Match the reactions in Column I with appropriate types of steps/reactive intermediate involved in these reactions as given in Column II.

Consider an ionic solid $\mathrm{MX}$, with $\mathrm{NaCl}$ structure. Construct a new structure $\left(\mathrm{Z}\right)$, whose unit cell is constructed from the unit cell of $\mathrm{MX}$, following the sequential instructions given below. Neglect the charge balance.
$\left(\mathrm{i}\right)$ Remove all the anions $\left(\mathrm{X}\right)$, except the central one.
$\left(\mathrm{ii}\right)$ Replace all the face centered cations $\left(\mathrm{M}\right)$, by anions $\left(\mathrm{X}\right)$.
$\left(\mathrm{iii}\right)$ Remove all the corner cations $\left(\mathrm{M}\right)$.
$\left(\mathrm{iv}\right)$ Replace the central anion $\left(\mathrm{X}\right)$, with cation $\left(\mathrm{M}\right)$.
The value of $\left(\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}\right)$ in $\mathrm{Z}$ is _____.

Statement 1 For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.
Statement 2 At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

In the following reaction sequence in aqueous solution, the species $\text{X,}\text{Y}$ and $\text{Z}$ respectively, are
\(S _2 O _3^{2-} \xrightarrow{ Ag ^{+}} \underset{\substack{\text { Clear } \\ \text { Solution }}}{ X } \xrightarrow{ Ag ^{+}} \underset{\substack{\text { White } \\ \text { Precipitate }}}{ Y }\) \(\xrightarrow{\text { With time }} \underset{\substack{\text { Black } \\ \text { Precipitate }}}{ Z }\)

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)

The structure of a peptide is given below.
If the absolute values of the net charge of the peptide at $\mathrm{pH}=2,\mathrm{pH}=6,$ and $\mathrm{pH}=11$ are $\left|{\mathrm{z}}_1\right|,\left|{\mathrm{z}}_2\right|,$ and $\left|{\mathrm{z}}_3\right|,$ respectively, then what is $\left|{\mathrm{z}}_1\right|+\left|{\mathrm{z}}_2\right|+\left|{\mathrm{z}}_3\right|$?

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 \(\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}\) \(\left.\mathrm{mol}^{-1}\right]\)

A circular coil of radius $R$ and $N$ turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge $Q$ through a switch. The coil is in a horizontal uniform magnetic field $B_o$ parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)

Let the straight line \(\mathrm{y}=2 \mathrm{x}\) touch a circle with center \((0, \alpha), \alpha>0\), and radius \(\mathrm{r}\) at a point \(\mathrm{A}_1\). Let \(\mathrm{B}_1\) be the point on the circle such that the line segment \(A_1 B_1\) is a diameter of the circle. Let \(\alpha+r=5+\sqrt{5}\).
Match each entry in List-I to the correct entry in List-II.

The correct option is

An ellipse intersects the hyperbola \(2 x^2-2 y^2=1\) orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

A ball moves over a fixed track as shown in the figure. From \(A\) to \(B\) the ball rolls without slipping. If surface \(B C\) is frictionless and \(K_A, K_B\) and \(K_C\) are kinetic energies of the ball at \(A, B\) and \(C\) respectively, then

A police car with a siren of frequency \(8 \mathrm{kHz}\) is moving with uniform velocity \(36 \mathrm{~km} / \mathrm{h}\) towards a tall building which reflects the sound waves. The speed of sound in air is \(320 \mathrm{~m} / \mathrm{s}\). The frequency of the siren heard by the car driver is

A horizontal force$F$is applied at the centre of mass of a cylindrical object of mass$m$and radius$R$, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is$\mu$. The centre of mass of the object has an acceleration$a$. The acceleration due to gravity is$g$. Given that the object rolls without slipping, which of the following statement(s) is (are) correct?