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 :

Let the position vectors of the vertices $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ of a triangle be $$2 \hat{i}+2 \hat{j}+\hat{k}, \hat{i}+2 \hat{j}+2 \hat{k}$$ and $$2 \hat{i}+\hat{j}+2 \hat{k}$$ respectively. Let $$l_1, l_2$$ and $$l_3$$ be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides $$\mathrm{AB}, \mathrm{BC}$$ and $$\mathrm{CA}$$ respectively, then $$l_1^2+l_2^2+l_3^2$$ equals: