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NDA Mathematics Practice Set 1.

(a)

(b)

(c)

(d) 2. What is the difference between the smallest five digit binary integer and the largest four digit binary integer? (a) The smallest four digit binary integer (b) The smallest one digit binary integer (c) The greatest one digit binary integer. (d) The greatest three digit binary integer 3.

(a) (b) (c)

(d) 4.

(a) R is symmetric but not reflexive (b) R is reflexive but not symmetric (c) R is symmetric and reflexive but not transitive (d) R is an equivalence relation 5.

(a)

(b)

(c)

(d) 6.

(a)

(b)

(c)

(d)

7. The number 0.0011 in binary system represents (a) rational number 3/8 in decimal system (b) rational number 1/8 in decimal system (c) rational number 3/16 in decimal system (d) rational number 5/16 in decimal system 8.

(a)

(b)

(c)

(d) 9.

(a) {(1, 1), (2, 1), (6, 1), (3, 2)} (b) {(1, 1), (1, 2), (2, 1), (2, 2)} (c) {(1, 1), (2, 2)} (d) {(1, 1), (1, 2), (2, 5), (2, 6)} 10. Out of 500 first year students, 260 passed in the first semester and 210 passed in the second semester. If 170 did not pass in either semester, how many passed in both semesters? (a) 30 (b) 40 (c) 70 (d) 140 11. If a non-empty set A contains n elements, then its power set contains how many elements?

(a)

(b)

(c)

(d) 12.

(a) a < 2 (b) a 8 (c) a > 8 (d) a is any integer < - 2 13.

(a) a = 2, b = 4

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(b) a = 2, b = -4 (c) a = 1, b = ½ (d) a = -1, b = -1/2 14.

(a) 1 (b) 2 (c) 3 (d) 4

15.

(a) 3 (b) 2 (c) 1 (d) 0 16.

(a)

(b)

(c)

(d) 17.

(a) a > 0, b > 0, c > 0 (b) a > 0, b > 0, c > 0 (c) a > 0, b > 0, c > 0 (d) a > 0, b > 0, c > 0 18.

(a) -7/2, 2 (b) -3/2, 4 (c) -5/3, 3 (d) 3/2, 4 19.

(a)

(b)

(c)

(d) 20. For an AP with first term u and common difference v, the p th term is 15 uv more than the qth term. Which one of the following is correct? (a) p = q + 15 v (b) p = q + 15 u (c) p = q + 14 v (d) p = q + 14 u 21. What is the value of 91/3. 91/19. 91/27 ...... ∞? (a) 9 (b) 3 (c) 91/3 (d) 1 22. The harmonic mean of two numbers is 21.6.If one of the numbers is 27, then what is the other number? (a) 16.2 (b) 17.3 (c) 18 (d) 20 23. The arithmetic mean of two numbers exceeds their geometric mean by 2 and the geometric mean exceeds their harmonic mean by 1.6. What are the two numbers? (a) 16, 4 (b) 81, 9 (c) 256, 16 (d) 625, 25 24. What is the geometric mean of 10, 40 and 60 (appox)? (a) 10 (b) 28 (c) 29.6 (d) 70 25. What is the geometric mean of the sequence 1, 2, 4, 8, ....., 2n? (a) 2n/2 (b) 2(n +1)/2 (c) 2(n +1) – 1 (d) 2(n –1) 26.

(a)

(b)

(c)

(d)

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27.

(a) 0 (b) 1 (c) i (d) -i 28.

(a)

(b)

(c)

(d) 29.

(a) 5π/4 (b) - 5π/4 (c) 3π/4 (d) None of the above 30.

(a) I only (b) II only (c) Both I and II (d) Neither I nor II 31. If all permutations of the letters of the word 'LAGAN' are arranged as in dictionary, then what is the rank of 'NAAGL'? (a) 48th word (b) 49th word (c) 50th word (d) 51st word 32. What is the smallest natural number n such that n! is divisible by 990? (a) 9 (b) 11

(c) 33 (d) 99 33. What is the value of n, if P(15, n – 1): P(16, n – 2) = 3: 4? (a) 10 (b) 12 (c) 14 (d) 15 34. If p be the length of the perpendicular from the orgin on the straight line x + 2by + 2p ,then what is the value of b? (a) 1/p (b) p (c) 1/2 (d) √3/2 35. What is the area of the triangle formed by the lines y – x = 0, y + x = 0, x = c? (a) c/ 2 (b) c2 (c) 2c2 (d) c2/2 36. What is the locus of a point which moves equidistant from the coordinate axes? (a) x y ± = 0 (b) x + 2y = 0 (c) 2x + y = 0 (d) None of these 37. What is the perimeter of the triangle with vertices A(– 4, 2), B(0, – 1) and C(3, 3)? (a) 7 + 3√2 (b) 10 + 5√2 (c) 11 + 6√2 (d) 5 + √2 38. What is the equation of a straight line which passes through (3, 4) and sum of whose x and y intercepts is 14? (a) 4x + 3y = 24 (b) x + y = 14 (c) 4x – 3y = 0 (d) 3x + 4y = 25 39. If the extremities of a diameter of a circle are (0, 0) and (a3 ,1/ a3), then the circle passes through which one of the following points? (a) (a2, 1/a2) (b) (a, 1/a) (c) (a, –a) (d) (1/a, a)

