EIT Mathematics and Statistics 4 — Questions and Answers
Question 1: The curl of vector field F = (y, -x, 0) at any point is:
- (0, 0, -2) (Correct answer)
- (0, 0, 2)
- (2, 0, 0)
- (0, -2, 0)
Correct answer: (0, 0, -2)
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?
- 20% (Correct answer)
- 5%
- 16%
- 25%
Correct answer: 20%
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?
- Jacobi method
- Gauss-Seidel method (Correct answer)
- LU decomposition
- Cramer's rule
Correct answer: Gauss-Seidel method
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)?
- (1/2)sin(2t) (Correct answer)
- cos(2t)
- sin(2t)
- (1/4)cos(2t)
Correct answer: (1/2)sin(2t)
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?
- Sum of absolute errors
- Maximum error
- Sum of squared residuals (Correct answer)
- Sum of cubed errors
Correct answer: Sum of squared residuals
Ordinary least squares regression finds the slope and intercept that minimize the sum of squared residuals (SSR).
Question 6: The unit vector in the direction of A = (3, 4) is:
- (3/5, 4/5) (Correct answer)
- (3/7, 4/7)
- (0.6, 0.8) — same as first choice
- (1/3, 1/4)
Correct answer: (3/5, 4/5)
|A| = √(9+16) = 5, so the unit vector is (3/5, 4/5) = (0.6, 0.8).
Question 7: A fair die is rolled twice. What is the probability of getting a sum of 7?
- 1/6 (Correct answer)
- 1/9
- 5/36
- 7/36
Correct answer: 1/6
There are 6 favorable outcomes {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} out of 36 total, so P = 6/36 = 1/6.
EIT Mathematics and Statistics 4
The curl of vector field F = (y, -x, 0) at any point is: