Paragraph: When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex \(\mathrm{P}\) is formed. In a strong acidic medium, the equilibrium shifts completely towards \(\mathrm{P}\). Addition of zinc chloride to \(\mathrm{P}\) in a slightly acidic medium results in a sparingly soluble complex Q.
Question: The number of moles of potassium iodide required to produce two moles of \(\mathbf{P}\) is

Statement I Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).
Statement II The conductivity of a solution having surfactant molecules deceases sharply at the CMC.

Monocyclic compounds \(\mathbf{P}, \mathbf{Q}, \mathbf{R}\) and \(\mathbf{S}\) are the major products formed in the reaction sequences given below.


The product having the highest number of unsaturated carbon atom(s) is-

Choose the correct statement(s) among the following.

Statement I Glucose gives a reddish-brown precipitate with Fehling's solution.
Statement II Reaction of glucose with Fehling's solution gives \(\mathrm{CuO}\) and gluconic acid.

For the cell $\mathrm{Zn} \left(\mathrm{s}\right)\left|{\mathrm{ZnSO}}_4 \left(\mathrm{aq}\right)\right|\left|{\mathrm{CuSO}}_4 \left(\mathrm{aq}\right)\right|\mathrm{Cu} \left(\mathrm{s}\right)$, when the concentration of ${\mathrm{Zn}}^{2+}$ is $10$ times the concentration of ${\mathrm{Cu}}^{2+}$, the expression for $\mathrm{\Delta G} \left(\mathrm{in}\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{mol}}^{-1}\right)$ is
$[\mathrm{F}=$Faraday's constant, $\mathrm{R}=$universal gas constant, $\mathrm{T}=$temperature, ${\mathrm{E}}^{\mathrm{o}}\mathrm{cell}=1.1\mathrm{V}]$

Paragraph I: An organic compound \(\mathbf{P}\) with molecular formula \(\mathrm{C}_9 \mathrm{H}_{18} \mathrm{O}_2\) decolorizes bromine water and also shows positive iodoform test. \(\mathbf{P}\) on ozonolysis followed by treatment with \(\mathrm{H}_2 \mathrm{O}_2\) gives \(\mathbf{Q}\) and \(\mathbf{R}\). While compound \(\mathbf{Q}\) shows positive iodoform test, compound \(\mathbf{R}\) does not give positive iodoform test. \(\mathbf{Q}\) and \(\mathbf{R}\) on oxidation with pyridinium chlorochromate (PCC) followed by heating give \(\mathbf{S}\) and \(\mathbf{T}\), respectively. Both \(\mathbf{S}\) and \(\mathbf{T}\) show positive iodoform test.
Complete copolymerization of 500 moles of \(\mathbf{Q}\) and 500 moles of \(\mathbf{R}\) gives one mole of a single acyclic copolymer \(\mathbf{U}\).
[Given, atomic mass: \(\mathrm{H}=1, \mathrm{C}=12, \mathrm{O}=16\)]
Question: Sum of number of oxygen atoms in \(\mathbf{S}\) and \(\mathbf{T}\) is

$\mathrm{M}{\mathrm{X}}_2$ dissociates in ${\mathrm{M}}^{2+}$ and ${\mathrm{X}}^{-}$ ions in an aqueous solution, with a degree of dissociation $\left(\mathrm{\alpha }\right)$ of 0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is

For every twice differentiable function $f:\mathbb{R}\to \left[-2, 2\right] \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} {\left(f\left(0\right)\right)}^2+{\left(f^{\prime }\left(0\right)\right)}^2=85$ , which of the following statement(s) is (are) TRUE?

A uniform magnetic field B exists in the region between $x=0$ and $x=\frac{3R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum p directed along $x$ -axis enters region 2 from region 1 at point $P_1\left(y=-R\right).$ Which of the following option(s) is/are correct?

List-I contains various reaction sequences and List-II contains different phenolic compounds.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

The cubic unit cell structure of a compound containing cation $\mathrm{M}$ and anion $\mathrm{X}$ is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

A steady current \(I\) goes through a wire loop \(P Q R\) having shape of a right angle triangle with \(P Q=3 x, P R=4 x\) and \(Q R=5 x\). If the magnitude of the magnetic field at \(P\) due to this loop is \(k\left(\frac{\mu_0 I}{48 \pi x}\right)\), find the value of \(k\).