Copyright © 2014 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.
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
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
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
MTG Work-Books / olympiad books CLASS 9
International Mathematics Olympiad
National Science Olympiad
Math IQ Challenge
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
International English Olympiad
NTSE Explorer
Master Mental Ability in 30 Days
Mat for NTSE
International English Olympiad
NTSE Explorer
Master Mental Ability in 30 Days
Mat for NTSE
CLASS 10
International Mathematics Olympiad
National Science Olympiad
Math IQ Challenge
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
Class
1 to 10
JEE Main & Advanced | AIPMT | BOARDS | OLYMPIAD | NTSE
FOUNDATION COURSE For Classes 8, 9 & 10 Class 8
Class 9
Class 10
4th
LEVEL - 2 Year 2010-11
SECTION I : LOGICAL REASONING 1.
If in a certain code, 'O' is written as 'E', 'A' as 'C', 'M' as 'I', 'S' as 'O', 'N' as 'P', 'E' as 'M', 'I' as 'A', 'P' as 'N' and 'C' as 'S', then how will 'COMPANIES' be written in that code ? (A) SEIACPAMO
2.
(B) SMINCPAMO
(C) SEINCPAMO
(D) SEINCPMIO
Find the missing number amongst the options at the place of sign of interrogation(?).
2 6
(A) 20 (B) 23
4
33 15
(C) 25
5 9
45 ?
7 5
3
(D) 28 3.
Select a figure amongst the four alternatives, which when placed in the blank space figure (X) would complete the pattern. (A)
(B)
(C)
(D)
? Figure (X)
4.
B is to the SouthWest of A, C is to the East of B and SouthEast of A and D is to the North of C in line with B and A. In which direction of A is D located ? (A) North
5.
(B) East
(C) SouthEast
(D) NorthEast
In the given question, there is a set of five figures labelled P, Q, R, S and T called the Problem Set. Select a suitable figure from the options which will substitute this question mark so that a series is formed by the figures P, Q, R, S and T taken in order. Problem Set
? P
(A) 6.
R
(B)
S
T
(C)
(D)
If '¸' means '–', '–' means '´', '´' means '+' and '+' means '¸' then 20 ´ 60 ¸ 40 – 20 + 10 = (A) 40
7.
Q
(B) 0
(C) 80
(D) 60
The minimum number of straight lines required to form the given figure is ____. (A) 13 (B) 15 (C) 12 (D) 11
8.
If 'W' means white, 'Y' means yellow, 'B' means black, 'G' means green, 'R' means red, which of the following will come next in the sequence given below ? W, W Y, W Y B, W Y B G, W Y B G R, W, W Y, W Y B, W Y B ___ ?__ . (A) Red
4 th IMO | LevelII | Class 10
(B) White
(C) Green 2
(D) Yellow
9.
The six faces of a cube have been marked with numbers 1, 2, 3, 4, 5 and 6 respectively. This cube is rolled down three times. The three positions are given in the figure below. Choose the figure that will be formed when the cube is unfolded. 1
6 2
4
2
5 3
6
3
2
5
6
1
3 4
3 6
2 4
2 3
(A)
1
(B)
6 5
(C)
1
(D)
1
2 4
6
3 5
5 4
10. Letters of the words given below have been of jumbled up. Each letter has been numbered and each word is followed by four options. Choose the option which gives the correct order of the letters as indicated by the numbers to form words. A M D E N R 1 2 3 4 5 6 (A) 1, 6, 2, 4, 3, 5
(B) 2, 1, 5, 3, 4, 6
(C) 3, 4, 5, 2, 1, 6
(D) 6, 4, 2, 1, 5, 3
11. There are seven figures, the first and last of which are unnumbered and the remaining are numbered as 1, 2, 3, 4 and 5. These seven figures form a series. However, one of the five numbered figures does not fit into the series. Choose the correct option.
1
(A) 1
2
3
(B) 2
4
5
(C) 3
(D) 4
12. In a certain code 'STREAM' is written as 'QSRNBF' and 'SUPERB' is written as 'OTRCSF'. How is 'BORING' written in that code ? (A) QNAHOJ
(B) CPSJOH
(C) QNAOJH
(D) ANQJOH
13. The given question consists of four figures marked (i), (ii), (iii) and (iv) called the Problem figures. Select a figure from the options which will continue the same series as established by the four problem figures. Problem Figures
(A)
(B)
(C)
(D)
? (i)
(ii)
(iv)
(iii)
14. Introducing a man, Neeraj said, "His wife is the only daughter of my wife." How is Neeraj related to that man ? (A) Father
(B) Grandfather
(C) Fatherinlaw
(D) Son
15. A matrix of certain characters is given. These characters follow a certain trend row wise or column wise. Find the missing number. (A) 13
11
(B) 15
17 12 ?
