  We study the superconducting phase with two component order parameter
scenario, such as, $d_{x^2-y^2} + e^{i\theta}s_{\alpha}$, where $\alpha = xy,
x^2+y^2$. We show, that in absence of orthorhombocity, the usual $d_{x^2-y^2}$
does not mix with usual $s_{x^2+y^2}$ symmetry gap in an anisotropic band
structure. But the $s_{xy}$ symmetry does mix with the usual d-wave for $\theta
=0$. The d-wave symmetry with higher harmonics present in it also mixes with
higher order extended $s$ wave symmetry. The required pair potential to obtain
higher anisotropic $d_{x^2-y^2}$ and extended s-wave symmetries, is derived by
considering longer ranged two-body attractive potential in the spirit of tight
binding lattice. We demonstrate that the dominant pairing symmetry changes
drastically from $d$ to $s$ like as the attractive pair potential is obtained
from longer ranged interaction. More specifically, a typical length scale of
interaction $\xi$, which could be even/odd multiples of lattice spacing leads
to predominant $s/d$ wave symmetry. The role of long range interaction on
pairing symmetry has further been emphasized by studying the typical interplay
in the temperature dependencies of these higher order $d$ and $s$ wave pairing
symmetries.
