MCQ in Advanced Engineering Math Part 1 | Mathematics Board Exam

DOMINATE ADVANCED ENGINEERING MATH: Your Ultimate Board Exam Weapon

ELEVATE your preparation with these crucial Advanced Engineering Mathematics MCQs that SEPARATE licensed engineers from the rest!

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MCQ Topic Outline included in the Mathematics Board Exam Syllabus

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 question.

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!) + …..

ex = 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

Online Questions and Answers in Advanced Engineering Math Series

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

Mathematics Board Examination Mastery | Math Engineering Pre-Board