Hi xeeshan74,
as Bill already stated this is a very poor design. Connecting a 12V relay in series with a 20Ω resistor the relay won't work at all if its coil resistance is almost the same as the series resistor.
The ULN2XXX don't switch ground directly, but they contain darlington transistors, so I'd assume at least 1.4V voltage drop between emitter and collector leaving 10.6V for the relay, which could work properly if there wasn't an additional voltage drop across the resistor of at least 0.5V. (assuming 400Ω coil resistance)
Considering you have to drive up to four relays that makes an unneccessary pin count of 32 pins overall. (Compared with 4 MosFet drivers of 8 pins and 4 ULN2003 of 16 pins). This method is not only unreliable, but requires much more board space.
You should convince your boss, or whoever is ordering you to use ULN type transistor arrays to control the relays, that the already suggested method will be the much better choice. (Or have him build the circuit with 100% repeatability.)
The suggested way is absolutely reliable and requires less board space!
Regards
Boncuk