(C) 16
25 34 19
(D) 9
19 28 11
3
6
8
4 th IMO | LevelII | Class 10
16. Choose the option which shows common feature in the relationship given. Slap : Hit : Kick (A) Each has no vowel
(B) They are the ways of striking a person
(C) They are exercises
(D) The terms are used in wrestling
17. In a school, the following codes were used during physical exercise period. '1' means "start walking", '2' means "keep standing", '3' means "start running at the same stop", '4' means "sit down". How many times will a student who performs the following sequence without error from the beginning to the end has to start walking ? 1 2 3 4 2 3 2 4 4 3 2 2 1 2 4 3 1 4 4 1 2 3 1 1 4 (A) 6
(B) 7
(C) 4
(D) 5
DIRECTION (1820) : The above building plan shows an office block for six officers A, B, C, D, E and F. Both B and C occupy offices to the right of the corridor (as one enters the office block) and A occupies an office to the left of the corridor. E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F 's office is further down the corridor than A's, but on the same side. 18. If E sits in his office and faces the corridor, whose office is to his left ? (A) A
(B) B
(C) C
(D) D
(C) D
(D) E
(C) C only
(D) B and C
19. Whose office faces A's office ? (A) B
(B) C
20. Who is/are F's neighbour(s) ? (A) A only
(B) A and D
SECTION II : MATHEMATICAL REASONING 21. If a, b are the roots of the equation x 2 + x a + b = 0 , then values of a and b are _____ . (A) a = 1, b = 1
(B) a = 1, b = –2
(C) a = 2, b = 1
(D) a = 2, b = 2
22. If a square and rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is _____ . (A) Greater than 1
(B) Equal to 1
(C) Equal to
1 2
(D) Equal to
1 4 A
23. In the given figure, AD = 4 cm, BD = 3 cm and CB = 12 cm. Find cot q. (A) 12 (B) 4/3
D
(C) 4/5 C
(D) 12/5
B
24. The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the yaxis at ____ . (A) (0, 13) 4 th IMO | LevelII | Class 10
(B) (0, –13)
(C) (0, 12) 4
(D) (13, 0)
25. How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 metres in length ? (A) 9.8 secs
(B) 12.1 secs
(C) 12.42 secs
(D) 14.3 secs
26. Calculate the area of the designed region in figure common between the two quadrants of circles of radius 8 cm each. 8 cm 90°
8 cm
8 cm
90° 8 cm
(A) 32 cm 2
(B)
256 2 cm 7
(C) 182 cm 2
(D)
352 2 cm 7
27. The value of 0.0396 ¸ 2.51 correct to 2 significant figures is ____ . (A) 0.015
(B) 0.0157
(C) 0.016
(D) 0.017
28. A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower (approximately) ? (A) 14 mins 35 secs
(B) 15 mins 49 secs
(C) 16 mins 26 secs
(D) 18 mins 5 secs
29. Find the diameter of a wheel that makes 113 revolutions to go 2 km 26 decametres. 4 (A) 4 metres 13
4 (B) 6 metres 11
4 (C) 12 metres 11
30. If r is the ratio of the roots of the equation ax 2 + bx + c = 0, then (A) 1
(B)
b 2 ac
(C)
ac b 2
8 (D) 12 metres 11
(r + 1) 2 = r
(D) b 2 – 4ac
31. In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors of 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been _____. (A) 24 32. If a = (A)
(B) 144 5 + 1 and b = 5 - 1
3 4
(C) 292
æ a2 + ab + b 2 ö 5 - 1 ÷ is ____ . , the value of çè 2 a - ab + b 2 ø 5 + 1 4 3 (B) (C) 3 5
(D) 584
(D)
5 3
33. Find the least multiple of 23, which when divided by 18, 21 and 24 leaves remainders 7, 10 and 13 respectively. (A) 3002
(B) 3013
34. Twothird of a positive number and (A)
5 12
(B)
(C) 3024
(D) 3036
25 of its reciprocal are equal. The number is ____. 216
12 5
(C) 5
25 144
(D)
144 25
4 th IMO | LevelII | Class 10
35. What is the unit digit in (A) 0
{(6374)1793 ´ (625)317 ´ (341)491 } ? (B) 2
(C) 3
(D) 5
36. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ? (A)
1 2
(B)
3 4
3 8
(C)
(D)
5 16
37. The value of (0.2 + 0.3 + 0.4 + 0.9 + 0.39) is (A) 0.57
20 (B) 1 33
1 (C) 2 3
13 (D) 2 33
38. A computer is available for ` 39, 000 cash or ` 17, 000 as cash down payment followed by 5 monthly installments of ` 4, 800 each. Bank also gives loan at the rate of 24% per annum to purchase the computer. Which option is better ? (A) Full cash payment
(B) Payment in Installments (C) Both are equal
(D) Can't be determined
39. It costs ` x each to make the first thousand copies of a compact disc and ` y to make each subsequent copy. If z is greater than 1000, how much will it cost to make z copies of the compact disc ? (A) zx – zy
(B) 1000x + yz
(C) 1000 (x – y) + yz
(D) 100 (z – y) + xz
40. In the given figure, ABCD is a rectangle in which line segments AP and AQ are drawn as shown. Find the length of (AP + AQ). Q
C
30° P 30° A
(A) 60 cm
60 cm
(B) 30 cm
30 cm
D
B
(C) 180 cm
(D) 120 cm
SECTION III : EVERYDAY MATHEMATICS 41. 200 logs are stacked in the following manner : 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows 200 logs are placed and how many logs are in the top row respectively ?
(A) 25, 4
(B) 18, 12
(C) 15, 3
(D) 16, 5
42. The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq. metres, its volume is _____ . (A) 3180 m 3
(B) 4620 m 3
(C) 5240 m 3
(D) 3250 m 3
43. Priyansh speaks truth in 75% cases and Mohit in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident ? (A) 5% 4 th IMO | LevelII | Class 10
(B) 15%
(C) 35% 6
(D) 45%
44. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was ` 4.20 and that of Y was ` 6.30, in which year commodity X will cost 40 paise more than the commodity Y ? (A) 2010
(B) 2011
(C) 2012
(D) 2013
45. Ankit, Armaan and Abhay start at the same time in the same direction to run around a circular stadium. Ankit completes a round in 252 seconds, Armaan in 308 seconds and Abhay 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
46. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is ____. (A) 400 kg
(B) 560 kg
(C) 600 kg
(D) 640 kg
47. A man at the top of a tower is watching a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 60 metres from tower. After 5 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water ? (A) 32 km/hr
(B) 36 km/hr
(C) 38 km/hr
(D) 40 km/hr
48. Water boils at 212°F or 100°C and melts at 32°F or 0°C. If the temperature of a particular day is 35°C, it is equivalent to _____. (A) 85°F
(B) 90°F
(C) 95°F
(D) 99°F
49. How many pieces of 85 cm length can be cut from a rod 42.5 metres long ? (A) 30
(B) 50
(C) 60
(D) 40
50. A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq. feet per day, then approximately what time will be taken by the cow to graze the whole field ? (A) 2 days
(B) 6 days
(C) 18 days
(D) 24 days
SPACE FOR ROUGH WORK
7
4 th IMO | LevelII | Class 10
5th
LEVEL - 2 Year 2011-12
2
| 5 th IMO | LevelII | Class 10
SECTION I : LOGICAL REASONING 1.
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
2.
(D) BDF
(B) 5 years
(C) 7 years
(D) 14 years
If second Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then how many working days are there in that month? (A) 25
4.
(C) BFC
Anita, Mahima, Rajan, Lata and Deepti are five cousins. Anita is twice as old as Mahima. Rajan is half the age of Mahima. Anita is half the age of Deepti and Rajan is twice the age of Lata. If Mahima is 16 years old, then what is the age of Lata ? (A) 4 years
3.
(B) ABD
(B) 22
(C) 24
(D) 23
If the same function is applied to reach the results in each of the three sets of numbers given then which number will replace the question mark in the third set of numbers? (A) 24 21 5 28 13 (B) 30 24 30 (C) 36 7 7 17 25 (D) 40
5.
16
2 ?
10
8
If the first and the second letters of the word UNPRECEDENTED are interchanged with the last and the second last letters and similarly the third and the fourth letters are interchanged with the third and the fourth letters from the last respectively and so on, then what will be the seventh letter to the right of the third letter from the left end ? (A) C
6.
(B) E
(C) P
(D) R
Ravi wants to go to the university. He starts from his home which is in the East and comes to a crossing. The road to the left ends in a theatre, and straight ahead is the hospital. In which direction is the university if all the four places are in different directions ? (A) North
7.
(B) South
(C) East
(D) West
Find out the wrong term in the number series. 105, 85, 60, 30, 0, – 45, – 90 (A) 105
8.
(C) 0
(D) – 45
Choose the numberletter group which is different from the others. (A) M5S
9.
(B) 60
(B) B9L
(C) T4Y
(D) F4J
Select a figure from amongst the options which will continue the series established by the five problem figures. Problem Figures
? (A)
(B)
(C)
(D)
3
5 th IMO | LevelII | Class 10 |
10. In the question, there are seven figures, the first and last of which are unmarked and the remaining are marked as P, Q, R, S and T. These seven figures form a series. However, one of the five marked figures does not fit into the series. Select that figure from the options.
P
(A) P
Q
R
(B) Q
S (C) R
T
(D) T
11. In the given figure, if the triangle represents girls, the circle represents athletes, the rectangle represents boys and the square represents disciplined, then the boys who are athletes and disciplined are indicated by which number ? (A) 1 (B) 2 (C) 6 (D) 10
10
7 6 9 5 3 2 4 1 8
12. Five boys took part in a race. Raj finished before Mohit but behind Gaurav. Ashish finished before Sanchit but behind Mohit. Who won the race? (A) Raj
(B) Gaurav
(C) Mohit
(D) Ashish
13. In a certain coding system, '816321' means 'the brown dog frightened the cat'; '64851' means 'the frightened cat ran away'; '7621' means 'the cat was brown'; '341' means 'the dog ran'. What is the code for 'the dog was frightened'? (A) 5438
(B) 8263
(C) 8731
(D) None of these
14. Choose that set of numbers from the options, that is similar to the given set : (9, 15, 21) (A) (10, 14, 16)
(B) (7, 21, 28)
(C) (5, 10, 25)
(D) (4, 8, 12)
15. Find the missing number? (A) 8C (B) 12B (C) 16C
3C 2B
4A
27A ?
