List of top Questions asked in GATE PH- 2025

A particle is scattered from a potential \( V_{\vec{r}} = g \delta^3(\vec{r}) \), where \( g \) is a positive constant. Using the first Born approximation, the angular \((\theta, \phi)\) dependence of the differential scattering cross section \( \frac{d\sigma}{d\Omega} \) is:
A circle with center at \( (x, y) = (0.5, 0) \) and radius = 0.5 intersects with another circle with center at \( (x, y) = (1, 1) \) and radius = 1 at two points. One of the points of intersection \( (x, y) \) is:
The sum of the following infinite series is: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \dots \]