What is role of R9 resistor at input to OPAMP in this circuit?
You can tell it's nothing to do with offset nulling because of the capacitor- it has no effect (or rather the same small effect) at DC regardless of the position of the wiper. 

\$R_C\$ is for offset nulling

\$R_{10}\$ adjusts the DC common-mode rejection

\$R_9\$ adjusts the AC common-mode rejection