64B
9B 4A 16C
(D) 18C 16. Find the odd one out. (A)
(B)
(C)
17. 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. Choose a figure from the options which would most closely resemble the unfolded form of fig. (Z). (A)
(B)
(C)
(D)
X
Y
(D)
Z
4
| 5 th IMO | LevelII | Class 10
18. Group the given figures into three classes using each figure only once. (A) 1, 2, 5; 3, 7, 8; 4, 6, 9 (B) 1, 7, 2; 3, 9, 6; 4, 5, 8
1
2
3
4
5
6
7
8
9
(C) 2, 3, 8; 4, 6, 9; 1, 5, 7 (D) 5, 6, 9; 3, 4, 1; 2, 7, 8 19. When the given figure is folded to form a cube, how many dots would lie opposite the face bearing five dots? (A) 1 (B) 2 (C) 3 (D) 4 20. Select a figure from the options which satisfies the same conditions of placement of the dots as in fig. (X).
Fig. (X)
(A)
(B)
(C)
(D)
SECTION II : MATHEMATICAL REASONING 21. A person invested some amount at the rate of 10% simple interest and some other amount at the rate of 12% simple interest. He received yearly interest of `130. But if he had interchanged the amounts invested, he would have received `4 more as interest. How much amount did he invest at different rates ? (A) ` 700 at 12%, ` 500 at 10% (C) ` 700 each at 10% and 12%
(B) ` 700 at 10%, ` 500 at 12% (D) ` 500 each at 10% and 12%
22. In D PQR, PD ^ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, then (a + b)(a – b) = _____. (A) 1 (B) (c + d)(d – c) (C) (c + d)(c – d) (D) 0 23. Two circles with radii a and b respectively touch each other externally. Let c be the radius of a circle that touches these two circles as well as a common tangent to these two circles. Then ___. (A)
1 1 1 = a b c
(B)
1 1 1 + + = 0 a b c
(C)
1 1 1 + = a b c
(D) None of these
24. DABC is right angled at A. DEFG is a square inscribed in triangle as side DE is on BC and G & F are two points at AB and AC respectively. Then DE 2 = (A) BD ´ EC (C) BD =
1 EC 2
A
(B) BD = 2EC (D) None of these
B
C
5
5 th IMO | LevelII | Class 10 |
25. If from twice the greater of two positive numbers 16 is subtracted, the result is half the other number. If from half the greater number 1 is subtracted, the result is still half the other number. What are the numbers ? (A) 16, 8
(B) 12, 10
(C) 6, 8
(D) 10, 8
æ a 2a ö 26. If P and Q are two points whose coordinates are (at 2 , 2at) and çè 2 , t ÷ø respectively and S is the point t 1 1 + (a, 0), then is _____. SP SQ
(A) Dependent of t
(B) Independent of t
(C) Independent of a
27. If T 1 , T 2 , T 3, ......., T n are consecutive terms of an A.P., then n - 1 (A) T × T 1 n
(B)
n T1 × Tn
(C)
(D) None of these
1 1 1 + + ...... + = ____. T1T2 T2T3 Tn -1 T n
T2 ( n - 1) T1 × Tn
(D) None of these
28. In the given figure, the diameters of two wheels have measures 2 cm and 4 cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angle. B
(A) 4 cm each
A
(B) 3 cm each O
(C) 5 cm each
P C
O¢ D
(D) 6 cm each 29. In the given figure, three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the approximate value of R.
A
(A) 5.4 cm (B) 5.0 cm
B
C
(C) 4.0 cm (D) 4.3 cm 30. A number is selected at random from the numbers : 5, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 24, 25, 25, 27, 30, 30, 36, 37, 37, 39, 40, 40, 46. Find the probability that the selected number is their average. (A) 0
(B) 1
(C)
1 6
(D)
1 12
31. A cone is cut into two parts by a horizontal plane passing through the midpoint of its axis. The ratio of the volume of the upper part to the volume of lower part is ____. (A) 1 : 7
(B) 1 : 8
(C) 7 : 1
(D) 7 : 8
32. The ratio of the areas of the right angled triangles ABC and DEF in which ÐA = 30°, ÐB = 90°, AC = 4 cm, ÐD = 60°, ÐE = 90° and DE = 4 cm is ___. (A) 1 : 2
(B) 4 : 1
(C) 1 : 4
(D) 2 : 1
33. If (x + a) is a factor of the polynomial x 2 + px + q and x 2 + mx + n, then a = ___. (A)
n - q m - p
(B)
m - q n - p
(C)
n - p m - q
(D) None of these
6
| 5 th IMO | LevelII | Class 10
34. If A is the area of a rightangled triangle and b is one of the sides containing the right angle, then the length of altitude on the hypotenuse is ____. 2 Ab
(A)
4
2 A 2
2 A 2
b + 4 A
(B)
4
2
b + 4 A
(C)
4
2 b 2
b + 4 A
(D)
4
b + 4 A 2
35. Find the interrelationship of the variables for the quadratic equation y = ax 2 + bx + c from given graph. y (A) a + b + c = 0 (B) a – b + c = 0 –x ¢ x (–1, 0) (2, 0) (C) 2a + b + c = 0 y¢ (D) 4a – 2b + c = 0 36. The houses of a row are numbered consecutively from 1 to 49. If there is a x such that the sum of the numbers of the house preceding the house numbered x is equal to the sum of the numbers of the house following it. Find the value of x. (A) 35
(B) 34
37. If sin q + cos q = a and (A) b =
2 a 2
a - 1
(C) 30
(D) 33
(C) ab = b 2 – 1
(D) a + b = 1
sin q + cos q = b, then ____. sin q cos q
(B) a =
2 b 2
b - 1
38. In the given figure, PT is a tangent to the circle at T. If PA = 4cm and AB = 5 cm, find PT. B
(A) 7 cm (B) 6 cm (C) 8 cm
A P
(D) 2 cm
T
3 cm. A string of width h cm, when wound around p the cylinder without keeping any space between two turns, covers the lateral surface of the cylinder completely. What is the required length of the string ?
39. Consider a cylinder of height n cm and radius
(A)
6 n cm h
(B)
12 h cm n
(C)
36 n cm h
(D) None of these
40. If a and b are roots of the equation A(x 2 + m 2 ) + Amx + cm 2 x 2 = 0, then A(a 2 + b 2 ) + Aab + ca 2b 2 = ____. (A) 0
(B) 1
(C) –1
(D) None of these
SECTION III : EVERYDAY MATHEMATICS 41. Piyush gave onefourth of the amount he had to Mahesh. Mahesh in turn gave half of what he received from Piyush to Suraj. If the difference between the remaining amount with Piyush and the amount received by Suraj is ` 500, how much money did Mahesh receive from Piyush ? (A) ` 100
(B) ` 200
(C) ` 400
(D) Data inadequate
42. 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age difference of 2 years), the present average age of the family is the same. The present age of the youngest child is ____. (A) 1 years
(B) 2 years
(C) 3 years
(D) 5 years
7
5 th IMO | LevelII | Class 10 |
43. A, B and C start cycling around a circular path in the same direction at same time. Circumference of the path is 1980 m. If the speed of A is 330 m/min, speed of B is 198 m/min and C is 220 m/min and they start from the same point, then after what time interval will they be together at the starting point? (A) 30 mins
(B) 9 mins
(C) 90 mins
(D) 60 mins
44. A part of the monthly expenses of a family is constant and the remaining varies with the price of wheat. When the price of wheat is ` 250 per quintal, the total monthly expenses are ` 1000 and when it is ` 240 per quintal, the total monthly expenses are ` 980. Find the total monthly expenses of the family when the cost of wheat is ` 350 per quintal. (A) ` 1100
(B) ` 1200
(C) ` 1300
(D) ` 1500
45. In the Maths Olympiad at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes : (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) The other committed an error in the coefficient of x and he got the roots as 12 and 4. In the meantime, they realised that they were wrong and together they managed to get it right. Find the quadratic equation. (A) x 2 + 4x + 14 = 0
(B) 2x 2 + 7x – 24 = 0
(C) x 2 – 14x + 48 = 0
(D) 3x 2 – 17x + 52 = 0
46. Hari wishes to determine the distance between two objects A and B, but there is an obstacle between these two objects which prevents him from making a direct measurement. He devises an clever way to overcome this difficulty. First he fixes a pole at a convenient point O so that from O, both A and B are
A
B
visible. Then he fixes another pole at the point D on the line AO (produced) such that AO = DO. In a similar way he fixes a third pole at the point C on the line BO (produced) such that BO = CO. Then he measures CD which is equal to 170 cm.
O
The distance between the objects A and B is ____. (A) 170 cm
(B) 340 cm
(C) 85 cm
(D) None of these
C
D
47. A, B, C are three points on the same horizontal line and CT is a vertical pole. The angle of elevation of T, as seen from A, is x° and the angle of elevation of T, as seen from B is y°(y° > x°). If AB = d, then the height of the pole is ____. (A)
d cos x ° cos y ° sin( y ° - x °)
(B)
d tan x° tan y ° tan y ° - tan x °
(C)
d cos x ° cos y ° cos( y ° - x °)
(D)
d sin x° sin y ° cos( y ° - x °)
48. A bucket is 40 cm in diameter at the top, 28 cm in diameter at the bottom and 21 cm deep. The cost of tin sheet used in making the bucket, if the cost of tin is ` 1.50 per sq. dm is ____. (A) ` 32.25
(B) ` 40.25
(C) ` 44.25
(D) None of these
49. There are 100 transistors in a box. 20 of them are defective. At random two transistors are taken one by one consecutively without replacement. What is the probability that both of them are good ? (A)
316 495
(B)
19 495
(C)
16 99
(D)
32 99
8
| 5 th IMO | LevelII | Class 10
50. A boy is standing on the ground and flying a kite with 100 m length of string at an elevation of 30°. Another boy is standing on the roof of a 10 m high building and is flying his kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet. (A) 50 3 m
(B) 40 2 m
(C) 50 m
SPACE FOR ROUGH WORK
(D) 100 m
6th
LEVEL - 2 Year 2012-13
| 6th IMO | Level-II | Class 10
2
Section-I : Logical Reasoning 1.
Study the following information carefully to answer the given question.
M K K I D N E T T Q O B F H AA G T U U X W L S R I
Each of these letters gets a numerical value based on its position in the above arrangement, such as, 1 for M, 2 for K, 4 for I and so on.
Value of A is exactly equal to the total value of which of the following pairs ?
