CDS 2008 Maths Question Paper -2

ORDERING OF SENTENCES

1. What is the number which has to be added to each term of the ratio 49 : 68 so that it becomes 3 : 4?
   • 3
   • 5
   • 8
   • 9
2. What number must be added to each of 4, 10, 12, 24 so that the resulting numbers are in proportion?
   • 6
   • 8
   • 10
   • 4
3. The marked price of a machine is Rs. 18000. By selling it at a discount of 20%, the loss is 4%.What is the cost price of the machine?
   • 10000
   • 12000
   • 14000
   • 15000
4. At what rate percent per annum simple interest, will a sum of money triple itself in 25 yr?
   • 8%
   • 9%
   • 10%
   • 12%
5. If m men can do a job in p days, then (m+ r) men can do the job in how many days?
   • (p+ r) days
   • mp/m+ r days
   • p/m+ r days
   • m + r/ p days

6. If one man or two women or three boys can do piece of work in 55 days, then one man, one woman and one boy will do it in how many days?
   • 20 days
   • 30 days
   • 40 days
   • 50 days
7. A train crosses a telegraph post in 8 s and a bridge 200mlong in 24 s. What is the length of the train?
   • 100 m
   • 120 m
   • 140 m
   • 160 m
8. 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?
   • 5 s
   • 6 s
   • 10 s
   • 15 s
9. What is the value of
   • 6
   • 2
   • 3
   • 1
10. If then what does x equal to?
    • 1
    • 2
    • 3
    • 4
11. What is the simplified form of 9 ?
    • 4√2
    • 3√2
    • 2√2
    • √2
12. 1A number, when divided by 987, gives a remainder 59. When the same number is divided by 21,what is the remainder?
    • 21
    • 19
    • 17
    • 15
13. Which one of the following statements is always correct?
    • The square of a prime number is prime
    • The sum of two square numbers is a square number
    • The number of digits in a square number is even
    • The product of two square numbers is a square number
14. In the figure given above, ABC is a right angled triangle, right angled at B.BC = 21 cm and AB = 28 cm. With AC as diameter of a semicircle and with BC as radius a quarter circle are drawn. What is the area of the shaded portion?
    
    • 425 cm²
    • 75 cm²
    • 428 cm²
    • 75 cm²

15. In the figure given above, ΔABC is a right angled triangle, right angled at A. Semicircles are drawn on the sides AB, BC and AC. Then the area of the shaded portion is equal to which one of the following?
    
    • Area of , ΔABC
    • 2 times the area of , ΔABC
    • Area of semicircle ABC
    • None of the above

16. In the figure given above, A is the centre of the circle and AB = BC = CD. What is the value of x?
    
    • 20°
    • 22 1/2°
    • 25°
    • None of these
17. Triangle ABC is right angled at A. AB = 3 unit, AC = 4 unit and AD is perpendicular to BC. What is the area of the triangle ABD?

• 9/25 sq unit
• 54/25 sq unit
• 72/25 sq unit
• 96/25 sq unit

18. If A is the area of a right angled triangle and b is one of the sides containing the right angle, then what is the length of the altitude on the hypotenuse?
    • 
19. If ABC is a triangle, right angled at B and M, N are mid points of AB and BC respectively, then what is 4 (AN²+ CM²) equal to?
    • 3AC²
    • 4AC²
    • 5AC²
    • 6AC²

20. In the figure given above AB is a diameter of the circle with centre O and EC= ED. What is ∠EFO?
    
    • 15°
    • 20°
    • 25°
    • 30°

21. In the figure given above, O is the centre of the circle. What is ∠AOC?
    
    • 160°
    • 150°
    • 120°
    • 100°
22. ABCD is a square. The diagonals AC and BD meet at O. Let K, L be the points on AB such that AO = AK , BO = BL. If=θ∠ LOK, then what is the value of tan q?
    • 1/√3
    • √3
    • 1
    • 1/2

23. In the figure given above, what is the value of (2x– y)?
    
    • 10°
    • 15°
    • 20°
    • 25°

24. The sides of a triangle are 50m, 40mand 30 m. What is the length of the altitude of the vertex opposite to the side 50mlong?
    • 22 m
    • 24 m
    • 25 m
    • 26 m
25. A ladder 34 m long is placed in a lane so as to reach awindow30mhigh and on turning the ladder to the other side of the lane and keeping its foot at the same place, it reaches a point 16mhigh.What is the breadth of the lane?
    • 18 m
    • 40 m
    • 46 m
    • 50 m
26. If the angles of a triangle are 90°, 60° and 30°, then what is the ratio of the sides opposite to these angles?
    • √3: √2: 1
    • 1: √2 : 2
    • 2: √3: 1
    • 3 : 2 : 1
27. In the given figure, ∠ABD= 90°, ∠BDA= 30° and ∠BCA = 20°.What is ∠CAD?
    
    • 10°
    • 20°
    • 30°
    • 15°
28. In the given figure, if AB CD, ∠PTB = 55° and ∠DVS = 45°, then what is the sum of the measures of ∠CUQ and ∠RTP?
    
    • 180°
    • 135°
    • 110°
    • 100°

29. ABC is a right angled triangle, right angled at C and p is the length of the perpendicular from C on AB. If a, b, c are the sides of the triangle, then which one of the following is correct?
    • (a²+ b²) p²= a²b²
    • a²+ b²= a²b²p²
    • p²= a²+ b²
    • p²= a² – b²
30. If a clock is started at noon, then what is the angle turned by hour hand at 3 : 45 pm?
    • 5°
    • 5°
    • 5°
    • 5°

31. In the figure given above, PQ = QS and QR = RS. If ∠SRQ = 100°, how many degrees is ∠QPS?
    
    • 40°
    • 30°
    • 20°
    • 15°
32. The angle of elevation and angle of depression both are measured with
    • the vertical only
    • the horizontal only
    • both horizontal and vertical
    • None of the above
33. A round ball on of unit radius subtends an angle of 90° at the eye of an observer standing at a point, say A. What is the distance of the centre of the balloon from the point A?
    • 1/√2
    • √2
    • 2
    • ½
34. If sin (x + 54°) = cos x, where 0 < x, x + 54° < 90°, then what is the value of x?
    • 54°
    • 36°
    • 27°
    • 18°
35. The hypotenuse of a right triangle is 3 √10 unit. If the smaller side is tripled and the longer side is doubled, new hypotenuse becomes 9 √5 unit. What are the lengths of the smaller and longer sides of the right triangle respectively?
    • 5 unit, 9 unit
    • 5 unit, 6 unit
    • 3 unit, 9 unit
    • 3 unit, 6 unit
36. If 1 + tan θ= √2, then what is the value of cot θ – 1?
    • 1/√2
    • √2
    • 2
    • ½

37. If sin (x – y) = 1/2 and cos (x+ y) = 1/2, then what is the value of x?
    • 15°
    • 30°
    • 45°
    • 60°
38. If α, β are the roots of ax² + bx + c = 0, then what is the value of
    • a² (b² – 4ac)/c⁴
    • b (b² – 4ac)/c²
    • (b²– 4ac)/c²
    • (b² – 4ac)/c⁴
39. The solution of the equations is given by which one of the following?
    • x = 2, y = 1
    • x = 1, y = 1
    • x = – 1, y = – 1
    • x = 1, y = 2
40. 10 yr ago Ram was 5 times as old as Shyam, but 20 yr later from now he will be twice as old as Shyam. How many years old is Shyam?
    • 20 yr
    • 30 yr
    • 40 yr
    • 50 yr
41. The sum of the age of a father and the age of son is 75 yr. If the product of their ages before 5 yr was 750, then what is the present age of the father?
    • 60 yr
    • 55 yr
    • 52 yr
    • 50 yr
42. What is the simplified form of

• x/x-3
• x-2/x-3
• x/x+3
• x+3/x+4

43. Which one of the following is a correct statement?
    • 
44. The set {2, 4, 16, 256, …} can be represented as which one of the following?
    
