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CDS MATHEMATICS PRACTICE SET Subject Questions Marks Time -Ve

Maths 100 100 2 hrs 1/3 Q1. A ten-digit number is divisible by 4 as well as by 5. What could be the possible digit at the ten’s place in the given number? (a) 0, 1, 2, 4 or 6 (b) 1, 2, 4, 6 or 8 (c) 2, 3, 4, 6 or 8 (d) 0, 2, 4, 6 or 8 Q2. let p denote the product 2,3,5,59,61 of all primes from 2 to 61.Consider the sequence p + n (2 d n d 59). What is the number of primes in this sequence (where n is a natural number)? (a) 0 (b) 16 (c) 17 (d) 58 Q3. What is the sum of positive integers less than 100 which leave a remainder 1 when divided by 3 and leave a remainder 2 when divided by 4? (a) 416 (b) 620 (c) 1250 (d) 1314 Q4. What least value must be given to, so that the number 84705 2 is divisible by 9? (a) 0 (b) 1 (c) 2 (d) 3 Q5. If k is any even positive integer, then (k 2 + 2k) is (a) divisible by 24 (b) divisible by 8 but may not be divisible by 24 (c) divisible by 4 but may not be divisible by 8 (d) divisible by 2 but may not be divisible by 4 Q6. If three sides of a right angled triangle are integers in their lowest form, then one of its sides is always divisible by (a) 6 (b) 5 (c) 7 (d) None of these Q7. How many numbers between – 11 and 11 are multiples of 2 or 3? (a) 11 (b) 14 (c) 15 (d) None of these

Q8. What is the harmonic mean of 10, 20, 25, 40 and 50? (a) 25 (b) 30 (c) 26.1 (d) 21.3 Q9. If k is a positive integer, then every square integer is of the form (a) only 4k (b) 4k or 4k + 3 (c) 4k + 1 or 4k + 3 (d) 4k or 4k + 1 Q10. If N 2 – 33, N 2 – 31 and N 2 – 29 are prime numbers, then what is the number of possible values of N, where N is an integer? (a) 1 (b) 2 (c) 6 (d) None of these Q11. What is the number of possible pairs of (P, Q) if the number 357P25Q is divisible by both 3 and 5? (a) 7 (b) 6 (c) 5 (d) None of the above Q12. The last digit in the expansion of 17256 is (a) 9 (b) 7 (c) 3 (d) 1 Q13. The LCM of three different numbers is 150. Which of the following cannot be their HCF? (a) 15 (b) 25 (c) 50 (d) 55 Q14. If the highest common factor of two positive integers is 24, then their least common multiple cannot be (a) 72 (b) 216 (c) 372 (d) 600

Q15. The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3 is (a) 423 (b) 843 (c) 1683 (d) 2523

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Q16. If for integers a, b and c, if HCF (a, b) = 1 and HCF (a, c) = 1, then which one of the following is correct? (a) HCF (a, bc) = 1 (b) HCF (a, bc) = a (c) HCF (a, bc) = b (d) None of these Q17. If 2.5252525... = p/q (in the lowest form), then what is the value of q/p ? (a) 0.4 (b) 0.42525 (c) 0.0396 (d) 0.396 Q18. Which one of the following numbers is an integer?

Q19.

(a) 1 (b) 2 (c) 3 (d) 4 Q20. The population of a village increases by 20% in one year and decrease by 20% by the next year. If at the beginning of the third year, the population is 5184, what was the population in the first year? (a) 5400 (b) 5500 (c) 5600 (d) 5800 Q21. To an examination, a candidate needs 40% marks. All questions carry equal marks. A candidate just passed by getting 10 answers correct by attempting 15 of the total questions. How many questions are there in the examination? (a) 25 (b) 30 (c) 40 (d) 45 Q22. A person sold an article from Rs 3600 and got a profit of 20%. Had he sold the article for Rs 3150, how much profit would he have got? (a) 4% (b) 5% (c) 6%

