Which of the following statement(s) (are) correct regarding the root mean square speed $\left({\mathrm{U}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\right)$ and average translational kinetic energy $\left({\mathrm{\epsilon }}_{\mathrm{a}\mathrm{v}}\right)$ of a molecule in a gas at equilibrium?

Based on VSEPR theory, the number of 90 degree \(\mathrm{F}-\mathrm{Br}-\mathrm{F}\) angles in \(\mathrm{BrF}_5\) is

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?

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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

Based on the compounds of group 15 elements, the correct statement(s) is (are)

The carboxyl functional group \((-\mathrm{COOH})\) is present in

Considering the following reaction sequence, the correct statement(s) is(are)

If the value of Avogadro number is $6.023\times {10}^{23}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{–1}$ and the value of Boltzmann constant is $1.380\times {10}^{-23}\mathrm{ }\mathrm{J}{\mathrm{K}}^{-1}$ , then the number of significant digits in the calculated value of the universal gas constant is

For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two $2{\mathrm{p}}_{\mathrm{z}}$ orbitals is(are)

A thin spherical insulating shell of radius $\mathrm{R}$ carries a uniformly distributed charge such that the potential at its surface is ${\mathrm{V}}_0$ . A hole with a small area $\mathrm{\alpha }4\mathrm{\pi }{\mathrm{R}}^2\left(\mathrm{\alpha }\ll 1\right)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

The compound(s) formed upon combustion of sodium metal in excess air is (are)

The function $\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)$ is the solution of the differential equation $\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}+\frac{\mathrm{x}\mathrm{y}}{{\mathrm{x}}^2-1}=\frac{{\mathrm{x}}^4+2\mathrm{x}}{\sqrt{1-{\mathrm{x}}^2}}$ in (- 1 , 1) satisfying $\mathrm{f}\left(0\right)=0.$ Then $\underset{-\frac{\sqrt{3}}{2}}{\overset{\frac{\sqrt{3}}{2}}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{ }\mathrm{d}\mathrm{x}$ is

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Thermal decomposition of gaseous \(\mathrm{X}_{2}\) to gaseous \(\mathrm{X}\) at \(298 \mathrm{~K}\) takes place according to the following equation:

\(\mathrm{X}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{X}(\mathrm{g})\)

The standard reaction Gibbs energy, \(\Delta_{r} G^{\circ}\), of this reaction is positive. At the start of the reaction, there is one mole of \(\mathrm{X}_{2}\) and no \(\mathrm{X}\). As the reaction proceeds, the number of moles of \(\mathrm{X}\) formed is given by \(\beta\). Thus, \(\beta_{\text {equilibrium }}\) is the number of moles of \(\mathrm{X}\) formed at equilibrium. The reaction is carried out at a constant total pressure of \(2\) bar. Consider the gases to behave ideally. (Given : \(R=0.083 \mathrm{~L}\) bar \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\) )

Question:
The INCORRECT statement among the following, for this reaction, is