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CDS MATHEMATICS PRACTICE SET Subject Questions Marks Time -Ve

Maths 100 100 2 hrs 1/3 Q1. Which one of the following numbers is a composite numbers? (a) 589 (b) 571 (c) 569 (d) 563 Q2. One dividing 4996 by a certain number, the quotient is 62 and the remainder is 36. What is the divisor? (a) 80 (b) 85 (c) 90 (d) 95 Q3. If we divide a positive integer by another positive integer, what is the resulting number? (a) It is always a natural number (b) It is always an integer (c) It is a rational number (d) It is an irrational number Q4. The remainder on dividing given integers a and b by 7 are, respectively 5 and 4. What is the remainder when a b is divided by 7? (a) 3 (b) 4 (c) 5 (d) 6 Q5. The product of a rational number and an irrational number is (a) a natural number (b) an irrational number (c) a composite number (d) a rational number Q6. ABC is a triangle and AD is perpendicular to BC. It is given that the lengths of AB, BC, CA are all rational numbers. Which one of the following is correct? (a) AD and BD must be rational (b) AD must be rational but BD need not be rational (c) BD must be rational but AD need not be rational (d) Neither AD nor BD need be rational Q7. How many rational numbers are there between 1 and 1000? (a) 998 (b) 999 (c) 1000 (d) Infinite Q8. Which one of the following numbers is divisible by 11?

(a) 45678940 (b) 54857266 (c) 87524398 (d) 93455120 Q9. Consider the following statements: I. 7710312401 is divisible by 11. II. 173 is a prime number. Which of the statements given above is/are correct? (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q10. How many pairs of X and Y are possible in the number 763X4Y2, if the number is divisible by 9? (a) 8 (b) 9 (c) 10 (d) 11 Q11. What is the maximum value of m if the number N = 35 × 45 × 55 × 60 × 124 × 75 is divisible by 5m? (a) 4 (b) 5 (c) 6 (d) 7 Q12. What is the remainder when 496 is divided by 6? (a) 4 (b) 3 (c) 2 (d) 1 Q13. If the HCF of (x 2 + x – 12) and (2x 2 – kx – 9) is (x – k), then what is the value of k? (a) – 3 (b) 3 (c) – 4 (d) 4 Q14. What is the smallest positive integer which when divided by 4, 5, 8 and 9 leaves remainder 3, 4, 7 and 8, respectively? (a) 119 (b) 319 (c) 359 (d) 719

Q15. The sum of two numbers is 232 and their HCF is 29. What is the number of such pairs of numbers satisfying the above condition? (a) One (b) Two (c) Four (d) None of these

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Q16. For any integer n, what is HCF (22n + 7, 33n + 10) equal to? (a) n (b) 1 (c) 11 (d) None of these Q17. Consider the following statements: I. 1/22 cannot be written as a terminating decimal. II. 2/15 can be written as a terminating decimal. III. 1/16 can be written as a terminating decimal. Which of the statements given above is/are correct? (a) Only I (b) Only II (c) Only I and III (d) II and III

Q18.

(a)

(b)

(c)

(d) Q19.

(a) 0 (b) 1 (c) 2 (d) 3 Q20. if the radius of the base and the height of a right circular cone are increased by 20%, then what is the approximate percentage increase in volume? (a) 60% (b) 68% (c) 73% (d) 75% Q21. What is the number whose 20% is 30% of 40? (a) 90 (b) 80 (c) 60 (d) 50 Q22. On a 20% discount sale, an article costs 596. What was the original price of the article? (a) Rs 720 (b) Rs 735 (c) Rs 745 (d) Rs 775

Q23. What number must be added to each of 4, 10, 12 and 24, so that the resulting numbers are in proportion? (a) 6 (b) 8 (c) 10 (d) 4 Q24. If x varies as the mth power of y, y varies as the nth power of z and x varies as the pth power of z, then which one of the following is correct? (a) p = m + n (b) p = m – n (c) p = mn (d) None of theses Q25. The fourth proportional to 7, 11, 14 is (a) 16 (b) 18 (c) 20 (d) 22 Q26. The ratio of ages of A and B is 2: 5 and the ratio of ages of B and C is 3: 4, What is the ratio of ages of A, B and C? (a) 6: 15: 20 (b) 8: 5: 3 (c) 6: 5: 4 (d) 2: 15: 4 Q27. In an examination, 40% of the candidates wrote their answers in Hindi and the others in English. The average marks of the candidates written in Hindi is 74 and the average marks of the candidates written in English is 77. What is the average marks of all the candidates? (a) 75.5 (b) 75.8 (c) 76.0 (d) 76.8 Q28. An amount of Rs x at compound interest at 20% per annum for 3 years becomes y. What is y: x? (a) 3: 1 (b) 36: 25 (c) 216: 125 (d) 125: 216 Q29. The sum which amounts to Rs 364.80 in 8 years at 3.5% simple interest per annum is (a) Rs 285 (b) Rs 280 (c) Rs 275 (d) Rs 270 Q30. An automobile financer claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest at the rate of 10%, the effective rate of interest becomes (a) 10.25%

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(b) 10.5% (c) 10.75% (d) 11% Q31. A person A sells a table costing Rs 2000 to a person B and earns a profit of 6%. The person B sells it to another person C at a loss of 5%. At what price did B sell the table? (a) Rs 2054 (b) Rs 2050 (c) Rs 2024 (d) Rs 2014 Q32. A person bought 8 quintal of rice for certain rupees. After a week, he sold 3 quintal of rice at 10% profit, 3 quintal of rice with neither profit nor loss and 2 quintal at 5% loss. In this transaction, what is the profit? (a) 10% (b) 20% (c) 25% (d) None of these Q33. A train 200 m long fully passes a platform of 200 m length in 15 s. What is the speed of the train? (a) 36 km/h (b) 48 km/h (c) 72 km/h (d) 96 km/h Q34. Two trains travel in the same direction at 50 km/h and 32 km/h, respectively. A man in the slower train observes that 15 s elapse before the faster train completely passes him. What is the length of the faster train? (a) 75 m (b) 125 m (c) 150 m (d) 625/3 M Q35. A wheel of radius 2.1 m of a vehicle makes 75 revolutions in 1 min. What is the speed of the vehicle? (a) 78 km/h (b) 59.4 km/h (c) 37.4 km/h (d) 35.4 km/h Q36. A train takes 10 s to cross a pole and 20 s to cross a platform of length 200 m. What is the length of the train? (a) 50 m (b) 100 m (c) 150 m (d) 200 m Q37. A person can do a job as fast as his two sons working together. If one son does the job in 6 days and the other in 12 days, how many days does it take the father to do the job? (a) 9 days (b) 6 days (c) 4 days

(d) 3 days Q38. The mess charges for 35 students for 24 days in Rs6300. In how many days will the mess charges be Rs 3375 for 25 students? (a) 12 (b) 15 (c) 18 (d) 21 Q39. A can do a piece of work in 4 days and B can complete the same work in 12 days. What is the number of days required to do the same work together? (a) 2 days (b) 3 days (c) 4 days (d) 5 days Q40. X can complete a job in 12 days. If X and Y work together, they can complete the job in 20/3 days. Y alone can complete the job in (a) 10 days (b) 12 days (c) 15 days (d) 18 days Q41. How many men will be required to plough 100 acres of land in 10 days, if 10 men require 8 days to plough 20 acres of land? (a) 30 (b) 40 (c) 50 (d) 60 Q42. What is/are the factor(s) of (x29 – x24 + x13 – 1)? (a) Only (x – 1) (b) Only (x + 1) (c) (x – 1) and (x + 1) (d) Neither (x – 1) nor (x + 1) Q43. What is x(y – z) (y + z) + y(z – x) (z + x) + z(x – y) (x + y) equal to? (a) (x + y) (y + z) (z + x) (b) (x – y) (x – z) (z – y) (c) (x + y) (z – y) (x – z) (d) (y – x) (z – y) (x – z) Q44. What are the factors of x 2 + 4y 2 + 4y – 4xy – 2x – 8? (a) (x – 2y – 4) and (x – 2y + 2) (b) (x – y + 2) and (x – 4y + 4) (c) (x – y + 2) and (x – 4y – 4) (d) (x + 2y – 4) and (x + 2y + 2) Q45. If the expression x 3 + 4x 2 + 4x + k has (x + 4) as a factor, then what is the value of k? (a) –16 (b) 16 (c) 32 (d) –32

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Q46. What is the remainder when (1235 × 4523 × 2451) is divided by 12? (a) 1 (b) 3 (c) 5 (d) 7 Q47. In a school there are 30 teachers who teach Mathematics or Physics. Of these teachers, 20 teach Mathematics and 15 teach Physics, 5 teach both Mathematics and Physics. The number of teachers teaching only Mathematics is (a) 5 (b) 10 (c) 15 (d) 20 Q48.

(a) 1 (b) 2 (c) 3 (d) 4 Q49. Which one of the following is correct?

(a)

(b)

(c)

(d)

Q50. (a) ½ (b) –1 (c) –1/2 (d) 3/2

Q51.

