The controller which is highly sensitive to noise is 

Proportional + Derivate:

The additive combination of proportional & Derivative control is known as P-D control.

The overall transfer function for a PD controller is given by:

\({G_C}\left( s \right) = \frac{{U\left( s \right)}}{{E\left( s \right)}} = {K_P} + s{K_D}\)

PD controller is nothing but a differentiator (or) a High Pass Filter.

The frequency of noise is very high. So this high pass filter will allow noise into the system which results in noise amplification.

Hence option 2 is correct. 

Effects of Proportional Derivative (PD) controllers:

• Decreases the type of the system by one
• Reduces the rise time and settling time
• Rise time and settling time decreases and Bandwidth increases
• The speed of response is increased i.e. the transient response is improved
• Improves gain margin, phase margin, and resonant peak
• Increases the input noise
• Improves the stability

Effects of Proportional Integral (PI) controllers:

• Increases the type of the system by one
• Rise time and settling time increase and Bandwidth decreases
• The speed of response decreased i.e. transient response becomes slower
• Decreases the steady-state error and steady-state response is improved
• Decreases the stability