X. How many hours after 5.30 pm will the plane B overtake plane A? 3 X hr 2 (E) None of these. (A)

(B)

3 hr 2Y

3 (C) 2(Y X) hr

3 X (D) 2(Y X) hr

48. A sells a bicycle to B at a profit of 20% , B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of bicycle for A, is (A) Rs. 110

(B) Rs. 125

(C) Rs. 120

(D) Rs. 150

(E) None of these. 49. 180 oranges are distributed among 70 boys and girls such that each boy get 2 and each girl 3 oranges. The number of boys are (A) 70

(B) 25

(C) 30

(D) 40

(E) None of these. 50. Twenty litres of a mixture contains milk and water in the ratio of 5 : 3. If four litres of this mixture is replaced by four litres of milk, then the ratio of the milk to that of the water in the container will be (A) 5 : 3 (E) None of these.

(B) 4 : 3

(C) 7 : 3

(D) 2 : 3

2nd

Year 2008

Class 10

2nd IMO - 2008

2

SECTION I : LOGICAL REASONING 1.

If '+' means '¸', '¸' means '×', '×' means '–' and '–' means '+', what will be the value of the following expression ? 15 ¸ 5 × 9 + 3 – 6 (A) 78

2.

(B) 72

(D)

30

(E) None of these.

The positions of how many digits in the number 4231576 will remain unchanged after the digits within the number are arranged in ascending order ? (A) None

3.

(C) 28

(B) One

(C) Two

(D) Three

(E) More than three.

If the same functions are applied to reach the results in each of the three sets of numbers, find what number should replace the ? in the last set: 21

5

28 13 30

?

7

25 7

10 8

24 17

(A) 30

16 2

(B) 36

(C) 32

(D) 35

(E) 25

Directions (Q.4 and 5) : Which one of the five answer figures should come after the problem figures, if the sequence were continued? × ×

×

×

× ×

D

1

Problem figures

×

D

×

×

4.

Answer figures 2

(A) 1

3

4

(B) 2

5

(C) 3

5.

(D) 4

(E) 5

Problem figures

Answer figures 1

(A) 1

2

3

(B) 2

4

5

(C) 3

(D) 4

(E) 5

Class 10 6.

What should come in place of the question mark in the following number series ? 6 (A) 1045

7.

16

(B) 941

51 208

?

6276

(C) 836

(D) 1254

(E) None of these.

(B) 5189

(C) 5289

(D) 5429

(E) None of these.

Without using any coins, can you determine below how many revolutions a coin will complete if it is rolled around another coin ? The coins are of same size. (A) 1

9.

7

In a certain code 'GEAR' is written as '5914' and 'ROUTE' is written as '47289'. How is 'GATE' written in that code ? (A) 5187

8.

2nd IMO - 2008

3

(B) 2

(C) 3

(D) 5

(E) 6

The largest box of shoes contains 459 pieces. The next size box contains 153 pieces. They also sell a box with 51 pieces and one smaller sized box. Based on this pattern, how many pieces are in the smaller sized box ? (A)

15

(B) 37

(C) 27

(D)

17

(E) None of these.

10. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ? (A) 35

(B) 28

(C) 56

(D) 42

11. What is the first term in the exponential sequence below? {_, __, __, 81, 243, 729, ...... } (A) 1 (B) 3 (C) 9 (D) 27

(E) 49

(E) None of these.

12. If A : B = 2 : 3, B : C = 2 : 4 and C : D = 2 : 5, then A : D is equal to (A) 2 : 15

(B) 2 : 5

(C) 1 : 5

(D) 3 : 5

(E) None of these.

13. If Blue is called Red, Red is called Black, Black is called White, White is called Yellow, Yellow is called Green and Green is called Orange, then what is the colour of turmeric powder ? (A) Black

(B) White

(C) Green

(D) Yellow

(E) None of these.

14. Which of the following distances is the longest ? (A) 2 kilometers (B) 500 centimeters (C) 2,300 meters (E) None of these.

(D) 25,000 millimeters

15. Onefourth of sixty percent of a number is equal to twofifths of twenty percent of another number. What is the respective ratio of the first number to the second number ? (A) 4 : 7 (B) 8 : 13 (E) None of these.

(C) 5 : 9

(D) Cannot be determined

16. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group ? (A) Cabbage (B) Brinjal (C) Sweet Gourd (D) Pumpkin (E) Bitter Gourd. 17. Southland Cellular Phone Company offers two different rate plans. PlanA : Rs 45 per month, plus Rs 0.15 per minute of calling time PlanB : Rs 25 per month, plus Rs 0.25 per minute of calling time For how many minutes of calling time do the plans cost the same amount ? (A) 50 minutes (B) 120 minutes (C) 175 minutes (D) 200 minutes (E) None of these.

Class 10

2nd IMO - 2008

4

18. Tree is to ground as chimney is to ? (A) Smoke

(B) Sky

(C) House

(D) Garage

(E) None of these.

19. Jack is taller than Paul, and Bill is shorter than Jack. Which of the following statements would be most accurate? (A) Bill is taller than Paul

(B) Bill is shorter than Paul

(C) Bill is as tall as Paul

(D) It is impossible to tell whether Bill or Paul is taller.

(E) None of these.

is to

20.

(A)

(B)

as

is to

(C)

(D)

(E) None of these.

SECTION II : MATHEMATICAL REASONING 21. If HCF of 65 and 117 is expressed in the form of 65m + 117n, then the value of m and n respectively is (A) 3, 2

(B) 3, –1

(C) 2, –1

(D) 2, –3

(E) None of these.

22. If a and b are the zeros of the quadratic polynomial f(x) = x 2 – x –2, which of the following is the polynomial whose zeros are 2a + 1 and 2b + 1 ? (A) k(x 2 – 4x – 5)

(B) k(x 2 + 4x – 5)

(C) k(x 2 – 5x + 4)

(D) k(x 2 – 2x – 3)

(E) None of these.

23. What is the value of a and b for which the following system of linear equations has infinite number of solutions ? 2x – 3y = 7, (A) a = – 5, b = – 2

(a + b)x – (a + b – 3) y = 4a + b

(B) a = 5, b = – 1

(C) a = – 3, b = – 2

(D) a = – 5, b = – 1

(E) None of these. 24. A swimming pool is filled with three pipes with uniform flow. The first two pipes operating simultaneously, fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool five hours faster than the first pipe and four hours slower than third pipe. What is the time required by third pipe to fill the pool ? (A) 6 hrs.

(B) 10 hrs.

