[en] The two well accepted models-the Hubbard model and the t-J model along with their extensions are used to explain the different anomalous features of high-T_c cuprates (HTC). As we get diverse results depending on the approximations used in studying both the models, the research in this field does not arrive at end. It has been found that the 2D t-J model, for the physical parameter range J/t ∼ 0.4 reproduce the experimental qualitative features of HTSC. Various interactions such as hole-phonon interaction, electron phonon interaction, next to near neighbour (NNN) hopping amplitude, inter-site Coulomb repulsion V etc. have been considered to elucidate the ground state properties of HTC. In this communication, we consider 2D t-t′-J-V model to explore the role of NNN hopping amplitude and inter-site Coulomb repulsion on thermodynamic properties relevant to HTC. We employ exact-diagonalization technique on a small 10-site cluster with two holes. Results show that an antiferromagnetic tendency is exist in the system at low temperature. The dependence of the antiferromagnetic correlation on t′ and V are explored. The system becomes more ordered with the increase of Coulomb repulsion and specific heat curves confirms non-Fermi liquid behaviour of the system for a specified value of NNN hopping. (author)