We have carried out near-infrared (NIR) imaging observations of the Carina Nebula for an area of ~400 sq. arcmin. including the star clusters Trumpler 14 (Tr 14) and Trumpler 16 (Tr 16). With 10 sigma limiting magnitudes of J ~ 18.5, H ~ 17.5 and K_s ~ 16.5, we identified 544 Class II and 11 Class I young star candidates. We find some 40 previously unknown very red sources with H-K_s > 2, most of which remain undetected at the J band. The red NIR sources are found to be concentrated to the south-east of Tr 16, along the `V shaped dust lane, where the next generation of stars seems to be forming. In addition, we find indications of ongoing star formation near the three MSX point sources, G287.51-0.49, G287.47-0.54, and G287.63-0.72. A handful of red NIR sources are seen to populate around each of these MSX sources. Apart from this, we identified two hard Chandra X-ray sources near G287.47-0.54, one of which does not have an NIR counterpart and may be associated with a Class I/Class 0 object. The majority of the Class II candidates, on the other hand, are seen to be distributed in the directions of the clusters, demarcating different evolutionary stages in this massive star-forming region. A comparison of the color-magnitude diagrams of the clusters with pre-main sequence model tracks shows that the stellar population of these clusters is very young (< 3 Myr). The K_s band luminosity function (KLF) of Tr 14 shows structure at the faint end, including a sharp peak due to the onset of deuterium burning, implying an age of 1-2 Myr for the cluster. The KLF of Tr 16, in contrast, is found to rise smoothly until it turns over. The slopes of the mass functions derived for the clusters are found to be in agreement with the canonical value of the field star initial mass function derived by Salpeter.
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