  WE derive exact and more general solutions of the two coupled
Gross-Pitaevskii equation with suitable parameters by demonstrating two
analytical methods. In the first method, equations are analysed and inferred
some of their mathematical and physical properties, which are then used to
derive the exact stationary solutions. In the second method, we demonstrate the
Darboux transformation method and construct exact and more general soliton
solutions for the Gross-Pitaevskii equation (NLS equation with external
potential term). We have proved that the solutions were more general one by
showcasing all kinds of soliton pairs by manoeuvring the parameters suitably.
