Step 1: Understand PM$_{2.5$ measurement.}
PM$_{2.5}$ is measured by mass-based techniques. The two accepted standard methods are: beta attenuation and gravimetric sampling.
Step 2: Evaluate options.
(A) Beta attenuation — correct; measures mass by radiation attenuation.
(C) Gravimetric method — correct; filters collect PM and are weighed.
(B) Chemiluminescence — measures NO/NO$_2$ gases, not PM.
(D) NDIR — used for CO and CO$_2$, not PM.
Therefore only (A) and (C) measure PM$_{2.5$.}
Final Answer: (A), (C)