Refer to figure.
A Constant Speed Unit (CSU), also called a constant speed propeller governor, is a hydromechanical device that automatically adjusts propeller blade pitch to maintain a pilot-selected RPM regardless of changes in power or airspeed. The pilot selects a desired RPM using the pitch control lever, which sets a flyweight spring tension in the governor. 

If engine torque increases (for example due to advancing the throttle), the propeller tends to accelerate. The governor detects this via its flyweight assembly: as RPM rises above the selected value, centrifugal force overcomes the spring and directs oil pressure to increase blade pitch (coarsen the propeller). Increasing blade pitch increases the aerodynamic load on the propeller, absorbing the additional engine torque and preventing RPM from rising. Conversely, if RPM tends to fall, the governor reduces pitch to decrease the load. 

The result is that the propeller pitch is continuously and automatically modulated to keep RPM at the selected value. Increasing power with a CSU therefore results in higher manifold pressure and more thrust output, but not in a change in RPM, which is held constant by the governor.

Continue to increase as the power is increased → INCORRECT. This describes the behaviour of a fixed-pitch propeller, not a constant speed propeller with a CSU. With a fixed-pitch propeller, advancing the throttle increases torque and the propeller accelerates, raising RPM. The CSU exists precisely to prevent this from happening, automatically increasing blade pitch to absorb the additional torque and maintain the selected RPM.

Decrease → INCORRECT. RPM would not decrease when power is increased with a CSU in normal operation. A decrease in RPM could occur if the governor were set to a lower value, if the propeller were feathered, or in an overpitch (propeller stall) condition. Increasing power with an unchanged RPM selection would cause the governor to coarsen pitch slightly to absorb torque but the RPM would not fall below the selected value.

Remain the same → CORRECT. The entire purpose of the CSU is to maintain constant RPM at the pilot-selected value regardless of power changes. When power is increased, the governor automatically increases propeller blade pitch to absorb the additional torque, keeping RPM at the selected value. The pilot achieves higher power output (higher manifold pressure and thrust) without any change in RPM.