Class 10 Imo 5 Years e Book

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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 10 4th. Year 2010. Copyright©2015. Science Olympiad Foundation (SOF).

(12) 4th IMO - 2010. SECTION I : LOGICAL REASONING 1. . 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 . T . (C) . (D) . How many triangles are contained in the given figure? . (A) 18 4 th IMO | LevelI | Class 10 . (B) 12 . (C) 16 2 . Copyright©2015. Science Olympiad Foundation (SOF). (D) None of these.

(13) 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 . Copyright©2015. Science Olympiad Foundation (SOF). (D) 65 4 th IMO | LevelI | Class 10 .

(14) 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 . Copyright©2015. Science Olympiad Foundation (SOF). (D) 6, 25.

(15) 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 . Copyright©2015. Science Olympiad Foundation (SOF). (D) 22.14 4 th IMO | LevelI | Class 10 .

(16) 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 . Copyright©2015. Science Olympiad Foundation (SOF). (D) 0. F . H . C .

(17) 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. 1 % 7 . 7 . Copyright©2015. Science Olympiad Foundation (SOF). (D) 16. 2 % 7. 4 th IMO | LevelI | Class 10 .

(18) Class 10 5th. Year 2011. Copyright©2015. Science Olympiad Foundation (SOF).

(19) 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 = ? (C) 2550 (D) 4357 (A) 5743 (B) 7534. 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? (B) D and F (C) B and E (A) A and F. 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). Copyright©2015. Science Olympiad Foundation (SOF). (D).

(20) 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. Copyright©2015. Science Olympiad Foundation (SOF). (D) 60 m East.

(21) 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. Copyright©2015. Science Olympiad Foundation (SOF). (D) None of these.

(22) 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. Copyright©2015. Science Olympiad Foundation (SOF).

(23) 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 C. hd (A). 2h + d. (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. Copyright©2015. Science Olympiad Foundation (SOF). (D) 750.

(24) 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. Copyright©2015. Science Olympiad Foundation (SOF). (D). 1 5.

(25) Class 10 6th. SET A Year 2012. Copyright©2015. Science Olympiad Foundation (SOF).

(26) 2. 6th IMO - SET A Section I : Logical Reasoning. 1.. Some of the letters are missing which are given in that order as one of the options below it. Choose the correct option.. a __ n __ b __ __ ncb __ __ ncb (A) abbbcc. (B) abcbcb. (C) abcaba. (D) bcabab. 2. Two ladies and two men are playing bridge a card game and seated at North, East, South and West of a table. No lady is facing East. Persons sitting opposite to each other are not of the same sex.. One man is facing South. Which directions are the two ladies facing? (A) East and West (B) South and East (C) North and West. (D) North and East. 3. If 'sand' is called 'air', 'air' is called 'plateau', 'plateau' is called 'well', 'well' is called 'island' and. 'island' is called 'sky', then from where will a woman draw water? (A) Well (B) Island (C) Sky. (D) Air. 4.. K is brother of N and X, Y is the mother of N, and Z is the father of K. Which of the following. statements is not definitely true ? (A) K is the son of Z (B) Y is the wife of Z. 5.. Read the following information carefully and answer the question given below.. (i) There are five types of cards viz. A, B, C, D and E. There are three cards of each type. These. (C) X is the son of Y. (D) Z is the father of X. are to be inserted in envelopes of three colours - Red, Yellow and Brown. There are five envelopes of each colour.. (ii) B, D and E type cards are inserted in red envelopes. A, B and C type cards are to be inserted in yellow envelopes and C, D and E type cards are to be inserted in brown envelopes.. (iii) Two cards each of B and D type are inserted in red envelopes.. Which of the following combinations of colour of the envelope and the number of cards is definitely. correct in respect of E - type cards? (A) Red-1, Yellow- 2 (B) Yellow -1, Brown-2. (C) Red - 1, Brown-2. (D) None of these. 6. The given question is based on the symbols/numeric/alphabets as given below:. A & f t Y↑ P Q n * M ≠ r @ Z & C £ ? 8 7 R u V B e. If the first half of the above series is written in the reverse order, then which letter/symbol will be. 7 th letter from the left of 15th letter from right end. (A) M (B) n (C) f. 7. If. means '×', D means '+',. means '+',. means '–',. (D) Q means '=',. means 'more' and. means. 'less', then which one of the options is incorrect?. (A) 10. 3. 7. (C) 10. 7. 5. 8.. At an office where an interview was conducted to select persons for clerical posts, they came to. 4D2 9D3. 5. 5. 4. 2. (B) 10 8. 2. (D) 10. 3 4. 15 D 3 8D4. 5 7. 7 8. 9 2. 2 5. know that out of 20 persons, 12 knew only typing and 5 knew only shorthand and the rest knew both typing and shorthand. Which of the following diagrams represents this fact?. (A). (B). (C). Copyright©2015. Science Olympiad Foundation (SOF). (D).

