List of top Mathematics Questions asked in Banaras Hindu University Postgraduate Entrance Test

Given the Bessel function:
$$ J_0(x) = 1 - \frac{x^2}{2^2} + \frac{x^4}{2^2 \cdot 2^2} - \frac{x^6}{2^2 \cdot 2^2 \cdot 2^2} + \dots $$ The Bessel function $ J_1(x) $ is given by:
One solution (about $ x = 0 $ ) of the differential equation
$$ x^2 \frac{d^2 y}{dx^2} - 3x \frac{dy}{dx} + 4y = 0 $$ is $ y_1(x) = c_1x^2$ . A second linearly independent solution (with another constant $ c_2 $ ) is:
The first non-zero Fourier coefficient in the expansion of \( \sin^3(x) \) is:
The unit vectors \( \hat{\theta} \) and \( \hat{\phi} \) (where \( \theta \) and \( \phi \) are the polar and azimuthal angles, respectively), in the spherical coordinate system, under the operation of inversion (i.e., reflection through the origin) have:
The only possible real eigenvalue of a Skew-Hermitian matrix is:
The matrix \( A = \begin{bmatrix} -2 & 1 & 2
1 & 2 & 1
2 & 1 & -2 \end{bmatrix} \) is:
Evaluate the integral:
\[ \int_{0}^{\infty} e^{-x} \delta(\lambda^2 - 4)dx \]