(C) 15 hrs.

(D) 18 hrs.

(E) 12 hrs.

25. A man borrows Rs 1000 and agrees to repay with a total interest of Rs 140 in 12 installments, each installment being less than the preceding by Rs.10. What should be his first installment ? (A) Rs. 120

(B) Rs. 140

(C) Rs. 150

(D) Rs. 180

(E) Rs. 100

26. What is the third vertex of a triangle, if two of its vertices are at (–3, 1) and ( 0, – 2) and the centroid is at the origin? (A) (2, 1)

(B) (3, 1)

(C) (3, 2)

(D) (4, 1)

(E) (0, 2)

27. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double of a red ball, what is the number of blue balls in the bag? (A) 5

(B) 8

(C) 10

(D) 12

(E) 3

Class 10

2nd IMO - 2008

5

28. The mean of the following frequency table is 50, but the frequencies f 1 and f 2 in class 20–40 and 60–80 are missing. What are the missing frequencies? Class interval 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Total Frequency

(A) 12, 18

17

(B) 20, 24

?

32

?

(C) 32, 28

19

120

(D) 28, 24

(E) None of these.

29. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If æ 1 ö its volume is ç ÷ è 27 ø (A) 15 cm

th

the volume of cone, the height at which the section is made is

(B) 20 cm

(C) 10 cm

(D) 25 cm

(E) None of these. B

30. In the given figure, O is the centre, PAQ is tangent, ÐPAB = 58°, then ÐAQB is (A) 58°

(B) 29°

(C) 106°

(D) 26°

O 58° P A

C Q

(E) None of these. 31. In the given figure, P and Q are midpoints of AC and BC, then 5AB 2 = (A) 4(AQ 2 + BP 2 )

(B) 4(AC 2 + BC 2 )

(D) 4(PC 2 + CQ 2 )

(E) None of these.

(C) (AP 2 + BQ 2 )

(D) can't be said

P C

32. In a quadrilateral ABCD, AD = BC. If P, Q, R, S are midpoints of AB, AC, CD and BD respectively, then PQRS is a (A) square (B) rectangle (C) rhombus

A

(E) None of these.

B

Q

R

D S A

C Q

P

B

33. The sum of the series 45 2 – 43 2 + 44 2 – 42 2 + 43 2 – 41 2 + 42 2 – 40 2 + ........ to 30 terms is (A) 2000 (B) 1590 (C) 2143 (D) 2220 (E) None of these. x + 10 -

6

= 5 has x + 10 (A) an extraneous root between –5 and –1 (C) two extraneous roots (E) None of these.

34. The equation

(B) an extraneous root between – 10 and – 6 (D) a real root between 20 and 25

35. The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, what is the speed of the aeroplane ? (A) 432.6 kmph

(B) 338.8 kmph

(C) 439.2 kmph

(D) 332.7 kmph

(E) None of these.

36. If cosec q – sin q = l and sec q – cos q = m, then what is the value of l 2 m 2 (l 2 + m 2 + 3) ? (A) 0

(B) 1

(C) 2

37. 50 circular plates each of radius 7 cm and thickness

(D) –3

(E) None of these.

1 cm are placed one above another to form a 2

solid right circular cylinder. What is the total surface area of the cylinder so formed ? (A) 1230 cm 2

(B) 1332 cm 2

(C) 1408 cm 2

(D) 1560 cm 2

(E) None of these.

Class 10

2nd IMO - 2008

6

38. PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi–circles are drawn on PQ and QS as shown in the figure. What is the perimeter of the shaded region ? (A) 6p cm

(B) 10p cm

(C) 12p cm

Q

P

R

S

(D) 16p cm

(E) None of these. 39. What annual installment will discharge a debt of Rs. 5445 due 4 years hence, the rate of interest being 14 % p.a. simple interest ? (A) Rs. 1125

(B) Rs. 1000

(C) Rs. 1225

(D) Rs. 1275

(E) None of these. D

40. ABCD is a trapezium in which AB | | CD and AB = 2CD. What

C O

is the ratio of the areas of triangles AOB and COD ? (A) 2 :1

(B) 4 :1

(C) 3 :1

(D) 3 : 2 B

A

(E) None of these.

SECTION III : EVERYDAY MATHEMATICS 41. In a soccer tournament the average of goals scored in Anupam’s first 5 games was 6.4. The average of his next four games was 6.5. If there were 9 goals scored in the tenth game what was the overall average ? (A) 7.6

(B) 6.7

(C) 9.2

(D) 4.8

(E) None of these.

42. If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased 9 by 150%, the resultant fraction is . What is the original fraction ? 35 (A)

3 10

(B)

2 15

(C)

3 16

(D)

2 17

(E) None of these.

43. Two girls agree to go on a road trip together. They travel (x + 5) km on the first day. On the second day they travel 2 km more than half of the distance they travelled on the first day. On the third day they drove 3 times as far as they did on the second day. If they drove 5000 km total, find the value of x. (A) 1670

(B) 1659

(C) 1750

(D) 1756

(E) None of these.

44. The average age of a group of teachers and professors is 40. If the teachers average 35 years and the professors 50 years, then what is the ratio of the number of teachers to professors ? (A) 1 : 2

(B) 2 : 1

(C) 5 : 3

(D) 3 : 5

(E) None of these.

45. The lookout on a pirate ship is keeping his eyes open for land. From his perch 6 m above the water he can only look down at a 60 degree angle. He cannot see the land (X) from his position at t = 0 but in 3 seconds it comes into view. What was the distance from the ship’s position at t = 0 to land ?

(A) 13.39 m (B) 15.39 m

60° 6m

(C) 14.39 m (D) 19.39 m (E) None of these.

30° A t = 0

1 m/s

B

X

Class 10

2nd IMO - 2008

7

46. The distance from an observation point X to a comet at a given time is known to be 3.5 million kilometers. Given that a line drawn from the comet to the observation point is parallel to a line going through the center of the earth, find the values of y. (A) 1.5 million kilometers (B) 1.3 million kilometers (C) 1.7 million kilometers

Comet y X

x

(D) 1.75 million kilometers 60°

(E) None of these.

Earth

47. Four children are playing with marbles. At the end of the day one child has 4 less than half the marbles, the second child has 6 more than one fifth of the marbles, the third child has one third of what the first child had and the fourth child has 1 less than the third child. How many marbles are there ? (A) 60

(B) 65

(C) 50

(D) 55

(E) none of these.

