You dont have javascript enabled! Please enable it! MCQ in Calculus Part 1 | Mathematics Board Exam

MCQ in Calculus Part 1 | Mathematics Board Exam

MCQ in Calculus Part 1

This is the Multiple Choice Questions Part 1 of the Series in Calculus topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

MCQ Topic Outline included in Mathematics Board Exam Syllabi

  • MCQ in Complex Variables | MCQ in Derivatives and Applications | MCQ in Integration and Applications | MCQ in Transcendental Functions | MCQ in Partial Derivatives | MCQ in Indeterminate forms | MCQ in Multiple Integrals | MCQ in Differential Equations | MCQ in Maxima/Minima and Time Rates

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each questions.

1. Evaluate:

How to Evaluate the Limit of a Function

A. 1/5

B. 2/5

C. 3/5

D. 4/5

View Answer:

Answer: Option B

Solution:

2. Evaluate:

How to Evaluate the Limit of a Function

A. Undefined

B. 0

C. Infinity

D. 1/7

View Answer:

Answer: Option D

Solution:

3. Evaluate:

How to Evaluate the Limit of a Function

A. 0

B. 1

C. 8

D. 16

View Answer:

Answer: Option C

Solution:

4. Evaluate:

How to Evaluate the Limit of a Function

A. 0

B. 2

C. 4

D. 6

View Answer:

Answer: Option C

Solution:

5. Evaluate:

How to Evaluate the Limit of a Function

A. 0

B. 1/2

C. 2

D. -1/2

View Answer:

Answer: Option B

Solution:

6. Compute the following limit:

How to Evaluate the Limit of a Function

A. 1

B. 0

C. 2

D. Infinite

View Answer:

Answer: Option A

Solution:

7. Evaluate:

How to Evaluate the Limit of a Function

A. Undefined

B. 3/5

C. Infinity

D. Zero

View Answer:

Answer: Option C

Solution:

8. Evaluate:

How to Evaluate the Limit of a Function

A. 24

B. 26

C. 28

D. 30

View Answer:

Answer: Option A

Solution:

9. Evaluate:

How to Evaluate the Limit of a Function

A. e^2x

B. e^(2/π)

C. 0

D. infinity

View Answer:

Answer: Option B

Solution:

10. Differentiate y = ex cos x2

A. – e^x sin x^2

B. e^x (cos x^2 – 2x sin x^2)

C. e^x cos x^2 – 2x sin x^2

D. -2xe^x sin x

View Answer:

Answer: Option B

Solution:

11. Differentiate y = sec (x2 + 2).

A. 2x cos ( x^2 + 2)

B. – cos (x^2 + 2) cot (x^2 + 2)

C. 2x sec (x^2 + 2) tan (x^2 + 2)

D. cos (x^2 + 2)

View Answer:

Answer: Option C

Solution:

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

A. 3x + 6

B. 3x – 3

C. 6x – 3

D. 6x + 3

View Answer:

Answer: Option D

Solution:

13. Differentiate y = log10 (x2 + 1)2

A. 4x (x2 + 1)

B. 4xlog10e/x2 + 1

C. log e(x) (x2 + 1)0

D. 2x(x2 + 1)

View Answer:

Answer: Option B

Solution:

14. Differentiate (x2 + 2)1/2

A. [(x2 + 2)(1/2)]/2

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

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

D. (x2 + 2)(3/2)

View Answer:

Answer: Option B

Solution:

15. If y = (t2 + 2)2 and t = x(1/2), determine dy/dx.

A. 3/2

B. (2x2+2x)/3

C. 2(x + 2)

D. x(5/2) + x(1/2)

View Answer:

Answer: Option C

Solution:

16. What is the first derivative of the expression (xy)x = ex?

A. 0

B. x/y

C. [-y(1 + ln xy)] / x

D. [-y(1 – lnxy)/x2]

View Answer:

Answer: Option C

Solution:

17. Find the derivative with respect to x the function sqrt(2 – 3x2)

A. -2x2/sqrt(2 – 3x2)

B. -3x/sqrt(2 – 3x2)

C. -3x2/sqrt(2 – 3x2)

D. 3x/sqrt(2 – 3x2)

View Answer:

Answer: Option B

Solution:

18. Find y’ if y = arc sin cos x

A. – 1

B. -2

C. 1

D. 2

View Answer:

Answer: Option A

Solution:

19. Find the derivative of arc cos 4x.

A. -4/(1 – 16x3)^(0.5)

B. 4/(1 – 16x3)^(0.5)

C. -4/(1 – 4x3)^(0.5)

D. 4/(1 – 16x3)^(0.5)

View Answer:

Answer: Option A

Solution:

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

A. {[(x+1)^2]/x} – {[(x+3)^3]/x}

B. {[4(x+1)^2]/x} – {[2(x+1)^3]/x}

C. {[2(x+1)^2]/x} – {[(x+1)^3]/x^3}

D. {[3(x+1)^2]/x} – {[(x+1)^3]/x^2}

View Answer:

Answer: Option D

Solution:

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

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

B. 2x/(x + 1)

C. 2x

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

View Answer:

Answer: Option A

Solution:

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

A. 2 sin (x2 + 2) cos (x2 + 2)

B. -2 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:

23. Find the second derivative of y by implicit differentiation from the equation 4x2 + 8y2 = 36.

A. 64x2

B. (-9/4)y3

C. 32xy

D. (-16/9)y3

View Answer:

Answer: Option B

Solution:

24. Find the partial derivatives with respect to x of the function xy2 – 5y + 6.

A. y2 – 5

B. y2

C. xy – 5y

D. 2xy

View Answer:

Answer: Option B

Solution:

25. Find the second derivative of x3 – 5x2 + x = 0.

A. 10x – 5

B. 6x – 10

C. 3x + 10

D. 3x2 – 5x

View Answer:

Answer: Option B

Solution:

26. Given the function f(x) = x to the 3rd power – 6x + 2. Find the first derivative at x = 2.

A. 6

B. 7

C. 3x2 – 5

D. 8

View Answer:

Answer: Option A

Solution:

27. Find the slope of the ellipse x2 + 4y2 – 10x – 16y + 5 = 0 at the point where y = 2 + 8^0.5 and x = 7.

A. -0.1463

B. -0.1538

C. -0.1654

D. -0.1768

View Answer:

Answer: Option D

Solution:

28. If y = 4 cos x + sin 2x, what is the slope of the curve when x = 2 radians?

A. -2.21

B. -4.94

C. -3.25

D. 2.21

View Answer:

Answer: Option B

Solution:

29. Find the slope of the tangent to the curve y = x3 – 2x + 1 at x = 1.

A. 1

B. 1/2

C. 1/3

D. 1/4

View Answer:

Answer: Option A

Solution:

30. Give the slope of the curve at the point (1, 1): y = [(x3)/4] – (2x+1).

A. 1/4

B. -1/4

C. 1 1/4

D. -1 1/4

View Answer:

Answer: Option D

Solution:

31. Find the slope of x^2y = 6 at the point (2, 2).

A. 2

B. -1

C. -1/2

D. -2

View Answer:

Answer: Option D

Solution:

32. Find the slope of the curve x2 + y2 – 6x + 10y + 5 = 0.

A. 1/5

B. 2/5

C. 1/4

D. 2

View Answer:

Answer: Option B

Solution:

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

A. 1

B. 2

C. 3

D. 4

View Answer:

Answer: Option B

Solution:

34. Find the coordinates 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:

35. Find the equation of the normal to x2 + y2 = 5 at the point (2, 1).

A. y = 2x

B. x = 2y

C. 2x + 3y = 3

D. x + y = 1

View Answer:

Answer: Option B

Solution:

36. What is the equation of the normal to the curve x2 + y2 = 25 at (4, 3)?

A. 5x + 3y = 0

B. 3x – 4y = 0

C. 3x + 4y = 0

D. 5x – 3y = 0

View Answer:

Answer: Option B

Solution:

37. Locate the points of inflection of the curve y = f(x) = x2ex

A. –2  ±  sqrt (3)

B. 2 ±  sqrt (2)

C. –2 ±  sqrt (2)

D. 2 ±  sqrt (3)

View Answer:

Answer: Option C

Solution:

38. In the curve 2 + 12x – x3, find the critical points.

A. (2, 18) & (-2, -14)

B. (2, 18) & (2, -14)

C. (-2, 18) & (2, -14)

D. (-2, 18) & (-2, 14)

View Answer:

Answer: Option A

Solution:

39. Find the radius of curvature of a parabola y2 – 4x = 0 at point (4, 4).

A. 22.36 units

B. 25.78 units

C. 20.33 units

D. 15.42 units

View Answer:

Answer: Option A

Solution:

40. Find the radius of curvature at any point in the curve y + ln cos x = 0.

A. cos x

B. 1.5707

C. sec x

D. 1

View Answer:

Answer: Option C

Solution:

41. Find the minimum distance from the point (4, 2) to the parabola y2 = 8x.

A. 4 sqrt (3)

B. 2 sqrt (2)

C. sqrt (3)

D. 2 sqrt (3)

View Answer:

Answer: Option B

Solution:

42. The sum of the two positive numbers is 50. What are the numbers if their product is to be the largest possible.

A. 24 & 26

B. 28 & 22

C. 25 & 25

D. 20 & 30

View Answer:

Answer: Option C

Solution:

43. A triangle has variable sides x, y, z subject to the constraint such that the perimeter is fixed to 18 cm. What is the maximum possible area for the triangle?

A. 15.59 sq. cm

B. 18.71 sq. cm

C. 17.15 sq. cm

D. 14.03 sq. cm

View Answer:

Answer: Option A

Solution:

44. A farmer has enough money to build only 100 meter of fence. What are the dimensions of the field he can enclose the maximum area?

A. 25 m x 25 m

B. 15 m x 35 m

C. 20 m x 30 m

D. 22.5 m x 27.5 m

View Answer:

Answer: Option A

Solution:

45. Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108 cu. inches in square inches.

A. 125.50

B. 127.50

C. 129.50

D. 123.50

View Answer:

Answer: Option A

Solution:

46. A box is to be constructed from a piece of zinc 20 sq. in by cutting equal squares from each corner and turning up the zinc to form the side. What is the volume of the largest box that can be so constructed?

A. 599.95 cu. in.

B. 592.59 cu. in.

C. 579.90 cu. in.

D. 622.49 cu. in.

View Answer:

Answer: Option B

Solution:

47. A poster is to contain 300 (cm square) of printed matter with margins of 10 cm at the top and bottom and 5 cm at each side. Find the overall dimensions if the total area of the poster is minimum.

A. 27.76 cm, 47.8 cm

B. 20.45 cm, 35.6 cm

C. 22.24 cm, 44.5 cm

D. 25.55 cm, 46.7 cm

View Answer:

Answer: Option C

Solution:

48. A normal window is in the shape of a rectangle surmounted by a semi-circle. What is the ratio of the width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter?

A. 1

B. 1/2

C. 2

D. 2/3

View Answer:

Answer: Option A

Solution:

49. Determine the diameter of a closed cylindrical tank having a volume of 11.3 cu. m to obtain minimum surface area.

A. 1.22

B. 1.64

C. 2.44

D. 2.68

View Answer:

Answer: Option C

Solution:

50. The cost of fuel in running a locomotive is proportional to the square of the speed and is $25 per hour for a speed of 25 miles per hour. Other costs amount to $100 per hour, regardless of the speed. What is the speed which will make the cost per mile a minimum?

A. 40

B. 55

C. 50

D. 45

View Answer:

Answer: Option A

Solution:

Online Questions and Answers in Calculus Series

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

MCQ in Calculus
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
Please do Subscribe on YouTube!

P inoyBIX educates thousands of reviewers and students a day in preparation for their board examinations. Also provides professionals with materials for their lectures and practice exams. Help me go forward with the same spirit.

“Will you subscribe today via YOUTUBE?”

Subscribe

What You Also Get: FREE ACCESS & DOWNLOAD via GDRIVE

TIRED OF ADS?

  • Become Premium Member and experienced fewer ads to ads-free browsing.
  • Full Content Access Exclusive to Premium members
  • Access to PINOYBIX FREEBIES folder
  • Download Reviewers and Learning Materials Free
  • Download Content: You can see download/print button at the bottom of each post.

PINOYBIX FREEBIES FOR PREMIUM MEMBERSHIP:

  • CIVIL ENGINEERING REVIEWER
  • CIVIL SERVICE EXAM REVIEWER
  • CRIMINOLOGY REVIEWER
  • ELECTRONICS ENGINEERING REVIEWER (ECE/ECT)
  • ELECTRICAL ENGINEERING & RME REVIEWER
  • FIRE OFFICER EXAMINATION REVIEWER
  • LET REVIEWER
  • MASTER PLUMBER REVIEWER
  • MECHANICAL ENGINEERING REVIEWER
  • NAPOLCOM REVIEWER
  • Additional upload reviewers and learning materials are also FREE

FOR A LIMITED TIME

If you subscribe for PREMIUM today!

You will receive an additional 1 month of Premium Membership FREE.

For Bronze Membership an additional 2 months of Premium Membership FREE.

For Silver Membership an additional 3 months of Premium Membership FREE.

For Gold Membership an additional 5 months of Premium Membership FREE.

Join the PinoyBIX community.

DaysHoursMinSec
This offer has expired!

Add Comment

THE ULTIMATE ONLINE REVIEW HUB: PINOYBIX . © 2014-2024 All Rights Reserved | | Follow me on Blogarama DMCA.com Protection Status