Multifrequency observations with the GMRT and the VLA are used to determine the spectral breaks in consecutive strips along the lobes of a sample of selected giant radio sources (GRSs) in order to estimate their spectral ages. The maximum spectral ages estimated for the detected radio emission in the lobes of our sources range from $sim$6 to 36 Myr with a median value of $sim$20 Myr using the classical equipartition fields. Using the magnetic field estimates from the Beck & Krause formalism the spectral ages range from $sim$5 to 38 Myr with a median value of $sim$22 Myr. These ages are significantly older than smaller sources. In all but one source (J1313+6937) the spectral age gradually increases with distance from the hotspot regions, confirming that acceleration of the particles mainly occurs in the hotspots. Most of the GRSs do not exhibit zero spectral ages in the hotspots, as is the case in earlier studies of smaller sources. This is likely to be largely due to contamination by more extended emission due to relatively modest resolutions. The injection spectral indices range from $sim$0.55 to 0.88 with a median value of $sim$0.6. We discuss these values in the light of theoretical expectations, and show that the injection spectral index appears to be correlated with luminosity and/or redshift as well as with linear size.
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