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.

#### MCQ Topic Outline included in Mathematics Board Exam Syllabi

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

#### Start Practice Exam Test Questions Part 1 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. โi

C. 1 + i

D. 1 โ i

Answer: **Option A**

Solution: Review: Solution for Number 1

**Problem 2: EE Board April 1997**

Simplify: i^{29} + i^{21} + i

A. 3i

B. 1 โ i

C. 1 + i

D. 2i

Answer: **Option A**

Solution: Review: Solution for Number 2

**Problem 3: EE Board April 1997**

Write in the form a + bi the expression i^{3217} โ i^{427} + i^{18}

A. 2i + 1

B. -1 + i

C. 2i โ 1

D. 1 + i

Answer: **Option C**

Solution: Review: Solution for Number 3

**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

Answer: **Option B**

Solution: Review: Solution for Number 4

**Problem 5: EE Board October 1993**

Write the polar form of the vector 3 + j4.

A. 6 โ 53.1ยฐ

B. 10 โ 53.1ยฐ

C. 5 โ 53.1ยฐ

D. 8 โ 53.1ยฐ

Answer: **Option C**

Solution: Review: Solution for Number 5

**Problem 6: ME Board April 1997**

Evaluate the value of โ-10 x โ-7

A. i

B. -โ70

C. โ70

D. โ17

Answer: **Option B**

Solution: Review: Solution for Number 6

**Problem 7: EE Board April 1996**

Simplify (3 โ i)^{2} โ 7(3 โ i) + 10

A. โ(3 + i)

B. 3 + i

C. 3 โ i

D. โ(3 โ i)

Answer: **Option D**

Solution: Review: Solution for Number 7

**Problem 8: EE Board April 1996**

If A = 40e^{j120ยฐ}, B = 20 โ -40ยฐ, C = 26.46 + j0, solve for A + B + C.

A. 27.7 โ 45ยฐ

B. 35.1 โ 45ยฐ

C. 30.8 โ 45ยฐ

D. 33.4 โ 45ยฐ

Answer: **Option C**

Solution:Review: Solution for Number 8

**Problem 9: EE Board October 1997**

What is 4i cube times 2i square

A. -8i

B. 8i

C. -8

D. -8i^{2}

Answer: **Option B**

Solution:Review: Solution for Number 9

**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

Answer: **Option A**

Solution:Review: Solution for Number 10

**Problem 11: ECE Board November 1998**

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

A. 1 โ i

B. -4(1 + i)

C. 1 + i

D. 4(1 + i)

Answer: **Option B**

Solution:Review: Solution for Number 11

**Problem 12: EE Board October 1997**

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

A. 1.9 + j1.1

B. 3.26 โ j2.1

C. 2.87 + j2.1

D. 2.25 โ j1.2

Answer: **Option A**

Solution:Review: Solution for Number 12

**Problem 13: ECE Board April 1999**

What is the quotient when 4 + 8i is divided by i^{3}?

A. 8 โ 4i

B. 8 + 4i

C. -8 + 4i

D. -8 โ 4i

Answer: **Option C**

Solution:Review: Solution for Number 13

**Problem 14: EE Board October 1997**

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

A. (18 โ i) / 25

B. (-18 โ i) / 25

C. (-18 + i) / 25

D. (18 + i) / 25

Answer: **Option B**

Solution:Review: Solution for Number 14

**Problem 15: EE Board October 1997**

Rationalize ((4 + 3i) / (2 โ i))

A. 1 + 2i

B. (11 + 10i) / 5

C. (5 + 2i) / 5

D. 2 + 2i

Answer: **Option A**

Solution:Review: Solution for Number 15

**Problem 16: EE Board October 1997**

Simplify

A. (221 โ 91i) / 169

B. (21 + 52i) / 13

C. (-7 + 17i) / 13

D. (-90 + 220i) / 169

Answer: **Option C**

Solution:Review: Solution for Number 16

**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 โ j0.66

D. -1.75 + j1.03

Answer: **Option B**

Solution:Review: Solution for Number 17

**Problem 18: EE Board April 1997**

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

A. Square root of 3 โ 2i

B. Square root of 3 โ i

C. Square root of 3 + i

D. Square root of 3 + 2i

Answer: **Option C**

Solution:Review: Solution for Number 18

**Problem 19: EE Board June 1990**

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

A. 6.47 โ 3ยฐ

B. 4.47 โ 3ยฐ

C. 7.47 โ 30ยฐ

D. 2.47 โ 53ยฐ

Answer: **Option A**

Solution:Review: Solution for Number 19

**Problem 20: EE Board March 1998**

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

A. 5 โ j5

B. -10 + j10

C. 10 โ j10

D. 15 + j15

Answer: **Option B**

Solution:Review: Solution for Number 20

**Problem 21: EE Board April 1999**

Evaluate cosh [j(ฯ/4)]

A. 0.707

B. 1.41 + j0.866

C. 0.5 + j0.707

D. j0.707

Answer: **Option A**

Solution:Review: Solution for Number 21

**Problem 22: EE Board April 1999**

Evaluate cosh [j(ฯ/3)]

A. 0.5 + j1.732

B. j0.866

C. j1.732

D. 0.5 + j0.866

Answer: **Option C**

Solution:Review: Solution for Number 22

**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

Answer: **Option D**

Solution:Review: Solution for Number 23

**Problem 24: EE Board October 1997**

Evaluate the terms of a Fourier series 2 e^{j10ฯt} + 2 e^{-j10ฯt} at t = 1.