(27) 3. 6th IMO - SET A 9.. Find the missing number from amongst the given options at the. 4 5 7 3 6 4 (B) 42 9 6 (D) 45 . place of sign of interrogation (?).. (A) 34 . (C) 44 . 3 4 4 5. 2 4 5 5. 0 21 22 ?. 10. A college starts from 10 a.m. and continues till 1.30 p.m. In this duration there are 5 periods. If 5 minutes are provided before each period to leave the room and enter the other, then what is the. duration of each period? (A) 41 mins (B) 38 mins. (C) 40 mins. (D) 42 mins. 11. If in each of the following groups of numbers, last two digits are interchanged and after that they are arranged in descending order, then what will be the first digit of the middle group?. (A) 7. 257, 491, 623, 846, 738 (C) 8. (B) 4. (D) 6. 12. In a certain code language,. (i) 'pit na som' means 'bring me water'; (ii) 'na jo tod' means 'water is life';. (iii) 'tub od pit' means 'give me toy'; (iv) 'jo lin kot' means 'life and death';. Which of the following represents 'is' in that language ?. (A) jo (B) na (C) tod (D) lin 13. How many triangles are there in the figure below?. (A) 5. (B) 6. (C) 8. (D) 10. 14. The question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. These three figures are followed by options from which you have to choose a figure which would most closely resemble the unfolded form of fig. (Z).. X. (A). (B). Y. Z (C). (D). 15. Which of the following options does not have the same relationship between them as is there between. DH : EG ? (A) VZ : XY. 16.. Find the missing term. (A) 10 (B) 13 (C) 12 (D) 14. (B) LP : MO. (C) BG : CF. Copyright©2015. Science Olympiad Foundation (SOF). (D) QT : RS F. I. D. M. 4. ? 6. 9.

(28) 4. 6th IMO - SET A. 17. Select a figure from the options which satisfies the same conditions of placement of the dots as in figure (X) ?. (A). (B). (C). (D). 18. On a peculiar clock shown here, the hands move in an unusual way. Discover the system as revealed from the five positions, (i to v) shown below, and find the next position to be formed in fig (vi) from the options given below. 1 1 9. 3 5. 2 (A) 9. 10. 8. 6 (iv). 10. ?. (v). (vi). 10 3. (B). 3. 9. 3 7 6 (iii). 6 (ii). (i). 10. (C) 9. 10 (D) 9. 3. 12. 6. 6. 19. Machine 'A' produces 60% cloth and remaining is produced on machine 'B'. 25% of each machine's production is defective. Choose the diagram that best represents the situation. The shaded portion depicts defective cloth.. (A). (B). (C). (D). 20. Select a figure from the options, which is not embedded in the given figure (X).. (A). (B). (C). (D). Section II : Mathematical reasoning 21. If.  a 2 x 2 + b2 y 2 + c 2 z 2  x y z = = , then   3 3 3 a b c  a x + b y + c z . (A). xyz. abc. (B). xyz abc. 3/2. = _______ . (C). xyz (abc )2. Copyright©2015. Science Olympiad Foundation (SOF). (D). ( xyz )2 abc.

(29) 5. 6th IMO - SET A. 22. A sports club has 130 members. An increase of 10% in the number of men and 20% in the number of women brought up the membership to 148. How many men and women were there originally?. (A) 90 men, 40 women. (B) 80 men, 50 women. (C) 60 men, 70 women. (D) 50 men, 80 women. 23. Radhika draws the figure of an aeroplane as given in the figure. Here the wings ABCD and GHIF forms a parallelogram. The tail DEF is an isosceles triangle, the cockpit CKI is a semi-circle and middle-part DCIF is a square. The measurements (in cms) are given in the figure. The area of the plane figure if BP ^ CD and HQ ^ FI is _____.. (A) 97.24 cm2 . (B) 98.14 cm2 . (C) 96.82 cm2 . (D) 90 cm2. 24. The average of five consecutive natural numbers is m. If the next three natural numbers are also. included, how much more than m will the average of these 8 numbers be ? (A) 1 (B) 1.4 (C) 1.5 (D) 2. 25. How many sides does a regular polygon have, whose interior angle is eight times its exterior. angle ? (A) 16. (B) 24. (C) 18. (D) 20. 26. In the given figure, BD is the diameter of the circle with centre O,. ∠COD = 92° and ∠ABD = 65°. Then y equals ______. (A) 65° (B) 46° (C) 44° (D) 21°. 27. The incomes of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9 : 15. If A saves (1/4)th of his income, then the savings of A, B and C are in the ratio _____.. (A) 56 : 99 : 69. (B) 69 : 56 : 99. (C) 99 : 56 : 69. (D) 99 : 69 : 56. 28. The given pie chart shows the hourly distribution of all the major activities of a student.. Find the difference between the time (in percent) the students spends in games and sleeping. Also, what is the difference in time (in hours) spent in school and in homework.. (A) 30%, 2 hrs . (B) 40%, 3 hrs . (C) 25%, 4 hrs. (D) None of these. 29. A conical vessel of radius 6 cm and height 8 cm is filled with water. A sphere is lowered into the water and its size is such that when it touches the sides of the conical vessel, it is just immersed. How much water will remain in the cone after the overflow ?. (A) 188.57 cm3 . (B) 160 cm3 . (C) 181.30 cm3 . (D) 175.46 cm3. Copyright©2015. Science Olympiad Foundation (SOF).

