A closed vessel contains $10 \mathrm{~g}$ of an ideal gas $\mathbf{X}$ at $300 \mathrm{~K}$, which exerts $2 \mathrm{~atm}$ pressure. At the same temperature, $80 \mathrm{~g}$ of another ideal gas $\mathbf{Y}$ is added to it and the pressure becomes $6 \mathrm{~atm}$. The ratio of root mean square velocities of $\mathbf{X}$ and $\mathbf{Y}$ at $300 \mathrm{~K}$ is

At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid $\left(\mathrm{HNO}_2\right)$ gives the species

Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is

Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other.

$$ \text { [en }=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2 \text { ] } $$

Among the following, the correct statement(s) for electrons in an atom is(are)

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)

The option(s) in which at least three molecules follow Octet Rule is(are)

Consider the following volume-temperature $(\mathrm{V}-\mathrm{T})$ diagram for the expansion of 5 moles of an ideal monoatomic gas.

Considering only $\mathrm{P}-\mathrm{V}$ work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence $\mathbf{X} \rightarrow \mathbf{Y} \rightarrow \mathbf{Z}$ is ____________.

[Use the given data: Molar heat capacity of the gas for the given temperature range, $\mathrm{C}_{\mathrm{V}, \mathrm{m}}=12 \mathrm{~J} \mathrm{~K}^{-1}$ $\mathrm{mol}^{-1}$ and gas constant, $\left.\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

Consider the following reaction,

$$ 2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) $$

which follows the mechanism given below :

$$ \begin{array}{ll} 2 \mathrm{NO}(\mathrm{g}) \stackrel{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g}) & \text { (fast equlibrium) } \\\\ \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_2} \mathrm{~N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) & \text { (slow reaction) } \\\\ \mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_3} \mathrm{~N}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) & \text { (fast reaction) } \end{array} $$

The order of the reaction is __________.

Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. $\mathrm{NaOH}$ solution, gives $\mathbf{P}$ and $\mathbf{Q}$. Compound $\mathbf{P}$ does not give Tollens' test, whereas $\mathbf{Q}$ on acidification gives positive Tollens' test. Treatment of $\mathbf{P}$ with excess cyclohexanone in the presence of catalytic amount of $p$-toluenesulfonic acid (PTSA) gives product $\mathbf{R}$.

Sum of the number of methylene groups $\left(-\mathrm{CH}_2-\right)$ and oxygen atoms in $\mathbf{R}$ is __________.

Among $\mathrm{V}(\mathrm{CO})_6, \mathrm{Cr}(\mathrm{CO})_5, \mathrm{Cu}(\mathrm{CO})_3, \mathrm{Mn}(\mathrm{CO})_5, \mathrm{Fe}(\mathrm{CO})_5,\left[\mathrm{Co}(\mathrm{CO})_3\right]^{3-},\left[\mathrm{Cr}(\mathrm{CO})_4\right]^{4-}$, and $\operatorname{Ir}(\mathrm{CO})_3$, the total number of species isoelectronic with $\mathrm{Ni}(\mathrm{CO})_4$ is _________.

[Given, atomic number: $\mathrm{V}=23, \mathrm{Cr}=24, \mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27, \mathrm{Ni}=28, \mathrm{Cu}=29, \mathrm{Ir}=77$ ]

In the following reaction sequence, the major product $\mathbf{P}$ is formed.

Glycerol reacts completely with excess $\mathbf{P}$ in the presence of an acid catalyst to form $\mathbf{Q}$. Reaction of $\mathbf{Q}$ with excess $\mathrm{NaOH}$ followed by the treatment with $\mathrm{CaCl}_2$ yields Ca-soap $\mathbf{R}$, quantitatively. Starting with one mole of $\mathbf{Q}$, the amount of $\mathbf{R}$ produced in gram is __________.

[Given, atomic weight: $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Na}=23, \mathrm{Cl}=35, \mathrm{Ca}=40$ ]

Among the following complexes, the total number of diamagnetic species is ___________.

$\left[\mathrm{Mn}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{MnCl}_6\right]^{3-},\left[\mathrm{FeF}_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_6\right]^{3+}$, and $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}$

[Given, atomic number: $\mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27$;

$$ \text { en } \left.=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right] $$

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition.

The limiting ionic conductivity $\left(\Lambda_0\right)$ values (in $\mathrm{mS} \mathrm{m}{ }^2 \mathrm{~mol}^{-1}$ ) for different ions in aqueous solutions are given below:

$$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline \text { Ions } & \mathrm{Ag}^{+} & \mathrm{K}^{+} & \mathrm{Na}^{+} & \mathrm{H}^{+} & \mathrm{NO}_3^{-} & \mathrm{Cl}^{-} & \mathrm{SO}_4^{2-} & \mathrm{OH}^{-} & \mathrm{CH}_3 \mathrm{COO}^{-} \\ \hline \Lambda_0 & 6.2 & 7.4 & 5.0 & 35.0 & 7.2 & 7.6 & 16.0 & 19.9 & 4.1 \\ \hline \end{array} $$

For different combinations of titrates and titrants given in List-I, the graphs of 'conductance' versus 'volume of titrant' are given in List-II.

Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

LIST-I	LIST-II
(P) Titrate: KCl Titrant: AgNO$_3$
(Q) Titrate: AgNO$_3$ Titrant: KCl
(R) Titrate: NaOH Titrant: HCl
(S) Titrate: NaOH Titrant: CH$_3$COOH

Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option.

List-I	List-II
(P) XeF$_2$	(1) Trigonal bipyramidal and two lone pair of electrons
(Q) XeF$_4$	(2) Tetrahedral and one lone pair of electrons
(R) XeO$_3$	(3) Octahedral and two lone pair of electrons
(S) XeO$_3$F$_2$	(4) Trigonal bipyramidal and no lone pair of electrons
	(5) Trigonal bipyramidal and three lone pair of electrons

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

List-I	List-II

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.

List-I	List-II