### Quantitative aptitude question

• 1. Page 1LPU Set - 3 LPU Set - 3LPU Set - 3LPU Set - 3LPU Set - 3LPU Set - 3 Quantitative AptitudeQuantitative AptitudeQuantitative AptitudeQuantitative AptitudeQuantitative Aptitude 1. A circular ring of radius 3 cm is suspended from a point I by four identical strings tied at equal intervals on its circumference. The ring is in a horizontal plane. The point I is 4 cm vertically above the ring’s center. If the angle between any two consecutive strings is θ, then find the value of cos θ. (a) 9 25 (b) 3 5 (c) 16 25 (d) 4 5 2. ABC∆ and ∆PQR are triangles such that PQ || BC, QR || AB and PR || AC as shown in the figure. In ∆PQR, 2PD = DQ and in ABC∆ , BI = AD = 2DI. Find the ratio of areas of ∆ABC and ∆PQR. A B C DP Q R I (a) 49 25 (b) 4 1 (c) 25 9 (d) 29 14 No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3No of questions: 60 Marks for correct answer: 3 Time: 90 minutesTime: 90 minutesTime: 90 minutesTime: 90 minutesTime: 90 minutes Negative mark: 1Negative mark: 1Negative mark: 1Negative mark: 1Negative mark: 1 3. In the figure (not drawn to scale) given below, if AD = CD = BC and BCE 96∠ = o , how much is the value of DBC∠ ? A B C D E 96° (a) 32° (b) 64° (c) 84° (d) 24° 4. A vertical tower OP stands at the center O of a square ABCD. Let h and b denote the height of OP and length AB respectively. Suppose distance from top of the tower to the vertices of the square is equal to the length of the square, then the relationship between h and b can be expressed as (a) 2b2 = h2 (b) 2h2 = b2 (c) 3b2 = 2h2 (d) 3h2 = 2b2 5. There are 8436 steel balls, each with a radius of 1 centimeter, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is (a) 34 (b) 38 (c) 36 (d) 32
• 2. Page 2 LPU Set - 3 6. In the figure below, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO is produced to meet the circle at D. If ACD∠ = y degrees and AOD∠ = x degrees such that x = ky, then the value of k is A B CD O (a) 3 (b) 2 (c) 1 (d) 4 7. As shown in the figure, PQ and PR are tangents to the circle from an external point P. If ∠QPR = 60°, find out ∠QOR and QSR. 60° Q S R PO (a) 130° and 65° (b) 140° and 70° (c) 150° and 75° (d) 120° and 60° 8. The perimeter of an isosceles right-angled triangle is 2p. Find out the area of the same triangle. (a) ( )+ 2 2 2 p (b) ( )− 2 2 2 p (c) ( ) 2 3 – 2 p (d) ( )− 2 3 2 2 p 9. ABCD is a square in which P and Q are mid- points of AD and DC respectively. The area of ∆BPQ constitutes what part of the whole area? A B CD P Q x x x 2 x 2 x 2 x 2 (a) 50% (b) 37.5% (c) 66.66% (d) 40% 10. In the square ABCD, E and F are the two points on its diagonals. If O is the intersection point of the two diagonals and OF = 1, OE = 2, then what is the length of the line segment EF? I. 3 cm II. 1 cm III. 5 cm (a) I or II only (b) II or III only (c) III only (d) I, II or III 11. Four discs of diameter 10 cm each are cut from the bigger circular disc of radius 20 cm. Find out the percentage of the left-out area with respect to the total area. (a) 75% (b) 66.66% (c) 33.33% (d) 50% 12. The interior angles of a convex polygon form an arithmetic progression with a common difference of 5 degrees. If the smallest interior angle is 120º, then the number of sides of the polygon could be (a) 8 (b) 9 (c) 12 (d) 16
