MCQs in Advanced Engineering Math Part I

This is the Multiple Choice Questions Part 1 of the Series in Advanced Engineering Math 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.

Multiple Choice Questions Topic Outline

• MCQs in Complex Numbers | MCQs in Mathematical Operation of Complex Numbers | MCQs in Matrices | MCQs in Sum of Two Matrices | MCQs in Difference of Two Matrices | MCQs in Product of Two Matrices | MCQs in Division of Matrices | Transpose Matrix | MCQs in Cofactor of an entry of a Matrix | Mcqs in Cofactor Matrix | MCQs in Inverse Matrix | MCQs in Determinants | MCQs in Properties of Determinants | MCQs in Laplace Transform | MCQs in Laplace transform of elementary functions

Online Questions and Answers in Advanced Engineering Math Series

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

Advanced Engineering Math MCQs

PART 1: MCQs from Number 1 – 50                        Answer key: PART I

PART 2: MCQs from Number 51 – 100                   Answer key: PART II

Start Practice Exam Test Questions Part I of the Series

Choose the letter of the best answer in each questions.

Problem 1: ECE Board April 1999

Simplify the expression i¹⁹⁹⁷ + i¹⁹⁹⁹, where i is an imaginary.

• A. 0
• B. –i
• C. 1 + i
• D. 1 – i

Problem 2: EE Board April 1997

Simplify: i²⁹ + i²¹ + i

• A. 3i
• B. 1 – i
• C. 1 + i
• D. 2i

Problem 3: EE Board April 1997

Write in the form a + bi the expression i³²¹⁷ – i⁴²⁷ + i¹⁸

• A. 2i + 1
• B. -1 + i
• C. 2i – 1
• D. 1 + i

Problem 4: CE Board May 1994

The expression 3 + 4i is a complex number. Compute its absolute value.

• A. 4
• B. 5
• C. 6
• D. 7

Problem 5: EE Board October 1993

Write the polar form of the vector 3 + j4.

• A. 6 ∠ 53.1°
• B. 10 ∠ 53.1°
• C. 5 ∠ 53.1°
• D. 8 ∠ 53.1°

Problem 6: ME Board April 1997

Evaluate the value of √-10 x √-7

• A. i
• B. -√70
• C. √70
• D. √17

Problem 7: EE Board April 1996

Simplify (3 – i)² – 7(3 – i) + 10

• A. –(3 + i)
• B. 3 + i
• C. 3 – i
• D. –(3 – i)

Problem 8: EE Board April 1996

If A = 40e^j120°, B = 20 ∠ -40°, C = 26.46 + j0, solve for A + B + C.

• A. 27.7 ∠ 45°
• B. 35.1 ∠ 45°
• C. 30.8 ∠ 45°
• D. 33.4 ∠ 45°

Problem 9: EE Board October 1997

What is 4i cube times 2i square

• A. -8i
• B. 8i
• C. -8
• D. -8i²

Problem 10: EE Board April 1997

What is the simplified expression (4.33 + j2.5) square?

• A. 12.5 + j21.65
• B. 20 + j20
• C. 15 + j20
• D. 21.65 + j12.5

Problem 11: ECE Board November 1998

Find the value of (1 + i)⁵, where i is an imaginary number.

• A. 1 – i
• B. -4(1 + i)
• C. 1 + i
• D. 4(1 + i)

Problem 12: EE Board October 1997

Find the principal 5^th root of [50(cos 150° + jsin 150°)].

• A. 1.9 + j1.1
• B. 3.26 – j2.1
• C. 2.87 + j2.1
• D. 2.25 – j1.2

Problem 13: ECE Board April 1999

What is the quotient when 4 + 8i is divided by i³?

• A. 8 – 4i
• B. 8 + 4i
• C. -8 + 4i
• D. -8 – 4i

Problem 14: EE Board October 1997

If A = -2 – 3i, and B = 3 + 4i, what is A / B?

• A. (18 – i) / 25
• B. (-18 – i) / 25
• C. (-18 + i) / 25
• D. (18 + i) / 25

Problem 15: EE Board October 1997

Rationalize ((4 + 3i) / (2 – i))

• A. 1 + 2i
• B. (11 + 10i) / 5
• C. (5 + 2i) / 5
• D. 2 + 2i

Problem 16: EE Board October 1997

Simplify

• A. (221 – 91i) / 169
• B. (21 + 52i) / 13
• C. (-7 + 17i) / 13
• D. (-90 + 220i) / 169

Problem 17: EE Board April 1996

What is the simplified expression of the complex number (6 + j2.5) / (3 + j4)?

• A. -0.32 + j0.66
• B. 1.12 + j0.66
• C. 0.32 – j0.66
• D. -1.75 + j1.03

Problem 18: EE Board April 1997

Perform the operation: 4(cos 60° + i sin 60°) divided by 2(cos 30° + i sin 30°) in rectangular coordinates.

• A. Square root of 3 – 2i
• B. Square root of 3 – i
• C. Square root of 3 + i
• D. Square root of 3 + 2i

Problem 19: EE Board June 1990

Find the quotient of (50 + j35) / (8 + j5)

• A. 6.47 ∠ 3°
• B. 4.47 ∠ 3°
• C. 7.47 ∠ 30°
• D. 2.47 ∠ 53°

Problem 20: EE Board March 1998

Three vectors A, B and C are related as follows: A / B = 2 at 180°, A + C = -5 + j15, C = conjugate of B. Find A.

