Class 11 Imo 4 Years e Book

Full text

(1)11. 4. (2008-2011). INSTANT.

(2) Copyright © 2012 MTG Learning Media (P) Ltd. 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 Publisher. 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) 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.

(4) 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.

(5) 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.

(6) 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.

(7) IIT-JEE | AIEEE | NEET | BOARDS | OLYMPIAD | NTSE. FOUNDATION COURSE For Classes 8, 9 & 10 Class 8. Class 9. Class 10.

(8) 2nd. Year 2008.

(9) Class 11 . 2nd IMO - 2008. 2 . SECTION I : LOGICAL REASONING 1. . Which number should come next in the series? 4, 5, 8, 17, 44, ? (A) 135 . 2. . (B) 120 . (C) 125 . (D) 130 . (E) None of these. . A matrix of certain characters is given. These characters follow a certain trend, rowwise or column wise. Choose the missing character. . (A) 1 . (B) 2 . 963 . 2 . 844 . 464 . ? . 903 . (C) 3 . (D) 4 . (E) None of these. 3. . There are four equally spaced beads on a circle. How many straight lines are needed to connect each bead with every other bead ? (A) 5 . 4. . 7. . (D) 7 . (E) None of these. . (B) . (C) . (D) . (E) None of these. . How many straight lines are needed to divide a regular hexagon into 6 identical triangles ? (A) 4 . 6. . (C) 8 . Which of the following figures is the odd one out ? (A) . 5. . (B) 6 . (B) 5 . (C) 3 . (D) 2 . (E) None of these. . Which of the following figures is the odd one out ? . (A) . (B) . (C) . (D) . (E) None of these. . How many four sided shapes does this diagram have ? . (A) 5 (E) None of these.. (B) 11 . (C) 16 . (D) 26 .

(10) Class 11 8. . 2nd IMO - 2008. 3 . Which of the cubes is the same as the unfolded cube on the right ? (A) . (B) . (C) . (D) . (E) None of these. 9. . At the end of a banquet 10 people shake hands with each other. How many handshakes will there be in total ? (A) 100 . (B) 20 . (C) 45 . (D) 50 . (E) None of these. . 10. The day before the day before yesterday is three days after Saturday. What day is it today ? (A) Monday . (B) Tuesday . (C) Wednesday . (D) Friday . (E) None of these. . (C) Loop . (D) Castle . (E) None of these. . 11. 165135 is to 'peace' as 1215225 is to (A) Lead . (B) Love . 12. A matrix of certain characters is given in the right side. These characters follow a . 11 . 6 . 8 . certain trend, rowwise or columnwise. Which character should replace the question . 17 12 ? . mark accordingly ? (A) 16 (C) 13 (E) None of these. . 25 34 19. (B) 9 (D) 15 . 19 28 11 . 13. Find the picture that follows logically from the diagrams below. ? . (A) . (B) . (C) . (D) . (E) None of these. . (D) 64 . (E) None of these. . (D) . (E) None of these. . 14. Which number comes next in the sequence ? 4, 6, 12, 14, 28, 30, ? (A) 32 . (B) 60 . (C) 62 . 15. Which of the diagrams follows in the given pattern ? . ? (A) . (B) . (C) . 16. Find the answer that best completes the analogy people : democracy : : wealthy : ? (A) Oligarchy . (B) Oligopoly . (C) Plutocracy . (D) Timocracy . (E) None of these..

(11) Class 11 . 2nd IMO - 2008. 4 . 17. Find two words, one from each group, that are closest in meaning. . (A) Raise and Elevate . Group A . Group B . Raise . Top . Floor . Elevate . Stairs . Basement . (B) Raise and Top . (C) Floor and Basement (D) Stairs and Top . (E) None of these. 18. Which of the following diagrams is the odd one out ? . (A) . (B) . (C) . (D) . (E) None of these. . 19. Find the picture that follows logically from the diagrams on the right. . (A) . (B) . (C) . (D) . (E) None of these. . 20. Which diagram results from folding the diagram on the right ? . (A) . (B) . (C) . (D) . (E) None of these. . SECTION II : MATHEMATICAL REASONING 21. What is the greatest term in the expansion of (4 + 3x) 7 when x = (A) 60614 . (B) 72632 . (C) 86016 . 22. If z 1 and z 2 be two complex numbers such that (A) 2 . (B) 3 . (C) 4 . 2 ? 3 . (D) 91206 . (E) None of these. . z1 2 z 2 = 1 and z 2 ¹ 1. What is the value of | z 1 | ? 2 z1z 2 . (D) 6 . (E) None of these. . 23. The circle x 2 + y 2 – 4x – 4y + 4 = 0 is inscribed in a triangle which has two of its sides along the coordinate axes. The locus of the circumcentre of the triangle is x + y – xy + k(x 2 + y 2 ) 1/2 = 0. What is the value of k ? (A) 4 . (B) 2 . (C) 0 . (D) 1 . (E) None of these..

