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
7 4 th IMO | LevelI | Class 11 SPACE FOR ROUGH WORK
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
5
Year 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 (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 (D) None of these
6. Select a figure from amongst the options which will continue the same series as established by the five Problem Figures.
(a) (B) (c) (D)
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 is formed by the Problem Figures taken in order.
(a) (B) (c) (D)
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
466341 250
398282
(c) 298 (D) 350 ?
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) (B) (c) (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 ?
E G 4 B H 7 5 @ K 8 D N & Q Z $ W 3 C 1 9 * L B 2 S 6
(a) 1 (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
16. Nalini, her brother, her daughter and her son are tennis players and are playing game of doubles. correct. Find the correct option.
16 – 8 ÷ 4 + 5 × 2 = 8
(a) ÷ and × (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 (c) Wife (D) Daughter-in-law
20. If D = 4 and COVER = 63 then BASIS = ?
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 ____.
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 ____.
(a) A B∩ (B) 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 sina – y cosa = b (a is a variable) is ____.
(a) 2(x2 + y2) = a2 + b2 (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 33. Two equations numbered I and II are given.
I. 12x2 + 11x + 12 = 10x2 + 22x II. 13y2 – 18y + 3 = 9y2 – 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 – p2 is ____.
(a) Independent of a (B) Independent of n (c) Dependent on a (D) None of thesef these
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° (D) None of these
36. The argument of the complex number z i
i i
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
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
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?
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
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 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