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40. Under which of the following conditions does a general second degree equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 (a ≠ 0) represents a circle? (a) h = g, a = b (b) h = g = f, a = b (c) h = 0, a = b (d) h = 0, g2 + f2 – c = a + b 41. Consider the parabolas S1 ≡ y2 – 4ax = 0 and S2 ≡ y2 – 4bx = 0. S2 will contain S1, if (a) a > b > 0 (b) b > a > 0 (c) a > 0, b < 0 but |b| > a (d) a < 0, b > 0 but b > |a| 42. What is the sum of the focal distances of a point of an ellipse x2/a2 + y2/b2 = 1? (a) a (b) b (c) 2a (d) 2b 43. In a triangle ABC, if cos A = cos B cos C, what is the value of tan A – tan B – tan C? (a) 0 (b) – 1 (c) 1 + tan A tan B tan C (d) tan A tan B tan C – 1 44. If 3 tan θ + 4 = 0,where (π/2)< θ < π, then what is the value of 2cot θ –5 cos θ + sin θ? (a) – 53/10 (b) 7/10 (c) 23/10 (d) 37/10 45.

(a)

(b)

(c)

(d) 46. For which acute angle θ, cosec2 θ = 3 √3 cot θ – 5? (a) 5π/12

(b) π/3 (c) π/6 (d) π/4 47. What is the value of tan 15° + cot 15°? (a) √3 (b) 2√3 (c) 4 (d) 2 48.

(a) 1/4 (b) 1/2 (c) 1/3 (d) None of these 49. If x = sinθ + cosθ and y = sinθ.cosθ, then what is the value of x4 – 4x2 y – 2x2 + 4y2 + 4y + 1? (a) 0 (b) 1 (c) 2 (d) None of these 50. What is the angle subtended by 1 m pole at a distance 1 km on the ground in sexagesimal measure? (a) 9/50π degree (b) 9/5π degree (c) 3.4 minute (d) 3.5 minute 51. If ABCD is a cyclic quadrilateral then what is sinA + sinB – sinC – sinD equal to? (a) 0 (b) 1 (c) 2 (d) 2(sin A + sin B) 52. What is the value of (sin4θ – cos4θ + 1) cosec2θ? (a) – 2 (b) 0 (c) 1 (d) 2 53.

(a) 1 (b) –1 (c) 0 (d) 2

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54. For finding the area of a triangle ABC, which of the following entities are required? (a) Angles A, B and side a (b) Angles A, B and side b (c) Angles A, B and side c (d) Either 55. DIRECTION : Read the following information carefully and give the answer. ABC is a triangle right-angled at B. The hypotenuse (AC) is four times the perpendicular (BD) drawn to it from the opposite vertex and AD < DC. Q. What is one of the acute angle of the triangle? (a) 15° (b) 30° (c) 45° (d) None of these 56. If tan–12, tan–13 are two angles of a triangle, then what is the third angle? (a) tan–12 (b) tan–14 (c) π/4 (d) π/3 57. The angle of elevation of the top of a flag post from a point 5 m away from its base is 75°. What is the approximate height of the flag post? (a) 15 m (b) 17 m (c) 19 m (d) 21 m 58. A man walks 10 m towards a lamp post and notices that the angle of elevation of the top of the post increases from 30° to 45°. The height of the lamp posts is: (a) 10 m (b) (5√3 + 5) m (c) (5√3 – 5) m (d) (10√3 + 10) m 59.

(a) (f (x))2 (b) 1 (c) 2f (x) (d) f (1 – x/1 + x) 60.

(a)

(b)

(c)

(d) 61.

(a)

(b)

(c)

(d) 62. Consider the following statements 1. Every function has a primitive. 2. A primitive of a function is unique. Which of the statements given above is/are correct? (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 63.

(a) 0 (b) 1 (c) 1/2 (d) Limit does not exist 64.

(a) 0 (b) 1 (c) – 1 (d) 1/2 65. In a lottery, 16 tickets are sold and 4 prizes are awarded. If a person buys 4 tickets,what is the probability of his winning a prize? (a) 4/164

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(b) 175/256 (c) 1/4 (d) 81/256 66. If P(A) = 0.8, P(B) = 0.9, P(AB) = p, which one of the following is correct? (a) 0.72 ≤ p ≤ 0.8 (b) 0.7 ≤ p ≤ 0.8 (c) 0.72 < p< 0.8 (d) 0.7 < p< 0.8 67. Three letters are randomly selected from the 26 capital letters of the English Alphabet. What is the probability that the letter ‘A’ will not be included in the choice? (a) 1/2 (b) 23/26 (c) 12/13 (d) 25/26 68. Three digital numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that the number has the same digits? (a) 1/16 (b) 1/25 (c) 16/25 (d) 1/645 69. What is the probability that a leap year selected at random contains 53 Mondays? (a) 1/7 (b) 2/7 (c) 7/366 (d) 26/183 70. Four coins are tossed simultaneously. What is the probability of getting exactly 2 heads? (a) 1/2 (b) 1/4 (c) 1/8 (d) 3/8 71. How many arbitrary constants are there in the equation of a plane? (a) 2 (b) 3 (c) 4 (d) Any finite number 72.

(a) 0 (b) 30 unit (c) 40 unit (d) 50 unit 73. What is the number of planes passing through three non-collinear points? (a) 3 (b) 2 (c) 1 (d) 0 74. DIRECTIONS: The vertices of a cube are (0, 0, 0), (2, 0, 0), (0, 2, 0), (0, 0, 2), (2, 2, 0), (2, 0, 2), (0, 2, 2), (2, 2, 2) respectively. Q. What is the angle between the diagonal of one of the faces of the cube and the diagonal of the cube intersecting the diagonal of the face of the cube?

(a)

(b)

(c)

(d) 75. What are the direction ratios of normal to the plane 2x – y + 2z + 1 = 0

(a)

(b)

(c)

(d) 76. If a line makes 30° with the positive direction of x-axis, angle β with the positive direction of y-axis and angle γ with the positive direction of z-axis, then what is cos2β + cos2γ equal to? (a) 1/4 (b) 1/2 (c) 3/4 (d) 1 77. A firm employing 30 workers and paying on an average Rs 500 is combined with another firm employing 20 workers

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paying on an average Rs What is the average pay of the workers of the combined firm? (a) Rs 540 (b) Rs 550 (c) Rs 560 (d) Rs 580 78.

(a) Pie diagram (b) Bar chart (c) Cubic chart (d) Histogram 79. What is the standard deviation of numbers 7, 9, 11, 13, 15? (a) 2.2 (b) 2.4 (c) 2.6 (d) 2.8 80. The standard deviation of some consecutive integers is found to be 2. Which of the following statements best describes the nature of the consecutive integers? (a) The integers are any set of eight consecutive integers (b) The integers are any set of eight consecutive positive integers (c) The integers are any set of seven consecutive integers (d) None of the above 81. Students of three sections of a class, having 30, 30 and 40 students appeared for a test of 100 marks. The arithmetic means of the marks of the three sections are 72.2, 69.0 and 64.1 in that order. What is the arithmetic mean of the marks of all the students of the three sections? (a) 66.6 (b) 67.3 (c) 68.0 (d) 70.6 82.

(a) 20000 (b) 21000 (c) 24000 (d) 27000 83. If the mean of few observations is 40 and standard deviation is 8, then what is the coefficient of variation? (a) 1% (b) 10% (c) 20% (d) 30% 84. What is the derivative of f (x) = x | x |? (a) | x | + x (b) 2x (c) 2 | x | (d) – 2 | x |

85.

(a) 1/2 (b) 1 (c) –1 (d) 2 86.

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(a)

(b)

(c)

(d) 87.

(a) 0 (b) 1 (c) 2 (d) None of the above 88. Which one of the following statements is correct in respect of the curve 4y – x2 – 8 = 0? (a) The curve is increasing in (– 4, 4) (b) The curve is increasing in (– 4, 0) (c) The curve is increasing in (0, 4) (d) The curve is decreasing in (– 4, 4) 89. What is the equation of the curve whose slope at any point is equal to 2x and which passes through the origin? (a) y(1–x)=x2 (b) y2(1+x2) = x4 (c) Y2= (x+1)2

(d) y = x 2 90. What is the maximum point on the curve x = ex y? (a) (1, e) (b) (1, e –1) (c) (e, 1) (d) (e–1, 1) 91. At an extreme point of a function f(x), the tangent to the curve is (a) parallel to the x-axis (b) perpendicular to the x-axis (c) inclined at an angle 45° to the x-axis (d) inclined at an angle 60° to the x-axis 92.

(a)

(b)

(c)

(d) 93.

(a) eln x (sin x – cos x) + c (b) (sin x – x cos x) + c (c) (x sin x + cos x) + c (d) (sin x + x cos x) – c 94.

