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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 is correct? The number 222222 is (a) divisible by 3 but not divisible by 7 (b) divisible by 3 and 7 but not divisible by 11 (c) divisible by 2 and 7 but not divisible by 11 (d) divisible by 3, 7 and 11 Q2. The set of integers is closed with respect to which one of the following? (a) Addition only (b) Multiplication only (c) Both addition and multiplication (d) Division Q3. When a natural number n is divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4? (a) 1 (b) 2 (c) 3 (d) 6 Q4. What can be said about the expansion of 212n – 64n, where n is positive integer? (a) Last digit is 4 (b) Last digit is 8 (c) Last digit is 2 (d) Last two digit are zero Q5. Which one of the following three-digit numbers divides 9238 and 7091 with the same remainder in each case? (a) 113 (b) 209 (c) 317 (d) 191 Q6. Consider the following statements: I. The product of any three consecutive integers is divisible by 6. II. Any integer can be expressed in one of the three forms 3k, 3k + 1, 3k + 2, where k is an integer. Which of the above statements is/are correct ? (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q7. Which one of the following is neither prime number nor composite number? (a) 1 (b) 2 (c) 3 (d) None of these

Q8. If x is positive even integer and y is negative odd integer, then x y is (a) odd integer (b) even integer (c) rational number (d) None of these Q9. What is the remainder when 41000 is divided by 7? (a) 1 (b) 2 (c) 4 (d) None of these Q10. What is the number of divisors of 360? (a) 12 (b) 18 (c) 24 (d) None do these Q11. Consider the following statements: 1. There exists only one prime number p such that (17p + 1) is a square. 2. If x is the product of 10 consecutive prime numbers starting from 2, then (x + 1) is also a prime number. Which of the above statements is/are correct? (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 Q12. LCM of two numbers is 16 times their HCF. The sum of LCM and HCF is 850. If one number is 50, then what is the other number? (a) 800 (b) 1200 (c) 1600 (d) 2400 Q13. If the HCF of x 3 – 27 and x 4 + 4x 2 + 12x + k is a quadratic polynomial, then what is the value of k? (a) 27 (b) 9 (c) 3 (d) – 3 Q14. What is the least number of square tiles required to pave the floor of a room 9 m 99 m cm long and 4 m 7 cm broad? (a) 247 (b) 277 (c) 297 (d) 307

Q15. The product of HCF and LCM of 18 and 15 is (a) 120

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(b) 150 (c) 175 (d) 270 Q16. There are 48 cricket balls, 72 hockey balls and 84 tennis balls and they have to be arranged in several rows in such a way that every row contains the same number balls of balls of one type. What is the minimum number of rows required for this to happen? (a) 12 (b) 16 (c) 17 (d) 19 Q17. What is 3.76 – 1.4576 equal to? (a) 2.3100191 (b) 2.3101091 (c) 2.3110091 (d) 2.3110901 Q18.

(a) 0 (b) 1 (c) 2 (d) –1 Q19. Out of a group of swans 7/2 times the square root of the number are swimming in the pool while the two remaining are playing outside the pool. What is the total number of swans? (a) 4 (b) 8 (c) 12 (d) 16 Q20. If salary of X is 20% more than salary of Y, then by how much percentage is salary of Y less than X? (a) 25 (b) 20 (c) 50/3 (d) 65/4 Q21. The price of an article is 25. After two successive cuts by the same percentage, the price becomes Rs20.25. If each time the cut was x%, then (a) x = 9 (b) x = 10 (c) x = 11 (d) x = 11.5 Q22. The age of a mother, before two years, was eight times the age of their daughter. After 1 year, mother’s age will be five times the daughter’s age. After how many years from now the mother’s age will become three times the daughter’s age?

(a) 6 years (b) 8 years (c) 10 years (d) 12 years Q23. If the ratio of x to y is 25 times the ratio of y to x, then what is the ratio of x to y? (a) 1: 5 (b) 5: 1 (c) 25: 1 (d) 1: 25 Q24. A certain amount of money has be divided between two persons P and Q in the ratio 3: 5. But it was divided in the ratio 2: 3 and thereby Q loses Rs 10. What was the amount? (a) Rs 250 (b) Rs 300 (c) Rs 350 (d) Rs 400 Q25. A milkman bought 15 kg of milk and mixed 3 kg of water in it. If the price per kg of the mixture becomes Rs 22, what is cost price of the milk per kg? (a) Rs 28.00 (b) Rs 26.40 (c) Rs 24.00 (d) Rs 22.00 Q26. An aeroplane flies along the four sides of a square at a speed of 100, 200, 300 and 400 km/h, respectively. What is the average speed of the plane in its flight around the square? (a) 192 km/h (b) 200 km/h (c) 250 km/h (d) None of these Q27. The average weight of a class of 15 boys and 10 girls is 38.4 kg. If the average weight of the boys is 40 kg, then what is the average weight of the girls? (a) 36.5 kg (b) 35 kg (c) 36 kg (d) 34.6 kg Q28. A person borrowed Rs 7500 at 16% compound interest. How much does he have to pay at the end of 2 years to clear the loan? (a) Rs 9900 (b) Rs 10092 (c) Rs 11000 (d) Rs 11052 Q29. When an article is sold at 20% discount, the selling price is Rs24. What will be the selling price when the discount is 30%? (a) Rs 25 (b) Rs 23 (a) Rs 21

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(d) Rs 20 Q30. A refrigerator and a camera were sold for Rs 12000 each. The refrigerator was sold at a loss of 20% of the cost and the camera at a gain of 20% of the cost. The entire transaction results in which one of the following? (a) No loss or gain (b) Loss of Rs 1000 (c) Gain of Rs 1000 (d) Loss of Rs 2000 Q31. A man bought a number of oranges at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%? (a) Rs 4 (b) Rs 5 (c) Rs 6 (d) Rs 7 Q32. Two lots of onions with equal quantity, one costing Rs 10 per kg and the other costing Rs15 per kg, are mixed together and whole lot is sold at Rs 15 per kg. What is the profit or loss? (a) 10% loss (b) 10% profit (c) 20% profit (d) 20% loss Q33. A train 110 m long is running with a speed of 60 km/h. What is the time in which it will pass a man who starts from the engine running at the speed of 6 km/h in the direction opposite to that of the train? (a) 5 s (b) 6 s (c) 10 s (d) 15 s Q34. A motorboat takes 2 h to travel a distance of 9 km down the current and it takes 6 h to travel the same distance against the current. What is the speed of the boat in still water 1 km/hr? (a) 3 (b) 2 (c) 1.5 (d) 1 Q35. A sailor sails a distance of 48 km along the flow of a river in 8 h. If it takes 12 h return the same distance, then the speed of the flow of the river is (a) 0.5 km/h (b) 1 km/h (c) 1.5 km/h (d) 2 km/h Q36. A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is (a) 18 km/hr

(b) 24 km/hr (c) 30 km/hr (d) 36 km/hr Q37. Ram can do a piece of work in 6 days and Shyam can finish the same work in 12 days. How much work will be finished, if both work together for 2 days? (a) One-fourth of the work (b) One-third of the work (c) Half of the work (d) Whole of the work Q38. Four taps can individually fill a cistern of water in 1h, 2h, 3h and 6h, respectively. If all the four taps are opened simultaneously, the cistern can be filled in how many minutes? (a) 20 (b) 30 (c) 35 (d) 40 Q39. 18 men can earn Rs 360 in 5 days. How much money will 15 men earn in 9 days? (a) Rs 600 (b) Rs 540 (c) Rs 480 (d) Rs 360 Q40. A and B can do a piece of work in 10 h. B and C can do it in 15 h, while A and C take 12 h to complete the work. B independently can complete the work in (a) 12h (b) 16h (c) 20h (d) 24h Q41. The efficiency of P is twice that of Q, whereas the efficiency of P and Q together is three times that of R. If P, Q and R work together on a job, in what ratio should they share their earnings? (a) 2: 1: 1 (b) 4: 2: 1 (c) 4: 3: 2 (d) 4: 2: 3 Q42. If a is a rational number such that (x – a) is a factor of the polynomial x 3 – 3x 2 – 3x + 9, then (a) a can be any integer (b) a is an integer dividing 9 (c) a cannot be an integer (d) a can take three values Q43. When x 40 + 2 is divided by x 4 + 1, what is the remainder? (a) 1 (b) 2 (c) 3 (d) 4

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Q44. If 3x 3 – 2x 2 y – 13xy 2 + 10y 3 is divided by x – 2y, then what is the remainder? (a) 0 (b) x (c) y + 5 (d) x – 3 Q45. If the expression x 3 + 3x 2 + 4x + p contains (x + 6) as a factor, then the value of p is (a) 132 (b) 141 (c) 144 (d) 151 Q46. In an examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% candidates failed in both English and Mathematics, what percentage of candidates passed in both the subjects? (a) 18% (b) 21% (c) 23% (d) 25% Q47.

