Match the reaction in Column I with appropriate options in Column II

The plot given below shows $\mathrm{P}-\mathrm{T}$ curves (where, $\mathrm{P}$ is the pressure and $\mathrm{T}$ is the temperature) for two solvents $\mathrm{X}$ and $\mathrm{Y}$ and isomolal solutions of $\mathrm{NaCl}$ in these solvents. $\mathrm{NaCl}$ is completely dissociates in both the solvents.

On the addition of equal number of moles of a non-volatile solute $\mathrm{S}$ in equal amount (in $\mathrm{kg}$) of these solvents, the elevation of boiling point of solvent $\mathrm{X}$ is three times that of solvent $\mathrm{Y}$. The solute $\mathrm{S}$ is known to undergo dimerization in these solvents. If the degree of dimerization is $0.7$ in the solvent $\mathrm{Y}$, the degree of dimerization in the solvent $\mathrm{X}$ is _______.

The thermal dissociation equilibrium of ${\mathrm{CaCO}}_3\left(\mathrm{s}\right)$ is studied under different conditions.
${\text{CaCO}}_3\left(s\right)\rightleftharpoons \text{CaO}\left(s\right)+{\text{CO}}_2\left(\text{g}\right)$
For this equilibrium, the correct statement(s) is/are

The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If ${\mathrm{\lambda }}_{{\mathrm{X}}^{-}}^0\approx {\mathrm{\lambda }}_{{\mathrm{Y}}^{-}}^0$ , the difference in their $\mathrm{p}{\mathrm{K}}_{\mathrm{a}}$ values, $\mathrm{p}{\mathrm{K}}_{\mathrm{a}}\left(\mathrm{H}\mathrm{X}\right)-\mathrm{p}{\mathrm{K}}_{\mathrm{a}}\left(\mathrm{H}\mathrm{Y}\right)$ , is (Consider degree of ionization of both acids to << 1)

For the reaction, \(\mathbf{X}(s) \rightleftharpoons \mathbf{Y}(s)+\mathbf{Z}(g)\), the plot of \(\ln \frac{p_{\mathbf{Z}}}{p^{\theta}}\) versus \(\frac{10^{4}}{T}\) is given below (in solid line), where \(p_{\mathbf{Z}}\) is the pressure (in bar) of the gas \(\mathbf{Z}\) at temperature \(T\) and \(p^{\theta}=1\) bar.

(Given, \(\frac{\mathrm{d}(\ln K)}{\mathrm{d}\left(\frac{1}{T}\right)}=-\frac{\Delta H^{\theta}}{R}\), where the equilibrium constant, \(K=\frac{p_{z}}{p^{\theta}}\) and the gas constant, \(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) )
The value of $∆{\mathrm{S}}^{\mathrm{o}}$ (in $\mathrm{kJ} {\mathrm{mol}}^{-1}$) for the given reaction, at $1000 \mathrm{K}$ is ___.

Paragraph:
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridisation easily explains the ease of sigma donation capability of \(\mathrm{NH}_3\) and \(\mathrm{PH}_3\). Phosphine is a flammable gas and is prepared from white phosphorus.
Question:
White phosphorus on reaction with \(\mathrm{NaOH}\) gives \(\mathrm{PH}_3\) as one of the products. This is a

When \(20 \mathrm{~g}\) of naphthoic acid \(\left(\mathrm{C}_{11} \mathrm{H}_8 \mathrm{O}_2\right)\) is dissolved in \(50 \mathrm{~g}\) of benzene \(\left(K_f=1.72 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\), a freezing point depression of \(2 \mathrm{~K}\) is observed. The van't Hoff factor \((i)\) is

A \(0.1 \mathrm{~kg}\) mass is suspended from a wire of negligible mass. The length of the wire is \(1 \mathrm{~m}\) and its cross-sectional area is \(4.9 \times 10^{-7} \mathrm{~m}^2\). If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency \(140 \mathrm{rad} \mathrm{s}^{-1}\). If the Young's modulus of the material of the wire is \(n \times 10^9 \mathrm{Nm}^{-2}\), the value of \(n\) is

Let $E$ denote the parabola $y^2=8x.$ Let $P=\left(-2,4\right)$, and let $Q$ and $Q^{\text{'}}$ be two distinct points on $E$ such that the lines $PQ$ and $P{Q}^{\text{'}}$ are tangents to $E$. Let $F$ be the focus of $E$. Then which of the following statements is (are) TRUE?

The number of points in $\left(-\infty ,\infty \right)$, for which $x^2-x\sin x-\cos x=0$, is:

The surface of copper gets tarnished by the formation of copper oxide. $N_2$ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the $N_2$ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:

$2Cu\left(s\right)+ H_{2}O\left(g\right)\to C{u}_{2}O\left(s\right) + H_2\left(g\right)$

$P_{H_2}$ Is the minimum partial pressure of $H_2$ (in bar) needed to prevent the oxidation at 1250 K. The value of $\ln \left(p{H}_2\right)$ is ____.

(Given: total pressure \(=1\) bar, R (universal gas constant) \(=8 J K ^{-1} mol^{-1}, \ln (10) =2.3 \cdot Cu (s)\) and \(Cu _2 O (s)\) are mutually immiscible.

At \(1250 K: 2 Cu ( s )+\frac{1}{2} O _2(g) \rightarrow Cu _2 O ( s ) ;\) \(\Delta G^{\ominus}=-78,000 J mol ^{-1}\)

\(H _2(g)+\frac{1}{2} O _2(g) \rightarrow H _2 O ( g ) ; \quad \Delta^{\ominus}=\)\(-1,78,000 J mol ^{-1} ; G\) is the Gibbs energy)/mi> \(\Theta=\) \(-78,000 J mol -1\)

\(H _2(g)+\frac{1}{2} O _2(g) \rightarrow H _2 O ( g ) ; \quad\)\(\Delta^{\ominus}=-1,78,000 J mol ^{-1} ; G\) is the Gibbs energy)

In a non-right-angled triangle $\mathrm{\Delta }PQR,$ let $p\mathit{,}q\mathit{,}r$ denote the lengths of the sides opposite to the angles at $P,Q,R$ respectively. The median from $R$ meets the side $PQ$ at $S,$ the perpendicular from $P$ meets the side $QR$ at $E$, and $RS$ and $PE$ intersect at $0.$ If $p=\sqrt{3},q=1,$ and the radius of the circumcircle of the $\mathrm{\Delta }PQR$ equals $1,$ then which of the following options is/are correct?

Electrolysis of dilute aq. \(\mathrm{NaCl}\) solution was carried out by passing \(10 \mathrm{~mA}\) current. The time required to liberate \(0.01\) mole of \(\mathrm{H}_2\) gas at the cathode is (1 Faraday \(=96500 \mathrm{C} \mathrm{mol}^{-1}\) )