Mathematical Physics Mock Tests

The curl of the gradient of any scalar function φ is always:

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

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

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

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

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