• 3. Page 3LPU Set - 3 13. It is given that AB and AC are the equal sides of an isosceles ∆ABC, in which an equilateral ∆DEF is inscribed. As shown in the figure, ∠BFD = a and ∠ADE = b, and ∠FEC = c. Then A B C D E F a b c (a) a = +b c 2 (b) b = +a c 2 (c) c = 2a + 2b (d) + = b c a 3 14. In the figure, where AB is tangent to the circle with centre O, find the ratio of the area of shaded region to the area of unshaded region of triangle AOB. O A C B 260° (a) − π 2 3 2 (b) − π 3 3 2 (c) − π 2 3 (d) − π 3 3 1 15. The coordinates of an equilateral triangle are as shown in the figure below. What is the length of the median? A (x, y) B D C (0, 0) (4 3, 0) (a) 4 3 (b) 4.5 (c) 6 (d) 6.5 16. In the given figure, BO and CO are the bisectors of ∠MBC and ∠NCB respectively. Find the value of ∠COB. A M N B C O 50° (a) 75° (b) 65° (c) 90° (d) 80° 17. A wheel with a rubber tyre has an outside diameter of 25 inches. When the radius has been decreased by a quarter of an inch, the number of revolutions of the wheel in one mile will be (a) increased by about 2% (b) increased by about 30% (c) increased by about 20% (d) increased by about 0.2%
• 4. Page 4 LPU Set - 3 Directionsforquestions18and19:Answerthequestions based on the information given below. A cube is divided into eight equal small cubes. Each of these small cube is further sub-divided into eight equal smaller cubes. 18. What is the surface area of the smallest cube as a fraction of the surface area of the original cube? (a) 0.625 (b) 0.0625 (c) 0.0156 (d) 0.0039 19. If the original cube’s sides were painted blue, then what is the probability that exactly two sides of any randomly selected small cube is painted blue? (a) 3 8 (b) 1 16 (c) 1 4 (d) 3 4 20. Three sides of an isosceles triangle are variably represented as (x + 1), (9 – x) and (5x – 3). How many such triangles are possible? (a) 0 (b) 1 (c) 2 (d) 3 21. Two vertices of a rectangle lie on the line Y = 2x + λ and coordinate of the rest two vertices opposite to each other are (1, 3) and ( 5, 1). Find the value of λ . (a) 4 (b) 5 (c) –4 (d) – 3 22. A ladder rests against a wall with its lower end at a distance x from the wall and its upper end at a height of 2x above the floor. If the lower end slides through a distance y away from the wall, from its earlier position then by how much distance does the upper end slide? D A E B Cx 2x y (a) − − +2 2 x 5 5x (x y) (b) − − −2 2 x 5 5x (x y) (c) − − +2 2 2x 5x (x y) (d) − − −2 2 2x 5x (x y) 23. A circle of radius R 2 is cut out of another circle of radius R. How much paint is needed to paint this circle (with a hole in it) if the original circle needed 20 L for the painting? (a) 16.66 L (b) 18 L (c) 12 L (d) 15 L 24. The interior angle of the regular polygon exceeds the exterior angle by 132°. The number of sides in the polygon will be (a) 10 (b) 16 (c) 12 (d) 15 25. The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are c, t and s, respectively. Then, (a) s > t > c (b) c > t > s (c) c > s > t (d) s > c > t
• 5. Page 5LPU Set - 3 26. The sum of the squares of first ten natural numbers is (a) 281 (b) 385 (c) 402 (d) 502 27. The largest number among the following is (a) (2 + 2 × 2)3 (b) 3 1/ 2 [(2 2) ]+ (c) 25 (d) (2 × 2 – 2)7 28. The smallest number among the following is (a) (7)3 (b) (8.5)3 (c) (4)4 (d) (34/5)5 29. Find the sum of the first 50 even numbers. (a) 1275 (b) 2650 (c) 5100 (d) 2550 30. Evaluate: 112 + 114 ÷ 113 – 11 + (0.5) 112 (a) 302.5 (b) 181.5 (c) 484.0 (d) 121 31. Which one of the following is incorrect? (a) Square root of 5184 is 72. (b) Square root of 15625 is 125. (c) Square root of 1444 is 38. (d) Square root of 1296 is 34. 32. The sum of first 45 natural numbers is (a) 2070 (b) 975 (c) 1280 (d) 1035 33. The greatest fraction among 2 3 1 7 4 , , , and 5 5 5 15 5 is (a) 4 5 (b) 3 5 (c) 2 5 (d) 7 15 34. The lowest four-digit number which is exactly divisible by 2, 3, 4, 5, 6 and 7 is (a) 1400 (b) 1300 (c) 1250 (d) 1260 35. The sum of the two numbers is twice their difference. If their product is 27, then the numbers are (a) 5, 15 (b) 10, 30 (c) 9, 6 (d) 9, 3 36. The largest fraction among the following is (a) 17 21 (b) 11 14 (c) 12 15 (d) 5 6 37. If the product of three consecutive integers is 720, then their sum is (a) 54 (b) 45 (c) 18 (d) 27 38. How many numbers between 200 and 600 are divisible by 4, 5 and 6? (a) 5 (b) 6 (c) 7 (d) 8 39. The number (10n – 1) is divisible by 11 for (a) even values of n (b) odd values of n (c) all values of n (d) n = multiples of 11 40. Solve: 3 3 1 3 1 3 3 + + + (a) 1 (b) 3 (c) 43 11 (d) 63 19 41. How many numbers are there between 500 and 600 in which 9 occurs only once? (a) 19 (b) 20 (c) 21 (d) 18 42. How many zeros are there at the end of the product × × × × × ×33 175 180 12 44 80 66 ? (a) 2 (b) 4 (c) 5 (d) 6
• 6. Page 6 LPU Set - 3 43. N = 5656 + 56. What would be the remainder when N is divided by 57? (a) 0 (b) 56 (c) 55 (d) 1 44. The largest number that always divides the product of 3 consecutive multiples of 2 is (a) 8 (b) 16 (c) 24 (d) 48 45. The sum of two natural numbers is 85 and their LCM is 102. Find the numbers. (a) 51 and 34 (b) 50 and 35 (c) 60 and 25 (d) 45 and 40 46. By what smallest number, 21600 must be multiplied or divided in order to make it a perfect square? (a) 6 (b) 5 (c) 8 (d) 10 47. If we write down all the natural numbers from 259 to 492 side by side we shall get a very large natural number 259260261262 L 490491492. How many 8’s will be used to write this large natural number? (a) 52 (b) 53 (c) 32 (d) 43 48. n3 + 2n for any natural number n is always a multiple of (a) 3 (b) 4 (c) 5 (d) 6 49. A number when divided by 238 leaves a remainder 79. What will be the remainder when that number is divided by 17? (a) 8 (b) 9 (c) 10 (d) 11 50. What is the remainder when 17 23 is divided by 16? (a) 0 (b) 1 (c) 2 (d) 3 51. 96 + 1 when divided by 8, would leave a remainder (a) 0 (b) 1 (c) 2 (d) 3 52. N = 2 × 4 × 6 × 8 × 10 × L 100. How many zeros are there at the end of N? (a) 24 (b) 13 (c) 12 (d) 15 53. It is given that 232 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number? (a) 296 + 1 (b) 216 – 1 (c) 216 + 1 (d) 7 × 233 54. 461 + 462 + 463 + 464 + 465 is divisible by (a) 3 (b) 5 (c) 11 (d) 17 55. What is the smallest perfect square that is divisible by 8, 9 and 10? (a) 4000 (b) 6400 (c) 3600 (d) 14641 56. In a group of 500 students, selected for admission in a business school, 64% opted for finance and 56% for operations as specialisations. If dual specialisation is allowed, how many have opted for both? Each student opts for at least one of the two specialisations. (a) 200 (b) 100 (c) 150 (d) 125 Directions for questions 57 to 59:Directions for questions 57 to 59:Directions for questions 57 to 59:Directions for questions 57 to 59:Directions for questions 57 to 59: Read the passage given below and answer the questions. In a locality, 30% of the residents read The Times of India and 75% read The Hindustan Times. 3 people read neither of the papers and 6 read both. Only The Times of India and The Hindustan Times newspapers are available. 57. How many people are there in the locality? (a) 60 (b) 120 (c) 126 (d) 130
• 7. Page 7LPU Set - 3 58. What is the percentage of people who read only The Times of India? (a) 15% (b) 20% (c) 25% (d) 30% 59. What percentage of residents read only one newspaper? (a) 11% (b) 43% (c) 85% (d) 20% 60. Each student in a class of 40, studies at least one of the subjects namely English, Mathematics and Economics. 16 study English, 22 study Economics and 26 study Mathematics, 5 study English and Economics, 14 study Mathematics and Economics and 2 study English, Economics and Mathematics. Find the number of students who study English and Mathematics. (a) 10 (b) 7 (c) 17 (d) 27