a) (e_max – e)
b) \(\frac{(e_{max} – e)}{(e_{min}-e)}\)
c) \(\frac{(e_{max} – e_{min})}{(e_{max}-e)}\)
d) \(\frac{(e_{max} – e)}{(e_{max}-e_{min})}\)

Answer: d
Explanation: The density index is defined as the difference between the voids ratio of the soil in its loosest state e_max and its natural void ratio e to the difference between the voids ratio in the loosest and densest state.
I_D=\(\frac{(e_{max} – e)}{(e_{max}-e_{min})}\).