How can we decipher the population density of tiger in national parks and tiger reserves ?

Pug marks and fecal pellets.

The correct answer is Option (3) – Pug marks and fecal pellets.

Sometimes, for certain ecological investigations, there is no need to know the absolute population densities (Population size, technically called population density, designated as N), need not necessarily be measured in numbers only; relative densities serve the purpose equally well. For example: the number of fish caught per trap is good enough measure of its total population density in the lake. We are mostly obliged to estimate population sizes indirectly, without actually counting them or seeing them. The tiger census in our national parks and tiger reserves is often based on pug marks and fecal pellets. Dead decaying body of prey, roar sounds and by Knowing the evenness in population of every species, we cannot calculate the accurate number of population density.