We present a far-ultraviolet (FUV) study of hot stellar populations in the second parameter pair globular clusters (GCs) M3 and M13, as a part of the GC UVIT Legacy Survey programme (GlobULeS). We use observations made with F148W and F169M filters of the Ultraviolet Imaging Telescope (UVIT) onboard AstroSat along with ground-based data (UBVRI filters), Hubble Space Telescope(HST) GC catalogue, and Gaia EDR3 catalogue. Based on the FUV-optical colour-magnitude diagrams, we classify the sources into the horizontal branch (HB) stars, post-HB stars, and hot white dwarfs (WDs) in both the GCs. The comparison of synthetic and observed colours of the observed HB stars suggests that the mass-loss at the red giant branch and He spread in both clusters have a simultaneous effect on the different HB distributions detected in M3 and M13, such that HB stars of M13 require a larger spread in He (0.247-0.310) than those of M3 (Y = 0.252-0.266). The evolutionary status of HB stars, post-HB stars, and WDs are studied using SED fit parameters and theoretical evolutionary tracks on the H-R diagram. We found that the observed post-HB stars have evolved from zero-age HB (ZAHB) stars of the mass range of 0.48-0.55 M_{sun} in M3 and M13. We detect 24 WD candidates in each cluster having log(Lbol/L{sun}_) in the range of -0.8 to +0.6 and log(Teff/K) in the range of 4.2-5.0. Placing the WDs on the H-R diagram and comparing them with models, it is found that M13 has a population of low-mass WDs, probably originating from binary evolution.

Cone search capability for table J/MNRAS/522/847/table2 (Stellar parameters along with their associated errors of 217 HBs of M3 and 678 HBs of M13 derived from SED fitting)