MCQ in Engineering Mathematics Part 2 | Math Board Exam

(Last Updated On: January 6, 2021)

MCQs in Engineering Mathematics

This is the Multiples Choice Questions in Engineering Mathematics Part 2 of the Series. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize each and every questions compiled here taken from various sources including past Board Exam Questions, Engineering Mathematics Books, Journals and other Engineering Mathematics References. In the actual board, you have to answer 100 items in Engineering Mathematics within 5 hours. You have to get at least 70% to pass the subject. Engineering Mathematics is 20% of the total 100% Board Rating along with Electronic Systems and Technologies (30%), General Engineering and Applied Sciences (20%) and Electronics Engineering (30%).

Continue Practice Exam Test Questions Part 2 of the Series

MCQ in Engineering Mathematics Part 1 | Math Board Exam

Choose the letter of the best answer in each questions.

51. Find the derivative of y with respect to x if y = x ln x – x.

a. x ln x

b. ln x

c. (ln x)/x

d. x/ln x

View Answer:

Answer: Option B

Solution:

52. If y = tanh x, find dy/dx.

a. sech2 (x)

b. csch2 (x)

c. sinh2 (x)

d. tanh2 (x)

View Answer:

Answer: Option A

Solution:

53. Find the derivative of y = xx.

a. xx (2 + ln x)

b. xx (1 + ln x)

c. xx (4 – ln x)

d. xx (8 + ln x)

View Answer:

Answer: Option B

Solution:

54. Find the derivative of y = loga 4x.

a. y’ = (loga e)/x

b. y’ = (cos e)/x

c. y’ = (sin e)/x

d. y’ = (tan e)/x

View Answer:

Answer: Option A

Solution:

55. What is the derivative with respect to x of (x + 1)3 – x3.

a. 3x + 3

b. 3x – 3

c. 6x – 3

d. 6x + 3

View Answer:

Answer: Option D

Solution:

56. What is the derivative with respect to x of sec2 (x)?

a. 2x sec2 (x) tan2 (x)

b. 2x sec (x) tan (x)

c. sec2 (x) tan2 (x)

d. 2 sec2 (x) tan2 (x)

View Answer:

Answer: Option A

Solution:

57. The derivative with respect to x of 2cos2 (x2 + 2).

a. 4 sin (x2 + 2) cos (x2 + 2)

b. -4 sin (x2 + 2) cos (x2 + 2)

c. 8x sin (x2 + 2) cos (x2 + 2)

d. -8x sin (x2 + 2) cos (x2 + 2)

View Answer:

Answer: Option D

Solution:

58. Find the derivative of [(x + 1)3]/x.

a. [3(x + 1)2]/x – [(x + 1)3]/x^2

b. [2(x + 1)3]/x – [(x + 1)3]/x3

c. [4(x + 1)2]/x – [2(x + 1)3]/x

d. [(x + 1)2]/x – [(x + 1)3]/x

View Answer:

Answer: Option A

Solution:

59. Determine the slope of the curve y = x2 – 3x  as it passes through the origin.

a. -4

b. 2

c. -3

d. 0

View Answer:

Answer: Option C

Solution:

60. If y1 = 2x + 4 and y2 = x2 + C, find the value of C such that y2 is tangent to y1.

a. 6

b. 5

c. 7

d. 4

View Answer:

Answer: Option B

Solution:

61. Find the slope of (x2)y = 8 at the point (2,2).

a. 2

b. -1

c. -1/2

d. -2

View Answer:

Answer: Option D

Solution:

62. What is the first derivative dy/dx of the expression (xy)x = e.

a. –y(1 – ln xy)/x2

b. –y(1 + ln xy)/x

c. 0

d. x/y

View Answer:

Answer: Option B

Solution:

63. Find y’ in the following equation y = 4x2 – 3x –1.

a. 8x – 3

b. 4x – 3

c. 2x – 3

d. 8x – x

View Answer:

Answer: Option A

Solution:

64. Differentiate the equation y = (x2)/(x + 1).

a. (x2 + 2x)/(x + 1)2

b. x/(x + 1)

c. 2x2/(x + 1)

d. 1

View Answer:

Answer: Option A

Solution:

65. If y = x/(x + 1), find y’.

a. 1/(x + 1)3

b. 1/(x + 1)2

c. x + 1

d. (x + 1)2

View Answer:

Answer: Option B

Solution:

66. Find dy/dx in the equation y = (x6 + 3x2 + 50)/(x2 + 1) if x = 1

a. -21

b. -18

c. 10

d. 16

View Answer:

Answer: Option A

Solution:

67. Find the equation of the curve whose slope is (x + 1)(x + 2) and passes through point (-3, -3/2).

a. y = x2 + 2x – 4

b. y = (x3)/3 + (3x2)/2 + 2x

c. y = 3x2 + 4x – 8

d. y = (3x2)/2 + 4x/3 + 2

View Answer:

Answer: Option B

Solution:

68. Find the equation of the curve whose slope is 3x4 – x2 and passes through point (0,1).

a. y = (3x5)/5 – (x3)/3 + 1

b. y = (x4)/4 – (x3) + 1

c. y = (2x5)/5 – 2x + 1

d. y = (3x5) – (x3)/3 + 1

View Answer:

Answer: Option A

Solution:

69. What is the slope of the tangent to y = (x2 + 1)(x3 – 4x) at (1,-6)?

a. -8

b. -4

c. 3

d. 5

View Answer:

Answer: Option A

Solution:

70. Find the coordinate of the vertex of the parabola y = x2 – 4x + 1 by making use of the fact that at the vertex, the slope of the tangent is zero.

a. (2,-3)

b. (3,2)

c. (-1,-3)

d. (-2,-3)

View Answer:

Answer: Option A

Solution:

71. Find the slope of the curve x2 + y2 – 6x + 10y + 5 = 0 at point (1,0).

a. 2/5

b. ¼

c. 2

d. 2

View Answer:

Answer: Option A

Solution:

72. Find the slope of the ellipse x2 + 4y2 – 10x + 16y +5 = 0 at the point where y = 2 + 80.5 and x = 7.

a. -0.1654

b. -0.1538

c. -0.1768

d. -0.1463

View Answer:

Answer: Option C

Solution:

73. Find the slope of the tangent to the curve y = 2x – x2 + x3 at (0,2).

a. 2

b. 3

c. 4

d. 1

View Answer:

Answer: Option A

Solution:

74. Find the equation of the tangent to the curve y = 2ex at (0,2).

a. 2x – y + 3 = 0

b. 2x – y + 2 = 0

c. 3x + y + 2 = 0

d. 2x + 3y + 2 = 0

View Answer:

Answer: Option B

Solution:

75. Find the slope of the curve y = 2(1 + 3x)2 at point (0,3).

a. 12

b. -9

c. 8

d. -16

View Answer:

Answer: Option A

Solution:

76. Find the slope of the curve y = x2(x + 2)3 at point (1,2).

a. 81

b. 48

c. 64

d. 54

View Answer:

Answer: Option A

Solution:

77. Find the slope of the curve y = [(4 – x)2]/x at point (2,2).

a. -3

b. 2

c. -2

d. 3

View Answer:

Answer: Option A

Solution:

78. If the slope of the curve y2 = 12x is equal to 1 at point (x,y), find the value of x and y.

a. x = 3, y = 6

b. x = 4, y = 5

c. x = 2, y = 7

d. x = 5, y = 6

View Answer:

Answer: Option A

Solution:

79. If the slope of the curve x2 + y2 = 25 is equal to -3/4 at point (x,y) find the value of x and y.

a. 3,4

b. 2,3

c. 3,4.2

d. 3.5,4

View Answer:

Answer: Option A

Solution:

80. If the slope of the curve 25x2 + 4y2 = 100 is equal to -15/8 at point (x,y), find the value of x and y.

a. 1.2, 4

b. 2, 4

c. 1.2, 3

d. 2, 4.2

View Answer:

Answer: Option A

Solution:

81. Determine the point on the curve x3 – 9x – y = 0 at which slope is 18.

a. x = 3, y = 0

b. x = 4, y = 5

c. x = 2, y = 7

d. x = 5, y = 6

View Answer:

Answer: Option A

Solution:

82. Find the second derivative of y = (2x + 1)2 + x3.

a. 8 + 6x

b. (2x + 1)3

c. x + 1

d. 6 + 4x

View Answer:

Answer: Option A

Solution:

83. Find the second derivative of y = (2x + 4)2 x3.

a. x2(80x + 192)

b. 2x + 4

c. x3(2x + 80)

d. x2(20x + 60)

View Answer:

Answer: Option A

Solution:

84. Find the second derivative of y = 2x + 3(4x + 2)3 when x = 1.

a. 1728

b. 1642

c. 1541

d. 1832

View Answer:

Answer: Option A

Solution:

85. Find the second derivative of y = 2x/[3(4x + 2)2] when x = 0.

a. -1.33

b. 1.44

c. 2.16

d. -2.72

View Answer:

Answer: Option A

Solution:

86. Find the second derivative of y = 3/(4x-3) when x = 1.

a. 4.5

b. -3.6

c. 2.4

d. -1.84

View Answer:

Answer: Option A

Solution:

87. Find the second derivative of y = x-2  when x = 2.

a. 0.375

b. 0.268

c. 0.148

d. 0.425

View Answer:

Answer: Option A

Solution:

88. Find the first derivative of y = 2cos(2 + x2).

a. -4x sin (2 + x2)

b. 4x cos (2 + x2)

c. x sin (2 + x2)

d. x cos (2 + x2)

View Answer:

Answer: Option A

Solution:

89. Find the first derivative of y = 2 sin^2 (3x2 – 3).

a. 24x sin (3x2 – 3) cos (3x2 – 3)

b. 12 sin (3x2 – 3)

c. 6x cos (3x2 – 3)

d. 24x sin (3x2 – 3)

View Answer:

Answer: Option A

Solution:

90. Find the first derivative of y = tan2 (3x2 – 4).

a. 12xtan(3x2 – 4)sec2 (3x2 – 4)

b. x tan (3x2 – 4)

c. sec^2 (3x2 – 4)

d. 2 tan2 (3x2 – 4)csc2 (3x2 – 4)

View Answer:

Answer: Option A

Solution:

91. Find the derivative of arc cos 4x

a. -4/(1 – 16x2)0.5

b. 4/(1 – 16 x2)0.5

c. -4/(1 – 4x2)0.5

d. 4/(1 – 4x2)0.5

View Answer:

Answer: Option A

Solution:

92. The equation y2 = cx is the general equation of.

a. y’ = 2y/x

b. y’ = 2x/y

c. y’ = y/2x

d. y’ = x/2y

View Answer:

Answer: Option C

Solution:

93. Find the slope of the curve y = 6(4 + x)1/2 at point (0,12).

a. 1.5

b. 2.2

c. 1.8

d. 2.8

View Answer:

Answer: Option A

Solution:

94. Find the coordinate of the vertex of the parabola y = x2 – 4x +1 by making use of the fact that at the vertex, the slope of the tangent is zero.

a. (2,-3)

b. (3,2)

c. (-1,-3)

d. (-2,-3)

View Answer:

Answer: Option A

Solution:

95. Find dy/dx by implicit differentiation at the point (3,4) when x2 + y2 = 25.

a. -3/4

b. ¾

c. 2/3

d. -2/3

View Answer:

Answer: Option A

Solution:

96. Find dy/dx by implicit differentiation at point (0,0) if (x3)(y3) – y = x.

a. -1

b. -2

c. 2

d. 1

View Answer:

Answer: Option A

Solution:

97. Find dy/dx by implicit differentiation at point (0,-2) if x3 – xy + y2 = 4.

a. ½

b. -2

c. -2/3

d. ¾

View Answer:

Answer: Option A

Solution:

98. Find the point of inflection of f(x) = x3 – 3x2 – x + 7.

a. 1,4

b. 1,2

c. 2,1

d. 3,1

View Answer:

Answer: Option A

Solution:

99. Find the point of inflection of the curve y = (9x2 – x3 + 6)/6.

a. 3,10

b. 2,8

c. 3,8

d. 2,10

View Answer:

Answer: Option A

Solution:

100. Find the point of inflection of the curve y = x3 – 3x2 + 6.

a. 1,4

b. 1,3

c. 0,2

d. 2,1

View Answer:

Answer: Option A

Solution:

Online Question and Answer in Engineering Mathematics Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Engineering Mathematics
PART 1: MCQ from Number 1 – 50                                 Answer key: PART 1
PART 2: MCQ from Number 51 – 100                             Answer key: PART 2
PART 3: MCQ from Number 101 – 150                            Answer key: PART 3
PART 4: MCQ from Number 151 – 200                            Answer key: PART 4
PART 5: MCQ from Number 201 – 250                            Answer key: PART 5
PART 6: MCQ from Number 251 – 300                            Answer key: PART 6
PART 7: MCQ from Number 301 – 350                             Answer key: PART 7
PART 8: MCQ from Number 351 – 400                             Answer key: PART 8
PART 9: MCQ from Number 401 – 450                             Answer key: PART 9
PART 10: MCQ from Number 451 – 500                           Answer key: PART 10

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