45. If y = (a^x )… , (a^x ) ^…°° then which one of the following is correct?
    • log y = x y log a
    • log y= x+ y log a
    • log y= y+ x log a
    • log y = (y+ x) log a
46. Suppose p* q = 2p + 2q – pq, where p, q are natural numbers. If 8* x = 4, then what is the value of x?
    • 1
    • 2
    • 3
    • 4
47. The set of integers is closed with respect to which one of the following?
    • Addition only
    • Multiplication only
    • Both addition and multiplication
    • Division
48. Which one of the following is one of the two consecutive positive integers, the sum of whose is 761?
    • 15
    • 20
    • 24
    • 25
49. What is the value of
    • 0
    • 1
    • 2
    • 3
50. Assume that population densities of 5major states of India are given. Which one of the following diagrams is suitable to represent the data?
    • Single bar diagram
    • Percentage bar diagram
    • Pie diagram
    • Since population density is a ratio, it cannot be represented by any diagram
51. 
    The table above gives the frequency distribution of a discrete variable X with two missing frequencies. If the total frequency is 25 and the arithmetic mean of X is 2, then what is the value of the missing frequency f ?
    • 4
    • 5
    • 6
    • 7
52. Which one of the following statements is not correct with reference to a histogram?

• Frequency curve is obtained by joining the mid points of the top of the adjacent rectangles with smooth curves
• Historgam is drawn for continuous data
• The height of the bar is proportional to the frequency of that class
• Mode of the distribution can be obtained from the histogram

53. 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 unit. What is the total cost of painting the two halves of the sphere in rupees?
    • 6 r²
    • 32 r²
    • 48 r²
    • Insufficient data to answer
54. If the number of square centimetres on the surface area of a sphere is three times the number of cubic centimetres in its volume, then what is its diameter?
    • 1cm
    • 2cm
    • 3cm
    • 6cm
55. The ratio of the surface areas of two hemisphere is 4 : 1.What is the ratio of their volumes?

• 8 : 1
• 4 : 1
• 3 : 1
• 2 : 1

56. A container is in the form of a right circular cylinder surmounted by a hemisphere of the same radius 15 cm as the cylinder. If the volume of the container is 32400 cm³, then the height h of the container satisfies which one of the following?
    • 135 cm < h < 150 cm
    • 140 cm < h < 147 cm
    • 145 cm < h < 148 cm
    • 139 cm < h < 145 cm
57. A hollow cylindrical iron pipe of length 1.4 m has bore radius 2.5 cm and thickness of the metal is 1 cm. What is the volume of the iron used in the pipe?
    • 2640 cm³
    • 2604 cm³
    • 2460 cm³
    • None of these
58. Aright circular cone is cut by a plane parallel to its base in such away 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?
    • 2 : 1
    • 3 :1
    • 4 : 1
    • 8 : 1
59. If C₁ is a right circular cone with base radius r₁ cm and height h₁ cm and C₂ is a right circular cylinder with base radius r₂ cm and height h₂ cm and if r₁ : r₂ = 1: n (where n is a positive integer) and their volumes are equal, then which one of the following is correct?
    • h₁ = 3nh₂
    • h₁ = 3n²h₂
    • h₁ = 3h₂
    • h₁ = n²h2

Directions: Each of the following four (4) items consists of two statements, one labelled as ‘Assertion (A)’ and the other as ‘Reason (R)’. You are to examine these two statements carefully and select the answers to these items using the code given below:

Codes:

• Both A and R are individually true and R is the correct explanation of A
• Both A and R are individually true but R is not the correct explanation of A
• A is true but R is false
• A is false but R is true

60. Assertion (A):The curved surface area of a right ciruclar cone of base radius r and height h is given by πr √(h2+r2).

Reason (R):The right circular cone of base radius r and height h when cut opened along the slant height, froms a rectangle of length r and breadth √h2+r2 .

61. Assertion (A):The volume of a cuboid is the product of the lengths of its coterminous edges.

Reason (R):The surface area of a cuboid is twice the sum of the products of lengths of its coterminous edges taken two at a time.

62. Assertion (A):Triangles on the same base and between the same parallel lines are equal in area.

Reason (R):The distance between two parallel lines is same everywhere.

63. Assertion (A):Two distinct lines cannot have more than one point in common.

Reason (R):Any number of lines can be drawn through one point.

64. The population of a State increased from100 million to 169million in two decades. What is the average increase in population per decade?
    • 20%
    • 5%
    • 69%
    • 30%
65. 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?
    • 85 kg
    • 120 kg
    • 125 kg
    • 130 kg
66. A truck made a trip of 200 km, covering the first 100 km at the rate of 50 km/h and the second 100 km at 40 km/h. What was the average speed of the truck in km/h?
    • 2
    • 2
    • 3
    • 4
67. Sets A, B and C contain 5 numbers each. The medians of the numbers in these sets are 3, 8 and 11 respectively. What is the median of the combined 15 numbers of the three sets?
    • 8
    • 7
    • 22/3
    • Median cannot be determined from the given data
68. Suppose X is some statistical variable with mean µ . Let x₁, x₂, …, x_n be its deviations from mean with the respective frequencies f₁, f₂, …, f_n. What is the value of the sum x₁f₁+ x₂f₂ + … + x_n f_n?
    • 0
    • 1
    • µ
    • µ+ 1
69. If a polynomial equation has rational coefficients and has exactly three real roots, then what is the degree of the polynomial?
    • Equal to 3
    • Greater than or equal to 3
    • Strictly greater than 3
    • Less than 3
70. The value of y which will satisfy the equations

2x² + 6x + 5y + 1 = 0

and 2x+ y + 3 = 0

may be found by solving which one of the following equations?

• y2 + 14y – 7 = 0
• y² + 8y + 1 = 0
• y² + 10y – 7 = 0
• y² – 8y + 7 = 0

71. Which one of the following is the quadratic equation whose roots are reciprocal to the roots of the quadratic equation 2x² – 3x – 4 = 0?
    • 3x² – 2x – 4 = 0
    • 4x² + 3x – 2 = 0
    • 3x² – 4x – 2 = 0
    • 4x² – 2x – 3 = 0
72. 7What is the LCM of (x + 2)² (x – 2) and x² – 4x-12?

(x+ 2) (x – 2)

(x+ 2)³ (x – 2) (x – 6)

(x+ 2) (x – 2)²

(x+ 2)² (x – 2) (x – 6)

73. What is the value of k for which the HCF of 2x² + kx –12 and x² + x–2k – 2 is (x + 4)?
    • 5
    • 7
    • 10
    • –4
74. f (x+ k) is the HCF of ax²+ ax + b and x²+ cx + d, then what is the value of k?

• b+ d/a+ c
• a+ b/c+ d
• a-b/c- d
• None of these

75. What should be subtracted from27x³–9x²–6x–5 to make it exactly divisible by (3x– 1)?
    • – 5
    • – 7
    • 5
    • 7
76. Which one of the following is a factor of 2x³ – 3x ²– 11x + 6?
    • x + 1
    • x – 1
    • x + 2
    • x – 2
77. If x² – 11x+ a and x² – 14x+ 2a have a common factor, then what are the values of a?
    • 0, 7
    • 5, 20
    • 0, 24
    • 1, 3
78. If a is a rational number such that (x– a) is a factor of the polynomial x³ – 3x² – 3x + 9, then
    • a can be any integer
    • a is an integer dividing 9
    • a cannot be an integer
    • a can take three values
79. If x + y + z = 6 and xy + yz + zx = 11, then what is the value of x³+ y³+ z³ – 3xyz?
    • 18
    • 36
    • 54
    • 66
80. If x² – 4x + 1 = 0, then what is the value of x³+1/x³?
    • 44
    • 48
    • 52
    • 64
81. If sin = m²-n²/m²+n² then what is the value of tan  ?

