A detailed study of the ultraviolet (UV) bright stars in the old open star cluster, M67 is presented based on the far-UV observations using the Ultra Violet Imaging Telescope (UVIT) on ASTROSAT. The UV and UV-optical colour-magnitude diagrams (CMDs) along with overlaid isochrones are presented for the member stars, which include blue straggler stars (BSSs), triple systems, white dwarfs (WDs) and spectroscopic binaries (SB). The CMDs suggest the presence of excess UV flux in many members, which could be extrinsic or intrinsic to them. We construct multi-wavelength spectral energy distribution (SED) using photometric data from the UVIT, Gaia DR2, 2MASS and WISE surveys along with optical photometry. We fitted model SEDs to 7 WDs and find 4 of them have mass > 0.5 M and cooling age of less than 200 Myr, thus demanding BSS progenitors. SED fits to 23 stars detect extremely low mass (ELM) WD companions to WOCS2007, WOCS6006 and WOCS2002, and a low mass WD to WOCS3001, which suggest these to be post mass transfer (MT) systems. 12 sources with possible WD companion need further confirmation. 9 sources have X-ray and excess UV flux, possibly arising out of stellar activity. This study demonstrates that UV observations are key to detect and characterise the ELM WDs in non-degenerate systems, which are ideal test beds to explore the formation pathways of these peculiar WDs. The increasing detection of post-MT systems among BSSs and main-sequence stars suggest a strong MT pathway and stellar interactions in M67.