At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid \(\left(\mathrm{HNO}_2\right)\) gives the species

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?

Among the following, the number of compounds than can react with \(\mathrm{PCl}_5\) to give \(\mathrm{POCl}_3\) is \(\mathrm{O}_2, \mathrm{CO}_2, \mathrm{SO}_2, \mathrm{H}_2 \mathrm{O}, \mathrm{H}_2 \mathrm{SO}_4, \mathrm{P}_4 \mathrm{O}_{10}\).

Which is correct statement if \(\mathrm{N}_2\) is added at equilibrium condition?

The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compounds, is

Match the complexes in Column I with their properties listed in Column II. Indicates your answer by darkening the appropriate bubbles of \(4 \times 4\) matrix given in the ORS.

The geometries of the ammonia complexes of $\mathrm{N}{\mathrm{i}}^{2+}\mathrm{ },\mathrm{ }\mathrm{P}{\mathrm{t}}^{2+}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }\mathrm{Z}{\mathrm{n}}^{2+}$ respectively, are :

The species which by definition has zero standard molar enthalpy of formation at \(298 \mathrm{~K}\) is

Let the eccentricity of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) be reciprocal to that of the ellipse \(x^2+4 y^2=4\). If the hyperbola passes through a focus of the ellipse, then

To form a complete monolayer of acetic acid on \(1 \mathrm{~g}\) of charcoal, \(100 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 \(\mathrm{mL}\) of \(1 \mathrm{M} \mathrm{NaOH}\) solution was required. If each molecule of acetic acid occupies \(\mathbf{P} \times 10^{-23} \mathrm{~m}^2\) surface area on charcoal, the value of \(\mathbf{P}\) is _______ [Use given data: Surface area of charcoal \(=1.5 \times 10^2 \mathrm{~m}^2 \mathrm{~g}^{-1} ;\) Avogadro's number \(\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}\) \(\left.\mathrm{mol}^{-1}\right]\)

Match each coordination compound in List-I with an appropriate pair of characteristics from List-II and select the correct answer using the code given below the lists
\(\left\{\right.\)en \(= H _2 NCH _2 CH _2 NH _2 ;\) atomic numbers \(\left.: T _{ i }=22, Cr =24 ; Co =27 ; Pt =78\right\}\)

	List – I		List – II
A.	$\left[\mathrm{C}\mathrm{r}{\left(\mathrm{N}{\mathrm{H}}_3\right)}_4\mathrm{C}{\mathrm{l}}_2\right]\mathrm{C}\mathrm{l}$	P.	Paramagnetic and exhibits ionization isomerism
B.	$\left[\mathrm{T}\mathrm{i}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5\mathrm{ }\mathrm{C}\mathrm{l}\right]{\left(\mathrm{N}{\mathrm{O}}_3\right)}_2$	Q.	Diamagnetic and exhibits cis - trans isomerism
C.	$\left[\mathrm{P}\mathrm{t}\left(\mathrm{e}\mathrm{n}\right)\left(\mathrm{N}{\mathrm{H}}_3\right)\mathrm{C}\mathrm{l}\right]\mathrm{N}{\mathrm{O}}_3$	R.	Paramagnetic and exhibits cis - trans isomerism
D.	$\left[\mathrm{C}\mathrm{o}{\left(\mathrm{N}{\mathrm{H}}_3\right)}_4{\left(\mathrm{N}{\mathrm{O}}_3\right)}_2\right]\mathrm{N}{\mathrm{O}}_3$	S.	Diamagnetic and exhibits ionization isomerism

Column I gives certain situations in which a straight metallic wire of resistance \(R\) is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the \(4 \times 4\) matrix given in the ORS.

Paragraph:

A small block of mass \(1 \mathrm{~kg}\) is released from rest at the top of a rough track. The track is a circular arc of radius \(40 \mathrm{~m}\). The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point \(Q\), as shown in the figure below, is \(150 \mathrm{~J}\). (Take the acceleration due to gravity, \(g=10 \mathrm{~m} \mathrm{~s}^{-2}\) ).





Question:

The speed of the block when it reaches the point \(Q\) is