Among \(H_2, H e_2^{+}, L i_2, B e_2, B_2, C_2, N_2, O_2^{-}\), and \(F_2\), the number of diamagnetic species is -
(Atomic number : \(H=1, H e=2, L i=3, B e=4, B=5,\) \(C=6, N =7, O=8, F=9\) )

An organic compound $\left({\mathrm{C}}_8{\mathrm{H}}_{10}{\mathrm{O}}_2\right)$ rotates plane-polarized light. It produces pink color with neutral ${\mathrm{FeCl}}_3$ solution. What is the total number of all the possible isomers for this compound?

Reaction of iso-propylbenzene with \(\mathrm{O}_2\) followed by the treatment with \(\mathrm{H}_3 \mathrm{O}^{+}\)forms phenol and a by-product \(\mathbf{P}\). Reaction of \(\mathbf{P}\) with 3 equivalents of \(\mathrm{Cl}_2\) gives compound \(\mathbf{Q}\). Treatment of \(\mathbf{Q}\) with \(\mathrm{Ca}(\mathrm{OH})_2\) produces compound \(\mathbf{R}\) and calcium salt \(\mathbf{S}\).
The correct statement(s) regarding \(\mathbf{P}, \mathbf{Q}, \mathbf{R}\) and \(\mathbf{S}\) is(are)

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure$1$). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure $2$), the volume (in ${\mathrm{m}}^3$) of the compartment A after the system attains equilibrium is _________.

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Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.
A solution \(M\) is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is \(0.9\)
Given Freezing point depression constant of water \(\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\)
Freezing point depression constant of ethanol \(\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of water \(\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of ethanol \(\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Standard freezing point of water \(=273 \mathrm{~K}\)
Standard freezing point of ethanol \(=155.7 \mathrm{~K}\)
Standard boiling point of water \(=373 \mathrm{~K}\)
Standard boiling point of ethanol \(=351.5 \mathrm{~K}\)
Vapour pressure of pure water \(=328 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Vapour pressure of pure ethanol \(=40 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Molecular weight of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\)
Molecular weight of ethanol \(=46 \mathrm{~g} \mathrm{~mol}^{-1}\)
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.

Question:
The freezing point of the solution \(M\) is

The spin only magnetic moment value (in Bohr magneton units) of \(\mathrm{Cr}(\mathrm{CO})_6\) is

The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula \(=\mathrm{C}_5 \mathrm{H}_{10}\) is

The ${\mathrm{K}}_{\mathrm{sp}}$ of ${\text{Ag}}_2{\text{CrO}}_4$ is $1.1\times 10^{-12}$ at $298 \mathrm{K}$. The solubility (in $\mathrm{mol} {\mathrm{L}}^{-1}$) of ${\text{Ag}}_2\mathrm{CrO}{}_4$ in a $0.1 \mathrm{M} {\text{AgNO}}_3$ solution is

If $\alpha =3{\sin }^{-1}\left(\frac{6}{11}\right) and \beta =3{\cos }^{-1}\left(\frac{4}{9}\right),$ where the inverse trigonometric functions take only the principal values, then the correct options(s) is(are)

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass \(m\) and radius \(r\) and it is in a uniform vertical magnetic field \(B_0\), as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity \(g\), on two conducting supports at \(\mathrm{P}\) and \(\mathrm{Q}\). When a current \(I\) is passed through the loop, the loop turns about the line \(\mathrm{PQ}\) by an angle \(\theta\) given by

A gas described by van der Waals' equation

Consider the following reactions (unbalanced)
$\mathrm{Z}\mathrm{n}+H\mathrm{o}\mathrm{t}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4\to \mathrm{G}+\mathrm{R}+\mathrm{X}$
$\mathrm{Z}\mathrm{n}+\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{c}.\mathrm{ }\mathrm{N}\mathrm{a}\mathrm{O}\mathrm{H}\to \mathrm{T}+\mathrm{Q}$
\(\text G +\text H _2\text S+ \text{NH} _4 \text{OH} \rightarrow\text Z ~(\)a precipitate\()+\text X +\text Y\)
Choose the correct option(s).

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 standard enthalpy, $∆{\mathrm{H}}^{\mathrm{o}}$ (in $\mathrm{kJ} {\mathrm{mol}}^{-1}$) for the given reaction is ___.