(d) 10% Q23. x varies directly as y and inversely as square of z. When y = 4 and z = 14, x =If y = 16 and z = 7, then what is value of x? (a) 180 (b) 160 (c) 154 (d) 140 Q24. A mixture contains milk and water in the ratio 5: 1. On adding 5l of water, the ratio of milk and water becomes 5: 2. What is the quantity of milk in the original mixture? (a) 5 l (b) 25 l (c) 27.5 l (d) 32.5 l Q25. A bag contains Rs 112 in the form of Rs 1,50 paise and 10 paise coins in the ratio 3: 8: 10. What is the number of 50 paise coins? (a) 112 (b) 108 (c) 96 (d) 84 Q26. If A: B = 2: 3, B: C = 5: 7 and C: D = 3: 10, then what is A: D equal to? (a) 1: 7 (b) 2: 7 (c) 1: 5 (d) 5: 1 Q27. A person invested part of Rs 45000 at 4% and the rest at 6%. If his annual income from both are equal, then what is the average rate of interest? (a) 4.6% (b) 4.8% (c) 5.0% (d) 5.2% Q28. Ram had Rs 2 lakh, part of which he lent at 15% per annum and rest at 12% per annum. Yearly interest accured was Rs 27600. How much did he lent at 15%? (a) Rs 120000 (b) Rs 100000 (c) Rs 80000 (d) Rs 60000 Q29. What is the least number of years in which a sum of money at 20% compound interest will be more than doubled? (a) 7 (b) 6 (c) 5 (d) 4 Q30. The difference between compound interest and simple interest at the same rate of interest R per cent

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per annum on Rs 15,000 for 2 years is Rs 96.What is the value of R? (a) 8 (b) 10 (c) 12 (d) Cannot be determined due to insufficient data Q31. A dishonest dealer professes to sell his good at cost price but uses a false weight and thus gains 20%. For a kilogram he uses a weight of (a) 700 g (b) 750 g (c) 800 g (d) 850 g Q32. A person sold an article for Rs 136 and got 15% loss. Had he sold it for Rs x, he would have got a profit of 15%. Which one of the following is correct? (a) 190 < x < 200 (b) 180 < x < 190 (c) 170 < x < 180 (d) 160 < x < 170 Q33. A man buys 200 oranges for Rs 1000. How many oranges for Rs 100 can be sold, so that his profit percentage is 25%? (a) 10 (b) 14 (c) 16 (d) 20 Q34. Two persons P and Q start at the same time from city A for city B, 60 km away. P travels 4 km/h slower than Q. Q reaches city B and at once turns back meeting P, 12 km from city B. What is the speed of P? (a) 8 km/h (b) 12 km/h (c) 16 km/h (d) 20 km/h Q35. A train 280 m long is moving at a speed of 60 km/h. What is the time taken by the train to cross a platform 220 m long? (a) 45 s (b) 40 s (c) 35 s (d) 30 s Q36. A train running at the speed of 72 km/h goes past a pole in 15 s. What is the length of the train? (a) 150 m (b) 200 m (c) 300 m (d) 350 m Q37. A runs 5/3 times as fast as B. If A gives B a start of 80 m, how far must the winning post from the starting point be so that A and B might reach it at the same time? (a) 200 m (b) 300 m

(c) 270 m (d) 160 m Q38. Two taps can fill a tub in 5 min and 7 min respectively. A pipe can empty it in 3 min. If all the three are kept open simultaneously, when will the tub be full? (a) 60 min (b) 85 min (c) 90 min (d) 105 min Q39. Consider the following statements: I. If 18 men can earn Rs 1440 in 5 days, then 10 men can earn Rs1280 in 6 days. II. If 16 men can earn Rs1120 in 7 days, then 21 men can earn Rs 800 in 4 days. Which of the above statements is/are correct? (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II Q40. 4 goats or 6 sheeps can graze a field in 50 days. 2 goats and 9 sheeps can graze the field in (a) 100 days (b) 75 days (c) 50 days (d) 25 days Q41. A can do a piece of work in 'x' days and B can do the same work 3x days, To finish the work together they take 12 days. What is the value of 'x' (a) 8 (b) 10 (c) 12 (d) 16 Q42. If (x3 + 5x2 + 10k) leaves remainder –2x when divided by (x2 + 2), then what is the value of k? (a) –2 (b) –1 (c) 1 (d) 2 Q43. What should be subtracted from 27x 3 – 9x 2 – 6x – 5 to make it exactly divisible by (3x – 1)? (a) –5 (b) –7 (c) 5 (d) 7 Q44. If u, v and w are real numbers such that u 3 – 8v 3 – 27w 3 = 18uvw, then which one of the following is correct? (a) u – v + w = 0 (b) u = –v = –w (c) u – 2v = 3w (d) u + 2v = –3w

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Q45. AB is a straight line. C is a point whose distance from AB is 3cm. What is the number of points which are at a distance of 1cm from AB and 5cm from C? (a) 1 (b) 2 (c) 3 (d) 4 Q46. If (x + k) is the common factor of x 2 + ax + b and x 2 + cx + d. of and then what is k equal to? (a) (d – b)/ (c – a) (b) (d – b)/ (a – c) (c) (d + b)/ (c + a) (d) (d – b)/ (c + a) Q47. Let x {2, 3, 4} and y {4, 6, 9, 10}. If A be the set of all order pairs (x, y) such that x is a factor of y. Then, how many elements does the set A contain? (a) 12 (b) 10 (c) 7 (d) 6 Q48.

(a) x is not a multiple of 360° (b) x is not an odd multiple of 180° (c) x is not a multiple of 180° (d) None of the above Q49. Which one of the following statements is true in respect of the expression sin 31° + sin 32°? (a) Its value is 0 (b) Its value is 1 (c) Its value is less than 1 (d) Its value is greater than 1. Q50.

(a) 1 (b) 2 (c) 0 (d) –1 Q51.

(a) 54º (b) 36º (c) 27º (d) 18º

Q52.

(a) x – y = 0 (b) x = 2y (c) y = 2x (d) x – y = 1º Q53.

(a)

(b)

(c)

(d) Q54.

(a)

(b)

(c)

(d) Q55.

(a)

(b)

(c)

(d)

Q56.

(a)

(b)

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(c)

(d) Q57. If A, B, C and D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D are equal to? (a) 4 (b) 2 (c) 1 (d) 0 Q58. Consider the following statements: I. The angular measure in radian of a circular arc of fixed length subtending at its centre decreases, if the radius of the arc increases. II. 1800° is equal to 5 π radian. Which of the above statements is/are correct? Only I Only II Both I and II Neither I nor II Q59. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a tower casts a shadow 30 m long. What is the height of the tower? (a) 37.5 m (b) 36 m (c) 32.5 m (d) 32 m Q60. The shadow of a tower is 15 m when the Sun’s altitude is 30º. What is the length of the shadow when the Sun’s altitude is 60º? (a) 3 m (b) 4 m (c) 5 m (d) 6 m Q61. A cycle wheel makes 1000 revolutions is moving 440 m. What is the diameter of the wheel? (a) 7 cm (b) 14 cm (c) 28 cm (d) 21 cm Q62. What is the maximum area of a rectangle, the perimeter of which is 18 cm? (a) 20.25 cm2 (b) 20.00 cm2 (c) 19.75 cm2 (d) 19.60 cm2 Q63. The length of a minute hand of a wall clock is 9 cm. What is the area swept (in cm2) by the minute hand in 20 min? (take p = 3.14) (a) 88.78 (b) 84.78 (c) 67.74

(d) 57.78 Q64. If the area of a rectangle whose length is 5 more than twice its width is 75 sq units. What is the perimeter of the rectangle? (a) 40 units (b) 30 units (c) 24 units (d) 20 units