(a) 2 cosec 2x + c (b) – 2 cot 2x + c (c) 2 sec 2x + c (d) – 2 tan 2x + c 95. What is the area of the region bounded by the line 3x – 5y = 15, x =1, x = 3 and x-axis in sq unit? (a) 36/5 (b) 18/5 (c) 9/5 (d) 3/5 96. What is the area under the curve f(x) = xex above the x-axis and between the lines x = 0 and x = 1? (a) 1/2 sq unit (b) 1 sq unit (c) 3/2 sq unit (d) 2 sq unit 97.

(a) 2 (b) 1 (c) 0 (d) –1 98.

(a) 1

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(b) 2 (c) 3 (d) 4 99. What is the solution of the differential equation – cosec2 (x + y) dy = dx? (a) y – c = sin (x + y) (b) x – c = sin (x + y) (c) y – c = tan (x + y) (d) None of the above 100.

(a)

(b)

(c)

(d) 101.

(a) 1 (b) 2 (c) –1 (d) Degree does not exist 102.

(a) 2 (b) 4 (c) 6 (d) 8 103. From the matrix equation AB = AC, which one of the following can be concluded? (a) B = C for any matrix A (b) B = C, if A is singular (c) B = C, if A is non-singular (d) A = B = C for any matrix A

104.

(a) –1/2 (b) ½ (c) 1 (d) 2 105.

(a) x = 5, y = 14 (b) x = – 5, y = 14 (c) x = – 5, y = – 14 (d) x = 5, y = – 14 106.

(a)

(b)

(c)

(d) 107. If A be a real skew- symmetric matrix of order n such that A2 + I = 0, I being the identity matrix of the same order as that of A, then what is the order of A? (a) 3 (b) Odd (c) Prime number (d) Even 108. Find the value of k in which the system of equations kx + 2y = 5 and 3x + y = 1 has no solution? (a) 0 (b) 3 (c) 6 (d) 15 109. The sum and product of matrices A and B exist. Which of the following implications are necessarily true?

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1. A and B are square matrices of same order. 2. A and B are non-singular matrices Select the correct answer using the code given below: (a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2 110.

(a) –9 (b) –7 (c) 7 (d) 0 111.

(a)

(b)

(c)

(d) 112.

(a)

(b)

(c)

(d) 113.

(a) a2 + b2 (b) 2(a2 + b2) (c) 4(a2 + b2) (d) 4ab 114.

(a)

(b)

(c)

(d) 115.

(a)

(b)

(c)

(d) 116.

(a) √5/2 (b) 19/9 (c) √5/4 (d) 11/3 117.

(a)

(b)

(c)

(d) 118.

(a) 2 only (b) 2 and 3 (c) 1 and 2 (d) 1 and 3 119.

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(a)

(b)

(c)

(d) 120.

(a)

(b)

(c)

(d) 1. b 2. c 3. d 4. d 5. b 6. a 7. c 8. d 9. b 10. d 11. b 12. b 13. b 14. c 15. a 16. c 17. b 18. a 19. d 20. b 21. b 22. c 23. a 24. c 25. a 26. b 27. c 28. d 29. a 30. a 31. b 32. b 33. c 34. d 35. b 36. a 37. b 38. a 39. d 40. c 41. b 42. c 43. a 44. c 45. a 46. c 47. c 48. d 49. a 50. a 51. a 52. d 53. a 54. c 55. a 56. c 57. c 58. b 59. c 60. d 61. a 62. b 63. a 64. a 65. c 66. b 67. b 68. b 69. b 70. d 71. c 72. b 73. c 74. c 75. b 76. a 77. a 78. b 79. d 80. c 81. c 82. b 83. c 84. c 85. c 86. d 87. c 88. c 89. d 90. b 91. a 92. b 93. b 94. a 95. b 96. b 97. c 98. d 99. d 100. d 101. b 102. c 103. c 104. b 105. c 106. b 107. a 108. c 109. a 110. b 111. a 112. c 113. d 114. d 115. c 116. b 117. c 118. a 119. b 120. b 1.

2.

3.

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5.

6.

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7.

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9.

10.

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12.

13.

14.

15.

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16. 17.

18.

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21.

22.

23. 24.

25.

26.

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27.

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29.

30. 31.

32.

33.

34.

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38.

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40.

41.

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47.

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48.

49.

50.

51.

52.

53.

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54.

55.

56.

57.

58.

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59.

60.

61. 62.

63.

64.

65.

66.

67.

68.

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69.

70.

71.

72.

73.

74.

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77.

78.

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81.

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82.

83.

84.

85.

86.

87.

88.

89.

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90.

91.

92.

93.

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95.

96.

97.

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98.

99.

100. 101.

102.

103.

104.

105.

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106.

107.

108.

109.

110.

111.

112.

113.

114.

115.

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116.

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118.

119.

120.