48. Mania and Sania graduated from university together. Sania became a teacher and earned half what Mania earned for 5 years. Mania spent 1/3 of her money; Sania spent 1/4 every year for those 5 years. Sania has Rs. 80,000 after 5 years. How much does Mania have ? (A) Rs. 15333.3

(B) Rs. 142222.22

(C) Rs. 15000

(D) Rs. 152222.52

(E) None of these.

49. How many minutes is it until 5:00 if forty minutes ago it was four times as many minutes past 2 o’clock ? (A) 30 mins

(B) 35 mins

(C) 28 mins

(D) 29 mins

(E) None of these.

50. If a tyre rotates at 150 revolutions/min when the truck is travelling 40 km/h, what is the circumference of the tyre ? (A) 4.44 m

(B) 5 m

(C) 5.44 m

(D) 6 m

SPACE FOR ROUGH WORK

(E) None of these.

3rd

Year 2009

3rd IMO - 2009


In how many ways can you join the two shapes shown here to make a figure with a line of symmetry? (A) 0

2.

(B) 320

(C) 550

(D) 2560

(B) put

(C) ta

(D) Can't be determined

(B) Jack

(C) Pawan

(D) Ashish

(B) 30 metres

(C) 60 metres

(D) 40 metres

Choose the venn diagram which best illustrates the three given classes. Citizens, Educated, Men (A)

8.

(D) 18

Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his original position ? (A) 20 metres

7.

(C) 20

Ashish is heavier than Govind. Mohit is lighter than Jack. Pawan is heavier than Jack but lighter than Govind. Who among them is the heaviest ? (A) Govind

6.

(B) 22

In a certain code language, 'dom put ta' means 'bring hot food', 'put tir sop' means 'food is good' and 'tak da sop' means 'good bright boy'. Which of the following means 'hot' in that language? (A) dom

5.

(D) 3

In the series given below, one term is wrong. Find out the wrong term. 5, 10, 40, 80, 320, 550, 2560 (A) 80

4.

(C) 1

In the given series one term is missing. Choose the correct alternative that will continue the same pattern. 0, 2, 8, 14, (.........), 34 (A) 24

3.

(B) 2

(B)

(C)

(D)

In the given matrix, the characters follow a certain trend, row wise or column wise. Find out this trend and choose the missing character accordingly. 18 24 32 12 14 16 3 ? 4 72 112 128

(A) 2 9.

(B) 3

(C) 4

(D) 5

The adjoining figure shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible directions of travel. B

C

A

F D

E

What is the number of distinct paths from A to F ? (A) 9 3 rd IMO | LevelI | Class 10

(B) 10

(C) 11 2

(D) None of these

3rd IMO - 2009

10. How many letters of English alphabet [A to Z ] appear same when looked at in a mirror? (A) 10

(B) 8

(C) 11

(D) 13

11. One white square is surrounded by four black squares, two white squares are surrounded by six black squares, three white squares are surrounded by 8 black squares. What is the largest possible number of white squares surrounded by n black squares? (A)

n - 1 2

(B)

n + 1 2

(C) n + 2

(D) 2(n + 1)

12. Choose the best option to complete the given matrix.

(A)

(B)

(C)

(D)

13. A normal duck has two legs. A lame duck has one leg. A sitting duck has no legs. Ninetynine ducks have total of one hundred legs. Given that there are half as many sitting ducks as normal ducks and lame ducks put together, find the number of lame ducks. (A) 32

(B) 33

(C) 34

(D) 36

14. Choose the waterimage of the Figure (X) from amongst the given alternatives. Fig. (X )

(A)

(B)

(C)

(D)

15. In the given figure, ABCD is a square of side 2008 cm. It is divided as shown in the figure into four equal squares. The top right hand side square is again divided into 4 equal squares. Again the top right hand square is divided into four equal squares. A

B O

D

C

The side of each smallest square is _______ (A) 1004 cm

(B) 1002 cm

(C) 502 cm

(D) 251 cm

16. A plank is placed on a tiled floor. What fraction of the floor is not covered by the plank?

(A)

1 4

(B)

3 8

(C)

3

17 64

(D)

5 8

3 rd IMO | LevelI | Class 10

3rd IMO - 2009

17. The following housepatterns were created using match sticks:

House 1 Houses 4 Houses 7 Sticks 5 Sticks 17 Sticks 29 Which one of the numbers given below cannot be the number of sticks used to create a complete row of houses ? (A) 2361

(B) 2369

(C) 2309

(D) 2008

18. What should be the number opposite 3?

(A) 1

2 1 3

3 1 5

4 2 3

(i)

(ii)

(iii)

(B) 6

(C) 5

(D) 4

19. 8 boxes, all of different sizes, are placed in a row; 2008 books are distributed in such a way that each box receives 2 books more than its next immediate smaller box. How many books does the largest box receive? (A) 258

(B) 244

(C) 236

(D) 264

20. The number of prime numbers less than 100, sum of whose digits is 2, is ______ (A) 1

(B) 2

(C) 3

(D) 4

SECTION II : MATHEMATICAL REASONING 21. If the sum of the number (a ´ 25) 2 and a 3 is divisible by 9, then which of the following is the value for a ? (A) 1

(B) 7

(C) 9

(D) 8

22. A pentagon with area 40 has equal sides but not necessarily equal angles. The sum of the five perpendicular distances from a point inside the pentagon to the sides of the pentagon is 16. The side length of the pentagon is ______ (A)

5 2

(B)

5 4

(C) 12

(D) 5

23. In the figure given below, AG = 6 cm and AB = BC = CD = DE = EF = FG = 1 cm. Semicircles are drawn as shown in the diagram. The total length of the path A to G along the smaller semicircles is x. The length of the path (B to F) along the bigger semicircle is y. Then ______

A

(A) x < y

B

C

D

(B) x = y

E

F

G

(C) x > y

24. In the adjoining figure, the parallel lines are marked by arrows. The value of the angle x is ______ (A) 60°

(B) 70°

(C) 80°

(D) 50°


4

(D) x + y = 6p 80° 70°

x

3rd IMO - 2009

25. In the adjoining figure, AC = 2006 cm, ÐACB = q, BD ^ AC, DE ^ BC, EF ^ AC. Then EF = A D

F q

B

(A) 2006 sin 4q

E

(B) 2006 sin 3q cosq

C

(C) 2006 sin 2qcos 2q

(D) 2006 sinq cos 3q

26. Four identical coins are placed in a square. For each coin, the ratio of the area to circumference is same as the ratio of circumference to area. Then, find the area of the square that is not covered by the coins. (A) 16(p – 1)

