EIT Mathematics and Statistics 4

Question 1

The curl of vector field F = (y, -x, 0) at any point is:

Accepted Answer

(0, 0, -2)

Answer

curl F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y) = (0, 0, -1-1) = (0, 0, -2).

Question 2

What is the coefficient of variation (CV) for a dataset with mean = 80 and standard deviation = 16?

Accepted Answer

20%

Answer

CV = (σ/μ) × 100% = (16/80) × 100% = 20%.

Question 3

Which iterative method for solving linear systems Ax = b splits A into lower and upper triangular parts and updates each variable using the most recent values?

Accepted Answer

Gauss-Seidel method

Answer

The Gauss-Seidel method uses each updated variable immediately within the same iteration, unlike Jacobi which uses only previous-iteration values.

Question 4

What is the inverse Laplace transform of 1/(s² + 4)?

Accepted Answer

(1/2)sin(2t)

Answer

L⁻¹{ω/(s²+ω²)} = sin(ωt), so L⁻¹{1/(s²+4)} = (1/2)sin(2t) since ω = 2.

Question 5

In linear regression y = mx + b fitted to data, the slope m minimizes which quantity?

Accepted Answer

Sum of squared residuals

Answer

Ordinary least squares regression finds the slope and intercept that minimize the sum of squared residuals (SSR).

(EIT) Engineer In Training Certification Practice Test

(EIT) Engineer In Training Certification Practice Test

EIT Mathematics and Statistics 4