Fundamentals of Engineering Engineering Mathematics 1 — Questions and Answers
Question 1: What is the derivative of f(x) = x³ - 5x² + 3x - 7?
- 3x² - 10x + 3 (Correct answer)
- 3x² - 5x + 3
- x² - 10x + 3
- 3x² - 10x - 7
Correct answer: 3x² - 10x + 3
Applying the power rule term by term yields 3x² - 10x + 3.
Question 2: Which method is used to solve a system of linear equations by reducing the augmented matrix to row echelon form?
- Gaussian elimination (Correct answer)
- Cramer's rule
- Newton-Raphson method
- Simpson's rule
Correct answer: Gaussian elimination
Gaussian elimination reduces the augmented matrix to row echelon form to solve systems of linear equations.
Question 3: What is the Laplace transform of f(t) = e^(at)?
- 1/(s - a) (Correct answer)
- 1/(s + a)
- a/(s - a)
- s/(s - a)
Correct answer: 1/(s - a)
The Laplace transform of e^(at) is 1/(s - a) for s > a.
Question 4: If a matrix A has eigenvalue λ, which equation must be satisfied?
- det(A - λI) = 0 (Correct answer)
- det(A + λI) = 0
- trace(A) = λ
- det(A) = λ
Correct answer: det(A - λI) = 0
The characteristic equation det(A - λI) = 0 is used to find eigenvalues of a matrix.
Question 5: What is the value of the definite integral ∫₀² (3x²) dx?
- 8 (Correct answer)
- 6
- 12
- 4
Correct answer: 8
Integrating 3x² gives x³, evaluated from 0 to 2 yields 8 - 0 = 8.
Question 6: Which numerical method uses the formula xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) to find roots?
- Newton-Raphson method (Correct answer)
- Bisection method
- Secant method
- Euler's method
Correct answer: Newton-Raphson method
The Newton-Raphson method iteratively refines root estimates using the function and its derivative.
Fundamentals of Engineering Engineering Mathematics 1
What is the derivative of f(x) = x³ - 5x² + 3x - 7?