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: i29 + i21 + 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 i3217 โ i427 + i18
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 = 40ej120ยฐ, 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. -8i2
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 5th 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 i3?
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 ej10ฯt + 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 (x3/3!) + (x5/5!) + โฆ..
Cos x = 1 โ (x2/2!) + (x4/4!) + โฆ..
ex = 1 + x + (x2/2!) + (x3/3!) + โฆ.
What relation can you draw from these series?
A. ex = cos x + sin x
B. eix = cos x + i sin x
C. eix = icos x + sin x
D. iex = 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 ej40ฯt
B. 5 ej40ฯt + 5 e-j40ฯt
C. 10 e-j40ฯt 0
D. 10 ej40ฯt
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 s2 + k2 is the inverse Laplace transform of,
A. cos kt
B. sin kt
C. ekt
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 / (s2 + w2)
B. w / (s2 + w2)
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 / (s2 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 / ( s2 + w2 )
A. sin wt
B. w
C. ewt
D. cos wt
Answer: Option D
Solution:Review: Solution for Number 48
Problem 49:
The inverse Laplace transform of ( 2s โ 18 ) / ( s2 + 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 / ( 4s2 โ 8s ).
A. ยผ et sinh t
B. ยฝ e2t sinh t
C. ยผ et cosh t
D. ยฝ e2t 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:
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