Mathematical Physics Mock Tests

The Laplace transform of f(t) = e^{-at} sin(ωt) for t > 0 is:

The eigenvalues of the 2×2 matrix [[3, 1], [1, 3]] are:

The Laplace transform of f(t) = e⁻ᵃᵗ (for t ≥ 0) is:

The eigenvalues of a real symmetric matrix are always:

The residue of the function f(z) = z/(z² + a²) at z = ia (a > 0) is:

The Legendre polynomial P₁(x) is:

The residue of the function f(z) = 1/(z² + 1) at z = i is:

The divergence of the vector field F = (x², y², z²) is: