We consider the adsorption of polymers on the surface of a solid, occupying the region z < 0 The usual approach to the problem is the one due to de Gennes. We show that the propagator of this approach can be represented in terms of path integrals, where the paths are unconstrained and can enter the region z < 0 too. Using this approach, we consider adsorption on a flat, but random surface-where the randomness causes the adsorption energy to be a random function of position. Using the replica trick and variational formalism, we study the size of the adsorbed polymer. To simplify the calculations, we use the ground-state dominance approximation. The calculations revealed a sudden decrease in the size of the polymer, in both the parallel and perpendicular directions, as randomness is increased beyond a certain value. Further, the size of the polymer in the perpendicular direction is found to become zero at a larger value of the randomness. To verify whether these are artifacts of the ground-state dominance approximation, we also did exact calculations for test cases. It was found that the sudden change in size was absent in the exact calculations. Increasing randomness leads to a smooth, continuous decrease in the size. Ultimately, however, the polymer was found to collapse in the perpendicular direction.