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**

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

**PART I**

**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 i^{1997} + i^{1999}, where ** i** is an imaginary.

- A. 0
- B. –i
- C. 1 + i
- D. 1 – i

**Problem 2: EE Board April 1997**

Simplify: i^{29} + i^{21} + 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 i^{3217} – i^{427} + i^{18}

- 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. -8i
^{2}

**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 i^{3}?

- 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(Ï€/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(Ï€/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^{j10Ï€t} + 2 e^{-j10Ï€t} 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 – (x^{3}/3!) + (x^{5}/5!) + …..

Cos x = 1 – (x^{2}/2!) + (x^{4}/4!) + …..

e^{x} = 1 + x + (x^{2}/2!) + (x^{3}/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 40Ï€t. Write it in exponential form.

- A. 5 e
^{j40Ï€t} - B. 5 e
^{j40Ï€t}+ 5 e^{-j40Ï€t} - C. 10 e
^{-j40Ï€t}0 - D. 10 e
^{j40Ï€t}

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

- A. sin wt
- B. w
- C. e
^{wt} - D. cos wt

**Problem 49: **

The inverse laplace transform of ( 2s – 18 ) / ( s^{2} + 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 / ( 4s^{2} – 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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