(isomeric products) \(\text C _5\text H _{11} \text{Cl} \xrightarrow{\text { fractional distillation }}\text M\) (isomeric products)
What are N and M ?

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.

For the process \(\mathrm{H}_2 \mathrm{O}(\mathrm{l})\) (1 bar, \(\left.273 \mathrm{~K}\right) \longrightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})\) (1 bar, \(\left.373 \mathrm{~K}\right)\), the correct set of thermodynamic parameters is

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\(P\) and \(Q\) are isomers of dicarboxylic acid \(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{4}\). Both decolorize \(\mathrm{Br}_{2} / \mathrm{H}_{2} \mathrm{O}\). On heating, \(\boldsymbol{P}\) forms the cyclic anhydride.

Upon treatment with dilute alkaline \(\mathrm{KMnO}_{4}, \boldsymbol{P}\) as well as \(\boldsymbol{Q}\) could produce one or more than one from \(\boldsymbol{S}, \boldsymbol{T}\) and \(\boldsymbol{U}\).




Question:
Compounds formed from \(\boldsymbol{P}\) and \(\boldsymbol{Q}\) are, respectively

The colour of the $X_2$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -

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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

Statement I Band gap in germanium is small.
Statement II The energy spread of each germanium atomic energy level is infinitesimally small.

Two bodies, each of mass $M$, are kept fixed with a separation of $2L$. A particle of mass $m$ is projected from the midpoint of the line joining their centers, perpendicular to the line. The gravitational constant is $G$. The correct statement (s) is (are) :

The correct acidity order of the following is

Statement I Molecules that are not superimposable on their mirror images are chiral.
Statement II All chiral molecules have chiral centres.

Let \(\mathbb{R}\) denote the set of all real numbers. Let \(a_{\mathrm{i}}, b_{\mathrm{i}} \in \mathbb{R}\) for \(\mathrm{i} \in\{1,2,3\}\).
Define the functions \(f: \mathbb{R} \rightarrow \mathbb{R}, g: \mathbb{R} \rightarrow \mathbb{R}\), and \(h: \mathbb{R} \rightarrow \mathbb{R}\) by
\(\begin{aligned} & f(x)=a_1+10 x+a_2 x^2+a_3 x^3+x^4, \\ & g(x)=b_1+3 x+b_2 x^2+b_3 x^3+x^4, \\ & h(x)=f(x+1)-g(x+2) .\end{aligned}\)
If \(f(x) \neq g(x)\) for every \(x \in \mathbb{R}\), then the coefficient of \(x^3\) in \(h(x)\) is

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

Let $b$ be a nonzero real number. Suppose $f:\mathrm{ℝ}\to \mathrm{ℝ}$ is a differentiable function such that $f\left(0\right)=1$. If the derivative $f^{\text{'}}$ of $f$ satisfies the equation $f^{\text{'}}\left(x\right)=\frac{f\left(x\right)}{b^2+x^2}$ for all $x\in \mathrm{ℝ},$ then which of the following statements is/are TRUE?