170 CDS MATHEMATICS PRACTICE SET Subject Questions Marks Time -Ve Maths 100 100 2 hrs 1/3 Q1. Which one of the following is correct? The sum of two irrational numbers (a) is always a natural or irrational (b) may be rational or irrational (c) is always a rational number (d) is always an irrational number Q2. What least value must be given to *, so that the number 8798546*5 is divisible by 11? (a) 0 (b) 1 (c) 2 (d) 3 Q3. There are four numbers forming a GP in which the third term is greater than the first by 9 and the second term is greater than the fourth by 18. What is the first term? (a) 2 (b) 3 (c) 2 (d) 3 Q4. What is the value of x for which x, x + 1, x + 3 are all prime numbers? (a) 0 (b) 1 (c) 2 (d) 101 Q5. When a positive integer n is divided by 5, the remainder is 2. What is the remainder when the number 3n is divided by 5? (a) 1 (b) 2 (c) 3 (d) 4 Q6. Consider the following statements: I. Every composite number is a natural number. II. Every whole number is a natural 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 Q8. What is the last digit in 7 402 + 3 402? (a) 0 (b) 4 (c) 8 (d) None of the above Q9. 7 10 5 10 is divisible by (a) 10 (b) 7 (c) 5 (d) 11 Q10. The digit in the units place of the product 81 82 83 84... 99 is (a) 0 (b) 4 (c) 6 (d) 8 Q11. Out of 532 saving accounts held in a post office, 218 accounts have deposits over Rs 10,000 each. Further, in 302 accounts, the first or sole depositors are men, of which the deposits exceed Rs 10,000 in 102 accounts. In how many accounts the first or sole depositors are women and the deposits are up to Rs 10,000 only? (a) 116 (b) 114 (c) 100 (d) Cannot be determined from the given data Q12. If HCF of m and n is 1, then what are the HCF of m + n, m and HCF of m n, n, respectively? (m > n) (a) 1 and 2 (b) 2 and 1 (c) 1 and 1 (d) Cannot be determined Q13. What is the least number which when divided by 42, 72 and 84 leaves the remainders 25, 55 and 67, respectively? (a) 521 (b) 512 (c) 504 (d) 487 Q14. What is the HCF of 3.0, 1.2 and 0.06? (a) 0.6 (b) 0.06 (c) 6.0 (d) 6.06 Q7. Which one of the following has least number of divisors? (a) 88 (b) 91 (c) 96 (d) 99
171 Q15. The LCM of two numbers is 2376 while their HCF is 33. If one of the numbers is 297, then the other number is (a) 216 (b) 264 (c) 642 (d) 792 Q16. The HCF of two natural numbers m and n is 24 and their product is 552. How many sets of values of m and n are possible? (a) 1 (b) 2 (c) 4 (d) No set of m and n is possible satisfying the given conditions Q17. What is the value of 0.007 17.83 310.0202? (a) 327.86638 (b) 327.86638 (c) 327.86683 (d) 327 Q18. (a) A and R are correct and R is correct explanation of A (b) A and R are correct but R is not correct explanation of A (c) A is correct but R is wrong (d) A is wrong but R is correct Q19. (a) a rational number less than 0.01 (b) a rational number (c) an irrational number (d) neither a rational number nor an irrational number Q20. If the height of a cone is increased by 50%, then what is the percentage increase in the volume of the cone? (a) 100/3 % (b) 40% (c) 50% (d) 200/3 % Q21. What is 5% of 50% of 500? (a) 12.5 (b) 25 (c) 1.25 (d) 6.25 Q22. The monthly incomes of A and B are in the ratio 4: 3. Each of them saves Rs 600. If the ratio of their expenditure is 3: 2, then what is the monthly income of A? (a) Rs 2400 (b) Rs 1800 (c) Rs 2000 (d) Rs 3600 Q23. If x: y = 1: 3, y: z = 5: k, z: t = 2: 5 and t: x = 3: 4, then what is the value of k? (a) 1/2 (b) 1/3 (c) 2 (d) 3 Q24. X is twice as old as Y 3 years ago, when X was as old as Y today. If the difference between their ages as present is 3 years, how old is X at present? (a) 18 years (b) 12 years (c) 9 years (d) 8 years Q25. Age of X is six times that of Y. After 4 years, X is four times elder to Y. What is the present age of Y? (a) 4 years (b) 5 years (c) 6 years (d) 7 years Q26. How much tea at Rs 9 per kg must be mixed with 100 kg of superior tea at Rs 13.50 per kg to give an average price of Rs 11 per kg? (a) 85 kg (b) 120 kg (c) 125 kg (d) 130 kg Q27. If the average of A and B is 30, the average of C and D is 20, then which of the following is/are correct? I. The average of B and C must be greater than 25. II. The average of A and D must be less than 25. Select the correct answer using the codes given below. (a) Only I (b) Only II (c) Either I or II (d) Neither I or II Q28. The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs 4000 for 2 years at 10% per annum. What is the sum placed on simple interest? (a) Rs 1550 (b) Rs 1650 (c) Rs 1750 (d) Rs 2000 Q29. The difference between compound interest and simple interest for 2 yr at the rate of 10% over principal amount of Rs X is Rs10. What is the value of X? (a) Rs 100 (b) Rs 1000 (c) Rs 500
172 (d) Rs 5000 Q30. Successive discounts of 25/2% and 15/2% are given on the marked price of a cupboard. If the customer pays Rs 2590, then what is the marked price? (a) Rs 3108 (b) Rs 3148 (c) Rs 3200 (d) Rs 3600 Q31. On selling an article for Rs 240, a trader loses 4%. In order to gain 10%, he must sell the article for (a) Rs 275 (b) Rs 280 (c) Rs 285 (d) Rs 300 Q32. A person selling an article for Rs 96 finds that his loss per cent is one fourth of the amount of rupees that he paid for the article. What can be the cost price? (a) Only Rs160 (b) Only Rs 240 (c) Either Rs 160 or Rs 240 (d) Neither Rs 160 nor Rs 240 Q33. A train of length 150 m takes 10 s to cross another train 100 m long coming from the opposite direction. If the speed of first train is 30 km/h. What is the speed of second train? (a) 72 km/h (b) 60 km/h (c) 54 km/h (d) 48 km/h Q34. Two trains each 200 m long move towards each other on parallel lines with velocities 20 km/h and 30 km/h, respectively. What is the time that elapses when they first meet until they have cleared each other? (a) 20 s (b) 24.8 s (c) 28.8 s (d) 30 s Q35. A man cycles with a speed of 10 km/h and reaches his office at 1 p.m. However, when he cycles with a speed of 15 km/h, he reaches his office at 11 am. At what speed should he cycle, so that he reaches his office at 12 noon? (a) 12.5 km/h (b) 12 km/h (c) 13 km/h (d) 13.5 km/h Q36. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is (a) 1 hour (b) 2 hours (c) 3 hours (d) 4 hours Q37. If one man or two women or three boys can do a piece of work in 55 days, then one man, one woman and one boy will do it how many days? (a) 20 days (b) 30 days (c) 40 days (d) 50 days Q38. X completes a job in 2 days and Y completes it in 3 days and Z takes 4 days to complete it. If they work together and get Rs3900 for the job, then how much amount does Y get? (a) Rs 1800 (b) Rs 1200 (c) Rs 900 (d) Rs 800 Q39. 20 workers working for 5 h per day complete a work in 10 days. if 25 workers are employed to work 10 h per day, what is the time required to complete the work? (a) 4 days (b) 5 days (c) 6 days (d) 8 days Q40. There are two taps A and B to fill up a water tank. The tank can be filled in 40 min, if both taps are on. The same tank can be filled in 60 min, if tap A alone is on. How much time will tap B alone take, to fill up the same tank? (a) 64 min (b) 80 min (c) 96 min (d) 120 min Q41. If (x + y + z = 0), then what is (x + y) (y + z) (z + x) equal to? (a) xyz (b) x 2 + y 2 + z 3 (c) x 3 + y 3 + z 3 + 3xyz (d) xyz Q42. If x 2 11x + a and x 2 14x + 2a have a common factor, then what are the values of a? (a) 0, 7 (b) 5, 20 (c) 0, 24 (d) 1, 3 Q43. Which one of the following statements is correct? (a) Remainder theorem is a special case of factor theorem (b) Factor theorem is a special case of remainder theorem (c) Factor theorem and remainder theorem are two independent results (d) None of the above