A. 2 + j

B. 2

C. 4

D. 2 + j2

Answer: **Option C**

Solution:Review: Solution for Number 24

**Problem 25: EE Board March 1998**

Given the following series:

Sin x = x โ (x^{3}/3!) + (x^{5}/5!) + โฆ..

Cos x = 1 โ (x^{2}/2!) + (x^{4}/4!) + โฆ..

ex = 1 + x + (x^{2}/2!) + (x^{3}/3!) + โฆ.

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

Answer: **Option B**

Solution:Review: Solution for Number 25

**Problem 26: EE Board October 1997**

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

A. 5 e^{j40ฯt}

B. 5 e^{j40ฯt} + 5 e^{-j40ฯt}

C. 10 e^{-j40ฯt} 0

D. 10 e^{j40ฯt}

Answer: **Option B**

Solution:Review: Solution for Number 26

**Problem 27: EE Board April 1997**

A. 4

B. 2

C. 5

D. 0

Answer: **Option C**

Solution:Review: Solution for Number 27

**Problem 28: ECE Board November 1991**

A. 110

B. -101

C. 101

D. -110

Answer: **Option B**

Solution:Review: Solution for Number 28

**Problem 29: EE Board April 1997**

A. 489

B. 389

C. 326

D. 452

Answer: **Option C**

Solution:Review: Solution for Number 29

**Problem 30: CE Board November 1996**

Compute the value of x by determinant.

A. -32

B. -28

C. 16

D. 52

Answer: **Option B**

Solution:Review: Solution for Number 30

**Problem 31: EE Board April 1997**

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

A. 1

B. -2

C. 3

D. 0

Answer: **Option C**

Solution:Review: Solution for Number 31

**Problem 32: EE Board April 1997**

Solve the equations by Cramerโs Rule: 2x โ y + 3z = -3, 3x + 3y โ z = 10, -x โ y + z = -4.

A. (2, 1, -1)

B. (2, -1, -1)

C. (1, 2, -1)

D. (-1, -2, 1)

Answer: **Option C**

Solution:Review: Solution for Number 32

**Problem 33: EE Board October 1997**

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

Answer: **Option A**

Solution:Review: Solution for Number 33

**Problem 34: EE Board October 1997**

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

Answer: **Option D**

Solution:Review: Solution for Number 34

**Problem 35: EE Board October 1997**

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

Answer: **Option A**

Solution:Review: Solution for Number 35

**Problem 36: EE Board April 1996**

A. 3

B. 1

C. 0

D. -2

Answer: **Option C**

Solution:Review: Solution for Number 36

**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

Answer: **Option A**

Solution:Review: Solution for Number 37

**Problem 38: EE Board April 1996**

A. 8

B. 1

C. -4

D. 0

Answer: **Option D**

Solution:Review: Solution for Number 38

**Problem 39: EE Board October 1997**

Answer: **Option D**

Solution:Review: Solution for Number 39

**Problem 40: EE Board April 1997**

Answer: **Option D**

Solution:Review: Solution for Number 40

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

Answer: **Option A**

Solution:Review: Solution for Number 41

**Problem 42: EE Board October 1997**

Answer: **Option B**

Solution:Review: Solution for Number 42

**Problem 43: **

Determine the inverse matrix of,

Answer: **Option A**

Solution:Review: Solution for Number 43

**Problem 44: EE Board April 1997**

k divided by s^{2} + k^{2} is the inverse Laplace transform of,

A. cos kt

B. sin kt

C. e^{kt}

D. 1.0

Answer: **Option B**

Solution:Review: Solution for Number 44

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

The Laplace transform of cos wt is,

A. s / (s^{2} + w^{2})

B. w / (s^{2} + w^{2})

C. w / (s + w)

D. s / (s + w)

Answer: **Option A**

Solution:Review: Solution for Number 45

**Problem 46: EE Board April 1997**

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

A. 2e^{-t} โ 4e^{-3t}

B. e^{-2t} + e^{-3t}

C. e^{-2t} โ e^{-3t}

D. (2e^{-t}) (1 โ 2e^{-3t})

Answer: **Option A**

Solution:Review: Solution for Number 46

**Problem 47: EE Board March 1998**

Determine the inverse Laplace transform of I(s) = 200 / (s^{2} โ 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

Answer: **Option A**

Solution:Review: Solution for Number 47

**Problem 48: EE Board April 1997**

The inverse Laplace transform of s / ( s^{2} + w^{2} )

A. sin wt

B. w

C. e^{wt}

D. cos wt

Answer: **Option D**

Solution:Review: Solution for Number 48

**Problem 49: **

The inverse Laplace transform of ( 2s โ 18 ) / ( s^{2} + 9 )

A. 2 cos x โ sin 3x

B. 2 cos 3x โ 6 sin 3x

C. 3 cos 2x โ 2 sin 6x

D. 6 cos x โ 3 sin 2x

Answer: **Option B**

Solution:Review: Solution for Number 49

**Problem 50: **

Determine the inverse Laplace transform of 1 / ( 4s^{2} โ 8s ).

A. ยผ e^{t} sinh t

B. ยฝ e^{2t} sinh t

C. ยผ e^{t} cosh t

D. ยฝ e^{2t} cosh t

Answer: **Option A**

Solution:Review: Solution for Number 50

#### 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**

**MCQ from Number 1 โ 50**Answer key:

**PART 1**

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

**PART II**

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