  The sensitivity of nuclear symmetry energy elements at the saturation density
to the binding energies of ultra neutron-rich nuclei (neutron to proton ratio
$\sim$ 2) and the maximum mass of neutron star is explored within a
relativistic mean field model. Values of the interaction parameters governing
the isovector strengths and the symmetry elements are determined in tighter
bounds. Assessments based on the sensitivity matrix reveal that the properties
of extreme neutron-rich systems play a predominant role in narrowing down the
uncertainties in the various symmetry energy parameters. The calculations are
extended over a wide range of nuclear matter density and the results are
discussed.
