SCE Engineering Mathematics 6

Question 1

Stokes' theorem relates a surface integral to:

Accepted Answer

A line integral around the boundary of the surface

Answer

A volume integral

Answer

A double integral

Answer

A point evaluation

Question 2

What is the primary purpose of singular value decomposition (SVD)?

Accepted Answer

Decomposing any matrix into orthogonal and diagonal components for analysis

Answer

Finding only the eigenvalues

Answer

Solving systems of nonlinear equations

Answer

Computing the trace of a matrix

Question 3

The error function erf(x) is commonly used in engineering for:

Accepted Answer

Calculating probabilities related to normal distributions

Answer

Solving algebraic equations

Answer

Computing Fourier coefficients

Answer

Evaluating matrix determinants

Question 4

In regression analysis, the coefficient of determination R² represents:

Accepted Answer

The proportion of variance in the dependent variable explained by the model

Answer

The slope of the regression line

Answer

The correlation between residuals

Answer

The standard error of estimate

Question 5

The trapezoidal rule approximation error is proportional to:

Accepted Answer

h² (the square of the step size)

Answer

h (the step size)

Answer

h³ (the cube of the step size)

Answer

1/h

Question 6

A homogeneous system of linear equations always has:

Accepted Answer

At least the trivial solution (all zeros)

Answer

Exactly one non-trivial solution

Answer

No solution

Answer

Infinitely many solutions