(i) DO (A) Only (i)
2.
Seven villages A, B, C, D, E, F and G are situated as follows:
(ii) QE (B) Only (ii)
(iii) MH (C) Only (iii)
(D) Both (i) and (ii)
E is 2 km to the west of B. F is 2 km to the north of A. C is 1 km to the west of A. D is 2 km to the south of G. G is 2 km to the east of C. D is exactly in the middle of B and E.
How far is E from F (in km)?
(A) 4
(B)
20
(C) 5
(D)
26
3. In the given diagram, the circle stands for educated, square for hard-working, triangle for urban and the rectangle for honest people. Different regions in the diagram are numbered from 1 to 12.
Region 4 is best described as consisting of ______.
(A) People who are non-urban, honest, uneducated and hard-working.
(B) People who are uneducated, urban, honest and hard-working.
(C) People who are uneducated, urban, hard-working and dishonest.
(D) People who are urban, hard-working, honest and educated.
4.
Read the following information carefully to answer the given question.
Fifty books belonging to different subjects, viz. History (8), Geography (7), Literature (13), Psychology (8) and Science (14), are placed on a shelf. They are arranged in an alphabetical order subject to the condition that no two books of the same subject are placed together so long as books of other subjects are available. Unless otherwise mentioned, all counting is done from the left.
Counting from the right end, the fifth book from the right of 39th book is ______. (A) History (B) Psychology (C) Geography (D) Science
5. If the word TERMINATION is coded as 12345671586, what should be the code for the word
MOTION ? (A) 438586
6.
Read the following information carefully and answer the question given below it . (i) A, B, C, D and E are five friends. (ii) B is elder to E, but not as tall as C. (iii) C is younger to A, and is taller to D and E. (iv) A is taller to D, but younger than E. (v) D is elder to A but is shortest in the group. Which of the following statements is correct about B ? (i) B is not the tallest. (ii) B is shorter to E. (iii) When they are asked to stand in ascending order with respect to their heights, B is in the
middle. (A) Only (i)
(B) 458586
(B) Only (i) and (ii)
(C) 481586
(C) (i), (ii) and (iii)
(D) 485186
(D) All are incorrect
6th IMO | Level-II | Class 10 |
3 7.
Pointing to a photograph, a person tells his friend, "She is the grand daughter of the elder brother
of my father." How is the girl in the photograph related to this man ? (A) Niece (B) Sister (C) Aunt
8.
Study the following information and answer the question given below it .
(D) Sister-in-law
The admission ticket for an exhibition bears a password which is changed after every clock hour based on set of words chosen for each day. The following is an illustration of the code and steps of rearrangement for subsequent clock hours. The time is 9 a.m. to 3 p.m.
Batch I (9 a.m. to 10 a.m.)
: is not ready cloth simple harmony burning
Batch II (10 a.m. to 11 a.m.)
: ready not is cloth burning harmony simple
Batch III (11 a.m. to 12 noon) : cloth is not ready simple harmony burning
Batch IV (12 noon to 1 p.m.) : not is cloth ready burning harmony simple
Batch V (1 p.m. to 2 p.m.)
: ready cloth is not simple harmony burning
Batch VI (2 p.m. to 3 p.m.)
: is cloth ready not burning harmony simple
If the password for Batch I was – 'rate go long top we let have', which batch will have the 9.
password–'go rate top long have let we' ? (A) II (B) III
(C) IV
(D) V
N ranks fifth in a class. S is eighth from the last. If T is sixth after N and just in the middle of N and S, then how many students are there in the class? (A) 23 (B) 24 (C) 25 (D) 26
10. Which one of the four interchanges in signs and numbers would make the given equation correct ? 4 × 6 – 2 = 14 (A) × to ÷, 2 and 4 (B) – to ÷ , 2 and 6 (C) – to +, 2 and 6 (D) × to +, 4 and 6 11. A total of 324 coins of 20 paise and 25 paise make a sum of ` 71. The number of 25 paise coins is _______. (A) 120 (B) 124 (C) 144 (D) 200 12. Select a figure from amongst the options which will continue the same series as established by the five Problem Figures.
(A)
(B)
(C)
(D)
13. In the given question, there are seven figures, the first and last of which are unnumbered and the remaining are numbered as 1, 2, 3, 4 and 5. These seven figures form a series. However, one of the five numbered figures does not fit into the series. The number of that figure is the answer.
(A) 1
S L P M E UH U EE S HS L S U 1 2 (B) 2
U E NN P 3 (C)
E Y J U SB S EU E B Y U S 4 5 4
(D) 5
| 6th IMO | Level-II | Class 10
4
14. There is a set of five figures labelled P, Q, R, S and T called the Problem figures. Fig. (R) contains a question mark. Select a suitable figure from the options which will substitute this question mark so that a series is formed by the figures P, Q, R, S and T taken in order.
(A)
(B)
(C)
(D)
15. There is a definite relationship between figures P and R. Establish a similar relationship between figures Q and S by selecting a suitable figure from the options that would replace the question mark (?) in fig. (S).
