Role of Ultra-fine Particles (UFPs) in causing adverse health effects among large population across the world, attributable to household smoke, is being increasingly recognized. However, there is very little theoretical perspective available on the complex behavior of the UFP metrics with respect to controlling factors, such as ventilation rate and particle emission rate from the combustion sources. This numerical study examines through coagulation dynamics, the dependence of UFP metrics, viz., number (PN), mass (PM_0.1) and surface area (PA_0.1) concentrations below 0.1 mm diameter, on ventilation and the number emission rate from household smoke. For strong sources, the steady-state concentrations of these metrics are found to increase initially with increasing Air Exchange Rate (AER), reach a peak value and then decrease. Counter correlations are seen between UFP metric and PM_2.5 concentrations. The concepts of Critical Air Exchange Rate (CAER) and Half-Value Air Exchange Rate (HaVAER) have been introduced which indicate a feasibility of mitigation of PM_0.1 and PA_0.1, unlike PN, by ventilation techniques. The study clearly brings forth complex differential behavior of the three UFP metrics. The results are further discussed.