This is the Uncategorized Multiples Choice Questions Part 1 of the Series in Engineering Mathematics. 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%).

### The Series

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

**Engineering Mathematics MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

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

**PART 2**

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

**PART 3**

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

**PART 4**

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

**PART 5**

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

**PART 6**

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

**PART 7**

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

**PART 8**

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

**PART 9**

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

**PART 10**

### Start Practice Exam Test Questions Part I of the Series

**Choose the letter of the best answer in each questions.**

1. Evaluate the lim (x^2 – 16)/(x – 4).

- a. 1
- b. 8
- c. 0
- d. 16

2. Evaluate the limit (x – 4)/(x^2 – x – 12) as x approaches 4.

- a. undefined
- b. 0
- c. infinity
- d. 1/7

3. What is the limit of cos (1/y) as y approaches infinity?

- a. 0
- b. -1
- c. infinity
- d. 1

4. Evaluate the limits of lim (x^3 – 2x + 9) /(2x^3 – 8).

- a. 0
- b. -9/8
- c. α
- d. ½

5. Evaluate the limit of (x^3 – 2x^2 – x + 2) /(x^2-4) as x approaches 2.

- a. α
- b. ¾
- c. 2/5
- d. 4/7

6. Evaluate the limit of √(x – 4)/√(x^2 – 16) as x approaches 4.

- a. 0.262
- b. 0.354
- c. 0
- d. α

7. Evaluate the limit of (x^2 – x – 6)/(x^2 – 4x + 3) as x approaches 3.

- a. 3/2
- b. 3/5
- c. 0
- d. 5/2

8. Evaluate the limit of (4x^2 – x)/ (2x^2 + 4) as x approaches α.

- a. 2
- b. 4
- c. α
- d. 0

9. Evaluate the limit of (x – 2)/(x^3 – 8) as x approaches 2.

- a. α
- b. 1/12
- c. 0
- d. 2/3

10. Evaluate the limit of θ/(2 sinθ) as θ approaches 0.

- a. 2
- b. ½
- c. 0
- d. α

11. Evaluate the limit of (1 – sec^2 (x)/ cos (x) – 1 as x approaches 0.

- a. -2
- b. α
- c. 0
- d. 1

12. Evaluate the limit (x^3 – 27)/(x – 3) as x approaches to 3.

- a. 0
- b. infinity
- c. 9
- d. 27

13. Evaluate the limit (3x^3 – 4x^2 – 5x + 2)/ (x^2 – x – 2) as x approaches to 2.

- a. α
- b. 5
- c. 0
- d. 7/3

14. Evaluate the limit of (4 tan^3 (x)/ 2sin(x) – x as x approaches 0.

- a. 1
- b. 0
- c. 2
- d. α

15. Evaluate the limit of 8x/(2x – 1) as x approaches α.

- a. 4
- b. 3
- c. 2
- d. -1

16. Evaluate the limit of (x^2-1)/ (x^2+3x-4) as x approaches 1.

- a. 2/5
- b. 1/5
- c. 3/5
- d. 4/5

17. Evaluate the limit of (x + 2)/(x – 2) as x approaches α.

- a. α
- b. -1
- c. 1
- d. 4

18. Evaluate the limit of (1 – cosx)/(x^2) as x approaches 0.

- a. α
- b. ½
- c. 1
- d. 0

19. Find the limit of [sqrt(x + 4) – 2]/x as x approaches 0.

- a. α
- b. ¼
- c. 0
- d. ½

20. Find the limit [sqrt(x + 9) – 3]/x as x approaches 0.

- a. α
- b. 1/6
- c. 0
- d. 1/3

21. Evaluate the limit (x^2 + x – 6)/(x^2 – 4) as x approaches to 2.

- a. 6/5
- b. 5/4
- c. 4/3
- d. 3/2

22. Evaluate the limit (x^4 – 81)/(x – 3) as x approaches to 3.

- a. 108
- b. 110
- c. 122
- d. 100

23. Evaluate the limit (x + sin2x)/ (x – sin2x) as x approaches to 0.

- a. -5
- b. -3
- c. 4
- d. -1

24. Evaluate the limit (ln sin x)/(ln tan x) as x approaches to 0.

- a. 1
- b. 2
- c. ½
- d. α

25. Compute the equation of the vertical asymptote of the curve y = (2x – 1)/(x + 2).

- a. x + 2 = 0
- b. x – 3 = 0
- c. x + 3 = 0
- d. x – 2 = 0

26. Compute the equation of the horizontal asymptote of the curve y = (2x – 1)/(x + 2).

- a. y = 2
- b. y = 0
- c. y – 1 = 0
- d. y – 3 = 0

27. The function y = (x – 4)/(x + 2) is discontinuous at x equals?

- a. -2
- b. 0
- c. 1
- d. 2

28. An elliptical plot of garden has a semi-major axis of 6 m and a semi-minor axis of 4.8 meters. If these are increased by 0.15 m each, find by differential equations the increase in area of the garden in sq. m.

