Class 9 Imo 5 Years EBook

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(2) Copyright © 2015 Science Olympiad Foundation. Printed with the permission of Science Olympiad Foundation. No part. of this publication may be reproduced, transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright holder. Ownership of an ebook does not give the possessor the ebook copyright. All disputes subject to Delhi jurisdiction only.. Disclaimer : The information in this book is to give you the path to success but it does not guarantee 100% success as the strategy is completely dependent on its execution. And it is based on last years papers of IMO exam.. Published by : MTG Learning Media (P) Ltd. Corporate Office : Plot 99, 2nd Floor, Sector 44 Institutional Area, Gurgaon, Haryana. Phone : 0124 - 4951200 Web: mtg.in Email: [email protected] Regd. Office : 406, Taj Apt., Ring Road, Near Safdarjung Hospital, New Delhi-110029. Visit. www.mtg.in for buying books online..

(3) CLASS 12. Contents ªª 4th IMO 2010 ªª 5th IMO 2011 ªª 6th IMO 2012 - SET A ªª 6th IMO 2012 - SET B ªª 7th IMO 2013 - SET A ªª 7th IMO 2013 - SET B ªª 8th IMO 2014 - SET A ªª 8th IMO 2014 - SET B.

(4) MTG Work-Books / olympiad books CLASS 1. International Mathematics Olympiad. National Science Olympiad. International English Olympiad. MTG CSS Series. CLASS 2. International Mathematics Olympiad. National Science Olympiad. National Cyber Olympiad. International English Olympiad. MTG CSS Series. International English Olympiad. MTG CSS Series. CLASS 3. International Mathematics Olympiad. National Science Olympiad. National Cyber Olympiad.

(5) MTG Work-Books / olympiad books CLASS 4. International Mathematics Olympiad. National Science Olympiad. National Cyber Olympiad. International English Olympiad. MTG CSS Series. International English Olympiad. MTG CSS Series. International English Olympiad. MTG CSS Series. CLASS 5. International Mathematics Olympiad. National Science Olympiad. National Cyber Olympiad. CLASS 6. International Mathematics Olympiad. National Science Olympiad. National Cyber Olympiad.

(6) MTG Work-Books / olympiad books CLASS 7. National Science Olympiad. International Mathematics Olympiad. National Cyber Olympiad. Science IQ Challenge. Math IQ Challenge. International English Olympiad. MTG CSS Series. Master Mental Ability in 30 Days. CLASS 8. International Mathematics Olympiad. National Science Olympiad. National Cyber Olympiad. International English Olympiad. MTG CSS Series. Math IQ Challenge. Science IQ Challenge. Psychology of Success. The Secrets of SUCCESS. Master Mental Ability in 30 Days.

(7) MTG Work-Books / olympiad books CLASS 9. International Mathematics Olympiad. Math IQ Challenge. National Science Olympiad. Science IQ Challenge. National Cyber Olympiad. Psychology of Success. The Secrets of SUCCESS. International English Olympiad. Master Mental Ability in 30 Days. CLASS 10. International Mathematics Olympiad. Math IQ Challenge. National Science Olympiad. Science IQ Challenge. National Cyber Olympiad. Psychology of Success. The Secrets of SUCCESS. International English Olympiad. Master Mental Ability in 30 Days.

(8) MTG Work-Books / olympiad books CLASS 11. International Mathematics Olympiad. Math IQ Challenge. Science IQ Challenge. National Science Olympiad. Psychology of Success. National Cyber Olympiad. The Secrets of SUCCESS. Master Mental Ability in 30 Days. CLASS 12. International Mathematics Olympiad. Math IQ Challenge. Science IQ Challenge. National Science Olympiad. Psychology of Success. National Cyber Olympiad. The Secrets of SUCCESS. Master Mental Ability in 30 Days.

(9) Class. 1 to 10.

(10) JEE (Main & Advanced) | AIPMT | BOARDS | OLYMPIAD | NTSE. FOUNDATION COURSE For Classes 7, 8, 9 & 10 Class 7. Class 8. Class 9. Class 10.

(11) Class 9 4th. Year 2010. Copyright©2015. Science Olympiad Foundation (SOF).

(12) 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.

(13) 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 .

(14) 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).

(15) 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 .

(16) 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.

(17) 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 . Copyright©2015. Science Olympiad Foundation (SOF). 4 th IMO | LevelI | Class 9 .

(18) Class 9 5th. Year 2011. Copyright©2015. Science Olympiad Foundation (SOF).

(19) 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.

(20) 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.

(21) 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.

(22) 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).

(23) 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.

(24) 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.

(25) Class 9 6th. SET A Year 2012. Copyright©2015. Science Olympiad Foundation (SOF).

(26) 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.

(27) 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).

(28) 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.

(29) 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.

(30) 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.

(31) 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).

(32) 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).

(33) Class 9 6th. SET B Year 2012. Copyright©2015. Science Olympiad Foundation (SOF).

(34) 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).

(35) 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.

(36) 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.

(37) 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).

(38) 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.

(39) 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.

(40) 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).

(41) Class 9 7th. SET A Year 2013. Copyright©2015. Science Olympiad Foundation (SOF).

(42) 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).

(43) 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).

(44) 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.

(45) 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).

(46) 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).

(47) 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).

(48) Class 9 7th. SET B Year 2013. Copyright©2015. Science Olympiad Foundation (SOF).

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