We report the first comparative study of strong MgII absorbers seen towards radio-loud quasars of core-dominated (CDQs) and lobe-dominated (LDQs) types and normal QSOs. The MgII associated absorption systems having a velocity offset v < 5000km/s from the systemic velocity of the background quasar were also excluded. Existing spectroscopic data for redshift-matched sightlines of 3975 CDQs and 1583 LDQs, covering a emission redshift range 0.39-4.87, were analysed and 864 strong MgII absorbers were found, covering the redshift range 0.45-2.17. The conclusions reached using this well-defined large dataset of strong MgII absorbers are: (i) The number density, dN/dz, towards CDQs shows a small, marginally significant excess over the estimate available for QSOs; (ii) In the redshift space, this difference is reflected in terms of a 1.6sigma excess of dN/dz over the QSOs, within the narrow redshift interval 1.2-1.8; (iii) The dN/dbeta distribution (with beta=v/c) for CDQs shows a significant excess over the distribution found for a redshift and luminosity matched sample of QSOs, at beta in the range 0.05-0.1. This leads us to infer that a significant fraction of strong MgII absorption systems seen in this offset velocity range are probably associated with the CDQs and might be accelerated into the line of sight by their powerful jets and/or due to the accretion-disk outflows close to our direction. Support to this scenario comes from a consistency check in which we only consider the spectral range corresponding to beta > 0.2. The computed redshift distribution for strong MgII absorbers towards CDQs now shows excellent agreement with that known for QSOs, as indeed is expected for purely intervening absorption systems. Thus, it appears that for CDQs the associated strong MgII absorbers can be seen at much larger velocities relative to the nucleus than the commonly adopted upper limit of 5000km/s.
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