(a) 25 cm (b) 20 cm (c) 5 cm (d) 4 cm Q52. If x + y = 90º and sin x: sin y = √3 :1, then what is x: y equal to? (a) 1: 1 (b) 1: 2 (c) 2: 1 (d) 3: 2 Q53.

(a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q54.

(a)

(b)

(c)

(d) Q55. If ABC is a right angled triangle at C and having u units, v units and w units as the lengths of its sides opposite to be vertices A, B and C respectively, then what is tan A + tan B equal to?

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(a)

(b)

(c)

(d) Q56. What is cot 15º cot 20º cot 70º cot 75º equal to? (a) –1 (b) 0 (c) 1 (d) 2 Q57. How many degrees are there in an angle which equals two-third of its complement? (a) 36º (b) 45º (c) 48º (d) 60º Q58.

(a) –139/60 (b) 139/60 (c) 119/60 (d) None of these Q59. The angle of elevation and angle of depression both are measured with (a) the vertical only (b) the horizontal line only (c) both horizontal and vertical (d) None of the above Q60. The angle of elevation of the tip of a tower from a point on the ground is 45º. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60º. What is the height of the tower, to the nearest meter? (a) 48 m (b) 49 m (c) 50 m (d) 51 m Q61. From a rectangular sheet of cardboard of size 5 cm × 2 cm, the greatest possible circle is cut-off. What is the area of the remaining part? (a) (25 – p) cm2 (b) (10 – p) cm2 (c) (4 – p) cm2 (d) (10 – 2p) cm2

Q62. What is the radius of the circle inscribed in a triangle having side lengths 35 cm, 44 cm and 75 cm? (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm Q63. If the area of a DABC is equal to area of square of side length 6 cm, then what is the length of the altitude of AB, where AB = 9 cm? (a) 18 cm (b) 14 cm (c) 12 cm (d) 8 cm Q64. Consider the following statements I. Area of a segment of a circle is less than area of its corresponding sector. II. Distance travelled by a circular wheel of diameter 2d cm in one revolution is greater than 6d cm. Which of the above statements is/are correct? (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II

Q65. The area of an isosceles triangle ABC with AB = AC and altitude AD = 3 cm is 12 sq cm. What is its perimeter? (a) 18 cm (b) 16 m (c) 14 cm (d) 12 cm Q66. ABC is a triangle right angled at A. AB = 6 cm and AC = 8 cm. Semi-circles drawn (outside the triangle) on AB, AC and BC as diameters which enclose areas x, z square units, respectively. What is x + y – z equal to? (a) 48 cm2 (b) 32 cm2 (c) 0 (d) None of these Q67. 27 drops of water form a big drop of water. If the radius of each smaller drop is 0.2 cm, then what is the radius of the bigger drop? (a) 0.4 cm (b) 0.6 cm (c) 0.8 cm (d) 1.0 cm Q68. A sphere is cut into two equal halves and both the halves are painted from all the sides. The radius of the sphere is r unit and the rate of painting is Rs 8 per sq

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unit. What is the total cost of painting the two halves of the sphere in rupees? (a) 6pr2 (b) 32pr2 (c) 48pr2 (d) Insufficient data to answer Q69. The dimensions of a rectangular box are in the ratio 2: 3: 4 and the difference between the cost of covering it with a sheet of some metal at Rs 8 and Rs 10 per sq m is Rs 234. What are the length, breadth and height of the box, respectively? (a) 2 m, 3 m, 4 m (b) 3 m, 4.5 m, 6 m (c) 4 m, 6 m, 8 m (d) 5 m, 7.5 m, 10 m Q70. From a cylindrical log whose height is equal to its diameter, the greatest possible sphere has been taken out. What is the fraction of the original log which is cut away? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3 Q71. The inner and outer radii of a 7 m long hollow iron right circular cylindrical pipe are 2 cm and 4 cm, respectively. If 1000 cm3 of iron weight 5 kg, then what is the weight of the pipe? (a) 264 kg (b) 132 kg (c) 396 kg (d) None of these Q72. If three cubic biscuits having edges 0.3 m, 0.4 m and 0.5 m respectively are melted and formed into a single cubic biscuit, then what is the total surface area of the cubic biscuit? (a) 1.08 sq m (b) 1.56 sq m (c) 1.84 sq m (d) 2.16 sq m Q73. A toy is in the form of a cone mounted on a hemisphere such that the diameter of the base of the cone is equal to that of the hemisphere. If the diameter of the base of the cone is 6 cm and its height is 4 cm, what is the surface area of the toy in sq cm? (take p = 3.14) (a) 93.62 (b) 103.62 (c) 113.62 (d) 115.50 Q74. 10 cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4 m. What is the cost of painting at the rate of Rs 5 per sq m? (a) Rs 400

