$$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)+\mathrm{C}(g)$$

For the given reaction, if the initial pressure is $$450 \mathrm{~mm} ~\mathrm{Hg}$$ and the pressure at time $$\mathrm{t}$$ is $$720 \mathrm{~mm} ~\mathrm{Hg}$$ at a constant temperature $$\mathrm{T}$$ and constant volume $$\mathrm{V}$$. The fraction of $$\mathrm{A}(\mathrm{g})$$ decomposed under these conditions is $$x \times 10^{-1}$$. The value of $$x$$ is ___________ (nearest integer)

The specific conductance of $$0.0025 ~\mathrm{M}$$ acetic acid is $$5 \times 10^{-5} \mathrm{~S} \mathrm{~cm}^{-1}$$ at a certain temperature. The dissociation constant of acetic acid is __________ $$\times ~10^{-7}$$ (Nearest integer)

Consider limiting molar conductivity of $$\mathrm{CH}_{3} \mathrm{COOH}$$ as $$400 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$$

Let $$S = \left\{ {z = x + iy:{{2z - 3i} \over {4z + 2i}}\,\mathrm{is\,a\,real\,number}} \right\}$$. Then which of the following is NOT correct?

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :