  We construct a rational extension of the truncated Calogero-Sutherland model
by Pittman et al. The exact solution of this rationally extended model is
obtained analytically and it is shown that while the energy eigenvalues remain
unchanged, however the eigenfunctions are completely different and written in
terms of exceptional X1 Laguerre orthogonal polynomials. The rational model is
further extended to a more general, the Xm case by introducing m dependent
interaction term. As expected, in the special case of m = 0, the extended model
reduces to the conventional model of Pittman et al. In the two appropriate
limits, we thereby obtain rational extensions of the celebrated
Calogero-Sutherland as well as Jain-Khare models.
