Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\mathrm{t}\mathrm{h}}$ orbit of the atom and List-II contains options showing how they depend on $n$ .
 

List - I	List - II
(I) Radius of the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{P}\right)$ $\propto n^{-2}$
(II) Angular momentum of the electron in the $n^{th}$ orbit	$\left(\mathrm{Q}\right)$ $\propto n^{-1}$
(III) Kinetic energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{R}\right)$ $\propto n^0$
(IV) Potential energy of the electron in the $n^{\mathrm{t}\mathrm{h}}$ orbit	$\left(\mathrm{S}\right)$ $\propto n^1$
	$\left(\mathrm{T}\right)$ $\propto n^2$
	$\left(\mathrm{U}\right)$ $\propto n^{1/2}$

Which of the following options has the correct combination considering List-I and List-II?

A monoatomic ideal gas undergoes a process in which the ratio of \(P\) to \(V\) at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

The mole fraction of urea in an aqueous urea solution containing $900\mathrm{ }\mathrm{g}$ of water is $0.05$ . If the density of the solution is $1.2\mathrm{ }\mathrm{g}\mathrm{ }{\mathrm{c}\mathrm{m}}^{-3}$ , the molarity of urea solution is _______
(Given data: Molar masses of urea and water are $60\mathrm{ }\mathrm{g}\mathrm{ }{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$ and $18\mathrm{ }\mathrm{g}\mathrm{ }{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$ , respectively)

Consider a reaction \(a G+b H \rightarrow\) products. When concentration of both the reactants \(G\) and \(H\) is doubled, the rate increases by eight times. However, when concentration of \(G\) is doubled keeping the concentration of \(H\) fixed, the rate is doubled. The overall order of the reaction is

After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is(are):

For the reduction of \(\mathrm{NO}_3^{-}\)ion in an aqueous solution \(E^{\circ}\) is \(+0.96 \mathrm{~V}\). Values of \(E^{\circ}\) for some metal ions are given below.
\(
\begin{aligned}
& \mathrm{V}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{V} ; E^{\circ}=-1.19 \mathrm{~V} \\
& \mathrm{Fe}^{3+}(a q)+3 e^{-} \longrightarrow \mathrm{Fe} ; \mathrm{E}^{\circ}=-0.04 \mathrm{~V} \\
& \mathrm{Au}^{3+}(a q)+3 e^{-} \longrightarrow \mathrm{Au} ; E^{\circ}=+1.40 \mathrm{~V}
\end{aligned}
\)
\(
\mathrm{Hg}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{Hg} ; E^{\circ}=+0.86 \mathrm{~V}
\)
The pair(s) of metals that is (are) oxidised by \(\mathrm{NO}_3^{-}\)in aqueous solution is (are)

Match the orbital overlap figures shown in List-I with the description given in List-II and select the correct
answer using the code given below the lists.

	List – I		List - II
A.		P	$\mathrm{p}-\mathrm{d}\mathrm{}\mathrm{\pi }$ antibonding
B.		Q	$\mathrm{d}-\mathrm{d}\mathrm{}\mathrm{\sigma }$ bonding
C.		R	$\mathrm{p}-\mathrm{d}\mathrm{}\mathrm{\pi }$ bonding
D.		S	$\mathrm{d}-\mathrm{d}\mathrm{}\mathrm{\sigma }$ antibonding

One mole of an ideal gas undergoes two different cyclic processes $\mathrm{I}$ and $\mathrm{II}$, as shown in the $P-V$ diagrams below. In cycle $\mathrm{I}$, processes $a, b, c$ and $d$ are isobaric, isothermal, isobaric and isochoric, respectively. In cycle $\mathrm{II}$, processes $a\text{'}, b\text{'}, c\text{'}$ and $d\text{'}$ are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle $\mathrm{I}$ is $W_{\mathrm{I}}$ and that during cycle $\mathrm{II}$ is $W_{\mathrm{II}}$. The ratio $\frac{W_{\mathrm{I}}}{W_{\mathrm{II}}}$ is _____.

Statement 1 Aniline on reaction with \(\mathrm{NaNO}_2 / \mathrm{HCl}\) at \(0^{\circ} \mathrm{C}\) followed by coupling with \(\beta\)-naphthol gives a dark coloured precipitate.
Statement 2 The colour of the compound formed in the reaction of aniline with \(\mathrm{NaNO}_2 / \mathrm{HCl}\) at \(0^{\circ} \mathrm{C}\) followed by coupling with \(\beta\)-naphthol is due to the extended conjugation.

Among P, Q, R and S, the aromatic compound(s) is/are

In the cyanide extraction process of silver from argentite ore, the oxidising and reducing agents used are

Paragraph :
Two plane harmonic sound waves are expressed by the equations.
\(
\begin{aligned}
& y_1(x, t)=A \cos (0.5 \pi x-100 \pi t) \\
& y_2(x, t)=A \cos (0.46 \pi x-92 \pi t)
\end{aligned}
\)
(All parameters are in MKS)
Question :
What is the speed of the sound?

All the energy released from the reaction $\mathrm{X}⟶\mathrm{Y},\mathrm{ }{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\mathrm{o}}=-193\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$ is used for oxidizing ${\mathrm{M}}^{+}$ as ${\mathrm{M}}^{+}⟶{\mathrm{M}}^{3+}+2{\mathrm{e}}^{-}\mathrm{ },\mathrm{ }{\mathrm{E}}^{\mathrm{o}}=\mathrm{ }-0.25\mathrm{ }\mathrm{V}$
Under standard conditions, the number of moles of ${\mathrm{M}}^{+}$ oxidized when one mole of X is converted to Y is
$[\mathrm{F}=96500\mathrm{ }\mathrm{C}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}]$