Near-IR spectra for a sample of 31 elliptical galaxies in the Coma cluster are obtained . The galaxies are selected to be ellipticals ( no lenticulars ) , with a large spatial distribution , covering both the core and outskirt of the cluster ( ie . corresponding to regions with large density contrasts ) . CO _ { sp } ( 2.3 \mu m ) absorption indices ] , measuring the contribution from intermediate-age red giant and supergiant stars to the near-IR light of the ellipticals , are then estimated . It is found that the strength of CO _ { sp } features in elliptical galaxies increases from the core ( r < 0.2 ^ { \circ } ) to the outskirts ( r > 0.2 ^ { \circ } ) of the Coma cluster . Using the Mg _ { 2 } strengths , it is shown that the observed effect is not due to metallicity and is mostly caused by the presence of a younger population ( giant and supergiant stars ) in ellipticals in outskirts ( low density region ) of the cluster . Using the CO _ { sp } features , the origin of the scatter on the near-IR Fundamental Plane ( relation between the effective diameter , effective surface brightness and velocity dispersion ) of elliptical galaxies is studied . Correcting this relation for contributions from the red giant and supergiant stars , the rms scatter reduces from 0.077dex to 0.073dex . Although measurable , the contribution from these intermediate-age stars to the scatter on the near-IR Fundamental Plane of ellipticals is only marginal . A relation is found between the CO _ { sp } and V - K colours of ellipticals , corresponding to a slope of 0.036 \pm 0.016 , significantly shallower than that from the Mg _ { 2 } - ( V - K ) relation . This is studied using stellar synthesis models .