(30) 6. 6th IMO - SET A. 30. A circle of radius 'r' has been inscribed in a triangle of area A. If the semi-perimeter of the triangle be S, then ____.. (A) S = Ar. (B) r 2 =. S. A. (C) r =. A. S. (D) r =. A2 S. 31. A group of girls planned a picnic. The budget for food was ` 2400. Due to illness, 10 girls could not go to the picnic and cost of food for each girl increased by ` 8. How many girls had planned. the picnic? (A) 60. (B) 50. (C) 65. (D) 57. 32. There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is the same. If 20 candidates are sent from B to A, the number of students. in A is double the number of students in B. Find the number of students in each room. (A) A = 60, B = 40 (B) A = 110, B = 60 (C) A = 95, B = 70 (D) A = 100, B = 80. 33. A number x is selected from the numbers 1, 2 & 3 and then a second number y is randomly selected from the numbers 1, 4 & 9. What is the probability that the product xy of the two numbers will be. less than 9? 5. (A) 9. (B). 9. 10. (C). 2. 9. (D). 7 10 E. 34. The given diagram represents some beams which supports part of a roof.. If AC = 8 metres, ∠BAC = 60°, ∠ACD = 30°, ∠ADC = 90° and ∠CAE = 90°, then the length of the beam AD is ______. (A) 5 cm (B) 8 cm (C) 4 cm (D) 12 cm. A. D. 60° 8. 30°. B. C. 35. The sum of n terms of the three arithmetical progressions are S1, S2 and S3. The first term of each is unity and the common differences are 1, 2 and 3 respectively, then _____.. (A) S1 + S 3 = 2S 2. (B) S1 – S 3 = S 2. (C) S1 + S 2 = S 3. (D) S1 + S 3 = S 2. 36. Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete the work in 7 days ?. (A) 14 (B) 8 (C) 7 (D) 12 37. In the adjoining figure, M is the midpoint of BC and AE is half of BE, then AD is _____.. (A) (B) (C) (D). 12.44 17.36 16.27 15.65. cm cm cm cm. 38. If 47.2506 = 4 A +. (A) 53.6003. 7 5 + 2C + + 6E, then the value of 5A + 3B + 6C + D + 3E is ______. B D (B) 53.603 (C) 153.6003 (D) 213.0003. 39. Kruti took a loan at simple interest at 6 % in the first year with an increase of 0.5 % in each. subsequent year. She paid ` 3375 as interest after 4 years. How much loan did she take? (A) ` 12500 (B) ` 15800 (C) ` 33250 (D) ` 30000 Copyright©2015. Science Olympiad Foundation (SOF).

(31) 7. 6th IMO - SET A. 40. What is more favourable for a buyer - discount series P of 20%, 15% and 10% or a discount series. Q of 25%, 12% and 8% ? (A) P (B) Q. (C) Both (P) and (Q). (D) None of these. Section III : Everyday Mathematics 41. Garima purchased a briefcase with an additional 10% discount on the reduced price after deducting 20% on the labelled price. If the labelled price was ` 1400, at what price did she purchase the briefcase?. (A) ` 980 (B) ` 1008 (C) ` 1056 (D) ` 1120 42. A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10 m wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing. its surface level by 25 cm. The depth of the drainlet is _______. (A) 1.375 m (B) 1.5 m (C) 1.227 m. (D) None of these. 43. There are three pipes fitted in a tank. First two pipes when operated simultaneously, fill the tank in the same time as filled by the third pipe alone. The second pipe fills the tank 7 hours faster than the first pipe and 3 hours slower than the third pipe. The approximate time required by each pipe to fill the tank simultaneously is _____.. (A) 12 hrs, 7 hrs, 3 hrs . (C) 15 hrs, 10 hrs, 6 hrs . 1 1 1 hrs, 8 hrs, 5 hrs 2 2 2 (D) 35 hrs, 30 hrs, 26 hrs. (B) 15. 44. Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as one another. Find the probability that both will. visit the shop on (i) the same day, (ii) consecutive days. 1 3 1 5 1 5 (A). (B). (C). , , , 6 18 5 18 6 18. (D). 1 3 , 5 18. 45. A cake of 6 cm radius is divided into 3 sectors with central angles 120°, 150° and 90° respectively. The ratio of the areas of the three sectors is ____.. (A) 4 : 3 : 5. (B) 5 : 3 : 4. (C) 3 : 4 : 5. (D) 4 : 5 : 3. 46. A, B and C starts cycling around a circular path in the same direction at same time. The circumference of the path is 2400 m. If the speed of A is 300 m/min, speed of B is 480 m/min and C is 150 m/min and they start from the same point, then after what time interval they will be together. at the starting point ? 2 (A) 1 hrs 3. 1 (B) 1 hrs 3. (C) 3. 1 hrs 3. (D) 3. 2 hrs 3. 47. A trader marks his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the. marked price. His total gain is ______. (A) 2 % (B) 4.5 % . (C) 13.5 %. (D) 15 %. 48. Mohit went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was one and a half times that from Chandigarh to Shimla. If the average speed for the entire. journey was 49 km/hr, what was the average speed from Chandigarh to Shimla ? (A) 39.2 km/hr (B) 63 km/hr (C) 42 km/hr (D) 35 km/hr Copyright©2015. Science Olympiad Foundation (SOF).