173 Q44. What is the remainder when (x 11 + 1) is divided by (x + 1)? (a) 0 (b) 2 (c) 11 (d) 12 Q45. 95. If the expression x 3 + 3x 2 + 4x + k has a factor x + 5, then what is the value of k? (a) 70 (b) 70 (c) 48 (d) 48 Q50. 15º 30º 45º 60º Q51. Q46. Consider the following statements: I. Set of points of a given line is a finite set. II. Intelligent students in a class is a set. III. Good books in a school library is a set. Which of the above statements is/are not correct? (a) Only I (b) Both II and III (c) Both I and II (d) I, II and III 0 1 2 4 Q52. If sin x + sin y = a and cos x + cos y = b, what is sin x. sin y + cos x. cos y equal to? Q47. Q53. Q48. Q49. Q54. 3/5 4/5 12/25 13/25 Q55. What is the value of cos 1º cos 2º cos 3º... cos 90º? 1/2
0 1 2 174 (b) 52.2 m (c) 67.2 m (d) 70 m Q56. Assume the Earth to be a sphere of radius R. What is the radius of the circle of latitude 40º S? R cos 40º R sin 80º R sin 40º R tan 40º Q57. Q58. The angle of elevation from the bank of a river of the top of a tree standing on the opposite bank is 60º. The angle of elevation becomes 30º when observed from a point 40 m backwards in a direction perpendicular to the length of the river. What is the width of the river? (a) 10 m (b) 20 m (c) 30 m (d) 40 m Q59. A ladder of 17 ft length reaches a window which is 15 ft above the ground on one side of the street. Keeping its foot at the same point the ladder is turned to the other side of the street and now it reaches a window 8 ft high. What is the width of the street? (a) 23 ft (b) 15 ft (c) 25 ft (d) 30 ft Q60. The angle of elevation of a cloud from a point 200 m above a lake is 30 and the angle of depression of its reflection in the lake is 60. The height of the cloud is (a) 200 m (b) 300 m (c) 400 m (d) 600 m Q61. A wire is in the form of a circle of radius 42 cm. If it is bent into a square, then what is the side of the square? (a) 66 cm (b) 42 cm (c) 36 cm (d) 33 cm Q62. The perimeter of a triangular field is 240 m. If two of its sides are 78 m and 50 m, then what is the length of the perpendicular on the side of length 50 m from the opposite vertex? (a) 43 m Q63. In the triangle ABC, the base BC is trisected at D and E. The line through D, parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. If EG and DF intersect at H, then what is the ratio of the sum of the area of parallelogram AGHF and the area of the triangle DHE to the area of the triangle ABC? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6 Q64. The area of a square inscribed in a circle of radius 8 cm is (a) 32 sq cm (b) 64 sq cm (c) 128 sq cm (d) 256 sq cm Q65. One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram? (a) 12.56 cm 2 (b) 14.56 cm 2 (c) 16.76 cm 2 (d) 22.56 cm 2 Q66. The ratio of the outer and inner perimeters of a circular path is 23: 22. If the path is 5 m wide, the diameter of the inner circle is (a) 55 m (b) 110m (c) 220 m (d) 230 m Q67. From a solid cylinder whose height is 4 cm and radius 3 cm a conical cavity of height 4 cm and base radius 3 cm is hollowed out. What is the volume of the remaining solid? (a) 9 pie cu cm (b) 15 pie cu cm (c) 21 pie cu cm (d) 24 pie cu cm Q68. A right circular cone is cut by a plane parallel to its base in such a way that the slant heights of the original and the smaller cone thus obtained are in the ratio 2: 1. If V1 and V2 are respectively the volumes of the original cone and of the new cone, then what is V1: V2? (a) 2: 1 (b) 3: 1 (c) 4: 1
175 (d) 8: 1 (d) 16 Q69. A roller of diameter 70 cm and length 2 m is rolling on the ground. What is the area covered by the roller in 50 revolutions? (a) 180 sq m (b) 200 sq m (c) 220 sq m (d) 240 sq m Q70. How many litres of water flow out of a pipe having an area of cross-section of 5 cm 2 in one minute, if the speed of water in the pipe is 30 cm/s? (a) 90 L (b) 15 L (c) 9 L (d) 1.5 L Q71. A cylinder having base of circumference 60 cm is rolling without sliding at a rate of 5 rounds per second. How much distance will the cylinder roll in 5 s? (a) 15 m (b) 1.5 m (c) 30 m (d) 3 m Q72. What is the height of the cone? (a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm Q73. If the diameter of a sphere is doubled, then how does its surface area change? (a) It increases two times (b) It increases three times (c) It increases four times (d) It increases eight times Q74. A cardboard sheet in the form of a circular sector of radius 30 cm and central angle 144º is folded to make a cone. What is the radius of the cone? (a) 12 cm (b) 18 cm (c) 21 cm (d) None of these Q75. What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm? (a) 10 cm (b) 12 cm (c) 15 cm (d) 16 cm Q76. A solid spherical ball of iron of radius 4 cm is melted to form spheres of radius 2 cm each. The number of spheres, so formed is (a) 8 (b) 9 (c) 10 Q77. For a plot of land of 100 m 80 m, the length to be raised by spreading the earth from stack of a rectangular base 10 m 8 m and vertical section being a trapezium of height 2 m. The top of the stack is 8 m 5 m. How many centimetres can the level raised? (a) 3 cm (b) 2.5 m (c) 2 cm (d) 1.5 cm 132 Q78. Consider the following statements: 1. The volume of the cone generated when the triangle is made to revolve about its longer leg is same as the volume of the cone generated when the triangle is made to revolve about its shorter leg. 2. The sum of the volume of the cone generated when the triangle is made to revolve about its longer leg and the volume of the cone generated when the triangle is made to revolve about its shorter leg is equal to the volume of the double cone generated when the triangle is made to revolve about its hypotenuse. Which of the above statements is/are correct? Q79. A rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper. The radius of the base of the cylinder so rolled is (a) 3.5 cm (b) 5 cm (c) 7 cm (d) 14 cm Q80. If a point P moves such that its distance from two given points A and B are equal. Then, what is the locus of the point P? (a) A straight line which is the right bisector of AB (b) A circle with centre at B (c) A straight line passing through A and B. (d) A straight line passing through either A or B Q81. If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are (a) neither equal nor supplementary (b) not equal but supplementary (c) equal but not supplementary (d) either equal or supplementary Q82. AB, EF and CD are parallel lines. If EG = 5 cm GC = 10 cm, AB = 15 cm and DC = 18 cm, then what is the value of AC? (a) 20 cm (b) 24 cm (c) 25 cm (d) 28 cm Q83. Consider the following statements I. If two triangles are equiangular, then they are similar. II. If two triangles have equal area, then they are similar. Which of the statements given above is/are correct?
176 (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q84. Consider the following statement in respect of an equilateral triangle ABC. I. There is a point P inside the triangle ABC such that each of its sides subtends an angle of 120º at P. II. There is a point P inside the triangle ABC such that the D PBC is obtuse angled and A is the orthocentre of triangle PBC. Which of the above statements is/are correct? (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q85. If triangles ABC and DEF are similar such that 2AB = DE and BC = 8 cm, then what is EF equal to? (a) 16 cm (b) 12 cm (c) 10 cm (d) 8 cm (a) 130 (b) 110 (c) 90 (d) 100 Q90. What is the number of tangents that can be drawn to a circle from a point on the circle? (a) 0 (b) 1 (c) 2 (d) 3 Q91. Q86. In a cricket match, the first 5 batsmen of a team scored runs: 30, 40, 50, 30 and 40. If these data represent a four sided figure with 50 as its one of the diagonals, then what does second diagonal represent? (a) 30 runs (b) 40 runs (c) 50 runs (d) 70 runs Q87. If two parallel lines are cut by two distinct transversals, then the quadrilateral formed by the four lines is always a (a) square (b) parallelogram (c) rhombus (d) trapezium Q88. How many equilateral triangles can be formed by joining any three vertices of a cube? (a) 0 (b) 4 (c) 8 (d) None of these (a) 20 (b) 30 (c) 35 (d) 40 Q92. Q89. (a) 5 cm (b) 4 cm (c) 10 cm (d) 20 cm
177 Q93. The distance between the centres of two circles having radii 4.5 cm and 3.5 cm respectively is 10 cm. What is the length of the transverse common tangent of these circles? (a) 8 cm (b) 7 cm (c) 6 cm (d) None of these Q94. A circular ring with centre O is kept in the vertical position by two weightless thin strings TP and TQ attached to the ring at P and Q. The line OT meets the ring at E whereas a tangential string at E meets TP and TQ at A and B, respectively. If the radius of the ring is 5 cm and OT = 13 cm, then what is the length of AB? (a) 10/3 cm (b) 20/3 cm (c) 10 cm (d) 40/3 cm Q95. A railroad curve is to be laid on a circle. What radius (approximate) should be used, if the track is to change direction by 25 in a distance of 120 m? (a) 300 m (b) 280 m (c) 275 m (d) 264 m Q96. If every number of a finite set is increased by any number k, the measure of central tendency should also increase by k. Which one of the following measures of central tendency does not have this property? (a) Arithmetic mean (b) Median (c) Mid-range, i.e. the arithmetic mean of the largest and smallest numbers (d) Geometric mean Q97. Examples of data are given below: I. Information on households collected by an investigator by door to door visits. II. Data on the percentage of literates, sexwise, for the different districts of a state collected from records of the census of India. III. General information about families, collected by telephonic interviews. Which one of the following in respect of the above is correct? (a) I and II are primary data (b) I and III are primary data (c) II and III are primary data (d) I, II and III are primary data Q98. Consider the following statements in respect of histogram. I. Histogram is an equivalent graphical representation of the frequency distribution. II. Histogram is suitable for continuous random variables, where the total frequency of an interval is evenly distributed over the interval. 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 Q99. If the population figures are given for each state of India, then the data can be classified as (a) qualitative (b) quantitative (c) chronological (d) geographical Q100. Which one of the following statements is correct? (a) A frequency polygon is obtained by connecting the corner points of the rectangles in a histogram (b) A frequency polygon is obtained by connecting the mid-points of the tops of the rectangles in a histrogram (c) A frequency polygon is obtained by connecting the corner points of the class intervals in a histogram (d) None of the above 1. b 2. d 3. b 4. c 5. a 6. a 7. b 8. c 9. d 10. a 11. b 12. c 13. d 14. b 15. b 16. d 17. b 18. c 19. b 20. c 21. a 22. a 23. a 24. c 25. d 26. c 27. d 28. c 29. b 30. c 31. a 32. c 33. b 34. c 35. b 36. a 37. b 38. b 39. a 40. d 41. a 42. c 43. b 44. a 45. b 46. d 47. d 48. c 49. c 50. c 51. b 52. d 53. c 54. b 55. b 56. a 57. c 58. b 59. a 60. c 61. a 62. c 63. b 64. c 65. c 66. c 67. d 68. d 69. c 70. c 71. a 72. a 73. c 74. a 75. d 76. a 77. d 78. d 79. c 80. a 81. b 82. c 83. a 84. a 85. a 86. c 87. d 88. c 89. a 90. b 91. b 92. b 93. c 94. b 95. c 96. d 97. b 98. c 99. d 100. b 1. 2. 3.
