11
4
(2008-2011)
INSTANT
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The Secrets of SUCCESS
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Master Mental Ability in 30 Days
IIT-JEE | AIEEE | NEET | BOARDS | OLYMPIAD | NTSE
FOUNDATION COURSE For Classes 8, 9 & 10 Class 8
Class 9
Class 10
2nd
Year 2008
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
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.
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.
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) 2y 3
(B) 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
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
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
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
4th
Year 2010
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
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
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
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) 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
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
5th
Year 2011
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)
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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
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5th IMO - 2011
16. Nalini, her brother, her daughter and her son are tennis players and are playing game of doubles.
Their positions on the court are as follows : (i) Nalini's brother is directly across the net from her daughter. (ii) Her daughter is diagonally across the net from the worst players sibling. (iii) The best and the worst players are on the same side of the net. Who is the best player ? (A) Nalini (B) Nalini's brother (C) Nalini's daughter (D) None of these
17. A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the
number of legs walking on the ground is 70, how many horses are there ? (A) 10 (B) 12 (C) 14 (D) 16
18. The given equation becomes correct due to the interchange of two signs. One of the four options under it specifies the interchange of signs in the equation which when made will make the equation correct. Find the correct option.
(A) ÷ and ×
16 – 8 ÷ 4 + 5 × 2 = 8 (B) – and ÷ (C) ÷ and +
(D) – and ×
19. Introducing a woman Shashank said, "She is the mother of the only daughter of my son." How
that woman is related to Shashank? (A) Daughter (B) Sister in-law
20. If D = 4 and COVER = 63 then BASIS = ? (A) 49 (B) 50
(C) Wife
(D) Daughter-in-law
(C) 54
(D) 55
Section II : Mathematical reasoning 21. The sum of the first n terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + ... is n is even. When n is odd the sum is _____.
3n(n + 1) 2
(A)
2
n(n + 1) (B) 2
n(n + 1) 2 4
(A) 2nπ +
5π 4
(B) nπ +
π 4
n 2 (n + 1) 2
(C)
22. The most general value of q satisfying both the equations cos θ = − (C) 2nπ +
π 4
n(n + 1)2 , when 2
(D)
1 and tan q = 1 is ____. 2 5π (D) nπ + 4
23. From the numbers 1, 2, 3, 4, ....,13; 4 numbers are drawn one by one. The probability that
the numbers will be in ascending order, is ____. 1 1 (B) (A) 13 24
(C)
1 12
(D) None of these
24. If |z – i Re(z)| = | z – Im(z)|, then z lies on ____.
(A) Re(z) = 2
(B) Im(z) = 2
(C) Re(z) + Im(z) = 2
(D) None of these
1 1 1 1 1 1 1 1 25. The value of the expression 1 + 1 + 2 + 2 + 2 + 2 + 3 + 3 + 2 + ..... + n + n + 2 , ω ω ω ω ω ω ω ω where w is an imaginary cube root of unity, is ____.
(A)
n( n 2 + 2) 3
(B)
n( n 2 − 2) 3
(C)
n(n 2 + 1) 3
(D) None of these
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5th IMO - 2011
26. If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}, then A – B is equal to ____.
(B) A ∩ B
(A) A ∩ B
(C) A ∩ B
(D) A ∩ B
27. The locus of the point of intersection of lines x cos a + y sin a = a and x sin a – y cos a = b (a is a variable) is ____.
(A) 2(x 2 + y 2) = a 2 + b 2
(B) x2 – y2 = a2 – b2
(C) x2 + y2 = a2 + b2
(D) None of these
28. Study the following Pie-chart carefully to answer the given question. What is the value of half of the difference between the number of students in MBA and MBBS?
(A) 800
(B) 1600
(C) 1300
(D) 650
29. A and B throw a die. The probability that A's throw is not greater than B's is ____.
(A)
1 2
(B) 1 6
(C)
7 12
(D)
5 12
30. P is a set containing n elements. A subset A of P is chosen and the set P is reconstructed by replacing the elements of A. A subset B of P is chosen again. The number of ways of choosing A and B such that A and B have no common elements is ____.
(B) 3n
(A) 2n
n 31. If Cr = Cr and S =
(A) S =
n 2
(C) 4n
(D) None of these
C C1 C C + 2 2 + 3 3 + ..... + n n , then which of the following is true ? C0 C1 C2 Cn −1 n −1 n(n − 1) (B) S = (C) S = (D) None of these 2 2
32. Let C 1 and C 2 be defined as follows :
C 1 : b 2 – 4ac ≥ 0
C 2 : a, –b, c are of same signs. The roots of ax 2 + bx + c = 0 are real and positive if ____.
(A) Both C1 and C2 are satisfied
(B) Only C2 is satisfied
(C) Only C1 is satisfied
(D) None of these
33. Two equations numbered I and II are given.
I.
12x 2 + 11x + 12 = 10x 2 + 22x
II.
13y 2 – 18y + 3 = 9y 2 – 10y
Solve both the equations and give answer if
(A) x > y
(B) x ≥ y
(C) x < y
(D) x ≤ y
34. If p and q are respectively the sum and the sum of the squares of n successive integers beginning with a, then nq – p 2 is ____.
(A) Independent of a
(B) Independent of n
(C) Dependent on a
(D) None of thesef these
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5th IMO - 2011
35. In a right angled triangle, the hypotenuse is four times as long as the perpendicular drawn to it from the opposite vertex. One of the acute angle is _____.
(A) 15°
(B) 30°
(C) 45°
36. The argument of the complex number z =
(A) p/6
(B) p/4
(D) None of these
(1 + i 3 )2 is _____. 4i (1 − i 3 ) (C) p/2
(D) None of these
37. Study the given graph carefully to answer the following question.
Number of girls from college R forms what percent of the total number of students from all the colleges together? (Rounded off to two digits after decimal).
(A) 8.26
(B) 5.18
(C) 6.54
(D) 4.92
38. The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : |x 2 – y 2| < 16} is given by ___.
(A) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}
(B) {(2, 2), (3, 2), (4, 2), (2, 4)}
(C) {(3, 3), (4, 3), (5, 4), (3, 4)}
(D) None of these
39. In a quadratic equation with leading coefficient 1, a student reads the coefficient 16 of x wrongly as 19 and obtain the roots as – 15 and – 4. The correct roots are ____.
(A) 6, 10
(B) – 6, –10
(C) – 7, –9
(D) None of these
40. A point moves in the xy-plane such that the sum of its distances from two mutually perpendicular lines is always equal to 3. The area enclosed by the locus of the point is _____.
(A) 18 sq. units
(B) 15 sq. units
(C) 9 sq. units
(D) 27 sq. units
Section III : Everyday Mathematics 41. AB is a vertical pole. The end A is on the level ground. C is the middle point of AB. P is a point on the level ground. The portion BC subtends an angle b at P. If AP = nAB, then tan b is equal to ____.
(A)
n 2
2n + 1
(B)
n 2
n −1
(C)
n 2
n +1
(D) None of these
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5th IMO - 2011
42. A lad was asked his age by his friend. The lad 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 lad is ____.
(A) 21 years
(B) 28 years
(C) 14 years
(D) 25 years
43. Divakar and Shubhank set out to meet each other from Delhi and Saharanpur, 330 km apart. Divakar travels 30 km on the first day, 28 km on the second day, 26 km on the third day and so on. Shubhank travels 20 km on the first day, 24 km on the second day, 28 km on the third day and so on. In how many days they meet, if they started moving towards each other at the same
time ? (A) 4
(B) 5
(C) 6
(D) None of these
44. An airgun can take a maximum of 4 shots at a balloon at some distance. The probabilities of hitting the balloon at the first, second, third and fourth shot are 0.1, 0.2, 0.3 and 0.4 respectively.
What is the probability that the balloon is hit ? (A) 0.6976 (B) 0.6576
(C) 0.786
(D) None of these
45. Raman scored 456 marks in an exam and Seeta got 54 per cent marks in the same exam which is 24 marks less than Raman. If the minimum passing marks in the exam is 34 per cent, then how
much more marks did Raman score than the minimum passing marks? (A) 184 (B) 196 (C) 190
(D) 180
46. In the entrance test of Wharton Business School, the maximum marks for each of three papers is n and that for the fourth paper is 2n. Find the number of ways in which a candidate can get
3n marks. 1 (n + 1)(n + 2) (A) 6
(B)
1 2 1 ( n + 3n − 6 ) (n + 1)(5n 2 + 10n + 6) (C) 2 6
(D) None of these
47. 7 sisters dine at a round table. They dine together till each of them dine with different neighbours i.e., they do not like to dine with same neighbours in any two arrangements. In a year how many
days they dine together. (A) 180 (B) 504
(C) 720
(D) 360
48. A shopkeeper buys a number of books for ` 80. If he had bought 4 more for the same amount,
each book would have cost Re. 1 less. How many books did he buy? (A) 8 (B) 16 (C) 24
(D) 28
49. Three horses are grazing within a semi-circular field. In the adjoining figure,
AB is the diameter of the semi-circular field with centre at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi circles with centres at P and R respectively, and S is the centre of the circle touching the two semi
circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi circles and the horses tied at S can graze within the circle centred at S. The percentage of the area
of the semi circle with diameter AB that cannot be grazed by the horses is nearest to _____. (A) 20 (B) 28 (C) 36 (D) 40
50. Varun joined as an area manager of a bank in the pay scale of ` 21,000 – 500 – 28,500. Minimum
how many years he has to work in the bank to avail the salary of ` 28,500 per month. (A) 12 years (B) 15 years (C) 13 years (D) 11 years
ANSWER KEYS 2 nd IMO (2008) 1. 8. 15. 22. 29. 36. 43. 50
(C) (A) (A) (A) (C) (C) (A) (A)
2. 9. 16. 23. 30. 37. 44
(B) (C) (C) (D) (B) (D) (C)
3. 10. 17. 24. 31. 38 45.
(B) (D) (A) (B) (C) (C) (C)
4. 11. 18. 25. 32. 39. 46.
(D) (B) (D) (B) (A) (B) (B)
5. 12. 19. 26. 33. 40. 47.
(C) (A) (A) (B) (C) (C) (B)
6. 13. 20. 27. 34. 41. 48.
(A) (C) (E) (A) (B) (C) (D)
7. 14. 21. 28. 35. 42. 49.
(E) (A) (C) (C) (A) (B) (D)
(C) (D) (D) (C) (A) (B) (C)
6. 13. 20. 27. 34. 41. 48.
(D) (C) (C) (C) (B) (D) (C)
7. 14. 21. 28. 35. 42. 49.
(B) (A) (B) (C) (D) (C) (A)
(C) (A) (D) (C) (C) (A) (B)
6. 13. 20. 27. 34. 41. 48.
(A) (B) (B) (D) (A) (B) (C)
7. 14. 21. 28. 35. 42. 49.
(D) (C) (B) (A) (C) (B) (D)
3 rd IMO (2009) 1. 8. 15. 22. 29. 36. 43. 50.
(C) (B) (B) (B) (B) (B) (C) (C)
2. 9. 16. 23. 30. 37. 44.
(D) (B) (C) (A) (A) (D) (B)
3. 10. 17. 24. 31. 38. 45.
(D) (A) (A) (B) (A) (D) (D)
4. 11. 18. 25. 32. 39. 46.
(B) (C) (C) (B) (A) (C) (D)
5. 12. 19. 26. 33. 40. 47.
4 th IMO (2010) 1. 8. 15. 22. 29. 36. 43. 50.
(A) (B) (B) (B) (D) (A) (C) (B)
2. 9. 16. 23. 30. 37. 44.
(D) (C) (C) (B) (B) (B) (D)
3. 10. 17. 24. 31. 38. 45.
(D) (C) (D) (B) (A) (D) (A)
4. 11. 18. 25. 32. 39. 46.
(C) (A) (B) (B) (A) (C) (B)
5. 12. 19. 26. 33. 40. 47.
5 th IMO (2011) 1.
(B)
2.
(C)
3.
(A)
4.
(B)
5.
(A)
6.
(B)
7.
(A)
8.
(D)
9.
(A)
10.
(D)
11.
(B)
12.
(A)
13.
(A)
14.
(B)
15.
(D)
16.
(B)
17.
(C)
18.
(B)
19.
(D)
20.
(B)
21.
(D)
22.
(A)
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(A)
24.
(D)
25.
(A)
26.
(B)
27.
(C)
28.
(D)
29.
(C)
30.
(B)
31.
(D)
32.
(A)
33.
(B)
34.
(C)
35.
(A)
36.
(C)
37.
(D)
38.
(D)
39.
(B)
40.
(A)
41.
(A)
42.
(C)
43.
(C)
44.
(A)
45.
(A)
46.
(B)
47.
(D)
48.
(B)
49.
(B)
50.
(B)
