If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:

Density $$\rho$$ is defined as mass per unit volume:
$$\rho = \dfrac{M}{L^{3}}$$

The given fundamental quantities are Force $$(F)$$, Length $$(L)$$ and Time $$(T)$$. We must first express mass $$(M)$$ in terms of $$F, L, T$$.

Begin with the definition of force:
$$F = M L T^{-2}$$

Solve this equation for $$M$$:
$$M = F \, L^{-1} \, T^{2}$$

Substitute this expression for $$M$$ into the formula for density:

$$\rho = \dfrac{M}{L^{3}} = \dfrac{F \, L^{-1} \, T^{2}}{L^{3}}$$

Simplify the powers of $$L$$:
$$\rho = F \, L^{-1-3} \, T^{2} = F \, L^{-4} \, T^{2}$$

Therefore, the dimensional formula of density in the $$[F, L, T]$$ system is $$[F L^{-4} T^{2}]$$.

Option A is correct.