(32) 8. 6th IMO - SET A. 49. In a Printing House, machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 a.m. While machine P is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished ?. (A) 11 : 30 a.m.. (B) 12 noon. (C) 12 : 30 p.m.. (D) 1 p.m.. 50. A railway half ticket costs half the full fare. But, the reservation charges are the same on the half ticket as on the full ticket. One reserved first class full ticket from Mumbai to Ahmedabad costs ` 216 while one full and one half reserved ticket costs ` 327. What is the value of the first class. full ticket and what is the reservation charge respectively? (A) ` 3, ` 210 (B) ` 210, ` 210 (C) ` 6, ` 220 SPACE FOR ROUGH WORK. Copyright©2015. Science Olympiad Foundation (SOF). (D) ` 210, ` 6.

(33) Class 10 6th. SET B Year 2012. Copyright©2015. Science Olympiad Foundation (SOF).

(34) 2. 6th IMO - SET B Section I : Logical Reasoning. (A) D. 2 A C 3 4. L. (B) D. DL2CA34 L A 4 (C) D C 3 2. L2 A 4 C 3 . (D) D. 2L. Find the water image of the given combination. A C 3. 4. 1.. 2. The different positions of a dice has been shown. What digit will be opposite to digit 4?. 3.. (A) 6. (B) 1. (C) 5. (D) 2. Find out the figure from amongst the options which can be formed from the pieces given in Fig. (X).. (A). 4.. Find out the wrong term in the given number series.. (B). (C). 1236, 2346, 3456, 4566, 5686 (B) 3456 (C) 4566. (D). (A) 1236. (D) 5686. 5.. Read the following letter-number sequence carefully and answer the question. J K P D F G H 6 9 2 8 Q E M 7 4 3 Z Y B T 5 4 2 3. If all the odd numbers are dropped from the above sequence, which of the following element would. be seventh to the right of twelfth element from the right end? (A) B (B) Z (C) Y. 6.. Mohit walks 6 km to the east and then turns to the south and walks 5 km. Again he turns to the. (D) 4. east and walks 6 km. Next, he turns northwards and walks 10 km. How far is he now from his. starting point? (A) 5 km. (B) 12 km. (C) 13 km. (D) 17 km. 7. Eight friends P, Q, R, S, T, U, V and W are sitting around a circle facing the centre. V is third to the right of Q and is second to the left of R. Q is second to the left of T and on the immediate right of S. U is between Q and T. P is not on the left of R.. Which of the following is the correct position of W?. (A) On the immediate left of V . (B) On the immediate right of V. (C) Between U and V . (D) On the immediate right of R. 8.. Pointing to a photograph a woman says : "He is the only son of the wife of my husband's father". How is the man related to the woman?. (A) Son. (B) Son-in-law. (C) Brother-in-law. Copyright©2015. Science Olympiad Foundation (SOF). (D) Husband.

(35) 3. 6th IMO - SET B 9.. Which of the following option figures will continue the same series as established by the Problem Figures?. (A). + + +. (B). (C). + + +. + + +. + + (D) +. 10. Find the mirror image of Fig. (X) from amongst options, if the mirror is placed to the right of Fig. (X).. (A). (B). (C). (D). 11. In a certain code language 'you require more concentration' is written as 'tig seeg loog roog'; 'stress require for arithmetic' is written as 'miya lota loog kota'; 'non-verbal is more easy' is written as 'seeg yoog beeg laa' and 'stress more on non-verbal' is written as 'seeg mota yoog miya'. Then. what is the code for 'require'? (A) yoog (B) loog. (C) miya. (D) seeg. 12. Following question is based on the 5 three-digit numbers given below: 517 394 823 976 465. If the position of the first and the second digits in each of the above numbers are interchanged,. which of the following will be the third digit of the highest number? (A) 7 (B) 4 (C) 3. (D) 6. 13. Nihal is taller than Sumit, who is shorter than Rohit. Vipin is taller than Akash. Anshu is shorter than Vivek. Neither Vipin nor Vivek is the tallest. If Rohit is standing second in decreasing order. of height, who will stand in the middle in the group of these seven persons? (A) Vipin (B) Vipin or Vivek (C) Anshu (D) Can't be determined. 14. Fig. (i) & (ii) of the Problem Figures bears a certain relationship. Select a Fig. (iii) from the options which bears the same relationship to the Fig. (iv) of the Problem Figures.. (A). (B). (C). (D). 15. How many pairs of letters are there in the word GOALKEEPER which have the same number of. letters between them as in English alphabet? (A) Five (B) Four. (C) Seven. Copyright©2015. Science Olympiad Foundation (SOF). (D) Six.