(B) 16(8 – p)

(C) 16(4 – p)

pö æ (D) 16 ç 4 - ÷ 2 è ø

27. If the roots of the equation x 2 – bx + c = 0 differ by 2, then which of the following is true ? (A) c 2 = 4(c – 1)

(B) b 2 = 4c + 4

(C) c 2 = b + 4

(D) b 2 = 4(c + 2)

28. A pair of fair dice are rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is ______ (A) 0.45

(B) 0.4

(C) 0.5

(D) 0.6

29. A rectangle has sides of integer lengths (in cm) and an area of 36 cm 2 . What is the maximum possible perimeter of the rectangle ? (A) 74 cm

(B) 84 cm

(C) 124 cm

(D) 64 cm

30. Given question has two statements. Statement 1 is Assertion (A) and Statement 2 is Reason (R). Assertion (A) : The measures of the angles of a convex polygon are in arithmetic series. The smallest angle of the polygon is 36°. Reason (R) : Each angle of a convex polygon should be less than or equal to 180°. (A) (A) and (R) both are true and (R) explains (A) (B) (A) and (R) both are true and (R) does not explain (A) (C) (A) is true but (R) is false

(D) (A) is false but (R) is true

31. In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ÐCBE = 65°, then what is the value of ÐDEC ? (A) 35°

(B) 55°

(C) 45°

(D) 25°

32. Find the value of x in (A) 1

x+2

x +2

B A

C E

x +2

D

3 x = x .

(B) 3

(C) 6

(D) 12

33. If a clock strikes once at one O'clock, twice at two O'clock and twelve times at 12 O'clock and again once at one O'clock and so on, how many times will the clock strike in the course of 2 days? (A) 156

(B) 312

(C) 78 5

(D) 288 3 rd IMO | LevelI | Class 10

3rd IMO - 2009

34. The area of a square inscribed in a semicircle to the area of a square inscribed in a quadrant of the same circle is _______ (A) 2 : 1

(B) 3 : 2

(C) 5 : 3

(D) 8 : 5

35. In a long jump contest, the average jump length of the successful competitors was 6.4 metres and that of the unsuccessful competitors was 4.4 metres. If the average jump length of all competitors was 4.8 metres, the percentage of successful competitors is ______ (A) 25%

(B) 20%

(C) 16%

(D) 4%

36. The sum of the perpendicular distances from a point P inside a regular hexagon of side 10 cm to its sides is _______ (A) Depends on the position of P

(B) 30 3 cm

(C) 60 3 cm

(D) 45 3 cm

37. When x 94 – 7x 19 + 5x 4 – x + K is divided by (x – 1), then the remainder is –1. The remainder obtained when it is divided by (x + 1), is _______ (A) 0

(B) 15

(C) –1

(D) 10

38. In the given multiplication, a and b are natural numbers. Then (a + b) is _____ (A) 5

(B) 6

(C) 8

(D) 9

3a ´ b2 70 140 1470

39. The number of pythagorean triplets (a, b, c) where a 2 + b 2 = c 2 and each a, b, c being odd is ___ (A) 3

(B) 1

(C) 0

(D) Infinite

40. When onefifth of the adults left a neighbourhood picnic, the ratio of adults to children was 2 : 3. Later, when 44 children left, the ratio of children to adults was 2 : 5. How many people remained at the picnic? (A) 56

(B) 65

(C) 85

(D) 58

SECTION III : EVERYDAY MATHEMATICS 41. I bought 10 pens, 14 pencils and 4 erasers. Ravi bought 12 pens, 8 erasers and 28 pencils for an amount which was half more than what I had paid. What percent of the total amount paid by me was paid for the pens? (A) 37.5%

(B) 62.5%

(C) 50%

(D) None of these

42. On Ashok Marg three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 A.M. sharp, at what time will they change simultaneously? (A) 9 : 08 : 04

(B) 9 : 08 : 24

(C) 9 : 08 : 44

(D) None of these

43. Ravi's monthly salary is A rupees. Of this, he spends X rupees. The next month he has an increment of C% in his salary and D% in his expenditure. The new amount saved is ______ C ö D ö æ æ (A) A ç 1 + ÷ - X ç 1 + ÷ è 100 ø è 100 ø

(C)

D ö æ A ö æ (B) ç ÷ (C - D ) X ç 1 + ÷ è 100 ø è 100 ø

X (C - D ) 100


(D)

6

X

(C + D ) 100

3rd IMO - 2009

44. A leap year started on Monday. The days appearing 53 times are _____ (A) Sunday and Monday

(B) Monday and Tuesday

(C) Tuesday and Wednesday

(D) Saturday and Sunday

45. A thief steals a car at 1.30 p.m. and drives it at 40 km an hour. The theft is discovered at 2 p.m. and the owner sets off in another car at 50 km an hour. He will overtake the thief at ______ (A) 3:30 p.m.

(B) 4 p.m.

(C) 4:30 p.m.

(D) 6:30 p.m.

A ' s share B ' s share C ' s share 2 46. A sum of Rs. 1300 is divided between A, B, C and D such that B ' s share = C ' s share = D ' s share = 3 . Then, A's share is _____

(A) Rs. 140

(B) Rs. 160

(C) Rs. 240

(D) Rs. 320

47. The given diagram represents the area swept by the wiper of a car. With the dimensions given in the figure, calculate the shaded area swept by the wiper. O

m 7 c

30°

D

A

c 14 m

B

(A) 102.67 cm 2

C

(B) 205.34 cm 2

(C) 51.33 cm 2

(D) 208.16 cm 2

48. A student is declared passed in the exam only if he/she clears at least two subjects. The number of students who were declared passed in this exam is ______ Maths 16

13

6 8

Physics 22

12

19 Chemistry

(A) 33

(B) 66

(C) 39

(D) 78

49. A circular swimming pool is surrounded by a concrete walk 4 m wide. If the area of the walk is

11 25

that of the pool, then the radius of the pool is _______ (A) 20 m

(B) 8 m

(C) 30 m

(D) 16 m

50. In a box there are coins and rings which are either silver or gold. If 30% of the objects in the box are coins and 40% of the rings are silver, what percentage of the objects in the box are gold rings? (A) 60%

(B) 30%

(C) 42% 7

(D) 70% 3 rd IMO | LevelI | Class 10

4th

Year 2010

4th IMO - 2010


If the positions of the fifth and twelfth letters of the word GLORIFICATIONS are interchanged, and likewise the positions of the fourth and fourteenth letters, the third and tenth letters, the second and eleventh letters and the first and the thirteenth letters are interchanged, which of the following will be the twelfth letter from the right end? (A) I

2.

