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

# MCQ in Advanced Engineering Math Part 1 | Mathematics Board Exam

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. โi

C. 1 + i

D. 1 โ i

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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. -โ70

C. โ70

D. โ17

View Answer:

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)

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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)

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

Answer: Option D

Solution:Review: Solution for Number 23

Problem 24: EE Board October 1997

Evaluate the terms of a Fourier series 2 ej10ฯt + 2 e-j10ฯt at t = 1.

A. 2 + j

B. 2

C. 4

D. 2 + j2

View Answer:

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!) + โฆ..

Cos x = 1 โ (x2/2!) + (x4/4!) + โฆ..

ex = 1 + x + (x2/2!) + (x3/3!) + โฆ.

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

View Answer:

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 40ฯt. Write it in exponential form.

A. 5 ej40ฯt

B. 5 ej40ฯt + 5 e-j40ฯt

C. 10 e-j40ฯt 0

D. 10 ej40ฯt

View Answer:

Answer: Option B

Solution:Review: Solution for Number 26

Problem 27: EE Board April 1997

Evaluate the determinant:

A. 4

B. 2

C. 5

D. 0

View Answer:

Answer: Option C

Solution:Review: Solution for Number 27

Problem 28: ECE Board November 1991

Evaluate the determinant:

A. 110

B. -101

C. 101

D. -110

View Answer:

Answer: Option B

Solution:Review: Solution for Number 28

Problem 29: EE Board April 1997

Evaluate the determinant:

A. 489

B. 389

C. 326

D. 452

View Answer:

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

View Answer:

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

View Answer:

Answer: Option C

Solution:Review: Solution for Number 31

Problem 32: EE Board April 1997

Solve the equations by Cramerโs 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)

View Answer:

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?

View Answer:

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?

View Answer:

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.

View Answer:

Answer: Option A

Solution:Review: Solution for Number 35

Problem 36: EE Board April 1996

A. 3

B. 1

C. 0

D. -2

View Answer:

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

View Answer:

Answer: Option A

Solution:Review: Solution for Number 37

Problem 38: EE Board April 1996

A. 8

B. 1

C. -4

D. 0

View Answer:

Answer: Option D

Solution:Review: Solution for Number 38

Problem 39: EE Board October 1997

What is A times B equal to?

View Answer:

Answer: Option D

Solution:Review: Solution for Number 39

Problem 40: EE Board April 1997

View Answer:

Answer: Option D

Solution:Review: Solution for Number 40

Problem 41: CE Board May 1996

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

View Answer:

Answer: Option A

Solution:Review: Solution for Number 41

Problem 42: EE Board October 1997

Transpose the matrix,

View Answer:

Answer: Option B

Solution:Review: Solution for Number 42

Problem 43:

Determine the inverse matrix of,

View Answer:

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

View Answer:

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)

View Answer:

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)

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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
PART 2: MCQ from Number 51 โ 100 Answer key: PART II
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