  We present results from our search for HI 21-cm and OH 18-cm absorption at
z~1-1.4 towards red quasars showing strong MgII absorption using uGMRT. The
quasars J1501+1822 and J1521+5508 show multiple strong associated MgII
absorption at z~1.1 and signature of reddening in their optical spectra. We
report the detection of HI 21-cm absorption towards J1521+5508 at the systemic
redshift of the quasar, with N(HI) =(1.2 +/- 0.2) x 10^{20} cm^{-2} for spin
temperature of 100 K and unit covering factor. The HI 21-cm absorption is
offset from the blueshifted strong MgII absorbers by >~1500 km/s. We do not
detect HI 21-cm absorption at the redshift of the associated MgII absorption
and at the systemic redshift towards J1501+1822. We argue that lack of
one-to-one correspondence between MgII and HI 21-cm absorption could be related
with clumpiness of the neutral gas and the radio and optical sightlines probing
different volume of the gas. We find that the presence of strong associated
MgII absorption and reddening in the optical spectra of the quasars lead to an
increased detection rate of associated HI 21-cm absorption at z>=1. We also
report non-detection of intervening OH absorption ([OH]/[HI] <= (1-4) x
10^{-8}) at z = 1.3 towards two red quasars, J0850+5159 and J0852+3435, which
show strong metal and HI 21-cm absorption and the 2175 A dust extinction bump.