- a. 0.62π
- b. 1.62π
- c. 2.62π
- d. 2.62π

29. The diameter of a circle is to be measured and its area computed. If the diameter can be measured with a maximum error of 0.001 cm and the area must be accurate to within 0.10 sq.cm. Find the largest diameter for which the process can be used.

- a. 64
- b. 16
- c. 32
- d. 48

30. The altitude of a right circular cylinder is twice the radius of the base. The altitude is measured as 12 cm. With a possible error of 0.005 cm, find the approximately error in the calculated volume of the cylinder.

- a. 0.188 cu cm
- b. 0.144 cu cm
- c. 0.104 cu cm
- d. 0.126 cu cm

31. What is the allowable error in measuring the edge of a cube that is intended to hold a cu m, if the error in the computed volume is not to exceed 0.03 cu m?

- a. 0.002
- b. 0.0025
- c. 0.003
- d. 0.001

32. If y = x^(3/2) what is the approximate change in y when x changes from 9 to 9.01?

- a. 0.045
- b. 0.068
- c. 0.070
- d. 0.023

33. The expression for the horsepower of an engine is P = 0.4 n x^2 where *n* is the number of cylinders and x is the bore of cylinders. Determine the power differential added when four cylinder car has the cylinders rebored from 3.25cm to 3.265cm.

- a. 0.156 hp
- b. 0.210 hp
- c. 0.319 hp
- d. 0.180 hp

34. A surveying instrument is placed at a point 180 m from the base of a bldg on a level ground. The angle of elevation of the top of a bldg is 30 degrees as measured by the instrument. What would be error in the height of the bldg due to an error of 15 minutes in this measured angle by differential equation?

- a. 1.05 m
- b. 1.09 m
- c. 2.08 m
- d. 1.05 m

35. If y = 3x^2 – x + 1, find the point x at which dy/dx assume its mean value in the interval x = 2 and x = 4.

- a. 3
- b. 6
- c. 4
- d. 8

36. Find the approximate increase by the use of differentials, in the volume of the sphere if the radius increases from 2 to 2.05.

- a. 2.51
- b. 2.25
- c. 2.12
- d. 2.86

37. If the area of a circle is 64π sq mm, compute the allowable error in the area of a circle if the allowable error in the radius is 0.02 mm.

- a. 1.01 sq mm
- b. 1.58 sq mm
- c. 2.32 sq mm
- d. 0.75 sq mm

38. If the volume of a sphere is 1000π/6 cu mm and the allowable error in the diameter of the sphere is 0.03 mm, compute the allowable error in the volume of a sphere.

- a. 6.72 cu mm
- b. 4.71 cu mm
- c. 5.53 cu mm
- d. 3.68 cu mm

39. A cube has a volume of 1728 cu mm. If the allowable error in the edge of a cube is 0.04 mm, compute the allowable error in the volume of the cube.

- a. 17.28 cu mm
- b. 16.88 cu mm
- c. 15.22 cu mm
- d. 20.59 cu mm

40. Find the derivative of y = 2^(4x).

- a. 3^(4x+2) ln 2
- b. 2^(4x+2) ln 2
- c. 6^(3x+2) ln 2
- d. 4^(4x+2) ln 2

41. Find the derivative of h with respect to u if h = π^(2u).

- a. π^(2u)
- b. 2u ln π
- c. 2π^(2u) ln π
- d. 2π^(2u)

42. Find y’ if y = ln x

- a. 1/x
- b. ln x^2
- c. 1/ln x
- d. x ln x

43. Find y’ if y = arc sin (x)

- a. √(1 – x^2)
- b. 1/√(1 – x^2)
- c. 1/(1 + x^2)
- d. (1 + x)/√(1 – x^2)

44. Find the derivative of loga u with respect to x.

- a. log u du/dx
- b. u du/ln a
- c. loga e/u
- d. log a du/dx

45. Find the derivative of arc cos (2x).

- a. -2/√(1 – 4x^2)
- b. 2/√(1 – 4x^2)
- c. 2/(1 + 4x^2)
- d. 2/√(2x^2 – 1)

46. Find the derivative of 4 arc tan (2x).

- a. 4/(1 + x^2)
- b. 4/(4x^2 + 1)
- c. 8/(1 + 4x^2)
- d. 8/(4x^2 + 1)

47. Find the derivative of arc csc (3x).

- a. -1/[x√(9x^2 – 1)]
- b. 1/[3x√(9x^2 – 1)]
- c. 3/[x√(1 – 9x^2)]
- d. 3/[x√9x^2 – 1)]

48. Find the derivative of arc sec (2x)

- a. 1/[x√(4x^2 – 1)]
- b. 2/[x√(4x^2 – 1)]
- c. 1/[x√(1 – 4x^2)]
- d. 2/[x√(1 – 4x^2)]

49. If ln (ln y) + ln y = ln x, find y’.

- a. x/(x + y)
- b. x/(x – y)
- c. y/(x + y)
- d. y/(x – y)

50. Find y” if y=a^u.

- a. a^u ln a
- b. u ln a
- c. a^u/ln a
- d. a ln u