The packing efficiency of the two-dimensional square unit cell shown below is

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\(\mathbf{X}\) and \(\mathbf{Y}\) are two volatile liquids with molar weights of \(10 \mathrm{~g} \mathrm{~mol}^{-1}\) and \(40 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively. Two cotton plugs, one soaked in \(\mathbf{X}\) and the other soaked in \(\mathbf{Y}\), are simultaneously placed at the ends of a tube of length \(L=24 \mathrm{~cm}\), as shown in the figure. The tube is filled with an inert gas at \(1\) atmosphere pressure and a temperature of \(300 \mathrm{~K}\). Vapours of \(\mathbf{X}\) and \(\mathbf{Y}\) react to form a product which is first observed at a distance \(\mathbf{d} \mathrm{~cm}\) from the plug soaked in \(\mathbf{X}\). Take \(\mathbf{X}\) and \(\mathbf{Y}\) to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.



Question:

The experimental value of \(\mathbf{d}\) is found to be smaller than the estimate obtained using Graham's law. This is due to

Match the chemical conversions in List I with the appropriate reagents in List II and select the correct answer using the code given below the lists :
 

List - I		List - II
(A)		(P)	$\left(\mathrm{i}\right) \mathrm{Hg}{\left(\mathrm{OAc}\right)}_2; \left(\mathrm{ii}\right) {\mathrm{NaBH}}_4$
(B)	​	(Q)	$\mathrm{NaOEt}$
(C)		(R)	$\mathrm{Et}-\mathrm{Br}$
(D)		(S)	$\left(\mathrm{i}\right) {\mathrm{BH}}_3; \left(\mathrm{ii}\right) {\mathrm{H}}_2{\mathrm{O}}_2/\mathrm{NaOH}$

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The reaction of compound \(\mathbf{P}\) with \(\mathrm{CH}_{3} \mathrm{MgBr}\) (excess) in \(\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}\) followed by addition of \(\mathrm{H}_{2} \mathrm{O}\) gives \(\mathbf{Q}\). The compound \(\mathbf{Q}\) on treatment with \(\mathrm{H}_{2} \mathrm{SO}_{4}\) at \(0^{\circ} \mathrm{C}\) gives \(\mathbf{R}\). The reaction of \(\mathbf{R}\) with \(\mathrm{CH}_{3} \mathrm{COCl}\) in the presence of anhydrous \(\mathrm{AlCl}_{3}\) in \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) followed by treatment with \(\mathrm{H}_{2} \mathrm{O}\) produces compound \(\mathbf{S}\). [Et in compound \(\mathbf{P}\) is ethyl group]


Question :
The reactions, \(\mathbf{Q}\) to \(\mathbf{R}\) and \(\mathbf{R}\) to \(\mathbf{S}\), are

The correct option(s) regarding the complex ${\left[Co\left(en\right){\left(N{H}_3\right)}_3\left(H_{2}O\right)\right]}^{3+}$ :-
(en $= H_{2}NC{H}_{2}C{H}_{2}N{H}_2$ ) is (are)

The complex(es), which can exhibit the type of isomerism shown by $\left[\mathrm{Pt}{\left({\mathrm{NH}}_3\right)}_2{\mathrm{Br}}_2\right]$, is(are) $\left[\mathrm{en}={\mathrm{H}}_2{\mathrm{NCH}}_2{\mathrm{CH}}_2{\mathrm{NH}}_2\right]$

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The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal \(\mathrm{M}\) is :
\(
M(s) \mid M^{+}(\alpha q ; 0.05 \text { molar }) \| M^{+}(a q ; 1 \text { molar })\) \(\mid M(s)
\)
For the above electrolytic cell the magnitude of the cell potential \(\left|E_{\text {cell }}\right|=70 \mathrm{mV}\).
Question:
If the \(0.05\) molar solution of \(M^{+}\)is replaced by a \(0.0025\) molar \(M^{+}\) solution, then the magnitude of the cell potential would be

For the given close packed structure of a salt made of cation $\mathrm{X}$ and anion $\mathrm{Y}$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction $=\frac{\mathrm{packing} \mathrm{efficiency}}{100}$)

An open-ended U-tube of uniform cross-sectional area contains water (density ${10}^3\mathrm{kg}{\mathrm{m}}^{-3}$ ). Initially the water level stands at $0.29\mathrm{m}$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800\mathrm{kg}{\mathrm{m}}^{-3}$ is added to the left arm until its length is $0.1\mathrm{m}$, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is

Two metallic rings \(A\) and \(B\), identical in shape and size but having different resistivities \(\rho_A\) and \(\rho_B\), are kept on top of two identical solenoids as shown in the figure. When current \(I\) is switched on in both the solenoids in identical manner, the rings \(A\) and \(B\) jump to heights \(h_A\) and \(h_B\), respectively, with \(h_A>h_B\). The possible relation(s) between their resistivities and their masses \(m_A\) and \(m_B\) is(are)

The reagent(s) that can selectively precipitate ${\mathrm{S}}^{2-}$ from a mixture of ${\mathrm{S}}^{2-}$ and $\mathrm{S}{\mathrm{O}}_4^{2-}$ in aqueous solution is (are)

The coordination number of \(\mathrm{Al}\) in the crystalline state of \(\mathrm{AlCl}_3\) is

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p-amino-N, N-dimethylaniline is added to a strongly acidic solution of \(X\). The resulting solution is treated with a few drops of aqueous solution of \(Y\) to yield blue colouration due to the formation of methylene blue. Treatment of the aqueous solution of \(Y\) with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves an excess addition of the reagent. Similarly, treatment of the solution of \(Y\) with the solution of potassium hexacyanoferrate(III) leads to a brown colouration due to the formation of \(Z\).
Question:
The compound \(Y\), is