(B) O

(C) R

(D) T

In a row of boys, Samrat is seventh from the left and Rohit is twelfth from the right. If they interchange their positions, Samrat becomes twentysecond from the left. How many boys are there in the row? (A) 19

3.

(B) 31

(D) 38

If L stands for +, M stands for –, N stands for ×, P stands for ¸, then 14 N 10 L 42 P 2 M 8 = ? (A) 153

4.

(C) 33

(B) 216

(C) 248

(D) 251

Deepa moved a distance of 75 metres towards the north. She then turned to the left and walked 25 metres, again turned to the left and walk 80 metres and finally turned to the right at an angle of 45°. In which direction was she moving finally? (A) Northeast

5.

(B) Northwest

(D) Southwest

What number should replace the question mark in the given figures ? 9

6

7

13

36

?

2

(A) 41 6.

(C) South

9

5

8

18

(B) 32

15

(C) 45

(D) 48

There is a set of five figures marked P, Q, R, S and T called as problem figures. Select a figure among the four options, which will continue the series established by the five problem figures. Problem Figures ? P

(A)

7.

Q

R

(B)

S

(C)

T

(D)

How many triangles are contained in the given figure?

(A) 18 4 th IMO | LevelI | Class 10

(B) 12

(C) 16 2

(D) None of these

4th IMO - 2010

8.

Complete the given series : 23, 48, 99, 203, 413, ___ ?__ (A) 927

9.

(B) 837

(C) 937

(D) 437

Choose from the given options, the box that will be formed when figure X is folded.

+

Fig. (X)

(A)

(B)

(C)

(D)

10. Sasha was facing east. She walked 20 metres. Turning left she moved 15 metres and then turning right moved 25 metres. Finally, she turned right and moved 15 metres more. How far is she from her starting point? (A) 25 metres

(B) 35 metres

(C) 50 metres

(D) 45 metres

11. Which one of the following Venn diagrams correctly illustrates the relationship among the classes: Elephants, Wolves, Animals?

(A)

(B)

(C)

(D)

12. Find the missing number in the given set of numbers.

(A) 13

25 17

38 18

89 16

6

8

?

(B) 15

(C) 17

(D) 19

13. If the first and second letters in the word DEPRESSION were interchanged, also the third and the fourth letters, the fifth and sixth letters and so on, which of the following would be the seventh letter from the right? (A) R

(B) O

(C) S

(D) P

14. If eye is called hand, hand is called mouth, mouth is called ear, ear is called nose and nose is called tongue, with which of the following would a person hear? (A) Eye

(B) Mouth

(C) Nose

(D) Ear

15. If P denotes ¸, Q denotes ×, R denotes + and S denotes –, then the value of 18 Q 12 P 4 R 5 S 6 is _____ . (A) 36

(B) 53

(C) 59

3

(D) 65 4 th IMO | LevelI | Class 10

4th IMO - 2010

16. There is a set of four figures marked P, Q, R and S called as Problem figures. Select a figure from the four alternatives which will continue the series established by the four problem figures. Problem F igures

P

(A)

Q

R

(B)

S

(C)

(D)

17. Between two ends of a bookshelf in your study, five of your favourite puzzle books are displaced. If you decide to arrange these five books in every possible combination and move just one book every minute, how long would it take you to do so? (A) One hour

(B) Two hours

(C) Three hours

(D) Four hours

DIRECTION (18 19) : Read the information carefully given below and answer the following questions: In a group of five boys P, Q, R, S and T, P and R are good in English and Maths, Q and R are good in English and General Knowledge, T and S are good in Science and Drawing, Q and S are good in Drawing and General Knowledge, while T is good in Drawing, Maths and Science. 18. Who is good in English, Drawing and General Knowledge ? (A) P

(B) Q

(C) T

(D) R

19. Who is good in English and Maths but weak in General Knowledge ? (A) T

(B) Q

(C) P

(D) S

20. If you count 21 letters in the English alphabet from the end and 20 letters from the beginning, which letter will exactly appear in the middle of the sequence thus formed? (A) N

(B) L

(C) K

(D) M

SECTION II : MATHEMATICAL REASONING 21. Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds respectively. If they first beep together at 12 noon, at what time will they beep together again ? (A) 12:20 p.m.

(B) 12:12 p.m.

(C) 12:11 p.m.

(D) None of these

22. Solve for x and y : 2 3 17 + = ; 3 x + 2y 3 x – 2y 5

(A) x = 1, y = 3

(B) x = –2, y = 1

5 1 + = 2 3 x + 2y 3 x – 2 y

(C) x = 1, y = 1

(D) x =

1 1 , y = 5 5

23. If tan A + cot A = 4, then tan 4 A + cot 4 A is equal to ______ . (A) 196

(B) 194

(C) 192

(D) 190

24. For x 2 + 2x + 5 to be a factor of x 4 + px 2 + q, the value of p and q respectively must be ____. (A) –2, 5 4 th IMO | LevelI | Class 10

(B) 5, 25

(C) 10, 20 4

(D) 6, 25

4th IMO - 2010

25. Match the column: 1. In DABC and DPQR ,

(a) AA similarity criterion

AB AC = , Ð A = Ð P PQ PR

2. In DABC and DPQR,

(b) SAS similarity criterion

ÐA = ÐP, ÐB = ÐQ Þ

DABC ~ DPQR

3. In DABC and DPQR, AB AC BC = = PQ PR QR Þ DABC ~ DPQR

(c) SSS similarity criterion

4. In DABC, DE || BC

(d) BPT

Þ

AD AE = BD CE

(A) 1 ® a, 2 ® b, 3 ® c, 4 ® d

(B) 1 ® d, 2 ® a, 3 ® c, 4 ® b

(C) 1 ® b, 2 ® a, 3 ® c, 4 ® d

(D) 1 ® c, 2 ® b, 3 ® d, 4 ® a

26. The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is 110 not 100. The true mean and median are _____. (A) 50.10, 52

(B) 50, 52

(C) 50.20, 52

(D) None of these

27. If sec A + tan A = x, then tan A = (A)

2 x

(B)

1 2x

(C)

x 2 - 1 2 x

(D)

2 x x 2 - 1

28. Two friends were discussing their marks in an examination. While doing so they realized that both the numbers had the same prime factors, although one got a score which had two more factors than the other. If their marks are represented by one of the options given below, which of the following options would correctly represent the number of marks they got? (A) 30, 60