(36) 4. 6th IMO - SET B. 16. In the question, two Problems Figures, followed by four Answer Figures (A), (B), (C) and (D) are given. The two Problem Figures have some common characteristics/features. Find out one figure out of the four Answer Figures which has the same features/characteristics. Problem Figures. (A). (B). + +. (C). +. ×. (D). 17. Select a figure from the options which completes the Fig. (X)?. (A). (B). (C). (D). 18. The question is based on the following information:. 'A @ B' means 'A is added to B'.. 'A * B' means 'A is multiplied by B'.. 'A # B' means 'A is divided by B'.. 'A $ B' means 'B' is subtracted from A'.. In the question below, some information is given. You have to find out which expression correctly represents the statement.. Number of boys (B) in a class is equal to one-fourth of three times the number of girls (G) in the. class. (A) B = (3 # G) * 4. (B) B = (3 * G) @ 4. (C) B = (3 * G) # 4. (D) B = (3 $ G) # 4. 19. '2' is subtracted from each odd digit and '1' is added to each even digit in the number 7652348. Which of the following will be the sum of the second digit from the right and the third digit from. the left of the new number thus formed? (A) 10 (B) 8. (C) 4. (D) 6. 20. The question below is based on the given diagram. You have to take the given diagram to be true even if it seems to be at variance from commonly known facts and then decide which of the given options logically follows the given diagram. BPO employees. A. E. C D B. Population earning more than ` 10,000 per month. Graduate population. Which of the following represents the population which is graduate, employed in BPO and earning. more than ` 10,000 a month? (A) Only C (B) C and D. (C) A, C and D. Copyright©2015. Science Olympiad Foundation (SOF). (D) Only B.

(37) 5. 6th IMO - SET B Section II : Mathematical reasoning. 21. H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 2 4 × 35 × 52 × 72. The third number. is ______. (A) 22 × 35 × 72. (B) 22 × 53 × 72. (C) 25 × 52 × 72. (D) 23 × 35 × 72. 22. In the given figure, BC = AC = AD, ∠EAD = 81°. Find the value of x.. (A) 45°. (B) 54°. (C) 63°. (D) 36°. 23. If x = 21/3 + 2–1/3, then the value of 2x 3 – 6x will be ______.. (A) 5 (B) –5 (C) 1. (D) 0. 3 , find the value of cotq + cosecq. 5 (B) 2. (D) 0. 24. If cosq =. (A) 1. (C) 3. 25. The following table gives weekly wages in rupees of workers in a certain commercial organization. The frequency of class 49 - 52 is missing. It is known that the mean of the frequency distribution is 47.2. Find the missing frequency. Weekly wages (`). 40 - 43. 43 - 46. 46 - 49. 49 - 52. 52 - 55. 31. 58. 60. ?. 27. Number of workers (A) 40. (B) 38. (C) 44. (D) 42. 26. ABCD is a parallelogram. The diagonals AC and BD intersect at a point O. If E, F, G, and H are the mid-points of AO, DO, CO and BO respectively, then the ratio of (EF + FG + GH + HE) to (AD + DC + CB + BA) is _____.. (A) 1 : 1 (B) 1 : 2 (C) 1 : 3 (D) 1 : 4 27. If the 3rd and 7th terms of an A.P. are 17 and 27 respectively. Find the first term of the A.P.. (A) 9 (B) 12 (C) 14 (D) None of these 28. What must be subtracted from the polynomial f(x) = x4 + 2x 3 – 13x 2 – 12x + 21 so that the resulting. polynomial is exactly divisible by x 2 – 4x + 3? (A) 2x – 3 (B) 2x + 3. (C) x + 3. (D) 3x – 2. 29. If –5 is a root of the quadratic equation 2x 2 + px – 15 = 0 and the quadratic equation p(x 2 + x) + k = 0 has equal roots, find the value of k. 4 7 7 8. (B). (C). (D). (A) 7 4 8 7 30. In the given figure, AB is diameter of the circle. C and D lie on the semicircle. If ∠ABC = 65° and ∠CAD = 45°, then ∠DCA is ______.. (A) 45°. (B) 25°. (C) 20°. Copyright©2015. Science Olympiad Foundation (SOF). (D) 10°.

(38) 6. 6th IMO - SET B. 31. Find the value of a for which the following system of equations has infinitely many solutions.. 2x + 3y = 7. (a – 1)x + (a + 2)y = 3a (C) a = 5. (A) a = 4 . (B) a = 7. (D) a = 6. 32. In the given figure, ∠A = ∠CED. Find the value of x.. (A) 8 cm. (B) 5 cm. (C) 7 cm. (D) 6 cm . 33. If 5 5 × 53 ÷ 5 −3/2 = 5 a +2 , then the value of a is ______.. (A) 4. (B) 5. (C) 9. (D) 16. 34. If x be a rational number and y be an irrational number, then _____.. (A) Both x + y and xy are necessarily irrational.. (B) Both x + y and xy are necessarily rational.. (C) xy is necessarily irrational, but x + y can be either rational or irrational.. (D) x + y is necessarily irrational, but xy can be either rational or irrational.. 35. If the sum of the zeroes of the quadratic polynomial f(t) = kt 2 + 2t + 3k is equal to their product, find the value of k.. (A) 5. (B) −. 36. If sin θ =. (A). 2. 3. (C) 7. (D) 0. 3 cosec2 θ − cot 2 θ , find . 4 sec2 θ − 1. 7. 3. 5. 3. (B). (C). 2. 3. 5 3. (D). 37. The following is the distribution of height of students of a certain class in a certain city. Height (in cms). 160 - 162. Number of students. Find the median height.. (A) 172.94. 163 - 165. 15. 166 - 168. 169 - 171. 172 - 174. 142. 127. 18. 118. (B) 161.36. (C) 150.53. (D) 167.13. 38. Which of the following statements is TRUE?. (A) The value of tan A is always less than 1.. (C) sinq =. 4 , for some angle q . 3. (B) sec A =. 12 , for some value of angle A. 5. (D) cot A is the product of cot and A.. 39. Two dice are tossed. The probability that the total score is a prime number is _____.. (A). 1. 6. (B). 5. 12. (C). 1. 2. Copyright©2015. Science Olympiad Foundation (SOF). (D). 7 9.

(39) 7. 6th IMO - SET B. 40. A spherical ball of lead 6 cm in radius is melted and recast into three spherical balls. The radii of. two of these balls are 3 cm and 4 cm. What is the radius of the third ball? (A) 4.5 cm (B) 5 cm (C) 6 cm (D) 7 cm. Section III : Everyday Mathematics 41. Shubham travels 760 km to his home partly by train and partly by car. He takes 8 hours if he travels 160 km by train and the rest by car. He takes 12 minutes more if he travels 240 km by train and the rest by car. Find the speed of the train and the car respectively (in km/hr).. (A) 40, 80. (B) 60, 120. (C) 80, 100. (D) 100, 120. 42. Titan sells a wrist watch to a wholesaler making a profit of 10%. The wholesaler, in turn, sells it to the retailer making a profit of 10%. A customer purchases it by paying ` 990. Thus the profit of retailer is 2. (A) ` 768. 3 % . What is the cost incurred by the Titan to produce it? 11 (B) ` 750 (C) ` 800 (D) ` 820. 43. A cell-phone is available for ` 2500 cash or ` 520 cash down payments followed by 4 equal monthly instalments. If the rate of interest charged is 25% per annum, calculate the monthly instalment.. (A) ` 520. (B) ` 480. (C) ` 550. (D) None of these. 44. A well with 14 m inside diameter is dugout 15 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. What is the height of the. embankment? (A) 2 m. (B) 1 m. (C) 3 m. (D) 4 m. 45. Two trains starting at the same time from two stations 300 km apart and going in opposite directions, cross each other at a distance of 160 km from one of them. The ratio of their speeds is _____.. (A) 7 : 9. (B) 16 : 20. (C) 8 : 7. (D) None of these. 46. The monthly salary of Megha and Beena together is ` 28,000. The salary of Megha and Beena is increased by 25% and 12.5% respectively, then the new salary of Beena becomes 120% of the new salary of Megha. The new (or increased) salary of Megha is ______.. (A) ` 15,000. (B) ` 18,000. (C) ` 14,000. (D) ` 16,000. 47. Latika, Garima and Priya are three sisters. Latika and Garima are twins. The sum of the ages of Latika and Garima is same as that of Priya alone. Three years earlier the ratio of age of Latika and Priya was 2 : 7. What will be the age of Garima 3 years hence?. (A) 21 years. (B) 16 years. (C) 8 years. (D) 12 years. 48. Two pencils are 24 cm and 42 cm. If we want to make them of equal size then minimum number of similar pencils is _____.. (A) 6. (B) 11. (C) 12. (D) None of these. 49. I know a two digit number, but when its digits interchanges their places, we get another two digit number. But when these two digit numbers are added, it amounts to 99. Further if I just consider the difference between these numbers, it comes out to be 45. What is the number which I know?. (A) 27. (B) 38. (C) 72. Copyright©2015. Science Olympiad Foundation (SOF). (D) Data insufficient.

