Step 1: Analyze Statement P.
According to the National Ambient Air Quality Standards (NAAQS), notified by the Central Pollution Control Board (CPCB) in 2009:
Annual average standard for \( \text{PM}_{10} = 60 \, \mu g/m^3 \)
Annual average standard for \( \text{PM}_{2.5} = 40 \, \mu g/m^3 \)
\[
\text{Since } 60 > 40, \quad \text{P is TRUE.}
\]
Step 2: Analyze Statement Q.
The National Air Quality Index (AQI) released in 2015 uses sub-indices for pollutants including \( \text{PM}_{10} \) and \( \text{PM}_{2.5} \).
Sub-index values are calculated based on concentration ranges. It is possible for \( \text{PM}_{10} \) levels to fall in a lower AQI category (e.g., 'Moderate'), while \( \text{PM}_{2.5} \) levels fall in a higher one (e.g., 'Poor'), based on their respective concentration thresholds.
\[
\text{Hence, it is possible that the sub-index of PM}_{10} \text{ is less than that of PM}_{2.5}.
\Rightarrow \text{Q is TRUE.}
\]
Final Conclusion:
Both statements P and Q are TRUE.