Mathematical Physics Mock Tests

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

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

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

The Dirac delta function can be represented as the limit of which function as ε → 0⁺:

The eigenvalues of a real symmetric matrix are always:

The Fourier transform of the Gaussian function f(x) = exp(-ax²/2) (where a > 0) is proportional to:

The Fourier transform of a Gaussian function f(x) = e^(-ax²) (a > 0) is proportional to:

The determinant of a 3 × 3 rotation matrix R is: