NCEES Mathematics 4

Question 1

Solve the differential equation y'' + 4y = 0. The general solution is:

Accepted Answer

y = C₁cos(2x) + C₂sin(2x)

Answer

y = C₁e^(2x) + C₂e^(-2x)

Answer

y = (C₁ + C₂x)e^(2x)

Answer

y = C₁cos(4x) + C₂sin(4x)

Question 2

The Fourier series of a function requires the function to be:

Accepted Answer

Periodic

Answer

Continuous everywhere

Answer

Differentiable everywhere

Answer

Always positive

Question 3

What is the cross product A × B if A = (1, 0, 0) and B = (0, 1, 0)?

Accepted Answer

(0, 0, 1)

Answer

(1, 1, 0)

Answer

(0, 0, -1)

Answer

(1, 0, 1)

Question 4

A binomial distribution with n = 10 and p = 0.3 has a mean of:

Accepted Answer

3

Answer

0.3

Answer

7

Answer

2.1

Question 5

Which method is best suited for finding roots of a nonlinear equation numerically?

Accepted Answer

Newton-Raphson method

Answer

Gaussian elimination

Answer

Simpson's rule

Answer

Euler's method

Question 6

The Divergence Theorem relates a volume integral of divergence to:

Accepted Answer

A surface integral over the bounding surface

Answer

A line integral around the boundary

Answer

A curl integral inside the volume

Answer

Another volume integral

Question 7

If the standard deviation of a data set is 0, what can be concluded?

Accepted Answer

All values are identical

Answer

The mean is 0

Answer

The data is normally distributed

Answer

There is only one data point