Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

A solution of a metal ion when treated with \(\mathrm{KI}\) gives a red precipitate which dissolved in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt (II) thiocyanate gives rise to a deep blue crystalline precipitqte. The metal ion is

The given graph represent the variations of compressibility factor \((Z)=\frac{P V}{n R T}\) versus \(P\), for three real gases \(A, B\) and \(C\). Identify the only incorrect statement

The unbalanced chemical reactions given in List I show missing reagent or condition (?) which are provided in list II. match List I with List II and select the correct answer using the code given below the lists :

List - I	List - II
A. \(PbO _2+ H _2 SO _4 \xrightarrow{?}\) \(PbSO _4 + O _2+\) other product	P. \(\text{NO}\)
B. \(Na _2 S_2 O _3+ H _2 O \xrightarrow{?}\) \(NaHSO _4~+\) other product	Q. \(\text{I}_2\)
C. \(N _2 H _4 \xrightarrow{?} N_2 +\) other product	R. Warm
D. \(XeF _2 \xrightarrow{?} Xe ~+\) other product	S. \(\text{Cl}_2\)

A closed vessel with rigid walls contains 1 mol of ${}_{92}{}^{238}\mathrm{U}$ and 1 mol of air at 298 K. Considering complete decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{P}\mathrm{b}$ , the ratio of the final pressure to the initial pressure of the system at 298 K is

A trinitro compound, $1,3,5$-tris-($4$-nitrophenyl) benzene, on complete reaction with an excess of $\mathrm{Sn}/\mathrm{HCl}$ gives a major product, which on treatment with an excess of ${\mathrm{NaNO}}_2/\mathrm{HCl}$ at $0°\mathrm{C}$ provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of ${\mathrm{H}}_2\mathrm{O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$. The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is $474 \mathrm{g} {\mathrm{mol}}^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is $172.5 \mathrm{g} {\mathrm{mol}}^{-1}$.
The total number of carbon atoms and heteroatoms present in one molecule of \(S\) is
[Use: Molar mass (in \(\text{gmol} ^{-1}\) ): \(\text H =1,\text C =12,\text N=14,\text O =16,\) \(\text{Br} =80, \text{Cl} =35.5\) Atoms other than C and H are considered as heteroatoms]

On decreasing the $\mathrm{pH}$ from $7$ to $2$, the solubility of a sparingly soluble salt $\left(\mathrm{MX}\right)$ of a weak acid $\left(\mathrm{HX}\right)$ increased from ${10}^{-4} \mathrm{mol} {\mathrm{L}}^{-1}$ to ${10}^{-3} \mathrm{mol} {\mathrm{L}}^{-1}$. The ${\mathrm{pK}}_{\mathrm{a}}$ of $\mathrm{HX}$ is

The function $\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)$ is the solution of the differential equation $\frac{\mathrm{d}\mathrm{y}}{\mathrm{d}\mathrm{x}}+\frac{\mathrm{x}\mathrm{y}}{{\mathrm{x}}^2-1}=\frac{{\mathrm{x}}^4+2\mathrm{x}}{\sqrt{1-{\mathrm{x}}^2}}$ in (- 1 , 1) satisfying $\mathrm{f}\left(0\right)=0.$ Then $\underset{-\frac{\sqrt{3}}{2}}{\overset{\frac{\sqrt{3}}{2}}{\int }}\mathrm{f}\left(\mathrm{x}\right)\mathrm{ }\mathrm{d}\mathrm{x}$ is

Let $E$ be the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$. For any three distinct points $P,Q$ and $Q^{\text{'}}$ on $E$, let $M\left(P,Q\right)$ be the mid-point of the line segment joining $P$ and $Q$, and $M\left(P,Q^{\text{'}}\right)$ be the mid-point of the line segment joining $P$ and $Q^{\text{'}}$. Then the maximum possible value of the distance between $M\left(P,Q\right)$ and $M\left(P,Q^{\text{'}}\right)$, as $P,Q$ and $Q^{\text{'}}$ vary on $E$, is _____.

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The amount of energy required to break a bond is same as the amount of energy released when the same bond is formed. In gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond Strength. BDE is affected by \(s\)-character of the bond and the stability of the radicals formed. Shorter bonds are typically stronger bonds. BDEs for some bonds are given below:












Question:
Correct match of the \(\mathbf{C}-\mathbf{H}\) bonds (shown in bold) in Column \(\mathbf{J}\) with their BDE in Column \(\mathbf{K}\) is

At \(25^{\circ} \mathrm{C}\), the concentration of \(\mathrm{H}^{+}\)ions in \(1.00 \times 10^{-3} \mathrm{M}\) aqueous solution of a weak monobasic acid having acid dissociation constant \(\left(K_a\right)=4.00 \times 10^{-11}\) is \(\boldsymbol{X} \times 10^{-7} \mathrm{M}\). The value of \(\boldsymbol{X}\) is _____ .
Use: Ionic product of water \(\left(K_w\right)=1.00 \times 10^{-14}\) at \(25^{\circ} \mathrm{C}\)

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An aqueous solution of a mixture of two inorganic salts, when treated with dilute \(H C\) ?, gave a precipitate \((\boldsymbol{P})\) and a filtrate \((\boldsymbol{Q})\). The precipitate \(\boldsymbol{P}\) was found to dissolve in hot water. The filtrate \((\boldsymbol{Q})\) remained unchanged, when treated with \(\mathrm{H}_{2} \mathrm{~S}\) in a dilute mineral acid medium. However, it gave a precipitate \((\boldsymbol{R})\) with \(H_{2} S\) in an ammoniacal medium. The precipitate \(\boldsymbol{R}\) gave a coloured solution \((\boldsymbol{S})\), when treated with \(\mathrm{H}_{2} \mathrm{O}_{2}\) in an aqueous \(\mathrm{NaOH}\) medium.
Question:
The coloured solution \(\boldsymbol{S}\) contains

For the given aqueous reactions, which of the statement (s) is (are) true?