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The reactions of \(\mathrm{Cl}_{2}\) gas with cold-dilute and hot-concentrated \(\mathrm{NaOH}\) in water give sodium salts of two (different) oxoacids of chlorine, \(\boldsymbol{P}\) and \(\boldsymbol{Q}\), respectively. The \(\mathrm{Cl}_{2}\) gas reacts with \(\mathrm{SO}_{2}\) gas, in presence of charcoal, to give a product \(\boldsymbol{R}\). \(\boldsymbol{R}\) reacts with white phosphorus to give a compound \(\boldsymbol{S}\). On hydrolysis, \(\boldsymbol{S}\) gives an oxoacid of phosphorus, \(\boldsymbol{T}\).
Question:
\(R, S\) and \(T\), respectively, are

If the value of Avogadro number is $6.023\times {10}^{23}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{–1}$ and the value of Boltzmann constant is $1.380\times {10}^{-23}\mathrm{ }\mathrm{J}{\mathrm{K}}^{-1}$ , then the number of significant digits in the calculated value of the universal gas constant is

(I) 1, 2-dihydroxy benzene
(II) 1, 3-dihydroxy benzene
(III) 1, 4-dihydroxy benzene
(IV) Hydroxy benzene
The increasing order of boiling points of above mentioned alcohols is

${}_{92}{}^{238}\mathrm{U}$ is known to undergo radioactive decay to form ${}_{82}{}^{206}\mathrm{Pb}$ by emitting alpha and bet a particles. A rock initially contained $68\times {10}^{-6}\mathrm{g}$ of ${}_{92}{}^{238}\mathrm{U}$. If the number of alpha particles that it would emit during its radioactive decay of ${}_{92}{}^{238}\mathrm{U}$ to ${}_{82}{}^{206}\mathrm{Pb}$ in three half-lives is $\mathrm{Z}\times {10}^{18}$, then what is the value of $\mathrm{Z}$?

In the reaction scheme shown below,$\mathrm{Q},\mathrm{R},$ and$\mathrm{S}$ are the major products.

The correct structure of

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)

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Thermal decomposition of gaseous \(\mathrm{X}_{2}\) to gaseous \(\mathrm{X}\) at \(298 \mathrm{~K}\) takes place according to the following equation:

\(\mathrm{X}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{X}(\mathrm{g})\)

The standard reaction Gibbs energy, \(\Delta_{r} G^{\circ}\), of this reaction is positive. At the start of the reaction, there is one mole of \(\mathrm{X}_{2}\) and no \(\mathrm{X}\). As the reaction proceeds, the number of moles of \(\mathrm{X}\) formed is given by \(\beta\). Thus, \(\beta_{\text {equilibrium }}\) is the number of moles of \(\mathrm{X}\) formed at equilibrium. The reaction is carried out at a constant total pressure of \(2\) bar. Consider the gases to behave ideally. (Given : \(R=0.083 \mathrm{~L}\) bar \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\) )

Question:
The equilibrium constant \(K_{P}\) for this reaction at \(298 \mathrm{~K},\) in terms of \(\beta_{equilibrium}\) is

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Tollen's reagent is used for the detection of aldehyde when a solution of \(\mathrm{AgNO}_3\) is added to glucose with \(\mathrm{NH}_4 \mathrm{OH}\) then gluconic acid is formed
\(\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \)
\( \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)\) \(+~2 \mathrm{H}^{+}+2 e^{-} ; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \)
\( \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ;\) \(E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\)
[Use \(2.303 \times \frac{R T}{F}=0.0592\) and \(\frac{F}{R T}=38.92\) at \(298 \mathrm{~K}\) ]
Question:
When ammonia is added to the solution, \(\mathrm{pH}\) is raised to 11 . Which half-cell reaction is affected by \(\mathrm{pH}\) and by how much?

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant $\mathrm{K}$ in terms of change in entropy is described by:

An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K . Its cell potential is \(\frac{\boldsymbol{X}}{\boldsymbol{F}} \times 10^3\) volts, where \(\boldsymbol{F}\) is the Faraday constant. The value of \(\boldsymbol{X}\) is \(\qquad\) .
Use : Standard Gibbs energies of formation at 298 K are : \(\Delta_f G_{\mathrm{CO}_2}^{\circ}=-394 \mathrm{~kJ} \mathrm{~mol}^{-1}\);
\(\Delta_f G_{\text {water }}^{\circ}=-237 \mathrm{~kJ} \mathrm{~mol}^{-1} ; \Delta_f G_{\text {butane }}^{\circ}\) \(=-18 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Suppose that
Box-I contains $8$ red, $3$ blue and $5$ green balls,
Box-ll contains $24$ red, $9$ blue and $15$ green balls,
Box-III contains $1$ blue, $12$ green and $3$ yellow balls,
Box-IV contains $10$ green, $16$ orange and $6$ white balls.
A ball is chosen randomly from Box-l; call this ball $b$. If $b$ is red then a ball is chosen randomly from Box-ll, if $b$ is blue then a ball is chosen randomly from Box-III, and if $b$ is green then a ball is chosen randomly from Box-IV. The conditional probability of the event 'one of the chosen balls is white' given that the event 'at least one of the chosen balls is green' has happened, is equal to

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.

	List I		List II
A.		$\mathrm{P}.$	$2\mathrm{r}$
B.		$\mathrm{Q}.$	$\frac{\mathrm{r}}{2}$
C.		$\mathrm{R}.$	$-\mathrm{r}$
D.		$\mathrm{S}.$	$\mathrm{r}$

The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is (are)