Fundamentals of Engineering Engineering Mathematics 2 — Questions and Answers
Question 1: What does the Fourier series represent for a periodic function?
- A sum of sinusoidal components at integer multiples of the fundamental frequency (Correct answer)
- A polynomial approximation of the function
- A Taylor expansion about a point
- A complex exponential representation only
Correct answer: A sum of sinusoidal components at integer multiples of the fundamental frequency
The Fourier series decomposes a periodic function into sinusoidal components at integer multiples of the fundamental frequency.
Question 2: In probability, if events A and B are mutually exclusive, then P(A ∪ B) equals:
- P(A) + P(B) (Correct answer)
- P(A) × P(B)
- P(A) + P(B) - P(A ∩ B)
- P(A) - P(B)
Correct answer: P(A) + P(B)
For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).
Question 3: What is the general solution to the ordinary differential equation dy/dx + 2y = 0?
- y = Ce^(-2x) (Correct answer)
- y = Ce^(2x)
- y = C·sin(2x)
- y = C + 2x
Correct answer: y = Ce^(-2x)
This first-order linear ODE has solution y = Ce^(-2x) obtained by separation of variables.
Question 4: The Taylor series expansion of sin(x) about x = 0 begins with which terms?
- x - x³/6 + x⁵/120 - ... (Correct answer)
- 1 - x²/2 + x⁴/24 - ...
- x + x³/6 + x⁵/120 + ...
- 1 + x + x²/2 + ...
Correct answer: x - x³/6 + x⁵/120 - ...
The Maclaurin series of sin(x) is x - x³/3! + x⁵/5! - ..., which matches x - x³/6 + x⁵/120.
Question 5: Which of the following is the correct formula for the determinant of a 2×2 matrix [a b; c d]?
- ad - bc (Correct answer)
- ac - bd
- ab - cd
- ad + bc
Correct answer: ad - bc
The determinant of a 2×2 matrix is calculated as ad - bc.
Question 6: What is the dot product of vectors A = (2, 3, 1) and B = (1, -1, 4)?
- 3 (Correct answer)
- 6
- -1
- 7
Correct answer: 3
The dot product A·B = (2)(1) + (3)(-1) + (1)(4) = 2 - 3 + 4 = 3.
Fundamentals of Engineering Engineering Mathematics 2
What does the Fourier series represent for a periodic function?