178 LCM of 42, 72 and 84 = 504 Difference between divisor and remainder = 25 42 = 55 72 = 67 84 = 17 Required number = 504 17 = 487. 14. 15. 4. 5. Let n = 5q + 2 3n = 3(5q + 2) Ÿ n = 15q + 6 = 5 (3q + 1) + 1 When 3n is divided by 5, then remainder is 1. 6. I. Composite Number: Natural numbers, which has more than 2 distinct factors are called composite number. It postulates that every composite number is a natural number. II. Every whole number is not a natural number (zero is not a natural number). So, only statement I is true. 7. Here, 88 = 2 2 2 11= (2) 3 (11) 1 91 = (7) 1 (13) 1 96 = 2 2 2 2 2 3 = (2) 5 (3) 1 and 99 = 3 3 11 = (3) 2 (11) 1 So, 91 has least number of divisors. 8. 16. 17. 9. 7 10 5 10 is divisible by 11. 10. 81 82 83 84... 99 It can be written as = 81 82 83 84... 90 99 When we multiply any number by multiple of 10, then resultant number always carry zero at unit place. 11. Number of account up to ` 10,000 = 532 218 = 314 accounts. Rest of accounts of men deposits = 302 102 = 200 accounts Number of accounts of women deposits = 314 200 = 114 12. HCF of m and n is 1.? HCF (m + n, m) = 1 and HCF (m n, n) = 1 13. 18. 19. 20.
179 21. 22. Let monthly incomes of A s and B s are 4x and 3x. And monthly expenditures of A s and B s are 3y and 2y. Each saving = ` 600? Income Expenditure = Saving? 4x 3y = 600...(i) 3x 2y = 600...(ii) On solving equations. (i) and (ii), we get x = 600? A s income = 4x = 4 600 = ` 2400 23. 29. 24. Let present age of X = x years Present age of Y = (x 3) years 3 years ago, age of X = (x 3) years Age of Y = (x 6) years According to the question, x 3 = 2(x 6) Ÿ x 3 = 2x 12 Ÿ 12 3 = 2x x x = 9 years 25. Let the age of X and Y are x years and y years respectively. Then, (x + 4) = 4(y + 4) Ÿ 6y + 4 = 4y + 16 Ÿ 2y = 12? y = 6? The present age of y = 6 years 26. 30. 27. 31. 32. 28.
180 33. 34. 37. 35. 38. 36.
181 44. 45. 39. 40. 41. Given, x + y + z = 0? (x + y) (y + z) (z + x) = ( z) ( x) ( y) = xyz 42. 46. I. The set of points of a given line is not a finite set. II. Here, we cannot decide, which students are intelligent. III. Here, we cannot decide, which books are good a school library. 47. 48. 49. 43. Factor theorem is a special case of remainder theorem.
182 50. 51. 52. 54. 53. 55. 56.
183 57. 60. 58. 61. 62. 59.
184 63. 64.
185 69. 65. 66. 70. 67. 71. 72. 68. 73.
186 74. 75. 76. 77. 79. 78. 80. The locus of P is a straight line which is the right bisector of AB. 81.
187 85. 86. Here we see (50) 2 = (30) 2 + (40) 2 Þ 2500 = 900 + 1600 Þ 2500 = 2500 It means given scores are the sides of a rectangle. So, other diagonal should be 50 runs. 87. 82. 88. 83. We know that, if two triangles are equiangular, then they are similar (refer similarity conditions). Statement II is not true. 84.
188 92. 89. 93. 90. 91. 94.
189 95. 96. 97. 98. 99. 100. Q