(A)
(B)
(C)
(D)
16. Which term comes next in the given series?
(A) UW
(B) VW
AC, FH, KM, PR, ? (C) UX
(D) TV
17. Count the number of pentagons in the given figure.
(A) 16
(B) 12
(C) 8
(D) 4
18. Choose the correct mirror-image of the Fig. (X) from amongst the four options given along with it, if the mirror is placed along M1 M2.
(A)
(B)
(C)
(D)
19. A cube, painted yellow on all faces is cut into 27 small cubes of equal size. How many small cubes
are painted on one face only ? (A) 1 (B) 6
(C) 8
(D) 12
6th IMO | Level-II | Class 10 |
5 20. Find out which of the options will complete the figure matrix .
(A)
(B)
(C)
(D)
?
Section-II : Mathematical reasoning 1 7 +2 5 5 5 11 21. The value of is _______. ÷ −4 7 17 7 1 4 11 + 8− −1 10 22 5 3 8+ 2 7 11 (A) 8 (B) 0 (C) 16
(D) 1
22. If a x – 1 = bc, by – 1 = ca and cz – 1 = ab then xy + yz + zx = ______. (A) xyz (B) x2y2z2 (C) 2xyz
(D) 1/(xyz)
3
23. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs ` 216 and one full and one half reserved first class tickets cost ` 327. What is the cost of basic first class full
fare and the reservation charge? (A) ` 105 and ` 6 (B) ` 216 and ` 12
(C) ` 210 and ` 12
(D) ` 210 and ` 6
24. If p and q are the roots of the equation x2 – bx + c = 0, then what is the equation if the roots are (pq + p + q)
and (pq – p – q)? (A) x2 – 2cx + (c2 – b2) = 0 (C) 3cx2 – 2(b + cx + c2) = 0
(B) x2 – 2bx + (b2 + c2) = 0 (D) x2 + 2bx – (c2 – b2) = 0
25. Given intersecting chords, find x.
(A) 20°
(B) 40°
(C) 60°
(D) 80°
A
C Ex °
40
80°
O
B
D
26. If ABC is a right angled triangle with ∠A = 90° and 2s = a + b + c, where a > b > c and notations
have their usual meanings, then which one of the following is correct? (A) (s – b) (s – c) > s(s – a) (B) (s – a) (s – c) > s(s – b) (C) (s – a) (s – b) < s(s – c) (D) 4s(s – a) (s – b) (s – c) = bc
27. Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at
random from the basket. Which of the following is the probability that the fruit is an apple? (A) 0.32 (B) 0.4 (C) 0.46 (D) 0.58
| 6th IMO | Level-II | Class 10
6
28. A is three times as old as B. Four years ago, C was twice as old as A. In four years time, A will
be 31. What are the present ages of B and C respectively? (A) 9, 46 (B) 9, 50 (C) 10, 46
(D) 10, 50
29. If a, b and g are in A.P., then cotb = _______.
(A)
sin a − sin g cos g − cos a
(B)
sin g − sin a cos g − cos a
(C)
sin a − sin g 2(cos a − cos g )
(D)
2(sin g − sin a ) cos g − cos a
30. Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
(A) 60 mins 15 secs
(B) 50 mins 15 secs
(C) 51 mins 12 secs
(D) 49 mins 8 secs
31. Points A, B, C and D are midpoints of the sides of square JETS. If the area of JETS is 36 sq. cm, then the area of ABCD is ________.
J
A
B
D
(A) 3 sq. cm
(B) 7.5 sq. cm
S
E
C
T
(C) 9 sq. cm
(D) 18 sq. cm
32. The mean of 1, 3, 4, 5, 7 and 4 is m. The numbers 3, 2, 2, 4, 3, 3 and p have mean m – 1 and
median q, then p + q = ______. (A) 7 (B) 6
(C) 5
(D) 4
33. What approximate value should come in place of the question mark (?) in the following equation?
(A) 35
158.25 × 4.6 + 21% of 847 + ? = 950.935045 (B) 44 (C) 50
(D) 45
34. If the ratio of mean and median of a certain data is 2 : 3, then find the ratio of its mode and
mean. (A) 2 : 5
(B) 3 : 2
(C) 5 : 2
(D) 1 : 2
35. In the given diagram, ABCD is a square, diagonal BD is extended through D to E. AD = DE and AE is drawn. What is m∠DAE?
(A) 22.5°
(B) 45°
(C) 112.5°
(D) 135°
B
C
A
D E
36. What is the probability of getting at least one six in a single throw of three unbiased dice?
(A)
1 6
(B)
125 216
(C)
1 36
(D)
91 216
37. ABC is a right angled triangle, right angled at A. A circle is inscribed in it and the lengths of the
two sides containing the right angle are 12 cm and 16 cm. Find the area of the circle. (A) 25.56 sq. cm (B) 50.28 sq. cm (C) 75.65 sq. cm (D) 20.34 sq. cm
6th IMO | Level-II | Class 10 |
7
38. A person of height 2 m wants to get a fruit which is on the top of a pole of height 4 m 3
stands at distance of
10 m if he 3
from the foot of the pole, then the angle at which he should throw
the stone, so that it hits the fruit is _____. (A) 15° (B) 30°
(C) 45°
(D) 60°
39. The point (–4, –2) lies on a circle. What is the length of the radius of this circle, if the centre is located at (–8, –10)?
(A)
48
(B)
80
(C)
108
(D)
288
40. The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is ______.
(A) 15360
(B) 153600
(C) 30720
(D) 307200
Section-III : Everyday Mathematics 41. In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is ______.
(A) 20 m
(B) 22 m
(C) 24 m
(D) 26 m
42. 3 years ago, the average age of a family of 5 members was 17 years. A baby having been born,
the average age of the family is the same today. The present age of the baby is _____. 1 (A) 1 year (B) 1 years (C) 2 years (D) 3 years 2 6 times his age at the time of his marriage. 5 Rajan's sister was 10 years younger to him at the time of his marriage. The present age of Rajan's
43. Rajan got married 8 years ago. His present age is sister is ______.
(A) 32 years
(B) 36 years
(C) 38 years
(D) 40 years
44. In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 95 marks and 20% scored 90 marks, what was the average marks of the remaining students
of the class? (A) 65.5
(B) 72.5
(C) 75
(D) 85
45. Padma purchased 30 kg of rice at the rate of ` 17.50 per kg and another 30 kg rice at a certain rate. She mixed the two and sold the entire quantity at the rate of ` 18.60 per kg and made 20% overall profit. At what price per kg did she purchase the lot of another 30 kg rice ?
(A) ` 12.50
(B) ` 13.50
(C) ` 14.50
(D) ` 15.50
46. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for
14 months, 8 months and 7 months respectively. What was the ratio of their investments ? (A) 5 : 7 : 8 (B) 28 : 49 : 64 (C) 38 : 28 : 21 (D) None of these
47. Simi can do a work in 3 days, while Meeta can do the same work in 2 days. Both of them finish
the work together and get ` 150. What is the share of Simi? (A) ` 30 (B) ` 60 (C) ` 70
(D) ` 75
| 6th IMO | Level-II | Class 10
8
48. A bicycle can be purchased on cash payment of ` 1500. The same bicycle can also be purchased at the down payment (initial payment, at the time of purchasing) of ` 350 and rest can be paid in 3 equal installments of ` 400 for next 3 months. The rate of SI per annum charged by the dealer is _____.
(A) 23 9 % 17
(B) 17
9 % 23
(C) 13 9 % 17
(D) None of these
49. The question given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. A solid metallic cone is melted and recast into a sphere. What is the radius of the sphere? I. The radius of the base of the cone is 2.1 cm. II. The height of the cone is four times the radius of its base. III. The height of cone is 8.4 cm. (A) Only I and II (B) Only II and III
(C) Only I and III
(D) Any two of three
50. Yash invested a certain sum of money at 8% p.a. simple interest for ‘n’ years. At the end of ‘n’
years, Yash got back 4 times his original investment. What is the value of n? (A) 50 years (B) 25 years (C) 12 years 6 months (D) 37 years 6 months SPACE FOR ROUGH WORK
ANSWER KEYS 4 th IMO 1. 8. 15. 22. 29. 36. 43. 50.
(C) (C) (C) (B) (B) (B) (C) (B)
2. 9. 16. 23. 30. 37. 44.
(B) (C) (B) (D) (B) (D) (B)
3. 10. 17. 24. 31. 38. 45.
(D) (D) (D) (A) (D) (A) (D)
4. 11. 18. 25. 32. 39. 46.
(D) (A) (C) (B) (B) (C) (C)
5. 12. 19. 26. 33. 40. 47.
(D) (A) (D) (B) (B) (C) (A)
6. 13. 20. 27. 34. 41. 48.
(B) (A) (A) (C) (A) (D) (C)
7. 14. 21. 28. 35. 42. 49.
(D) (C) (B) (C) (A) (B) (B)
5. 12. 19. 26. 33. 40. 47.
(D) (B) (C) (B) (A) (A) (B)
6. 13. 20. 27. 34. 41. 48.
(A) (C) (D) (A) (A) (B) (C)
7. 14. 21. 28. 35. 42. 49.
(C) (D) (B) (B) (B) (C) (A)
5. 12. 19. 26. 33. 40. 47.
(C) (D) (B) (C) (D) (B) (B)
6. 13. 20. 27. 34. 41. 48.
(A) (D) (A) (D) (C) (B) (D)
7. 14. 21. 28. 35. 42. 49.
(A) (C) (B) (B) (A) (C) (D)
5 th IMO 1. 8. 15. 22. 29. 36. 43. 50.
(A) (D) (A) (C) (D) (A) (C) (B)
2. 9. 16. 23. 30. 37. 44.
(A) (B) (D) (C) (D) (A) (B)
3. 10. 17. 24. 31. 38. 45.
(C) (A) (D) (A) (A) (B) (C)
4. 11. 18. 25. 32. 39. 46.
(B) (B) (A) (D) (C) (A) (A) 6 th IMO
1. 8. 15. 22. 29. 36. 43. 50.
(C) (C) (A) (A) (A) (D) (C) (D)
2. 9. 16. 23. 30. 37. 44.
(A) (B) (A) (D) (C) (B) (C)
3. 10. 17. 24. 31. 38. 45.
(B) (C) (B) (A) (D) (B) (B)
4. 11. 18. 25. 32. 39. 46.
(A) (B) (B) (C) (A) (B) (D)
