The initial setting of cement is primarily due to which of the following?

$A$ metal $M$ and its compound can give the following observable changes in a sequence of reactions: $M$ $\xrightarrow{\text{dil. } HNO_3} M(NO_3)_2$ $\xrightarrow{NaOH} \text{White ppt.}$ $\xrightarrow{\text{Excess } NaOH} \text{Colourless solution}$ $\xrightarrow{H_2S} \text{White ppt.}$. Identify the metal $M$.

The product of the lengths of perpendiculars drawn from any point on the hyperbola $x^2 - 2y^2 - 2 = 0$ to its asymptotes is:

Given that $\Delta H_f(H) = 218 \ kJ/mol$,express the $H-H$ bond energy in $kcal/mol$.

Identify $B$ in the following reaction:
$H_4SiO_4$ $\xrightarrow[1000^{\circ}C]{-2H_2O} A$ $\xrightarrow[\Delta]{\text{Carbon}} B + CO$

$A$ variable plane passes through a fixed point $(1, 2, 3)$. The foot of the perpendicular from the origin to the plane lies on: