Volume of $$3 \mathrm{M} \mathrm{~NaOH}$$ (formula weight $$40 \mathrm{~g} \mathrm{~mol}^{-1}$$ ) which can be prepared from $$84 \mathrm{~g}$$ of $$\mathrm{NaOH}$$ is __________ $$\times 10^{-1} \mathrm{dm}^3$$.

Total number of ions from the following with noble gas configuration is _________.

$$\mathrm{Sr}^{2+}(z=38), \mathrm{Cs}^{+}(z=55), \mathrm{La}^{2+}(z=57), \mathrm{Pb}^{2+}(z=82), \mathrm{Yb}^{2+}(z=70)$$ and $$\mathrm{Fe}^{2+}(z=26)$$

For a certain thermochemical reaction $$\mathrm{M} \rightarrow \mathrm{N}$$ at $$\mathrm{T}=400 \mathrm{~K}, \Delta \mathrm{H}^{\ominus}=77.2 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta \mathrm{S}=122 \mathrm{~JK}^{-1}, \log$$ equilibrium constant $$(\log K)$$ is __________ $$\times 10^{-1}$$.

Considering only the principal values of inverse trigonometric functions, the number of positive real values of $$x$$ satisfying $$\tan ^{-1}(x)+\tan ^{-1}(2 x)=\frac{\pi}{4}$$ is :