If a projectile is sent from the surface of the earth,then its escape velocity is (under root 2GM/R).But if the same is projected from the centre of the earth,then what would be is escape velocity?

IT WILL BE INFINITY

any motion inside the earth is simple harmonic.hence when u throw a body at the centre of the earth it has max velocity at the centre of the earth(mean position).Its velocity continuously decreases and its velocity is 0 at the surface of the earth(extreme position)and u would need to project it with escape velocity to overcome the gravitational force.