(B) 20, 80

(C) 40, 80

(D) 20, 60

29. If sinq and cosq are the roots of the equation ax 2 – bx + c = 0, then a, b, c satisfy the relation ____. (A) b 2 – a 2 = 2ac

(B) a 2 – b 2 = 2ac

(C) a 2 + b 2 = c 2

(D) a 2 + b 2 = 2ac

30. Find the mode of the given data : Classes

Frequencies

10 - 15

30

15 - 20

45

20 - 25

75

25 - 30

35

30 - 35

25

35 - 40

15

Total

(A) 22.89

225

(B) 15.68

(C) 20.35 5

(D) 22.14 4 th IMO | LevelI | Class 10

4th IMO - 2010

A

31. In the given figure, AD = 3 cm, AE = 5 cm, BD = 4 cm, CE = 4 cm, CF = 2 cm, BF = 2.5 cm, then D

(A) DE || BC

E

(B) DF || AC (C) EF || AB B

(D) None of these

C

F

32. The median of a given frequency distribution is found graphically with the help of ____. (A) Histogram

(B) Ogive

(C) Bar Graph

(D) None of these

33. The value of q will be _____ , if sin 2q = 1 – cos 2q. (A) 45°

(B) 30°

(C) 60°

(1) 2x + 3y = 40 6x + 5y = 10

(a) Coincident lines

(2) 2x + 3y = 40 6x + 9y = 50

(b) Intersecting lines

(3) 2x + 3y = 10 4x + 6y = 20

(c) Parallel lines

(D) All of these

34. Match the column :

(A) 1 ® a, 2 ® b, 3 ® c (B) 1 ® b, 2 ® a, 3 ® c

(C) 1 ® b, 2 ® c, 3 ® a (D) 1 ® c, 2 ® a, 3 ® b

35. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is divided by 2 the quotient is 33. The other number is _____. (A) 66

(B) 130

(C) 132

(D) 196

36. Find the missing frequencies in the given frequency distribution if it is given that the mean is 1.46. Variables 0 1 2 3 4 5 Total Frequency 46 ? ? 25 10 5 200 (A) 76, 36

(B) 37, 38

(C) 76, 38

(D) 70, 38

37. If one zero of the polynomial 5z 2 + 13z – p is reciprocal of the other, then p is ____ (A) 4

(B) –5

(C) 1

(D) –8

38. In the given figure, ABC is a triangle and GHED is a rectangle. BC = 12 cm, HE = 6 cm, FC = BF and altitude AF is 24 cm. The area of the rectangle is _____. A

2

(A) 56 cm

(B) 54 cm 2 E

D 2

(C) 60 cm

B

(D) 72 cm 2

G

39. Evaluate : cos 2 20° + cos 2 70° + sin 48° sec 42° + cos 40° cosec 50°. (A) 1 4 th IMO | LevelI | Class 10

(B) 3

(C) 2 6

(D) 0

F

H

C

4th IMO - 2010

40. There are two positive numbers such that sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is _____. (A) 6

(B) 8

(C) 9

(D) 10

SECTION III : EVERYDAY MATHEMATICS 41. P can do a piece of work in 10 days. Q can do it in 24 days. If R also works with them then it takes only 6 days to complete the whole work. In how many days R alone can complete the whole work? (A) 25

(B) 40

(C) 50

(D) 75

42. 1854 seats in a theatre form a perfect square except for five seats at the back. The number of seats in each row is _____. (A) 42

(B) 43

(C) 47

(D) 48

43. The average weight of Meenu, Binu and Dia is 45 kg. If the average weight of Meenu and Binu is 40 kg and the average weight of Binu and Dia is 43 kg, then the weight of Binu is _____. (A) 17 kg

(B) 20 kg

(C) 26 kg

(D) 31 kg

44. A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. The speed of the boat in standing water is _____. (A) 6.5 km/hr

(B) 6 km/hr

(C) 5.5 km/hr

(D) 5 km/hr

45. If 20 typists can type 480 pages in 6 hours, how many pages will be typed by 25 typists in 4 hours? (A) 256

(B) 576

(C) 900

(D) 400

46. A dealer buys 200 quintals of wheat at ` 1200 per quintal. He spends ` 10,000 on transportation and storage. Then he sells the wheat at ` 13 per kg. His profit percentage is _____. (A) 4%

(B) 5%

(C) 6%

(D) 7%

47. A student who secures 20% marks in an examination fails by 30 marks. Another student who secures 32% marks gets 42 marks more than those required to pass. The percentage of marks required to pass is ______. (A) 20%

(B) 25%

(C) 28%

(D) 30%

48. A sum is being lent at 20% p.a. compound interest. What is the ratio of increase in amount of 4 th year to 5 th year? (A) 4 : 5

(B) 5 : 4

(C) 5 : 6

(D) Can't be determined

49. Pipes A and B can fill a cistern in 10 hours and 15 hours respectively. When a third pipe C which works as an outlet pipe is also open then the cistern can be filled in 18 hours. The outlet pipe can empty a full cistern in _____. (A) 12 hours

(B) 8 hours

(C) 9 hours

(D) 14 hours

50. By selling 8 bananas, a fruit seller gains the selling price of 1 banana. His gain per cent is ____. (A) 12%

(B) 14

2 % 7

(C) 14 7

1 % 7

(D) 16

2 % 7

4 th IMO | LevelI | Class 10

5th

Year 2011

2

5th IMO - 2011

Section I : Logical Reasoning 1.

Using first, third, sixth and seventh digits of the number 9 3 4 2 6 1 8 5, one time each, how many numbers of two digits are possible which are perfect squares of a number. What is that number? If two such numbers are possible then answer 11, if no such number is possible then answer zero. (A) 0 (B) 7 (C) 9 (D) 11

2.

If 323 × 41 = 14323; 137 × 72 = 27731 and 48 × 87 = 7884, then 34 × 75 = ? (A) 5743 (B) 7534 (C) 2550 (D) 4357

3.

There is a matrix followed by four answer figures. In the matrix there are eight designs and one space is left blank as shown by a question mark. Find which answer figures will replace the question mark.

(A)

(B)

(C)

(D)

4.

If the expressions ‘E < J ≤ H > Z’, ‘H ≤ Y’ and ‘E > F’ are true, which of the following conclusions

will be definitely false ? (A) F < Y (B) Y > E

5.

Six people A, B, C, D, E and F are sitting on the ground in a hexagonal shape. All the sides of

?

(C) F < H

(D) All are true

the hexagon so formed are of same length. A is not adjacent to B or C; D is not adjacent to C or E; B and C are adjacent; F is in the middle of D and C.

Which of the following is not a correct neighbour pair? (A) A and F (B) D and F (C) B and E

6.

In a shop, there were 4 dolls of different heights A, B, C and D. D is neither as tall as A nor as

(D) C and F

short as C. B is shorter than D but taller than C. If Mani wants to purchase the tallest doll, which 7.

one should she purchase ? (A) Only A (B) Only D

(C) Either A or D

(D) Either B or D

Find the missing number in the adjoining figure. S T W 3 15 D J

10 ? P T G

(A) 5

(B) 9

(C) 11

(D) 13

8.

Select a figure from amongst the four alternatives, which when placed in the blank space of the given figure would complete the pattern.

? ?

(A)

(B)

(C)

(D)

3

5th IMO - 2011 9.

In a row of 40 boys, Satish was shifted 10 places to the right of Rohan and Kewal was shifted 10 places to the left of Vilas. If Vilas was twenty-sixth from the left and there were three boys between

Kewal and Satish after shifting, what was the position of Rohan in the row ? (B) 10th from the left end (A) 10th from the right end th (D) Data inadequate (C) 39 from the right end

10. ‘+’ stands for division, ‘÷’ stands for multiplication, ‘×’ stands for subtraction and ‘–’ stands for

addition. Which one of the following equations is correct ? (A) 18 ÷ 6 – 7 + 5 × 2 = 20 (B) 18 + 6 ÷ 7 × 5 – 2 = 18 (C) 18 × 6 + 7 ÷ 5 – 2 = 16 (D) 18 ÷ 6 × 7 + 5 – 2 = 22

11. At a farm, there are hens, cows, bullocks and keepers to look after them. There are 69 heads less than legs. The number of cows is double than that of the bullocks but the number of cows and hens is the same. There is one keeper per 10 birds and cattle. The total number of hens plus cows

and bullocks and their keepers does not exceed 50. How many cows are there ? (A) 10 (B) 14 (C) 16 (D) 12

12. All the faces of a cube are painted with blue colour. Then it is cut into 125 small equal cubes.

How many small cubes will be formed having no face coloured ? (A) 27 (B) 8 (C) 16

(D) 24

13. In a certain code language, ‘123’ means ‘bright little boy’, ‘145’ means ‘tall big boy’ and ‘637’ means

‘beautiful little flower’. Which digit in that language means ‘bright’ ? (A) 1 (B) 2 (C) 3

(D) 4

14. Which letter will be sixth to the left of the nineteenth letter from the right end of the English

alphabet series ? (A) M

(B) N

(C) X

(D) None of these

15. If animals that live on land and the animals that live in water are represented by two big circles and animals that live both in water and on land are represented by a small circle, the combination of these three can be best represented as _____.

(A)

(B)

(C)

(D)

16. Find the figure from the options which will continue the series established by the problem figures.

(A)

(B)

(C)

(D) None of these

17. Rohit walked 25 m towards south. Then he turned to his left and walked 20 m. He then turned to his left and walked 25 m. He again turned right and walked 15 m. At what distance is he from the starting point and in which direction ?

(A) 35 m East

(B) 35 m North

(C) 40 m East

(D) 60 m East

4

5th IMO - 2011

18. The adjoining diagram represents those students who play cricket, football and kabaddi. Study the diagram and identify the students who play all the three games. Kabaddi A

B

C

D

E

F

Football G

Cricket

(A) A + B + C

(B) G + E

(C) D + E + G

(D) D

19. In the adjoining figure, find out how the figure will look like after rotation.

(A)

(B)

(C)

(D)

20. In the adjoining figure, count the number of triangles and squares.

(A) 23 triangles, 7 squares

(B) 18 triangles, 8 squares

(C) 20 triangles, 8 squares

(D) None of these

Section II : Mathematical reasoning 21. A set of numbers consists of four 5’s, six 7’s, ten 9’s, eleven 12’s, three 13’s, two 14’s. The approximate difference between mean and median of this set of numbers is _____.

(A) 1

(B) 2

(C) 5

(D) 4

22. In the given figure, ABCD and AEFG are squares. Then in DAGE and DADC which of the following holds ? E

A G

D

(A)

GF AC = AG AD

(B) CF = AF AG DG

B F

C

(C) AF = AC AD AG

(D) None of these

5

5th IMO - 2011

23. An equilateral triangle is inscribed in a circle of circumference equal to perimeter of a square with side 22 cm. Find its side.

(A) 7 3 cm

(B) 14 cm

(C) 14 3 cm

(D) 17 cm

24. L.C.M. of two prime numbers x and y (x > y) is 161. The value of 3y – x is _____. (A) – 2 (B) – 1 (C) 1 (D) 2 25. If a quadratic polynomial of the form x2 + ax + b has no linear term and the constant term is

negative, then _____. (A) One of the zeroes is reciprocal of the other. (C) One of the zeroes is twice of the other.

(B) One of the zeroes is negative of the other. (D) One of the zeroes is half of the other.

(A) 6, 1

(B) 3, 2

(C) 4, 1

(D) 13, 7

3x + y

26. Find the values of x and y in the given rectangle if its length is cube root of 2197 and width is x + 3y one less than the fourth multiple of first prime number.

27. If l is the last term, d is the common difference and ‘s’ is the sum of n terms of an A.P. be connected by the equation 8ds = (d + 2l)2, then d = _____.

(A) a

(B) 2a

(C) 3a

(D) –a

28. A bridge across a river makes an angle of 30° with the river bank (Fig. given). If the length of the bridge across the river is sum of the arithmetic progression 5, 10, 15, ....., 55, what is the width of the river ?

(A) 160 m

(B) 150 m

(C) 165 m

(D) 155 m

29. If (2, –2), (–2, 1) and (5, 2) are vertices of a right angled triangle, then the area of the triangle is _____.

(A) 12.5 sq. units

(B) 22.5 sq. units

(C) 12 sq. units

(D) 20 sq. units

30. A number is chosen at random among the first 120 natural numbers. The probability of the number

chosen being a multiple of 5 is _____. (A) 1/5 (B) 1/6

(C) 1/7

(D) 1/9

31. If area of a parallelogram with sides ‘l’ and ‘b’ is ‘A’ and that of a rectangle with sides ‘l’ and ‘b’

is ‘B’, then _____. (A) A < B

(B) A = B

(C) A > B

(D) None of these

p q 32. If the roots of a quadratic equation are  , −  , then the equation is _____. q p (B) pqx2 – (p 2 – q2)x – pq = 0 (A) qx2 – (q2 + p 2)x – pq = 0

(C) px2 – (p 2 + 1)x + p = 0

(D) p 2x2 – (p 2 – q2)x – pq = 0

6

5th IMO - 2011

33. If x = 7 − 5 , y = 5 − 3 , z = 3 − 7 , then find the value of x3 + y3 + z3 – 2xyz.

(A) − 4 5 − 12 3 + 7 (B) − 4 5 + 2 3 + 2 7

(C) 4 5 + 12 3 + 2 7

(D) 4 5 − 12 3 + 7

34. A hemispherical container with radius 6 cm contains 325 ml of milk. Calculate the volume of milk that is needed to fill the container completely. (p = 3.142)

(A) 117.45 ml

(B) 107.40 ml

(C) 127.45 ml

(D) 127 ml

35. Without using trigonometric tables, evaluate the following :

cos2 20° + cos2 70° sec2 50° − cot 2 40° (A) 1

+ 2 cosec2 58° – 2 cot 58° tan 32° – 4 tan 13° tan 37° tan 45° tan 53° tan 77° (B) 2

(C) – 1

(D) – 2

36. If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have ?

5 3

(A)

37. If

(B)

(C)

19

13 3

(D) None of these

2 3 + 5 + 7 + ..... + n terms units , then the = Volume of cylinder with diameter 7 units and height 11 5 + 8 + 11 + ..... + 10 terms

value of n is _____.

(A) 35

(B) 36

(C) 37

(D) 40

38. A bag contains tickets marked with numbers 179, 180, 172, 127, 155, 115, 143, 122, 175, 222, 232, 162, 112, 132, 192, 182, 174, 132, 32, 131. A ticket is drawn at random. Find the probability that

the ticket drawn has an even digit at ten’s place. (A) 7/19 (B) 3/20 (C) 7/20

(D) 6/19

39. Point A is on x-axis, point B is on y-axis and the point P lies on line segment AB, such that P=

(

)

(2n + 1)2 − (2n − 1)2 , 3 50n + 5 n ; where n = 2 and AP : PB = 5 : 3. Find the coordinates of

points A and B.

 32  (A)  , 0  ,( 0, 8 ) 3

32  (B) ( 3, 0 ),  0,  3 

(C) (4, 0), (0, 3)

32 (D)  , 0  , ( 0, 3 ) 3 

40. In the right triangle shown here, AB + AD = BC + CD, if AB = x, BC = h and CD = d, then x is equal to _____.

A B

hd (A) 2h + d

C

(B) d – h

D

(C) h + d

(D)

1 h 2

Section III : Everyday Mathematics 41. A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets

are sold, how many tickets has she bought ? (A) 40 (B) 240

(C) 480

(D) 750

7

5th IMO - 2011

42. Raghav buys a watch for ` 1,20,000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of ` 5000 each. If the rate of interest is 12% and he pays with the instalment the interest due on the unpaid amount, find the total cost of the watch.

(A) 1,27,750

(B) 1,27,000

(C) 1,28,000

(D) None of these

43. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point ?

(A) 26 minutes 18 seconds

(B) 42 minutes 36 seconds

(C) 45 minutes

(D) 46 minutes 12 seconds

44. Assume that a mango and its seed, both are spherical. The radius of the seed is 2/5 of the thickness of the pulp. The seed lies exactly at the centre of the fruit. What per cent of the total volume of the mango is its pulp ?

(A) 90%

(B) 92%

(C) 97.66%

(D) 93%

45. One fourth of a herd of cows is in the forest. Twice the square root of the herd has gone to mountains, and of the remaining, 15 are on the bank of a river. The total number of cows is ____.

(A) 6

(B) 100

(C) 63

(D) 36

46. Vidushi and Sanya distributed ` 100 each in charity. Vidushi distributes money to 5 more people than Sanya and Sanya gives ` 1 more than Vidushi to each person. How many people are recipients of the charity ?

(A) 45

(B) 60

(C) 90

(D) None of these

47. Rahman bought 30 stamps consisting of 20 paise and 30 paise stamps. Given that the stamps cost ` 7.80 altogether, how many 20 paise stamps did he buy ?

(A) 12

(B) 14

(C) 16

(D) 18

2 3 of the votes cast. If, after of the votes have been 3 4 5 of what he needs, then what part of the remaining ratio does he still counted, a candidate has 6 need ?

48. To win an election, a candidate needs

(A)

1 10

(B)

1 8

(C)

1 4

(D)

3 8

49. Raju has 64 small cubes of 1 cm3. He wants to arrange all of them in a cuboidal shape, such that the surface area will be minimum. What is the diagonal of this larger cuboid ?

(A) 4 3 cm

(B) 2 3 cm

(C) 4 cm

(D) 2 cm

50. The Gurgaon office of Microsoft has 1500 executives. Of these 900 subscribe to the Hindustan Times and 750 subscribe to The Hindu. 150 subscribe to both Hindustan Times and The Hindu. If an executive is picked at random, what is the probability that he has subscribed to Hindustan Times?

(A)

2 5

(B)

3 5

(C)

4 5

(D)

1 5

ANSWER KEYS 1st IMO (2007) 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4 11. 18. 25. 32. 39. 46.

(A) (A) (E ) (D) (A) (B) (A)

5. 12. 19. 26. 33. 40. 47.

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

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

6. 13. 20. 27. 34. 41. 48.

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

7. 14. 21. 28. 35. 42. 49.

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

2 nd IMO (2008) 1. 8. 15. 22. 29. 36. 43. 50

(A) (B) (E) (A) (B) (B) (B) (A)

2. 9. 16. 23. 30. 37. 44

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

3. 10. 17. 24. 31. 38 45.

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

4. 11. 18. 25. 32. 39. 46.

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

5. 12. 19. 26. 33. 40. 47.

3 rd IMO (2009) 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 32. 39. 46.

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

5. 12. 19. 26. 33. 40. 47.

4 th IMO (2010) 1. 8. 15. 22. 29. 36. 43. 50.

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

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 32. 39. 46.

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

5. 12. 19. 26. 33. 40. 47.

5 th IMO (2011) 1. 8. 15. 22. 29. 36. 43.

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

50.

(B)

2. 9. 16. 23. 30. 37. 44.

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

3. 10. 17. 24. 31. 38. 45.

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

4. 11. 18. 25. 32. 39. 46.

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

5. 12. 19. 26. 33. 40. 47.

CLASS 10 IMO WORKBOOK

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