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The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.
The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2,+4\) and \(+6 . \mathrm{XeF}_4\) reacts violently with water to give \(\mathrm{XeO}_3\). The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.
Question:
The structure of \(\mathrm{XeO}_3\) is

What is the order of basicity among the following compounds?

The correct stability order for the following species is

Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction as shown in the given scheme.

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Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper include chalcanthite \(\left(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\right)\), atacamite \(\left(\mathrm{Cu}_2 \mathrm{Cl}(\mathrm{OH})_3\right)\), cuprite \(\left(\mathrm{Cu}_2 \mathrm{O}\right)\), copper glance \(\left(\mathrm{Cu}_2 \mathrm{~S}\right)\) and malachite \(\left(\mathrm{Cu}_2(\mathrm{OH})_2 \mathrm{CO}_3\right)\). However, 80\% of the world copper production comes from the ore chalcopyrite \(\left(\mathrm{CuFeS}_2\right)\). The extraction of copper from chalcopyrite involves partial roasting, removal of iron and self-reduction.
Question:
Partial roasting of chalcopyrite produces

Match the conversions in Column I with the type(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

The total number of \(\alpha\) and \(\beta\)-particles emitted in the nuclear reaction \({ }_{92} \mathrm{U}^{238} \longrightarrow{ }_{82} \mathrm{~Pb}^{214}\) is

For each positive integer $n$, let $y_n={\frac{1}{n}\left((n+1)(n+2)\mathrm{...}(n+n)\right)}^{\frac{1}{n}}$. If $\underset{n\to \infty }{\lim }{y}_n=L,$ then the value of $\left[L\right]$ (where $\left[x\right]$ is the greatest integer less than or equal to $x$) is ____

In the decay sequence:
${}_{92}{}^{238}\mathrm{U}\stackrel{-{\mathrm{x}}_1}{\to }{}_{90}{}^{234}\mathrm{T}\mathrm{h}\stackrel{-{\mathrm{x}}_2}{\to }{}_{91}{}^{234}\mathrm{P}\mathrm{a}\stackrel{-{\mathrm{x}}_3}{\to }{}_{\mathrm{ }}{}^{234}\mathrm{Z}\stackrel{-{\mathrm{x}}_4}{\to }{}_{90}{}^{234}\mathrm{T}\mathrm{h}$
${\mathrm{x}}_1,\mathrm{ }{\mathrm{x}}_2,\mathrm{ }{\mathrm{x}}_3$ and ${\mathrm{x}}_4$ are the particles/ radiation emitted by the respective isotopes. The correct option(s) is/are:

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $\mathrm{T}$ . Assuming the gases are ideal, the correct statement(s) is (are)

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Consider an evacuated cylindrical chamber of height \(h\) having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius \(r \ll h\). Now a high voltage source \((HV)\) is connected across the conducting plates such that the bottom plate is at \(+V_{0}\) and the top plate at \(-V_{0} .\) Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)



Question :

Which one of the following statements is correct?

Let $P_1=I=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right], P_2=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 0& 1& 0\end{array}\right], P_3=\left[\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$$P_4=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}\right], P_5=\left[\begin{array}{ccc}0& 0& 1\\ 1& 0& 0\\ 0& 1& 0\end{array}\right],P_6=\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right],$ and
$X=\sum _{k=1}^6{P}_K\left[\begin{array}{ccc}2& 1& 3\\ 1& 0& 2\\ 3& 2& 1\end{array}\right]P_K^T$
where $P_K^T$ denotes the transpose of the matrix $P_K.$ Then which of the following options is/are correct?

Among the following, the correct statement(s) is(are)