(b) Rs 440 (c) Rs 480 (d) Rs 500 Q75. 10 circular plates each of thickness 3 cm, each are placed one above the other and a hemisphere of radius 6 cm is placed on the top just to cover the cylindrical solid. What is the volume of the solid so formed? (a) 264p cu cm (b) 252p cu cm (c) 236p cu cm (d) None of these Q76. The length, breadth and height of a box are respectively 14 m, 12 m and 13 m. The length of the greatest rod that can be put in it is (a) 22.31 m (b) 22.56 m (c) 20 m (d) 19.5 m Q77. Let A be a pyramid on a square base and B be a cube. If a, b and c denote the number of edges, number of faces and number of corners, respectively. Then, the result a = b + c is true for (a) Only A (b) Only B (c) Both A and B (d) Neither A nor B Q78. A cylinder circumscribes a sphere. What is the ratio of volume of the sphere to that of the cylinder ? (a) 2:3 (b) 1:2 (c) 3:4 (d) 3:2 Q79. A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by (a) 1.5 cm (b) 2 cm (c) 2.25 cm (d) 4.5 cm Q80. The angle between the legs of a compass is 60º and each leg is 10 cm long. How far apart are the points on which the legs of the compass rest? (a) 5 cm (b) 10 cm (c) 5 root 3 cm (d) 10 root 3 cm Q81. Let A and B be two points. What is the locus of the point P such that triangle APB = 90º? (a) The line AB itself (b) The point P itself (c) The circumference of the circle with AB as diameter (d) The line perpendicular to AB and bisecting AB

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Q82. BAC is triangle with angle A = 90°. From A, a perpendicular AD is drawn on BC. Which one of the following is correct? (a) Only angle ABC ~ D DAC (b) Only angle DAC ~ D DBA (c) Only angle ABC ~ DDBA ~ D DAC (d) Only angle ABC ~ angle DAB where ~ stands for the notation of similarity. Q83. If the medians of two equilateral triangles are in the ratio 3: 2, then what is the ratio of their sides? (a) 1: 1 (b) 2: 3 (c) 3: 2 (d) 3: 2 Q84. The centroid of a DABC is 8 cm from the vertex A. What is the length of the median of the triangle through A? (a) 20 cm (b) 16 cm (c) 12 cm (d) 10 cm Q85. The side AC of a triangle ABC is produced to D such that BC = CD. If triangle ACB is 70°, then what is triangle ADB equal to? (a) 35º (b) 45º (c) 70º (d) 110º Q86. For a triangle, the radius of the circumcircle is double the radius of the inscribed circle, then which one of the following is correct? (a) The triangle is a right-angled (b) The triangle is an isosceles (c) The triangle is an equilateral (d) None of the above Q87. The quadrilateral formed by joining the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD is (a) a trapezium but not a parallelogram (b) a quadrilateral but not a trapezium (c) a parallelogram only (d) a rhombus Q88. Let ABCD be a parallelogram. Let X and Y be the mid– points of the sides BC and AD, respectively. Let M and N be the mid–points of the sides AB and CD, respectively. Consider the following statements: 1. The straight line MX cannot be parallel to YN. 2. The straight lines AC, BD, XY and MN meet at a point. Which of the above statements is/are correct? (a) Only 1 (b) Only 2 (c) Both 1 and 2 (d) Neither 1 nor 2

Q89. The area of a rhombus with side 13cm and one diagonal 10 cm will be (a) 140 square cm (b) 130 square cm (c) 120 square cm (d) 110 square cm Q90.

(a) 2 6 (b) 34 (c) 4 6 (d) 6 2 Q91.

(a) 11 cm (b) 14 cm (c) 15 cm (d) 16 cm Q92.

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(a) 44° (b) 46° (c) 67° (d) 78.5° Q93.

(a) 40° (b) 45° (c) 50° (d) 60° Q94. A bicycle is running straight towards North. What is the locus of the centre of the front wheel of the bicycle whose diameter is d? (a) A line parallel to the path of the wheel of the bicycle at a height d cm (b) A line parallel to the path of the wheel of the bicycle at a height d/2 cm (c) A circle of radius d/2 cm (d) A circle of radius d cm Q95. The diameter of a circle with centre at C is 50 cm. CP is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP = 18 cm, then what is the length of AB? (a) 24 cm (b) 32 cm (c) 40 cm (d) 48 cm Q96. What type of classification is needed to enumerate the female population of India? (a) Geographical (b) Chronological (c) Qualitative (d) Quantitative

Q97. Which one of the following represents statistical data? (a) The names of all owners of shops located in a shopping complex (b) A list giving the names of all states of India (c) A list of all European countries and their respective capital cities (d) The volume of a rainfall in certain geographical area, recorded every month for 24 consecutive months Q98. DIRECTIONS : Read the following information carefully to answer the questions that follow. The average age of 6 persons living in a house is 23.5 years. Three of them are majors and their average age is 42 years. The difference in ages of the three minor children is same. 34. What is the mean of the ages of minor children? (a) 3 years (b) 4 years (c) 5 years (d) 6 years Q99. Which one among the following statements is correct? (a) Simple bar diagrams are those diagrams which show two characteristics of the data (b) In pie diagrams all the items are converted into angles (c) A bar diagram is one in which data are shown in terms of bars (d) Bar diagrams present data through length and breadth

Q100. Which of the following is/are correctly matched? I. Weight of a person: Continuous variable. II. Educational qualification of the person: Attribute Select the correct answer using the codes given below. (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II 1. a 2. a 3. c 4. d 5. b 6. c 7. d 8. d 9. c 10. d 11. c 12. a 13. b 14. c 15. b 16. b 17. c 18. c 19. c 20. c 21. c 22. c 23. d 24. c 25. d 26. a 27. b 28. c 29. a 30. a 31. d 32. d 33. d 34. a 35. b 36. d 37. c 38. c 39. b 40. c 41. b 42. a 43. b 44. a 45. b 46. b 47. c 48. c 49. c 50. b 51. a 52. c 53. c 54. c 55. d 56. c 57. a 58. c 59. b 60. c 61. b 62. d 63. d 64. c 65. a 66. c 67. b 68. c 69. b 70. d 71. b 72. d 73. c 74. b 75. d 76. b 77. d 78. a 79. c 80. b 81. c 82. c 83. c 84. c 85. b 86. c 87. c 88. b 89. c 90. c 91. b 92. c 93. b 94. b 95. d 96. d 97. d 98. c 99. a 100. a 1.

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2.

3.

4.

5. We know that the product of a rational number and an irrational number is an irrational number. 6. Since, D is a point of BC. As BC is rational so BD must be rational but AD need not to be rational. 7. There are an infinite of rational numbers between any two given numbers. 8.

9.

10.

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11.

12.

13.

14. LCM of (4, 5, 8, 9) = 360 Difference between divisor and remainder. = 3 – 4 = 4 – 5 = 7 – 8. = 8 – 9 = – 1 Hence, Required value = 360 – 1 = 359. 15. Let two numbers by 29x and 29y. ? 29x + 29y = 232 Ÿ x + y = 8 Ÿ (x, y) = (1, 7), (3, 5) Since, one such pair is 87 and 145. Hence, the other pairs is 203 and 29. 16.

17.

18.

19.

20.

21.

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22.

s 23.

24.

25. Let fourth proportional be x. 7: 11:: 14: x Ÿ 7/11 = 14/x Ÿ x = 2 × 11 ? x = 22 26. A: B = 2: 5 o × 3 B: C = 3: 4 o × 5 Now, A: B = 6: 15 B: C = 15: 20 So A: B: C = 6: 15: 20 27.

28.

29.

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31.

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32.

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50.

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59. The angle of elevation and angle of depression are measured with the horizontal line only. 60.

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84.

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85.

86.

87.

The quadrilateral formed by joining the mid-points of the sides is a parallelogram. 88.

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90.

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91.

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93.

94.

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95.

96. Quantitative is needed to enumerate the female population of India. 97. The volume of rainfall in certain geographical area, recorded every month for 24 consecutive months. 98. Total age of six persons = 23.5 × 6 = 141 years Total age of three major persons = 42 × 3 = 126 years \ Total age of three minor children = 411 – 126 = 15 years The difference in ages of the three minor children is same. Therefore, we take ages may be: 5, 5, 5; 3, 5, 7; 2, 5, 8 and 1, 5, 9 In all the cases, median will be 5 years. 99. Simple Bar Diagram represents only one variable. For examples: Sales, Production, Population, Figures, etc. For various years may be shown by simple bar charts. Since these are of the same width and vary only in heights (or lengths). It becomes very easy for readers to study the relationship. Simple bar diagrams are very popular in practice. A bar can be either vertical or horizontal; vertical bars are more popular. 100. Continuous Variable: It is available whose value is obtained by measuring. Examples: (i) Height of students in class. (ii) Weight of students in class. (iii) Weight of a person. Here, weight of a person is continuous variable while educational qualification of the person is Discrete Variables.