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

Answer: **Option B**

Solution:

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

a. sech^{2} (x)

b. csch^{2} (x)

c. sinh^{2} (x)

d. tanh^{2} (x)

Answer: **Option A**

Solution:

53. Find the derivative of y = x^{x}.

a. x^{x} (2 + ln x)

b. x^{x} (1 + ln x)

c. x^{x} (4 – ln x)

d. x^{x} (8 + ln x)

Answer: **Option B**

Solution:

54. Find the derivative of y = log_{a} 4x.

a. y’ = (log_{a} e)/x

b. y’ = (cos e)/x

c. y’ = (sin e)/x

d. y’ = (tan e)/x

Answer: **Option A**

Solution:

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

a. 3x + 3

b. 3x – 3

c. 6x – 3

d. 6x + 3

Answer: **Option D**

Solution:

56. What is the derivative with respect to x of sec^{2} (x)?

a. 2x sec^{2} (x) tan^{2} (x)

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

c. sec^{2} (x) tan^{2} (x)

d. 2 sec^{2} (x) tan^{2} (x)

Answer: **Option A**

Solution:

57. The derivative with respect to x of 2cos^{2} (x^{2} + 2).

a. 4 sin (x^{2} + 2) cos (x^{2} + 2)

b. -4 sin (x^{2} + 2) cos (x^{2} + 2)

c. 8x sin (x^{2} + 2) cos (x^{2} + 2)

d. -8x sin (x^{2} + 2) cos (x^{2} + 2)

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}]/x^{3}

c. [4(x + 1)^{2}]/x – [2(x + 1)^{3}]/x

d. [(x + 1)^{2}]/x – [(x + 1)^{3}]/x

Answer: **Option A**

Solution:

59. Determine the slope of the curve y = x^{2} – 3x as it passes through the origin.

a. -4

b. 2

c. -3

d. 0

Answer: **Option C**

Solution:

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

a. 6

b. 5

c. 7

d. 4

Answer: **Option B**

Solution:

61. Find the slope of (x^{2})y = 8 at the point (2,2).

a. 2

b. -1

c. -1/2

d. -2

Answer: **Option D**

Solution:

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

a. –y(1 – ln xy)/x^{2}

b. –y(1 + ln xy)/x

c. 0

d. x/y

Answer: **Option B**

Solution:

63. Find y’ in the following equation y = 4x^{2} – 3x –1.

a. 8x – 3

b. 4x – 3

c. 2x – 3

d. 8x – x

Answer: **Option A**

Solution:

64. Differentiate the equation y = (x^{2})/(x + 1).

a. (x^{2} + 2x)/(x + 1)^{2}

b. x/(x + 1)

c. 2x^{2}/(x + 1)

d. 1

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}

Answer: **Option B**

Solution:

66. Find dy/dx in the equation y = (x^{6} + 3x^{2} + 50)/(x^{2} + 1) if x = 1

a. -21

b. -18

c. 10

d. 16

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 = x^{2} + 2x – 4

b. y = (x^{3})/3 + (3x^{2})/2 + 2x

c. y = 3x^{2} + 4x – 8

d. y = (3x^{2})/2 + 4x/3 + 2

Answer: **Option B**

Solution:

68. Find the equation of the curve whose slope is 3x^{4} – x^{2} and passes through point (0,1).

a. y = (3x^{5})/5 – (x^{3})/3 + 1

b. y = (x^{4})/4 – (x^{3}) + 1

c. y = (2x^{5})/5 – 2x + 1

d. y = (3x^{5}) – (x^{3})/3 + 1

Answer: **Option A**

Solution:

69. What is the slope of the tangent to y = (x^{2} + 1)(x^{3} – 4x) at (1,-6)?

a. -8

b. -4

c. 3

d. 5

Answer: **Option A**

Solution:

70. Find the coordinate of the vertex of the parabola y = x^{2} – 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)

Answer: **Option A**

Solution:

71. Find the slope of the curve x^{2} + y^{2} – 6x + 10y + 5 = 0 at point (1,0).

a. 2/5

b. ¼

c. 2

d. 2

Answer: **Option A**

Solution:

72. Find the slope of the ellipse x^{2} + 4y^{2} – 10x + 16y +5 = 0 at the point where y = 2 + 8^{0.5} and x = 7.

a. -0.1654

b. -0.1538

c. -0.1768

d. -0.1463

Answer: **Option C**

Solution:

73. Find the slope of the tangent to the curve y = 2x – x^{2} + x^{3} at (0,2).

a. 2

b. 3

c. 4

d. 1

Answer: **Option A**

Solution:

74. Find the equation of the tangent to the curve y = 2e^{x} at (0,2).

a. 2x – y + 3 = 0

b. 2x – y + 2 = 0

c. 3x + y + 2 = 0

d. 2x + 3y + 2 = 0

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

Answer: **Option A**

Solution:

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

a. 81

b. 48

c. 64

d. 54

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

Answer: **Option A**

Solution:

78. If the slope of the curve y^{2} = 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

Answer: **Option A**

Solution:

79. If the slope of the curve x^{2} + y^{2} = 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

Answer: **Option A**

Solution:

80. If the slope of the curve 25x^{2} + 4y^{2} = 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

Answer: **Option A**

Solution:

81. Determine the point on the curve x^{3} – 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

Answer: **Option A**

Solution:

82. Find the second derivative of y = (2x + 1)^{2} + x^{3}.

a. 8 + 6x

b. (2x + 1)^{3}

c. x + 1

d. 6 + 4x

Answer: **Option A**

Solution:

83. Find the second derivative of y = (2x + 4)^{2} x^{3}.

a. x^{2}(80x + 192)

b. 2x + 4

c. x^{3}(2x + 80)

d. x^{2}(20x + 60)

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

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

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

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

Answer: **Option A**

Solution:

88. Find the first derivative of y = 2cos(2 + x^{2}).

a. -4x sin (2 + x^{2})

b. 4x cos (2 + x^{2})

c. x sin (2 + x^{2})

d. x cos (2 + x^{2})

Answer: **Option A**

Solution:

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

a. 24x sin (3x^{2} – 3) cos (3x^{2} – 3)

b. 12 sin (3x^{2} – 3)

c. 6x cos (3x^{2} – 3)

d. 24x sin (3x^{2} – 3)

Answer: **Option A**

Solution:

90. Find the first derivative of y = tan^{2} (3x^{2} – 4).

a. 12xtan(3x^{2} – 4)sec^{2} (3x^{2} – 4)

b. x tan (3x^{2} – 4)

c. sec^2 (3x^{2} – 4)

d. 2 tan^{2} (3x^{2} – 4)csc^{2} (3x^{2} – 4)

Answer: **Option A**

Solution:

91. Find the derivative of arc cos 4x

a. -4/(1 – 16x^{2})^{0.5}

b. 4/(1 – 16 x^{2})^{0.5}

c. -4/(1 – 4x^{2})^{0.5}

d. 4/(1 – 4x^{2})^{0.5}

Answer: **Option A**

Solution:

92. The equation y^{2} = cx is the general equation of.

a. y’ = 2y/x

b. y’ = 2x/y

c. y’ = y/2x

d. y’ = x/2y

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

Answer: **Option A**

Solution:

94. Find the coordinate of the vertex of the parabola y = x^{2} – 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)

Answer: **Option A**

Solution:

95. Find dy/dx by implicit differentiation at the point (3,4) when x^{2} + y^{2} = 25.

a. -3/4

b. ¾

c. 2/3

d. -2/3

Answer: **Option A**

Solution:

96. Find dy/dx by implicit differentiation at point (0,0) if (x^{3})(y^{3}) – y = x.

a. -1

b. -2

c. 2

d. 1

Answer: **Option A**

Solution:

97. Find dy/dx by implicit differentiation at point (0,-2) if x^{3} – xy + y^{2} = 4.

a. ½

b. -2

c. -2/3

d. ¾

Answer: **Option A**

Solution:

98. Find the point of inflection of f(x) = x^{3} – 3x^{2} – x + 7.

a. 1,4

b. 1,2

c. 2,1

d. 3,1

Answer: **Option A**

Solution:

99. Find the point of inflection of the curve y = (9x^{2} – x^{3} + 6)/6.

a. 3,10

b. 2,8

c. 3,8

d. 2,10

Answer: **Option A**

Solution:

100. Find the point of inflection of the curve y = x^{3} – 3x^{2} + 6.

a. 1,4

b. 1,3

c. 0,2

d. 2,1

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**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

**MCQ from Number 51 – 100**Answer key:

**PART 2**

**MCQ from Number 101 – 150**Answer key:

**PART 3**

**MCQ from Number 151 – 200**Answer key:

**PART 4**

**MCQ from Number 201 – 250**Answer key:

**PART 5**

**MCQ from Number 251 – 300**Answer key:

**PART 6**

**MCQ from Number 301 – 350**Answer key:

**PART 7**

**MCQ from Number 351 – 400**Answer key:

**PART 8**

**MCQ from Number 401 – 450**Answer key:

**PART 9**

**MCQ from Number 451 – 500**Answer key:

**PART 10**

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