(40) 8. 6th IMO - SET B. 50. Samay has a right circular cylinder which he inserted completely into a right circular cone of height 30 cm. The vertical angle of the cone is 60° and the diameter of the cylinder is 8 3 cm. What is the volume of the cone?. (A). 3000 π cm3 7. (B) 3000p cm3. (C) 4860p cm3. SPACE FOR ROUGH WORK. Copyright©2015. Science Olympiad Foundation (SOF). (D) Can't be determined.

(41) Class 10 7th. SET A Year 2013. Copyright©2015. Science Olympiad Foundation (SOF).

(42) 2. 7th IMO - Set A. logical reasoning 1.. Choose the correct option that will continue the same pattern and replace the question mark in the given series. 3, 12, 27, 48, 75, 108, ?. A. B. C. D.. 2.. 147 162 183 192. A.. In a certain code, PLEADING is written as FMHCQMFB. How is SHOULDER written in that code?. B.. A. B. C. D.. C.. 3.. Q's mother is sister of P and daughter of M. S is daughter of P and sister of T. How is M related to T?. KCDQTIPV QDCKVPIT QDCKTIPV TIPVQDCK. A. B. C. D.. 4.. Read the following information carefully and answer the question that follows :. (i) Five friends P, Q, R, S and T travelled to five different cities; Chennai, Kolkata, Delhi, Bangalore and Hyderabad by different modes of transport; Bus, Train, Aeroplane, Car and Boat from Mumbai. (ii) The person who travelled to Delhi did not travel by boat. (iii) R went to Bangalore by car and Q went to Kolkata by aeroplane. (iv) S travelled by boat whereas T travelled by train. (v) Mumbai is not connected by bus to Delhi and Chennai. Which of the following combinations of place and mode is not correct ? A. Delhi-Train B. Kolkata-Aeroplane C. Hyderabad-Car D. Chennai-Boat. 5.. Aunt. Father Sister Maternal Grandfather or Maternal Grandmother. The given question consists of five figures marked P, Q, R, S and T called the Problem Figures. Select a figure from the options which will continue the same series as established by the five Problem Figures.. D.. 6.. Find the number of triangles in the given figure.. A. B. C. D.. 7.. The door of Aditya's house faces East. From the back side of his house, he walks straight 50 metres, then turns to the right and walks 50 metres again. Finally, he turns towards left and stops after walking 25 metres. Now, Aditya is in which direction from the starting point ?. A. B. C. D.. 8.. Forty boys are standing in a row facing the North. Arun is eleventh from the left and Deepak is thirtyfirst from the right end of the row. How far will Shreya, who is third to the right of Arun in the row, be from Deepak ?. A. B. C. D.. 12. 15 14 None of these. South-east North-east West North-west. 2nd 3rd 4th 5th. Copyright©2015. Science Olympiad Foundation (SOF).

(43) 3. 7th IMO - Set A 9.. If 'Q' denotes '+', 'J' denotes '×', 'T' denotes '–' and 'K' denotes '÷', then 30 K 2 Q 3 J 6 T 5 = ?. A. B. C. D.. 18 28 31 103. 10. Which of the following is the mirror image of the given word, if the mirror is placed vertically left? N otification. A. B. C. D.. 15. If the third, fourth, fifth, seventh and tenth letters of the word PERSONALITY forms a meaningful word then first letter of the word is the answer. If no word is possible, then 'X' is the answer and if more than one such word is formed, then 'M' is the answer.. A. B. C. D.. R X O M. 16. Find the missing character.. T W 3. 11. Find out how many such pairs of letters are there in the given word each of which has as many letters between them in the word as in the English alphabet. ADVERTISEMENT. A. Three. B. Four. C. Five. D. More than five. J. A. B. C. D.. T. 10. 15. S. D. ? P G. 5 9 11 13. 17. The number of cubes required to make the given figure is ______.. 12. The triangle represents females, rectangle represents housewife and circle represents school teachers, then the number representing females who are school teachers but unmarried is. A. B. C. D.. 2 4 3 8. 13. How many 8's are there in the following number series each of which is exactly divisible by its immediately preceding and also divisible by its immediately succeeding number?. A. B. C. D.. 31 32 33 34. 18. Select the figure from the options which is embedded in the given Fig. (X).. 824517284842282698454832843183. A. B. C. D.. 1 4 3 2. 14. Choose the group which is different from the rest.. A. B. C. D.. MEWGN PBQTX DRYSN CGHKV. A.. B. C.. D.. Copyright©2015. Science Olympiad Foundation (SOF).