Q48.

Q49.

cosec x 2 cosec x 2 sin x 2 cos x Q50.

Q51. I and II II and III I and III All of these Q52.

–1 0 1 2 Q53.

35/0 –35/8 –11/8 11/8 Q54.

√7 7/3 3 √3 Q55.

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Q56.

Q57. Only I Only II Both I and II Neither I nor II Q58. What is the value of sec (90 – θ)°. sin θ sec 45º?

Q59. A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45º with the man’s eye when at a distance of 60 m from the bottom of tower. After 5 s, the angle of depression becomes 30º. What is the approximate speed of the boat assuming that it is running in still water? (a) 31.5 km/h (b) 36.5 km/h (c) 38.5 km/h (d) 40.5 km/h Q60. The angles of elevation of the top of a tower from two points P and Q at distances m 2 and n 2 respectively, from the base and in the same straight line with it are complementary. The height of the tower is (a) (mn) 1/2

(b) mn 1/2 (c) m 1/2 n (d) mn Q61. A horse is tied to a pole fixed at one corner of a 50 m × 50 m square field of grass by means of a 20 m long rope. What is the area of that part of the field which the horse can graze? (a) 1256 m2 (b) 942 m2 (c) 628 m2 (d) 314 m2 Q62. The two diagonals of a rhombus of lengths 55 cm and 48 cm. If p is the perpendicular height of the rhombus, then which one of the following is correct? (a) 36 cm < p < 37 cm (b) 35 cm < p < 36 cm (c) 34 cm < p < 35 cm (d) 33 cm < p < 34 cm Q63. If the area of a rectangle whose length is 5 units more than twice its width is 75 sq units, then what is the width? (a) 3 units (b) 5 units (c) 7 units (d) 10 units Q64. The area of a rectangular field is 4500 sq m. If its length and breadth are in the ratio 9: 5, then its perimeter is (a) 90 m (b) 150 m (c) 280 m (d) 360 m

Q65. The perimeter of a rectangle having area equal to 144 cm2 and sides in the ratio 4: 9 is (a) 52 cm (b) 56 cm (c) 60 cm (d) 64 cm Q66. The sides of a triangular field are 41 m, 40 m and 9 m. The number of rose beds that can be prepared in the field if each rose bed, on an average, needs 900 square cm space, is (a) 2000 (b) 1800 (c) 900 (d) 800 Q67. From a wooden cylindrical block, whose diameter is equal to its height, a sphere of maximum possible

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volume is carved out. What is the ratio of the volume of the utilised wood to that of the wasted wood? (a) 2: 1 (b) 1: 2 (c) 2: 3 (d) 3: 2 Q68. A hollow cylindrical iron pipe of length 1.4 m has base radius 2.5 cm and thickness of the metal is 1 cm. What is the volume of the iron used in the pipe? (a) 2640 cu cm (b) 2604 cu cm (c) 2460 cu cm (d) None of these Q69. A cylindrical vessel of base radius 14 cm is filled with water to some height. If a rectangular solid of dimensions 22 cm × 7 cm × 5 cm is immersed in it, what is the rise in water level? (a) 0.5 cm (b) 1.0 cm (c) 1.25 cm (d) 1.5 cm Q70. How many litres of water (approximately) can a hemispherical container of radius 21 cm hold? (a) 19.4 L (b) 38.8 L (c) 194 L (d) 388 L Q71. The volume of a cone is equal to that of a sphere. If the diameter of base of cone is equal to the diameter of the sphere, then what is the ratio of height of cone to the diameter of the sphere? (a) 2: 1 (b) 1: 2 (c) 3: 1 (d) 4: 1 Q72. The volume of a sphere is 8 times that of another sphere. What is the ratio of their surface areas? (a) 8: 1 (b) 4: 1 (c) 2: 1 (d) 4: 3 Q73. A cylindrical vessel of height 10 cm has base radius 60 cm. If d is the diameter of a spherical vessel of equal volume, then what is d equal to? (a) 30 cm (b) 60 cm (c) 90 cm (d) 120 cm Q74. The curved surface area of a right circular cone of radius 14 cm is 440 sq cm. What is the slant height of the cone? (a) 10 cm (b) 11 cm

(c) 12 cm (d) 13 cm Q75. The diameter of base of a right circular cone is 7 cm and slant height is 10 cm, then what is its lateral surface area? (a) 110 sq cm (b) 100 sq cm (c) 70 sq cm (d) 49 sq cm Q76. From a solid wooden right circular cylinder, a right circular cone whose radius and height are same as the radius and height of the cylinder, respectively is curved out. What is the ratio of the volume of the utilised wood to that of the wasted wood? (a) 1: 2 (b) 2: 1 (c) 2: 3 (d) 1: 3 Q77. A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of the cylinder is 24 m. The height of the cylindrical portion is 11 m, while the vertex of the cone is 16 m above the ground. What is the area of the curved surface for conical portion? (a) 3434/9 sq m (b) 3431/8 sq m (c) 3432/7 sq m (d) 3234/7 sq m Q78. What is the surface area of the double cone so formed? (a) 1101.2 cm2 (b) 1111.4 cm2 (c) 1310.4 cm2 (d) 1318.8 cm2 Q79. Water flows through a cylindrical pipe of internal diameter 7 cm at the rate of 5 m/s. The time, in minutes, the pipe would take to fill an empty rectangular tank 4m × 3m × 2.31m is (a) 28 (b) 24 (c) 20 (d) 12 Q80. Let AB and AC be two rays intersecting at A. If D, E be the points lying on AB, AC respectively and P be the point such that P divides the line DE such that PD: PE = AD: AE. Then, what is the locus of the point P? (a) The angle bisector of angle A (b) The angle trisect or of angle A (c) The perpendicular bisector of angle A (d) None of the above Q81. Consider the following statements I. The locus of points which are equidistant from two parallel lines is a line parallel to both of them and drawn mid way between them.

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II. The perpendicular distances of any point on this locus line from two original parallel lines are equal. Further, no point outside this locus line has this property. Which of the above statements is/are correct? (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q82. Consider the following statements A triangle can be constructed if its I. two sides and the included angles are given. II. three angles are given. III. two angles and the included side are given. Which of the statements given above are correct ? (a) I and II (b) I and III (c) II and III (d) All of these Q83. Consider the following statements I. Congruent triangles are similar. II. Similar triangles are congruent. III. If the hypotenuse and a side of one right triangle are equal to the hypotenuse and a side of another right triangle respectively, then the two right triangles are congruent. Which of the statement given above is/are correct? (a) Only I (b) Only I (c) Both II and III (d) Both I and III Q84. Which one among the following is not correct? (a) Two congruent triangles are necessarily similar (b) All equiangular triangles are similar (c) Two isosceles right triangles are similar (d) All isosceles triangles are similar Q85. Consider the following statements I. The perpendicular bisector of a chord of a circle does not pass through the centre of the circle. II. The angle in a semi-circle is a right angle. 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 Q86. Assertion (A) If the side of a rhombus is 10 cm. Its diagonals should have values 16 cm and 12 cm. Reason (R) The diagonals of a rhombus cut at right angles. (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 Q87. If the diagonals of a quadrilateral are equal and bisect each other at right angles, then the quadrilateral is a

(a) rectangle (b) square (c) rhombus (d) trapezium Q88. What is the number of pairs of perpendicular planes in a cuboid? (a) 4 (b) 8 (c) 12 (d) None of these Q89. T 6 cm 4 cm P A B In the figure given above, PT = 6 cm and PA = 4 cm. What is the length of AB? (a) 9 cm (b) 5 cm (c) 4 cm (d) 6 cm Q90. If two circles C1 and C2 have three points in common, then which of the following is correct? (a) C1 and C2 are concentric (b) C1 and C2 are the same circle (c) C1 and C2 have different centres (d) None of the above Q91. ABCD is noncyclic quadrilateral. The tangents at A and C intersect each other at P. If ANGLE ABC = 100°, then what is ANGLE APC equal to? (a) 10° (b) 20° (c) 30° (d) 40° Q92. What is the locus of centres of circles which touch a given line at a given point? (a) A line perpendicular to the given line, passing through the given point (b) A line parallel to the given line (c) A circle tangent to the given line at the given point (d) A closed curve other than a circle Q93. Consider the following statements I. Let P be a point on a straight line L. Let Q, R and S be the points on the same plane containing the line L such that PQ, PR and PS are perpendicular to L. Then, there exists no triangle with vertices Q, R and S. II. Let C be a circle passing through three distinct points D, E and F such that the tangent at D to the circle C is parallel to EF. Then, DEF is an isosceles triangle. Which of the statement (s) given above is/are correct? (a) Only I (b) Only II (c) Both I and II (d) Neither I and II Q94. Let AB be a line segment such that a point P on the locus satisfies AB2 – AP2 – BP2 = 0. What is the locus? (a) The straight line AB itself

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(b) The perpendicular bisector of AB (c) A straight line parallel to AB (d) A circle Q95. In a DABC, AB = BC = CA. The ratio of the radius of the circum circle to that of the incircle is (a) 2: 1 (b) 3: 1 (c) 3: 2 (d) None of these Q96. From a series of 50 observations, an observation with value 45 is dropped but the mean remains the same. What was the mean of 50 observations? (a) 50 (b) 49 (c) 45 (d) 40 Q97. Which one of the following can be obtained from a histogram? (a) Mean (b) Median (c) Mode (d) None of these Q98. For a set of positive numbers, consider the following statements: I. If each number is reduced by 2, then the geometric mean of the set may not always exist. II. If each number is increased by 2, then the geometric mean of the set is increased by 2. Which of the above statements is/are correct? (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q99. Let the observations at hand be arranged in increasing order. Which one of the following measures will not be affected when the smallest and the largest observations are removed? (a) Mean (b) Median (c) Mode (d) Standard deviation

Q100. Consider the following statements: I. A frequency distribution condenses the data and reveals its important features. II. A frequency distribution is an equivalent representation of original data. Which of the above statements is/are correct? (a) Only I (b) Only II

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

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5. Difference between the digit = 9238 – 7091 = 2147 2147 is completely divided by 113. 6.

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7. Prime number: A number that is divisible by itself and one excluding one. So, 1 is not prime number. Composite Number: Natural numbers, which has more than 2 distinct factors are called composite numbers. 1 is not composite numbers. 8. If x is a positive even integer and y is negative odd integer, then x y is a rational number. 9.

10. 360 = 23 × 32 × 5 ? Number of divisors = (3 + 1) (2 + 1) (1 + 1) = 4 × 3 × 2 = 24 11.

12. Let first number = x, second number = y ? LCM × HCF = Product of numbers = x × y Also, LCM = 16 HCF, LCM + HCF = 850 and x = 5017 HCF = 850 Ÿ HCF = 50 Now, LCM = 16 × 50 = 800 ? 800 × 50 = 50 × y ? y = 800 13.

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15. HCF of 18 and 15 = 3 LCM of 18 and 15 = 2 × 3 × 3 × 5 = 90 ? Product of HCF and LCM of both numbers = 3 × 90 = 270 16.

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22. Let present age of mother and daughter be x and y. 2 years ago, x – 2 = 8(y – 2) Ÿ x – 8y = – 14 ...(i) 1 year after, x + 1 = 5(y + 1) Ÿ x – 5y = 4 ...(ii) On solving equations. (i) and (ii), we get y = 6 years and x = 34 years Let after z years mother will be three times of her daughter. 34 + z = 3 (6 + z) Ÿ z = 8 years 23.

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83. It is true that congruent triangles are similar but converse is not true. Also, Statement III is true. 84.

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All isosceles triangles are similar. 85.

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87. We know that in a square diagonals are equal and bisect each other at 90°. Hence, the required quadrilateral is a square. 88. In a cuboid, 4 perpendicular face pairs in bottom surface, 4 perpendicular face pairs in top surface and 4 perpendicular face pairs in vertical surface. Total perpendicular pairs are 12. 89.

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97. Mode can be obtained from a histogram. 98.

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In an increasing order arrangements of observations, the median will not be affected when the smallest and the largest observations are removed. 100. A frequency distribution is a summary of the data set in which the interval of possible values is divided into sub-intervals known as class.