• m²+n²/m²-n²
• 2mn/m²+n²
• m²-n²/2mn
• m²+n²/2mn

82. In the given figure, BC = 15 cm and sin B = 4/5.What is the value of AB?
    
    • 25 cm
    • 20 cm
    • 5cm
    • 4cm
83. If sin x = cos y and angle x and angle y are acute, then what is the relation between x and y?
    • x – y = π/2
    • x + y = 3 π/2
    • x + y = π/2
    • x + y = π/4
84. If cos A = 5/13, then what is the value of sin A-cot A/2 tan A?
    • 395/3644
    • 395/3844
    • 395/3744
    • 385/3744

85. If sin² 60° + cos² (3x – 9°) = 1, then what is the value of x?
    • 24°
    • 23°
    • 22°
    • 21°
86. What is the value of cot² θ– (1/sin² θ)?
    • 1/2
    • – 1
    • – 1/2
    • 3/2
87. What is the value of log₁₀₀1?
    • 1/2
    • – 1/2
    • – 2
    • 2
88. 21mango trees, 42 apple trees and 56 orange trees have to be planted in rows such that each row contains the same number of trees of one variety only. What is the minimum number of rows in which the above trees may be planted?
    • 3
    • 15
    • 17
    • 20
89. What least value must be given to * so that the number 8798546*5 is divisible by 11?
    • 0
    • 1
    • 2
    • 3
90. What is the sum of all prime numbers between 100 and 120?
    • 652
    • 650
    • 644
    • 533
91. What is the value of the polynomial r(x) so that f(x)= g(x) q(x)+ r(x) and deg r(x) < deg g(x), where f(x)= x² + 1 and g(x) = x+ 1?
    • 1
    • – 1
    • 2
    • – 2
92. The radius and height of a right circular cone are in the ratio 3 : 4 and its volume is 96 πcm³. What is its lateral surface area?
    • 24 πcm²
    • 36 πcm²
    • 48 πcm²
    • 60 πcm²
93. From a sπolid cube of edge 3m, a solid of largest sphere is carved out. What is the volume of solid left?
    • (27 – 2.25 π) m³
    • (27 – 4.5 π) m³
    • 25 πm³
    • 4.5 πm³
94. 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 square metre is Rs. 234. What are the length, breadth and height of the box respectively.
    • 2m, 3 m, 4 m
    • 3m, 4.5m, 6 m
    • 4m, 6 m, 8 m
    • 5m, 7.5 m, 10 m
95. A solid metallic cube of edge 4 cm is melted and recast into solid cubes of edge 1 cm. If x is the surface area of the melted cube and y is the total surface area of all the cubes recast, then what is x : y?
    • 2 : 1
    • 1 : 2
    • 1 : 4
    • 4 : 1
96. What is the total surface area of a one-side open cubical box of outer side of length 5cm and thickness 0.5 cm?
    • 125 cm²
    • 222 cm²
    • 180 cm²
    • 205 cm2

97. Afield is 125mlog and 15mwide.A tank 10 × 7.5 m× 6mwas dug in it and the earth thus dug out was spread equally on the remaining field. The level of the field thus raised is equal to which one of the following?
    • 15 cm
    • 20 cm
    • 25 cm
    • 30 cm

98. ABCD is a rectangular of dimensions 8 unit and 6 unit. AEFC is a rectangle drawn in such away that diagonal AC of the first rectangle is one side and side opposite to it is touching the first rectangle at Das shown in the figure given above. What is the ratio of the area of rectangle ABCD to that of AEFC ?
    
    • 2
    • 3/2
    • 1
    • 8/9
99. If the area of a circle, inscribed in an equilateral traingle is 4  cm², then what is the area of the triangle?

• 12 √3cm²
• 9√3 cm²
• 8 √3cm²
• 18 cm²

100. If x and y are respectively the areas of a square and a rhombus of sides of same length, then what is x : y?
     • 1 : 1
     • 2:√3
     • 4:√3
     • 3 : 2