(44) 4. 7th IMO - Set A. 19. 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 of numbers is to be answered. The operations of numbers progress from left to right.. Rules. I.. If an odd number is followed by a two-digit even number, then they are to be added. II. If an odd number is followed by a two-digit odd number, then the second number is to be subtracted from the first number. III. If an even number is followed by a number which is a perfect square of a number, then the second number is to be divided by the first number. IV. If an even number is followed by a two-digit even number, then the first number is to be multiplied by the second number. 13 11 4 17 13 12. A. B. C. D.. 48 69 75 96. 20. Which of the following options will complete the figure matrix?. A.. B. C.. If the resultant of the first set of numbers is multiplied by the resultant of the second set of numbers, what will be the outcome?. D.. MATHEMATICAL REASONING 21. If one root of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 is 1, then the other root is ___. b (c − a ) a (b − c). B.. A. a (b − c) c ( a − b) a (b − c) c ( a − b). C.. D. b (c − a ) a (b − c) 22. If H.C.F of (x – 5)(x2 – x – a) and (x – 4) (x2 – 2x – b) is (x – 4)(x – 5), find the values of a and b respectively.. A. B. C. D.. 15, 10, –8, 12,. 18 7 10 15. 24. ABCD is a cyclic quadrilateral. AE is drawn parallel to CD and BA is produced. If ∠ ABC = 92° and ∠FAE = 20°, then ∠BCD =. A. B. C. D.. 88° 108° 115° 72°. 25. If xcos3q + ysin3q = sinqcosq and xcosq = ysinq, then x2 + y 2 =. 23. What is the sum of an A.P. whose first term is a, the second term is b and the last term is c? (b + c − 2a )(a + c). A.. 2(b − a ) (b + c + a)(a + c). B.. 2b − a 2(a + c)(b − c + 2a ) C.. b+a (b + c − 2a )(a − c) D.. b+a. A. B. C. D.. 0 4 1 2. 26. Find the coordinates of the points which trisect the line joining (–3, 5) and (6, –7).. A. B. C. D.. (0, 1) and (3, –3) (–1, –1) and (0, 3) (2, 0) and (1, 1) (2, 2) and (0, 1). Copyright©2015. Science Olympiad Foundation (SOF).

(45) 5. 7th IMO - Set A. 31. The product of 12% of an integer and 20% of the next integer is 61.2. Find the integer.. x8 − a 8 27. Express in lowest terms : 6 x − a6 2 2 2 2 ( x + a )( x − a ). A. ( x 2 + ax + a 2 )2. B.. C.. D.. ( x 2 + a 2 )( x 4 + a 4 ) ( x 2 + ax + a 2 )( x 2 − ax + a 2 ) 2. 2. 4. A.. ( x + a )( x + a ) ( x 2 − ax + a 2 )2 ( x 2 + a 2 )( x 4 + a 4 ). ( x 2 + ax − a 2 )( x 2 − ax + a 2 ). 33. Find the value of x in the given figure, where O is the centre of the circle.. (3 x 2 − 14). B.. C.. D.. 50 –51 63 Both A and B. 32. Find the values of p and q respectively for which the following system of linear equations has infinite solutions. 2x + 3y = 7 (p + q)x + (2p – q)y = 21. A. 2, 6. B. –7, 3. C. –3, –5. D. 5, 1. 4. 28. Express as a rational expression. 1 1 2 4 − − − x − 1 x + 1 x2 + 1 x4 + 1. A. B. C. D.. x2 − 1 ( x 2 + 3) x4 + 1 8 8 ( x − 1) 2( x + 4) x +1. 29. A point D is on the side BC of an equilateral DABC 1 such that DC = BC. Then AD 2 = 4. A. 13 CD2. B. 9 AB2. C. 6 CD2. D. 12 BC 2 30. In the given figure, AB, EF and CD are parallel lines. Given that EG = 5 cm, GC = 10 cm and DC = 18 cm, then EF =. A. 9 cm. B. 25 cm. C. 13 cm. D. 16 cm. A. B. C. D.. 80° 160° 100° 105°. 34. If sinq + cosq =. A.. B.. 2 −1. C. D.. 2 +1 –1. 2 sin(90° – q), then cotq =. 1. 35. Find k, so that 4k + 8, k3 + 3k + 6 and 3k2 + 4k + 4 are three successive terms of an A.P.. A. C.. 0 –1. B. D.. 2 Both A and B. EVERYDAY MATHeMATICS 36. A lot of 24 bulbs contains 25% defective bulbs. A bulb is drawn at random from the lot. It is found to be not defective and it is not put back. Now, one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?. A. B. C. D.. 18/23 15/24 17/23 20/23. 37. The mean height of the 10 girls of a class is 1.4 m and the mean height of the 30 boys of the class is 1.45 m. Find the approximate mean height of the 40 students of the class.. A. B. C. D.. 1.39 1.46 1.42 1.44. m m m m. Copyright©2015. Science Olympiad Foundation (SOF).

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