• A. 5 – j5
• B. -10 + j10
• C. 10 – j10
• D. 15 + j15

Problem 21: EE Board April 1999

Evaluate cosh [j(π/4)]

• A. 0.707
• B. 1.41 + j0.866
• C. 0.5 + j0.707
• D. j0.707

Problem 22: EE Board April 1999

Evaluate cosh [j(π/3)]

• A. 0.5 + j1.732
• B. j0.866
• C. j1.732
• D. 0.5 + j0.866

Problem 23: EE Board April 1999

Evaluate ln (2 + j3)

• A. 1.34 + j0.32
• B. 2.54 + j0.866
• C. 2.23 + j0.21
• D. 1.28 + j0.98

Problem 24: EE Board October 1997

Evaluate the terms of a Fourier series 2 e^j10πt + 2 e^-j10πt at t = 1.

• A. 2 + j
• B. 2
• C. 4
• D. 2 + j2

Problem 25: EE Board March 1998

Given the following series:

Sin x = x – (x³/3!) + (x⁵/5!) + …..

Cos x = 1 – (x²/2!) + (x⁴/4!) + …..

e^x = 1 + x + (x²/2!) + (x³/3!) + ….

What relation can you draw from these series?

• A. e^x = cos x + sin x
• B. e^ix = cos x + i sin x
• C. e^ix = icos x + sin x
• D. ie^x = icos x + i sin x

Problem 26: EE Board October 1997

One term of a Fourier series in cosine form is 10 cos 40πt. Write it in exponential form.

• A. 5 e^j40πt
• B. 5 e^j40πt + 5 e^-j40πt
• C. 10 e^-j40πt 0
• D. 10 e^j40πt

Problem 27: EE Board April 1997

Evaluate the determinant:

• A. 4
• B. 2
• C. 5
• D. 0

Problem 28: ECE Board November 1991

Evaluate the determinant:

• A. 110
• B. -101
• C. 101
• D. -110

Problem 29: EE Board April 1997

Evaluate the determinant:

• A. 489
• B. 389
• C. 326
• D. 452

Problem 30: CE Board November 1996

Compute the value of x by determinant.

• A. -32
• B. -28
• C. 16
• D. 52

Problem 31: EE Board April 1997

Given the equations: x + y + z = 2, 3x – y – 2z = 4, 5x – 2y + 3z = -7. Solve for y by determinants.

• A. 1
• B. -2
• C. 3
• D. 0

Problem 32: EE Board April 1997

Solve the equations by Cramer’s Rule: 2x – y + 3z = -3, 3x + 3y – z = 10, -x – y + z = -4.

• A. (2, 1, -1)
• B. (2, -1, -1)
• C. (1, 2, -1)
• D. (-1, -2, 1)

Problem 33: EE Board October 1997

What is the cofactor of the second row, third column element?

Problem 34: EE Board October 1997

What is the cofactor with the first row, second column element?

Problem 35: EE Board October 1997

IF a 3 x 3 matrix and its inverse are multiplied together, write the product.

Problem 36: EE Board April 1996

• A. 3
• B. 1
• C. 0
• D. -2

Problem 37: CE Board November 1997

Given the matrix equation, solve for x and y,

• A. -4, 6
• B. -4, 2
• C. -4, -2
• D. -4, -6

Problem 38: EE Board April 1996

• A. 8
• B. 1
• C. -4
• D. 0

Problem 39: EE Board October 1997

What is A times B equal to?

Problem 40: EE Board April 1997

Problem 41: CE Board May 1996

Find the elements of the product of the two matrices, matrix BC.

Problem 42: EE Board October 1997

Transpose the matrix,

Problem 43:

Determine the inverse matrix of,

Problem 44: EE Board April 1997

k divided by s² + k² is the inverse laplace transform of,

• A. cos kt
• B. sin kt
• C. e^kt
• D. 1.0

Problem 45: EE Board April 1996, EE Board April 1997

The laplace transform of cos wt is,

• A. s / (s² + w²)
• B. w / (s² + w²)
• C. w / (s + w)
• D. s / (s + w)

Problem 46: EE Board April 1997

Find the laplace transform of [ 2 / (s + 1) ] – [ 4 / (s + 3) ].

• A. 2e^-t – 4e^-3t
• B. e^-2t + e^-3t
• C. e^-2t – e^-3t
• D. (2e^-t) (1 – 2e^-3t)

Problem 47: EE Board March 1998

Determine the inverse laplace transform of I_(s) = 200 / (s2 – 50s + 10625)

• A. I_(s) = 2e^-25t sin 100t
• B. I_(s) = 2te^-25t sin 100t
• C. I_(s) = 2e^-25t cos 100t
• D. I_(s) = 2te^-25t cos 100t

Problem 48: EE Board April 1997

The inverse laplace transform of s / ( s² + w² )

• A. sin wt
• B. w
• C. e^wt
• D. cos wt

Problem 49:

The inverse laplace transform of ( 2s – 18 ) / ( s² + 9 )

• A. 2 cos x – sin 3x
• B. 2 cos 3x – 6 sin 3x
• C. 3 cos 2x – 2 sin 6x
• D. 6 cos x – 3 sin 2x

Problem 50:

Determine the inverse laplace transform of 1 / ( 4s² – 8s ).

• A. ¼ e^t sinh t
• B. ½ e^2t sinh t
• C. ¼ e^t cosh t
• D. ½ e^2t cosh t

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