NCEES Mathematics 4

Question 1

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

Accepted Answer

y = C₁cos(2x) + C₂sin(2x)

Answer

The characteristic equation r² + 4 = 0 gives r = ±2i, leading to a sinusoidal solution.

Question 2

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

Accepted Answer

Periodic

Answer

Fourier series represent periodic functions, though convergence conditions (Dirichlet conditions) may vary.

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

i × j = k, so (1,0,0) × (0,1,0) = (0,0,1).

Question 4

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

Accepted Answer

3

Answer

The mean of a binomial distribution is μ = np = 10 × 0.3 = 3.

Question 5

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

Accepted Answer

Newton-Raphson method

Answer

Newton-Raphson is an iterative root-finding method for nonlinear equations.

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