(12) Class 11 . 24.. If. 2nd IMO - 2008. 5 . cos 4 x cos2 y. +. sin 4 x sin 2 y . (A) 0 . = 1, then what is the value of. (B) 1 . 25. What is the value of lim n. cos2 x. (C) 2 . +. sin 4 y sin 2 x . ? . (D) 4 . 1 öæ 1 ö 1 ö ö æ æ ç (n + 1) ç n + 2 ÷ ç n + 2 ÷ .......... ç n + n 1 ÷ ÷ 2 ø 2 ø ø è øè è è. - n 2 æ. n ®¥. (B) e 2 . (A) e . cos4 y. 26. Common tangent of the ellipses . (C) e –2 x2 a2. +. (E) None of these. . n . ? . (D) Does not exist (E) None of these. . y 2 . 2 x x 2 y 2 -2 x = and + = subtends an angle at the origin. c b2 c b 2 a 2 . What is that angle ? (A) 45° . (B) 90° . (C) 135° . (D) 60° . (E) None of these. . 27. If S 1 , S 2, S 3 be respectively the sum of n, 2n, 3n terms of a G.P, then S 1(S 3 – S 2 ) equals 2 (A) (S 2 – S 1) . (B) (S 2 – 2S 1 ) 2 . (C) (2S 1 – 3S 2 ) 2 . (D) S 3 – 3S 1 . (E) None of these. . 28. Given 5 different green dyes, four different blue dyes and 3 different red dyes, how many combination of dyes can be chosen taking at least one green and one blue dye ? (A) 2840 . 29. Let y =. (C) 3720 . (D) 3988 . (E) None of these. . mx 2 + 3 x - 4 , find the interval of m so that y takes all real values for real values of x. m + 3 x - 4 x 2 . (A) 0 £ m £ 6 . 30.. (B) 2972 . (B) 1 £ m £ 9 . (C) 1£ m £ 7 . (D) 0 £ m £ 8 . (E) None of these. . p pü ì If A = í x : £ x £ ý and f ( x ) = cos x - x (1 + x ), then f(A) is equal to 6 3 î þ (A). é 1 p p2 3 p p 2 ù , + ê + ú 9 2 6 36 úû êë 2 3. (B). é 1 p p2 3 p p 2 ù , - ê - ú 9 2 6 36 úû êë 2 3. (C). é 1 p p2 3 p p 2 ù , - + ê - + ú 9 2 6 36 úû ëê 2 3. (D). é 3 p p 2 1 p p 2 ù - + , - ê ú 6 36 2 3 9 úû ëê 2. (E) None of these. 31. The value of a for which the inequality (x–3a) (x–a–3) < 0 is satisfied for all x such that 1 £ x £ 3, is 1 ö æ (A) çè -2, 3 ÷ø. (B) (0, 1) . (C) . æ 1 ö çè 0, 3 ÷ø. 1 ö æ (D) çè -1, 3 ÷ø. (E) None of these. . 32. Which of the following is the domain of the function f ( x ) = 3 - 2 x - 21- x + sin -1 x ? (A) [0, 1] . (B) [0, 2] . (C) [–1, 2] . (D) [–1, 3] . (E) None of these. . d æ d 2 y ö 33. If y 2 = p(x) is a polynomial of degree 3, then which of the following is equal to 2 ç y 3 2 ÷ ? dx è dx ø. (A) p¢(x). p¢¢(x) . (B) p¢(x). p¢¢¢(x) . (C) p(x). p¢¢¢(x) . (D) p(x). p¢(x) . (E) None of these..

(13) Class 11 . 2nd IMO - 2008. 6 . 34. The independent probabilities that A, B and C solve a mathematical problem are . 1 1 1 , and 3 3 4 . respectively. What is the probability that just two of them only solve the problem ? . (A) . 5 36 . (B) . 7 36 . (C) . 11 36 . (D) . 13 36 . (E) None of these. . æ A + B - Cö æ B + C - Aö æ C + A - Bö 35. If A + B + C = p and tan ç tan ç tan ç ÷ ÷ ÷ø = 1, t h e n w h a t i s t h e v a l u e o f 4 4 4 è ø è ø è SinA + SinB + SinC + SinA SinB SinC ? (A) 0 . (B) 1 . (C) 2 . (D) 3 . (E) None of these. . 36. A straight line through P(–2, –3) cuts the pair of straight lines x 2 + 3y 2 + 4xy – 8x – 6y – 9 = 0 in Q and R. What is the equation of the line if PQ × PR = 20 ? (A) 2x – 3y + 4 = 0 and 3x – 2y + 5 = 0 . (B) 3x – y + 3 = 0 and x + y = 1 . (C) x – y = 1 and 3x – y + 3 = 0 . (D) 2x – y = 3 and 3x + y – 3 = 0 . (E) None of these. 37. Which of the following is the value of x for the equation |2x – 1| = 3[x] + 2{x} ([∙] is greatest integer function and { } is fractional part function) ? (A) . 1 2 . (B) 2 . (C) 1 . (D) . 1 4 . (E) None of these. . 38. Which of the following is the solution of C 1 + 2C 2 + 3C 3 + ....... + nC n ? (A) n (2 n ) . (B) 2 n–1 . (C) n(2 n–1 ) . (D) (n–1)2 n . (E) None of these. . 39. The series of natural numbers is divided into groups : (1); (2, 3, 4) ; (5, 6, 7, 8, 9) and so on. The sum of numbers in the n th group is (A) (n + 1) 2 + n 3 (B) (n – 1) 3 + n 3 . (C) (n – 1) 2 + n 3 . (D) n 3 . (E) None of these. . 40. Which of the following is the complex number z which satisfies the condition | z – 2 + 2i | = 1 and has the least absolute value ? 1 ö 1 ö æ æ (A) çè 2 ÷ø + i çè 2 + ÷ 2 2 ø. 1 ö 1 ö æ æ (B) çè 2 + ÷ø + i çè 2 ÷ 2 2 ø. 1 ö æ æ 1 ö - 2 ÷ (C) çè 2 ÷ø + i çè 2 2 ø. 1 ö æ æ 1 ö + 2 ÷ (D) çè 2 ÷ø + i çè 2 2 ø. (E) None of these. . SECTION III : EVERYDAY MATHEMATICS 41. My married neighbour has reached an age that is a square of some number. The product of the digits of his age is his wife’s age. The age of their daughter is the sum of the digits of the mother’s age. How old is my neighbour ? (A) 81 . (B) 94 . (C) 49 . (D) 36 . (E) None of these..

(14) Class 11 . 2nd IMO - 2008. 7 . 42. Car A starts travelling east along a road. At the same time, from the same point car B starts travelling north at a speed 15 km/hr faster than that of car A. After one hour and twenty minutes, the cars are 100 km apart. At what speed car B was travelling ? (A) 40 km/hr . (B) 60 km/hr . (C) 65 km/hr . (D) 80 km/hr . (E) None of these. C . D . 43. Squares ABCD and EFGH are congruent, AB = 10 cm, and G is the centre of . G . square ABCD. The area of the shaded region in the plane is A . (A) 75 cm 2 . (B) 100 cm 2 . (D) 175 cm 2 . (E) None of these. . 44. If . = 7 , . (A) 670 . (C) 125 cm 2 . E . = 27 and . (B) 680 . B F . H . = 81; . (C) 689 . then . (D) 700 . = ? . (E) None of these. . 45. It is an odd number with three digits. All the digits are different and add up to 12. The difference between the first two digits equals the difference between the last two digits. What is the number ? (A) 742 . (B) 740 . (C) 741 . (D) 841 . (E) None of these. . 46. A dog is chasing a rabbit, which has a start of 45 m, jumps 3 m every time while rabbit jumps 2 m. In how many leaps does the dog overtake the rabbit ? (A) 40 jumps . (B) 45 jumps . (C) 47 jumps . (D) 50 jumps . (E) None of these. . 47. Tony and his brother have each agreed to mow half of the front lawn, which is a 20 m by 40 m rectangle. The mower cuts a 1 m wide strip. If Tony starts at the corner and mows around the lawn toward the center, about how many times around must he go before he has mowed his half ? (A) . 1 2 . 1 (B) 3 2 . (C) . 1 2 2 . 1 (D) 1 2 . 1 (E) 4 2 . 48. Anu has an income which is five eighths that of Bonny. Anu’s expenses are onehalf those of Bonny and Anu saved 40% of her income. What is the percentage of his income that Anu saves? (A) 50% . (B) 45% . (C) 30% . (D) 25% . (E) None of these. . 49. The exterior angle of a regular polygon exceeds the interior angle by 132°. Then the number of sides in the polygon is (A) 12 . (B) 13 . (C) 14 . (D) 15 . (E) None of these. . 50. In a plane, four distinct lines intersect the interior of a circle forming regions within the circle. If m represents the maximum number of regions and n represents the minimum number, then m + n = (A) 16 . (B) 18 . (C) 17 . (D) 20 . (E) None of these..

(15) 3rd. Year 2009.

(16) 3rd IMO - 2009. SECTION I : LOGICAL REASONING 1. . Three sequences of letters/numerals are given which correspond to each other in some way. You have to find out the letters/numerals that come in the vacant places marked by (?). Of the four options given below choose the correct one. C B _ _ D _ B A B C C B – – 1 2 4 3 – – ? ? ? ? a – a b – c – b – – – – (A) 3, 4, 4, 3 . 2. . (B) 3, 2, 2, 3 . (C) 3, 1, 1, 3 . (D) 1, 4, 4, 1 . Which one of the following sets is best represented in the adjoining diagram ? (A) Animals, Insects, Cockroaches (B) Country, States, Districts (C) Animals, Males, Females and Hermaphrodites (D) States, Districts, Union Territory . 3. . In the following sequence of instructions, 1 stands for Run, 2 stands for Stop, 3 stands for Go, 4 stands for Sit and 5 stands for Wait. If the sequence were continued, which instruction will come next ? 4 4 5 4 5 3 4 5 3 1 4 5 3 1 2 4 5 4 5 3 4 5 3 (A) Wait . 4. . (B) Sit . (C) Go . (D) Run . The priest told the devotee, " The temple bell is rung at regular intervals of 45 minutes. The last bell was rung five minutes ago. The next bell is due to be rung at 7.45 a.m." At what time did the priest give this information to the devotee? (A) 7.40 a.m. . 5. . (B) 7.05 a.m. . (C) 7.00 a.m. . (D) 6.55 a.m. . In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 persons can speak Hindi and 6 persons can speak Gujarati. In that group, none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group? (A) 21 . 6. . (C) 23 . (D) 24 . A matrix of certain characters is given. These characters follow a certain trend, row . 2 4 . wise or columnwise. Find out this trend and choose the missing character . 1 . 2 4 . accordingly. . 3 . 1 3 . (A) 25 7. . (B) 22 . (B) 48 . (C) 59 . (D) 73 . Count the number of triangles in the figure given below. . (A) 8 3 rd IMO | LevelI | Class 11 . (B) 10 . (C) 11 . 2 . (D) 12. 0 . 36 ? 91 .

(17) 3rd IMO - 2009. 8. . Which of the figures in (X) is embedded in Figure (Y)? . p u . r s . Figure (X ) . Figure (Y ) . (A) r 9. . (B) s . (C) u . (D) p . Complete the missing portion of the given pattern (X) by selecting from the given choices. . ? (X ) . (A) . (B) . (C) . (D) . 10. A cube painted yellow on all faces is cut into 27 small cubes of equal sizes. How many small cubes are not painted on any face? (A) 1 . (B) 4 . (C) 6 . (D) 8 . 11. Different designs can be made by placing a maximum of nine matchsticks. Which of the following designs cannot be made at all? . (A) . (B) . (C) . (D) . 12. In the following options, four words have been given, out of which three are alike in some manner and the fourth one is different. Choose out the odd one. (A) Yuri Gagarin . (B) Rakesh Sharma . (C) Neil Armstrong . (D) Edmund Hillary . 13. Which is the number that comes next in the given sequence? 0, 6, 24, 60, 120, 210, ? (A) 240 . (B) 290 . (C) 336 . (D) 504 . 14. If MISTAKE is coded as 9765412 and NAKED is coded as 84123, then how is the following word coded? DISTANT (A) 3765485 . (B) 4798165 . (C) 3697185 . (D) 4768296 . 15. If 'sky' is called 'sea', 'sea' is called water, 'water' is called air, 'air' is called 'cloud' and 'cloud' is called 'river', then what do we drink when thirsty ? (A) Sky . (B) Air . (C) Water 3 . (D) Sea 3 rd IMO | LevelI | Class 11 .

(18) 3rd IMO - 2009. 16. A man pointing to a photograph says "The lady in the photograph is my nephew's maternal grandmother." How is the lady in the photograph related to the man's sister who has no other sister? (A) Cousin . (B) Sisterinlaw . (C) Mother . (D) Motherinlaw . 17. There are six persons A, B, C, D, E and F . C is the sister of F . B is the brother of E 's husband. D is the father of A and grandfather of F. There are two fathers, three brothers and a mother in the group. Which of the following is a group of brothers ? (A) ABF . (B) ABD . (C) BFC . (D) BDF . 18. Choose the correct mirror image of the figure (Z) X . X . X . (A) . (B) . X . (C) . (D) . X . Fig. (Z ) . 19. Two ladies and two men are playing cards and are 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 ladies facing ? (A) East and West . (B) South and East . (C) North and East . (D) North and West . 20. In the following question, find the figure from the answer set which will continue the series given in the problem set. Problem set . B . A . C . Answer set . D . (A) 4 . E . 1 . (B) 3 . 2 . 3 . (C) 2 . 4 . (D) 1 . SECTION II : MATHEMATICAL REASONING 21. If y =. 1 1+ x. n -m. +x. p -m. (A) 1 . +. 1 m -n. 1+ x +x (B) 0 . p -n. +. 1 1 + x. m-p. dy , then is equal to dx + x n - p (C) m + n + p (D) m – n + p . 22. The graph of function y = f (x) has a unique tangent at (e a , 0) through which the graph passes, then log(1 + 7f ( x )) - sin(f ( x )) equals to 3f ( x ) x ®e (A) 1 (B) 2 lim . a . (C) 7 . (D) 9 . 23. The point (a 2 , a + 1) lies in the angle between the lines 3x – y + 1 = 0 and x + 2y – 5 = 0 containing the origin, if (A). æ 1 ö a Î ( -3,0) È ç ,1 ÷ è 3 ø. æ 1 ö (B) a Î ( -¥,3) È ç ,1 ÷ è 3 ø. 1 ö æ (C) a Î ç -3, ÷ è 3 ø. 24. If a, b are complex numbers, then the maximum value of (A) 1 . 3 rd IMO | LevelI | Class 11 . (B) 2 . ab + ab is | ab |. (C) Greater than 2 . 4 . æ 1 ö (D) a Î ç , ¥ ÷ è 3 ø. (D) Less than 1.

(19) 3rd IMO - 2009. 1 ö æ 2 25. The coefficient of x in the expansion of (1+x ) . ç x + 2 + 2 ÷ è x ø (A) 30 C 10 (B) 30 C 25 (C) 1 20 . 2 40 . -5 . is __________ (D) 1/3 . 26. If a x = b y = c z , where x, y, z are unequal positive numbers and a, b, c are in G.P., then x 3 + z 3 (A) > 2y 3 . (B) < 2y 3 . (C) > 2y 3 . (D) 1 . 27. Equation of the circle of radius 2 containing the point (3, 1) and touching the line |x – 1| = |y – 1|, is (A) x 2 + y 2 – 3x + 4y + 7 = 0 . (B) x 2 + y 2 – 6x + 2y – 4 = 0 . (C) x 2 + y 2 – 6x – 2y + 8 = 0 . (D) x 2 + y 2 – 3x – 4y + 7 = 0 . 28. The sum of the maximum and minimum values of function f (x) = sin –1 2x + cos –1 2x + sec –1 2x is ____ (A) p. (B). p 2 . (C) 2p. (D). 3 p 2 . 29. A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is (A) 12 . (B) 10 . (C) 60 . (D) 84 . 30. The sum of the real roots of cos 6 x + sin 4 x = 1 in the interval – p < x < p is equal to (B) p. (A) 0 . (C) – p. (D) 1 . 31. If A, B, C are acute positive angles such that A + B + C = p and cot A cot B cot C = k, then (A). k £. 1 3 3 . (B). k ³. 1 . (C) k < 1 9 . 3 3 . (D). k >. 1 3 . 32. The tangent drawn at any point P on a parabola, meets the Yaxis at Q and the Xaxis at R. Then the ratio PQ : QR, is (A) 1 . (B) 2/3 . (C) 1/3 . (D) –4 . 33. If z = x + i y and x 2 + y 2 = 16, then the range of ||x | – |y || is ________ (A) [0, 4] . (B) [0, 2] . (C) [2, 4] . (D) [3, 4] . 1 ö 1 2 a æ 1 + + = , then the value of (x 3 – 5x 2 + 33x – 19) is equal 34. If x = 2 + 5i (where i 2 = –1) and 2 ç ÷ 1! 9! 3! 7! 5! 5! b ! è ø to. (A) a . (B) b . (C) a – b . (D) a + b . 35. Suppose A, B, C are defined as A = a 2 b + ab 2 – a 2 c – ac 2 , B = b 2 c + bc 2 – a 2 b – ab 2 and C = a 2 c + c 2 a – cb 2 – c 2 b, where a > b > c > 0 and the equation Ax 2 + Bx + C = 0 has equal roots, then a, b, c are in _______ (A) A.P. . (B) G.P. . (C) A.G.P. . 5 . (D) None of these. 3 rd IMO | LevelI | Class 11 .

(20) 3rd IMO - 2009. 36. A series of concentric ellipses E 1 , E 2 , ........., E n are drawn such that E n touches the extremities of the major axis of E n –1 and the foci of E n coincide with the extremities of minor axis of E n–1 . If the eccentricity of the ellipses is independent of n, then the value of the eccentricity is ____ (A) . 5 3 . (B). 5 - 1 2 . (C). 5 + 1 2 . (D) . 1 5 . 37. Two numbers are chosen from 1, 3, 5, 7, ........, 147, 149 & 151 and multiplied together in all possible ways. The number of ways which will give us the product a multiple of 5, is_____ (A) 74 . (B) 75 . (C) 76 . (D) 195 . 38. If a, b, c Î {1,2,3, 4} , the number of equations of the form 4ax 2 + 2bx + c = 0, which have real roots, is (A) 25 39. Given that (A) . (B) 12 . (C) 10 . (D) 16 . p 1 - sin x 1 + sin x < x < p, then the value of the expression + is _____ 2 1 + sin x 1 - sin x. 2 cos x . (B) . 1 sin x . (C) -. 2 cos x. (D). -. 1 sin x . 40. The sides of a quadrilateral are given by xy (x – 2) (y – 3) = 0. The equation of the line parallel to x – 4y = 0, which divides the quadrilateral into two equal regions, is _____ (A) x – 4y – 1 = 0 . (B) x – 4y + 5 = 0 . (C) x – 4y + 1 = 0 . (D) x – 4y + 3 = 0 . SECTION III : EVERYDAY MATHEMATICS 41. Anshuman bought some toys with 20% discount on original price. The original price of each toy is Rs. 40. If he makes a total saving of Rs. 240, how many toys did he buy ? (A) 8 . (B) 12 . (C) 24 . (D) 30 . 42. A dishonest milkman purchased milk at Rs. 10 per litre and mixed 5 litres of water in it. By selling the mixture at the rate of Rs. 10 per litre he earns a profit of 25%. The quantity of the amount of the mixture that he had was ? (A) 15 litres . (B) 20 litres . (C) 25 litres . (D) 30 litres . 43. The height of a triangle is increased by 40%. What can be the maximum percentage increase in length of the base so that the increase in area is restricted to a maximum of 60% ? (A) 50% . (B) 20% . (C) 14.28% . (D) 25% . 44. A watch dealer pays 10% custom duty on a watch that costs Rs. 250 abroad. For how much should he mark it, if he desires to make a profit of 20% after giving a discount of 25% to the buyer? (A) Rs. 400 . (B) Rs. 440 . (C) Rs. 275 . (D) Rs. 330 . 45. In the adjoining figure, AOBCA represents a quadrant of a circle of radius 3.5 cm with centre O. B . Calculate the area of the shaded portion. (A) 35 cm 2 . (B) 7.875 cm 2 . (C) 9.625 cm 2 . (D) 6.125 cm 2. C . 2 cm A . 3 rd IMO | LevelI | Class 11 . D . 6 . 3.5 cm . O .

(21) 3rd IMO - 2009. 46. A circle with radius 2 cm is placed against a right angle. Another small circle is placed in the gap between the circle and the right angle. What is the radius of the smaller circle ? (A). 3 - 2 2 . (B). (C) 7 - 4 2 . 4 - 2 2 . (D). 6 - 4 2 . 47. A tank can be filled by one tap in 20 mins and by another in 25 mins. Both the taps are kept open for 5 mins and then the second is turned off. In how many minutes more is the tank completely filled? 1 (A) 17 min. 2 . (B) 12 min. . (C) 11 min. . (D) 6 min. . 48. Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water, is ____ (A) 1 : 2 . (B) 2 : 3 . (C) 3 : 2 . (D) 19 : 135 . 49. A dog after travelling 50 km meets a swami who counsels him to go slower. He then proceeds at 3/4 of his former speed and arrives at his destination 35 minutes late. Had the meeting occurred 24 km further the dog would have reached its destination 25 minutes late. The speed of the dog is (A) 48 km/hr . (B) 36 km/hr . (C) 54 km/hr . (D) 58 km/hr . 50. Aditya and Rehaan invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and Aditya's share is Rs. 855, total profit is _____ (A) Rs. 1576 . (B) Rs. 1582 . (C) Rs. 1500 . (D) Rs. 1595 . SPACE FOR ROUGH WORK. 7 . 3 rd IMO | LevelI | Class 11 .

(22) 4th. Year 2010.

(23) 4th IMO - 2010. SECTION I : LOGICAL REASONING 1. . 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 . 2. . 4. . (C) 248 . (D) 251 . Which one of the following four logical diagrams represents correctly the relationship between "Sea, Island, Mountain". (A) . 3. . (B) 216 . (B) . (C) . (D) . 1 1 2 2 Which fraction comes next in the given sequence 11 , 12 , 14 , 16 ,..... ? 9 2 7 3 1 1 (B) 9 (C) 10 (D) 20 (A) 8 3 11 . The digits of each of the following five numbers are written in reverse order and five new numbers are obtained. Which of the following will be the third digit of the second highest new number ? 513, 726, 492, 865, 149 (A) 1 . 5. . (D) 8 . (B) 875 . (C) 876 . (D) 886 . Which of the letter series follows the given rule. Rule : The group of letters should not contain more than two vowels. (A) BDEJOLY . 7. . (C) 7 . If 123 stands for 987, then 234 stands for (A) 768 . 6. . (B) 5 . (B) JKAPIXU . (C) PRAQEOS . (D) ZILERAM . The given characters follows a certain rule, find the missing character. ? . 406 5 . 3 . 81 16 . (A) 1 8. . (B) 731 . (D) 2031 . In three out of the given four pairs of figures, Fig. I is related to Fig. II in the same particular manner. Spot out the pair in which this relationsh ip does not exist between figures I and II. . I . II . P. (A) P 9. . (C) 1625 . I . I . II . Q. II . R. (B) Q . I . II . S . (C) R . Find the number of triangles in the given figure. (A) 15 . (B) 19 . (C) 17 . (D) None of these. 4 th IMO | LevelI | Class 11 . 2 . (D) S .

(24) 4th IMO - 2010. 10. Study the figure given below carefully and answer the following question. 5 1 3 . 4 . 6 . 3 2 . 7 8 9 . 4 . 1 . What is the sum of the numbers which belong to two figures only? (A) 6 . (B) 15 . (C) 20 . (D) None of these . 11. Find the next term in the given series : AC, FH, KM, PR ? (A) UW . (B) VW . (C) UX . (D) TV . 12. In the following alternatives, find out which one is the rearrangement of the parts of the given figure (X). . Fig. (X) . (A) . (B) . (C) . (D) . 13. The following question is based on the following alphabetseries : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Which letter is exactly midway between G and Q in the given alphabet series ? (A) K . (B) L . (C) M . (D) N . 14. Akshat goes North, turn right, then right again and then goes left. In which direction is he now? (A) North . (B) South . (C) East . (D) West . 15. How many times will you write even numerals if you write all the numbers from 291 to 300? (A) 11 . (B) 13 . (C) 15 . (D) 17 . 16. Select from the given alternatives which satisfy the same conditions of placement of the dot as in figure (X). . Fig. (X) . (A) . (B) . (C) . (D) . 17. Find the missing character from among the given alternatives. 4 7 5 1 64 3 11 27 ? 8 8 2 . (A) 0 . (B) 8 . (C) 125 3 . (D) 216 4 th IMO | LevelI | Class 11 .

(25) 4th IMO - 2010. 18. Select a figure from amongst the four alternatives, which when placed in the blank space of Fig. (X) would complete the pattern. . ? Fig. (X) . (A) . (B) . (C) . (D) . 19. The given question consists of four problem figures marked X, Y, Z and W. Select a figure from the options which will continue the series. Problem Figures . ? X. (A) . Y. Z. W . (B) . (C) . (D) . 20. Select a figure from amongst the four alternatives, which when placed in the blank space of Fig. (X) would complete the pattern. . ? . Fig. (X) . (A) . (B) . (C) . (D) . SECTION II : MATHEMATICAL REASONING 21. If A = {1, 2, 3}, B = {3, 8}, then (A ÈB) ´ (A ÇB) is equal to ____. (A) {(3, 1), (3, 2), (3, 3), (3, 8)} . (B) {(1, 3), (2, 3), (3, 3), (8, 3)} . (C) {(1, 2), (2, 2), (3, 3), (8, 8)} . (D) {(8, 3), (8, 2), (8, 1), (8, 8)} . 22. If tan A =. a 1 and tan B = , then the value of A + B is ____ . a + 1 2a + 1 . (A) 90° . (B) 45° . (C) 135° . (D) None of these . 23. A card is accidently dropped from a pack of 52 playing cards. The probability that it is an ace is_____. (A) . 1 4 . (B) . 1 13 . (C) . 1 52 . (D) . 12 13 . 24. In an experiment with 15 observations, it was found that å x i2 = 2830, å x i = 170. One observation 20 was found to be wrong and was replaced by 30. The correct variance of the data is _____. (A) 80.33 4 th IMO | LevelI | Class 11 . (B) 78.00 . (C) 60.22 4 . (D) None of these.

(26) 4th IMO - 2010. ì 8p 8 p ö ü æ + i ç 1 + cos ÷ ý is equal to 25. Amp í sin è 5 5 ø þ î. (A) . 3 p 5. (B) . 7 p 10. (C) . 4 p 5. 3 p 10. (D) . 26. If a, b, c are in G.P., then the line a 2 x + b 2 y + ac = 0 will always pass through the fixed point ___. (A) (0, 1) . (B) (1, 0) . (C) (0, –1) . (D) (1, –1) . 27. The smallest positive integer 'n' for which 2 n (1 × 2 × 3 × .... × n) < n n holds is _____ . (A) 5 . (B) 3 . (C) 4 . (D) 6 . 10 . æ x 3 ö 28. The coefficient of x in ç - 2 ÷ è 2 x ø 4 . (A) . 405 256 . (B) . is equal to _____. . 504 259 . (C) . 450 263 . (D) None of these . 29. For any complex number z, which of the following is true? (A) Re( z ) =. z + z 2 . (B) Im( z ) =. z - z 2 i . (C) | z | 2 = z z. (D) All of these . (C) – 4 . (D) 3.5 . 30. The value of 6 + 6 + 6 + .... is _____. (A) 4 . (B) 3 . 31. The sum of the squares of the perpendiculars on any tangent to the ellipse points on the minor axis, each at a distance a 2 - b 2 (A) 2a 2 . (B) 2b 2 . x2 2. a from the centre is ___. . (C) a 2 + b 2 . +. y 2 b2 . = 1 from two . (D) a 2 – b 2 . 32. If cos (a + b) = 0, then sin (5a + 6b) is equal to ____. (A) sin a. (B) –cos b. (C) cos b. (D) cos a. 33. If f (x) = x 2 – 3x + 1 and f (2a) = 2f (a) then a is equal to _____. (A) . 1 2 . (B) -. 1 . (C) . 2. 1 2. or -. 1 2. (D) None of these . 34. If the area of the triangle formed by the points (x, 2x), (–2, 6) and (3, 1) is 5 square units, then x = (A) . 2 3 . (B) . 3 5 . (C) 3 . (D) 5 . 35. If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is _____. (A) . ab 2(b - a ) . (B) . ab b-a. (C) . 3 ab 2(b - a ) . (D) None of these . 1 1 1 , P ( A Ç B ) = , and P ( A) = , where A stands for 6 4 4 complement of event A. Then events A and B are (A) Independent but not equally likely (B) Mutually exclusive and not independent (C) Equally likely and mutually exclusive (D) Equally likely but not independent.. 36. Let A and B be two events such that P ( A È B ) =. 5 . 4 th IMO | LevelI | Class 11 .

(27) 4th IMO - 2010. 37. If S n denotes the sum of first n terms of an A.P. whose common difference is d, then S n – 2S n – 1 + S n – 2 (n > 2) is equal to ____. (A) 2d . (B) d . (C) –d . (D) None of these . 38. If x = a secq and y = b tanq, then b 2 x 2 – a 2 y 2 = _____. (B) a 2 – b 2 . (A) ab 39. Domain of the function . æ 2 ö (A) ç - , ¥ ÷ è 3 ø. (C) a 2 + b 2 . (D) a 2 b 2 . ì 2 ü (C) R - í - ý î 3 þ. (D) None of these . 1 is 3 x + 2 . é 2 ö (B) ê - , ¥÷ø ë 3. 40. A convex polygon has 65 diagonals. The number of its sides is equal to _____. (A) 13 . (B) 10 . (C) 22 . (D) 11 . SECTION III : EVERYDAY MATHEMATICS 41. A rectangular carpet has an area of 60 sq. m. Its diagonal and longer side together equal 5 times the shorter side. The length of the carpet is ____. (A) 5 m . (B) 12 m . (C) 13 m . (D) 14.5 m . 42. A town has total population 25,000, out of which 13,000 read 'The Hindustan Times' and 10,500 read 'The Indian Express' and 2,500 read both papers. The percentage of population who read neither of these newspapers is _____. (A) 10% . (B) 16% . (C) 27% . (D) 30% . 43. A lady was asked her age by her friend. The lady said, "the number you get when you subtract 25 times my age from twice the square of my age will be thrice your age". If the friend's age is 14, then the age of the lady is _____ . (A) 21 years . (B) 28 years . (C) 14 years . (D) 25 years . 44. There are two bags each of which contains n balls. A man has to select an equal number of balls from both the bags. The number of ways in which a man can choose at least one ball from each bag is (A) . 2n . C n . (B) ( n C n ) 2 . (C) . 2n . C 1 . (D) . 2n . C n – 1 . 45. The minute hand of a wall clock is of length 10.5 cm. The area covered by it in 1 hour is ____. (A) 346.5 cm 2 . (B) 348.5 cm 2 . (C) 300.5 cm 2 . (D) 350 cm 2 . 46. A man standing on a horizontal plane, observes the angle of elevation of the top of a tower to be a. After walking a distance equal to double the height of the tower, the angle of elevation becomes 2a, then a is _____ . (A) . p 18. 4 th IMO | LevelI | Class 11 . (B) . p 12. (C) . 6 . p 6. (D) . p 2.

(28) 4th IMO - 2010. 47. Astha and Soumya each have certain number of oranges. Astha says to Soumya, "If you give me 10 of your oranges, I will have twice the number of oranges left with you. "Soumya replies, "If you give me 10 of your oranges, I will have the same number of oranges as left with you." Find the number of oranges with Astha and Soumya respectively. (A) 60, 40 . (B) 70, 50 . (C) 60, 80 . (D) 70, 90 . 48. Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all the five balls. In how many ways can we place the balls so that no box remains empty? (A) 5 C 3 . (B) 5! . (C) 150 . (D) 5 3 . 49. A jogging park has two identical circular tracks touching each other and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track, A jogs along the rectangular track while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point? (A) 3.88% . (B) 4.22% . (C) 4.44% . (D) 4.72% . 50. If the sum of the radius and the height of a closed cylinder is 35 cm and the total surface area of the cylinder is 1540 cm 2 , then the circumference of the base of the cylinder is ____ . (A) 66 cm . (B) 44 cm . (C) 56 cm . (D) Can't be determined. SPACE FOR ROUGH WORK . 7 . 4 th IMO | LevelI | Class 11 .

(29) 5th. Year 2011.

(30) 2. 5th IMO - 2011. Section I : Logical Reasoning 1.. Which of the following meanings of the arithmetical signs will yield the value 'zero' for the expression given below ?. 50 + 150 ÷ (0.2) + 20 × 100 – 10 = 10 (A) + means –, – means ×, × means ÷, ÷ means + (B) + means –, – means ÷, × means +, ÷ means × (C) + means ×, – means –, × means ÷, ÷ means + (D) + means ÷, – means +, × means –, ÷ means ×. 2.. If first 6 letters of the English alphabet are written in reverse order then next 6 letters are written in reverse order and so on but the last two letters Y and Z are interchanged, then which will be. the 4th letter to the left of the letter which is 13th from the right? (A) J (B) H (C) I. (D) O. 3. Two positions of a dice are given. How many dots are contained on the face opposite to the face. containing four dots ? (A) 2 (C) 5 . 4.. In the given number series, two terms have been put within brackets.. (B) 3 (D) 6. 4, 6, 10, (12), 16, (14), 22 Which of the following statements is CORRECT ? (A) Both the bracketed terms are right. (B) The first bracketed term is right and second is wrong. (C) The first bracketed term is wrong and second is right. (D) Both the bracketed terms are wrong.. 5. At a dinner party every two guests used a bowl of rice between them, every three guests used a bowl of dal between them and every four guests used a bowl of meat between them. There were. altogether 65 dishes. How many guests were present at the party ? (A) 60 (B) 65 (C) 90. 6.. Select a figure from amongst the options which will continue the same series as established by. (D) None of these. the five Problem Figures.. (A). 7.. If WORK is coded as 4 – 12 – 9 – 16, then how will you code WOMAN? (A) 4 – 12 – 14 – 26 – 13 (B) 4 – 26 – 14 – 13 – 12 (C) 23 – 12 – 26 – 14 – 13 (D) 23 – 15 – 13 – 1 – 14. 8.. Select a suitable figure from the options which will substitute this question mark so that a series. (B). (C). (D). is formed by the Problem Figures taken in order. . (A). (B). (C). (D).

(31) 3. 5th IMO - 2011. 9.. A set of figures carrying certain characters is given. Assuming that the characters. in each set follow a similar pattern, find the missing character. (A) 232 (B) 268 (C) 298 (D) 350. 466 341 250. 398 282 ?. 10. If it is possible to form a number which is perfect square of a two-digit odd number using the second, the fourth and the seventh digits of the number 739142658 using each only once, which. of the following is the second digit of that two-digit odd number? (A) 3 (B) 4 (C) 5. (D) None of these. 11. Choose the correct water-image of the Fig. (X) from amongst the options.. (A). (C). (B). (D). 12. Select a figure from the options which satisfies the same conditions of placement of the dots as in fig. (X).. (A). (B). (C). (D). 13. Find out which of the options completes the figure matrix .. (A). . (B). . (C). . (D). 14. In the given arrangement, how many such consonants are there each of which is immediately preceded by a symbol and immediately followed by a digit ?. (A) 1. E G 4 B H 7 5 @ K 8 D N & Q Z $ W 3 C 1 9 * L B 2 S 6 (B) 2 (C) 0 (D) 3. 15. How many pairs of letters are there in the word 'DEFORM' which have as many letters between. them in the word as in the English alphabet ? (A) 1 (B) 2. (C) 3. (D) 4.

No results found