Role of RC in MOSFET Driver circuit
The pulse transformer and it's load aren't given and that may be needed to calculate quantities. But \$M_2\$ is operating as an open-drain, active-sourcing driver and that means there's no active sink there. This fact leaves \$C_1\$ to resonate with the pulse transformer's inductive component. \$R_1\$ does double-duty, adding to the primary resistance of the pulse transformer when \$M_2\$ pulls high and dissipating some resonance energy when \$M_2\$ becomes inactive. However, I think \$C_1\$ is also there to help absorb energy from the transformer and protect a potentially sensitive \$M_2\$ device, when driven inactive.