Q65. What is the area of a circle whose area is equal to that of a triangle with sides 7 cm, 24 cm and 25 cm? (a) 80 cm2 (b) 84 cm2 (c) 88 cm2 (d) 90 cm2 Q66. How many circular plates of diameter d be taken out of a square plate of side 2d with minimum loss of material? (a) 8 (b) 6 (c) 4 (d) 2 Q67. A cone is inscribed in a hemisphere such that their bases are common. If C is the volume of the cone and H that of the hemisphere, then what is the value of C: H? (a) 1: 2 (b) 2: 3 (c) 3: 4 (d) 4: 5 Q68. In which one of the following pairs does the first number represent the perimeter of one face of a cube and the second number represent the volume of the cube? (a) (16, 32) (b) (20, 125) (c) (9, 27) (d) (10, 100) Q69. 26. The radius and height of a right circular cone are in the ratio 3: 4 and its volume is 96x cm3. What is its lateral surface area? (a) 24p cm2 (b) 36p cm2 (c) 48p cm2 (d) 60p cm2 Q70. Three cubes each of side 5 cm are joined end to end. What is the surface area of the resulting cuboid? (a) 300 sq cm (b) 350 sq cm (c) 375 sq cm

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(d) 400 sq cm Q71. The ratio of volumes of two cones is 4: 5 and the ratio of the radii of their bases is 2: 3. What is the ratio of their vertical heights? (a) 5: 6 (b) 6: 5 (c) 9: 5 (d) 5: 9 Q72. The length, breadth and height of a rectangular parallelepiped are in ratio 6: 3: 1. If the surface area of a cube is equal to the surface area of this parallelepiped, then what is the ratio of the volume of the cube to the volume of the parallelepiped? (a) 1: 1 (b) 5: 4 (c) 7: 5 (d) 3: 2 Q73. The outer and inner diameters of a circular pipe are 6 cm and 4 cm, respectively. If its length is 10 cm, then what is the total surface area in sq cm? (a) 35 pie (b) 110 pie (c) 150 pie (d) None of these Q74. The radii of two cylinders are in the ratio 2: 3 and their curved surface areas are in the ratio 5: 3. What is the ratio of their volumes? (a) 20: 27 (b) 10: 9 (c) 9: 10 (d) 27: 20 Q75. What are the dimensions (length, breadth and height, respectively) of a cuboid with volume 720 cu cm, surface area 484 sq cm and the area of the base 72 sq cm? (a) 9, 8 and 10 cm (b) 12, 6 and 10 cm (c) 18, 4 and 10 cm (d) 30, 2 and 12 cm Q76. What is the volume of the largest sphere that can be curved out from a cube of edge 3 cm? (a) 9p cu cm (b) 6p cu cm (c) 4.5p cu cm (d) 3p cu cm Q77. The diameter of the Moon is approximately one-fourth of the diameter of the Earth. What is the ratio (approximate) of their volumes? (a) 1: 16 (b) 1: 64 (c) 1: 4 (d) 1: 128

Q78. The dimensions of a field are 15 m by 12 m. A pit 8 m long, 2.5 m wide and 2 m deep is dug in one corner of the field and the earth removed is evenly spread over the remaining area of the field. The level of the field is raised by (a) 15 cm (b) 20 cm (c) 25 cm (d) 200/9 cm Q79. Consider the following statements in respect of four spheres A,B, C and D having respective radii 6, 8, 10 and 12 cm. 1. The surface area of sphere C is equal to the sum of surface areas of sphere A and B. 2. The volume of sphere D is equal to the sum of volumes of sphere A, B and C. Which of the above statements is/ are correct? (a) Only 1 (b) Only 2 (c) Both 1 and 2 (d) Neither 1 nor 2 Q80. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone (a) remains unaltered (b) decreases by 25% (c) increases by 25% (d) increases by 50% . Q81. The line segments AB and CD intersect at O, OF is the internal bisector of obtuse ANGLEBOC and OE is the internal bisector of acute ANGLEAOC. If ANGLEBOC = 130º, what is the measure of ANGLEFOE? (a) 90º (b) 110º (c) 115º (d) 120º Q82. A triangle ABC is permitted to move around when its vertex A is fixed. What is the locus of the circumcentre? (a) A straight line (b) A circle (c) A point (d) A curve other than a circle Q83. The sides of a triangle are 50 m, 40 m and 30 m. What is the length of the altitude of the vertex opposite to the side 50 m long? (a) 22 m (b) 24 m (c) 25 m (d) 26 m Q84. In a triangle, if sum of two angles is equal to the third angle (considering the interior angles only), then the triangle is (a) right angled

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(b) acute angled (c) equilateral (d) obtuse angled Q85. Consider the following statements I. If G is the centroid of DABC, then GA = GB = GC. II. If H is the orthocentre of DABC, then HA = HB = HC. 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. Let ABC is triangle right angled at B. If AB = 6 cm and BC = 8 cm, then what is the length of the circum radius of the triangle ABC? (a) 10 cm (b) 7 cm (c) 6 cm (d) 5 cm Q87. Two sides of a parallelogram are 10 cm and 15 cm. If the altitude corresponding to the side of length 15 cm is 5 cm, then what is the altitude to the side of length 10 cm? (a) 5 cm (b) 7.5 cm (c) 10 cm (d) 15 cm Q88. A quadrilateral ABCD is inscribed in a circle. If AB is parallel to CD and AC = BD, then the quadrilateral must be a (a) parallelogram (b) rhombus (c) trapezium (d) None of these Q89. AD is the diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is (a) 17 cm (b) 15 cm (c) 13 cm (d) 8 cm Q90.

(a) 45°

(b) 37.5° (c) 30° (d) 22.5° Q91.

(a) 160° (b) 150° (c) 120° (d) 100° Q92.

(a) 50° (b) 60° (c) 70° (d) 80° Q93. The diameter of two circles are 18 cm and 8 cm. The distance between their centres is 13 cm. What is the number of common tangents? (a) 1 (b) 2 (c) 3 (d) None of these Q94. Two unequal circle are touching each other externally at P, APB and CPD are two secants cutting the circles at A, B, C and D. Which one of the following is correct? (a) ACBD is parallelogram (b) ACBD is a trapezium (c) ACBD is a rhombus (d) None of the above Q95. Consider a circle with centre at O and radius r. Points A and B lie on its circumference and a point M lies

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outside of it such that M, A and O lie on the same straight line. Then, the ratio of MA to MB is (a) equal to 1 (b) equal to r (c) greater than 1 (d) less than 1 Q96. If the angle between the radii of a circle is 130°, then the angle between the tangents at the ends of the radii is (a) 90° (b) 70° (c) 50° (d) 40° Q97. Which one of the following statements is not correct with reference to a histogram? (a) Frequency curve is obtained by joining the mid-points of the top of the adjacent rectangles with smooth curves (b) Histogram is drawn for continuous data (c) The height of the bar is proportional to the frequency of that class (d) Mode of the distribution can be obtained from the histogram Q98. Consider the following pairs of numbers: I. (8, 12) II. (9, 11) III. (6, 24) Which pairs of number have the same harmonic means? (a) I and II (b) II and III (c) I and III (d) I, II and III Q99. The arithmetic mean of 100 numbers was computed as 89.05. It was later found that two numbers 92 and 83 have been misread as 192 and 33, respectively. What is the correct arithmetic mean of the numbers? (a) 88.55 (b) 87.55 (c) 89.55 (d) Cannot be determined

Q100. Which one of the following relations for the numbers 10, 7, 8, 5, 6, 8, 5, 8 and 6 is correct? (a) Mean = Median (b) Mean = Mode (c) Mean > Median (d) Mean > Mode 1. d 2. a 3. a 4. b 5. b 6. b 7. c 8. d 9. d 10. c 11. a 12. d 13. d 14. c 15. b 16. a 17. d 18. c 19. a 20. a 21. a 22. b 23. b 24. b 25. a 26. a 27. b 28. a 29. d 30. a 31. c 32. b 33. c 34. a 35. d 36. c 37. a 38. d 39. d 40. d 41. d 42. c 43. b 44. c 45. d 46. a 47. d 48. c 49. d 50. b 51. d 52. a 53. c 54. c 55.

a 56. b 57. d 58. a 59. a 60. c 61. b 62. a 63. b 64. a 65. b 66. c 67. a 68. b 69. d 70. b 71. c 72. d 73. c 74. b 75. a 76. c 77. b 78. c 79. c 80. b 81. a 82. b 83. b 84. a 85. b 86. d 87. b 88. c 89. d 90. b 91. d 92. d 93. c 94. d 95. d 96. c 97. c 98. c 99. a 100. a 1.

2.

3.

4.

5.

6. Let the lowest sides of a right triangle be 3, 4, 5. By Pythagoras theorem, (3)2 + (4)2 = (5)2 Hence, one of its sides is always divisible by 5. 7.

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8.

9. For square integer 25, 4k + 1 mean 4 × 6 + 1 and for 36 4k mean 4 × 9 Now, if k is a positive integer, then every square integer is of the form 4k or 4k + 1 10. From option (c) By Hook and Crook N = 6 N2 – 33 = 62 – 33 = 36 – 33 = 3, which is prime. N2 – 31 = 62 – 31 = 36 – 31 = 5, which is prime. N2 – 29 = 62 – 29 = 36 – 29 = 7, which is prime. So, N = 6 only. possible value 11. 357P25Q If it is divided by 3, then sum of the digit must be divided by 3 and if it is divided by 5 then its unit digit must be 0 or 5. = 3 + 5 + 7 + P + 2 + 5 + Q 1st Case Q = 0 3 + 5 + 7 + P + 2 + 5 + 0 = 22 + P Possible values of P = 2, 5, 8 2nd Case when Q = 5 3 + 5 + 7 + P + 2 + 5 + 5 = 27 + P Possible values of P = 0, 3, 6, 9 Possible pairs of (P,Q) = (2, 0), (5, 0), (8, 0) (0, 5), (3, 5) (6, 5) (9, 5) Total no. of pairs = 7. 12. 17256 Last digit is 7 so We know that 7 repeats its unit digit after 4 times. = (17)64×4 Unit of 7 × 7 × 7 × 7 = 2401 Now, 256 is completely divided by 4 so unit digit = 1 13.

We know that LCM is the multiple of HCF. So that 55 cannot be HCF because it is not divisor of 150. 14. In the given options, only 372 is not divisible by 24. Therefore, LCM of numbers cannot be 372. 15. We find out the LCM of given numbers. ? LCM (5, 6, 7, 8) = LCM (5, 2 × 3, 7, 2 × 4) = 2 × 5 × 3 × 7 × 4 = 840 ? Required number = 840 + 3 = 843 16. For integers a, b and c, if HCF (a, b) = 1 and HCF (a, c) = 1, then HCF (a, bc) = 1 17.

18.

19.

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20.

21.

22.

23.

24. Let quantities of milk and water are 5x and x l. According to the question, 5x/x+5

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= 5 2 Ÿ 10x = 5x + 25 Ÿ 5x = 25 ? x = 5 Hence, the quantity of milk in the original mixture = 5 × 5 = 25 l 25.

26. 27.

28.

29.

30.

31.

32.

33.

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34.

35.

36.

37.

38.

39.

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40.

41.

42.

43.

44.

45.

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46.

47.

48.

49.

50.

51.

52.

53.

54.

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55.

56.

57.

58.

59.

60.

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61.

62.

63.

64.

65.

66.

67.

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68.

69.

70.

71.

72.

73.

74.

75.

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76.

77.

78.

79.

80. 81.

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82. When triangle ABC is moved around fixed ponit A then its locus is circle. 83.

84. In a triangle, if sum of two angles is equal to the third angle, then triangle is right angled. 85.

86.

87.

88.

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The quadrilateral must be a trapezium because a quadrilateral where only one pair of opposite sides are parallel (in this case AB || CD) is a trapezium. 89.

90.

91.

92.

93.

94.

95.

96.

97. The height of the bar is not proportional to the frequency of the class.

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98.

99.

100.