The complex(es), which can exhibit the type of isomerism shown by $\left[\operatorname{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Br}_2\right]$, is(are) :

[en $=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2$ ]

Atoms of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$ form face-centred cubic (fcc) unit cell of edge length $\mathrm{L}_{\mathrm{x}}$, body-centred cubic (bcc) unit cell of edge length $\mathrm{L}_y$, and simple cubic unit cell of edge length $\mathrm{L}_z$, respectively.

If $\mathrm{r}_{\mathrm{z}}=\frac{\sqrt{3}}{2} r_{\mathrm{y}} ; \mathrm{r}_{\mathrm{y}}=\frac{8}{\sqrt{3}} \mathrm{r}_{\mathrm{x}} ; M_{\mathrm{z}}=\frac{3}{2} M_{\mathrm{y}}$ and $M_{\mathrm{z}}=3 M_{\mathrm{x}}$, then the correct statement(s) is(are) :

[Given: $M_x, M_y$, and $M_z$ are molar masses of metals $x, y$, and $z$, respectively.
$\mathrm{r}_{\mathrm{x}}, \mathrm{r}_{\mathrm{y}}$, and $\mathrm{r}_{\mathrm{z}}$ are atomic radii of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$, respectively.]

In the following reactions, $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ are the major products.



The correct statement(s) about $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ is(are) :

$\mathrm{H}_2 \mathrm{S}$ (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is $\mathbf{x}$, and the number of moles of electrons involved is $\mathbf{y}$. The value of $(\mathbf{x}+\mathbf{y})$ is ________.