Among the following, intensive property is (properties are)

A decapeptide (molecular weight 796) on complete hydrolysis gives glycine (molecular weight 75), alanine and phenylalanine. Glycine contributes \(47.0 \%\) to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is

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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

The conductance of $0.0015\mathrm{ }\mathrm{M}$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $\mathrm{Pt}$electrodes. The distance between the electrodes is $120\mathrm{ }\mathrm{cm}$ with an area of cross-section of $1 {\mathrm{cm}}^2$. The conductance of this solution was found to be $5\times {10}^{-7}\mathrm{S}$ . The $\mathrm{pH}$of the solution is $4$. The value of limiting molar conductivity of this weak monobasic acid in aqueous solution is $\mathrm{ }\mathrm{Z}\mathrm{ }\times \mathrm{ }{10}^2\mathrm{S}\mathrm{ }{\mathrm{cm}}^{-1}{\mathrm{mol}}^{-1}.$ The value of $\mathrm{Z}$is.

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.

Match the rate expressions in LIST-I for the decomposition of \(\mathrm{X}\) with the corresponding profiles provided in LIST-II. \(X_s\) and \(\mathrm{k}\) are constants having appropriate units.

The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown below is

When water is filled carefully in a glass, one can fill it to a height $h$ above the rim of the glass due to the surface tension of water. To calculate $h$ just before water starts flowing, model the shape of the water above the rim as a disc of thickness $h$ having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are ${10}^3\mathrm{kg}{\mathrm{m}}^{-3},0.07\mathrm{N}{\mathrm{m}}^{-1}$ and $10\mathrm{m}{\mathrm{s}}^{-2}$ respectively, the value of $h$(in $\mathrm{mm}$)is ________.

Which of the following liberates ${\mathrm{O}}_2$ upon hydrolysis?

Among the following, the correct statement(s) about polymers is(are)

For \(r=0,1, \ldots, 10\), let \(A_r, B_r\) and \(C_r\) denote, respectively, the coefficient of \(x^r\) in the expansions of \((1+x)^{10}\), \((1+x)^{20}\) and \((1+x)^{30}\). Then \(\sum_{r=1}^{10} A_r\left(B_{10} B_r-C_{10} A_r\right)\) is equal to

Let ${\ell }_1$ and ${\ell }_2$ be the lines ${\overrightarrow{r}}_1=\lambda \left(\hat{i}+\hat{j}+\hat{k}\right)$ and ${\overrightarrow{r}}_2=\left(\hat{j}-\hat{k}\right)+\mu \left(\hat{i}+\hat{k}\right)$, respectively, Let $X$ be the set of all the planes $H$ that contain the line ${\ell }_1$. For a plane $H$, let $d\left(H\right)$ denote the smallest possible distance between the points of ${\ell }_2$ and $H$. Let $H_0$ be a plane in $X$ for which $d\left(H_0\right)$ is the maximum value of $d\left(H\right)$ as $H$ varies over all planes in $X$. Match each entry in List-I to the correct entries in List-II.

	List-I		List-II
$\left(\mathrm{P}\right)$	The value of $d\left(H_0\right)$ is	$\left(1\right)$	$\sqrt{3}$
$\left(\mathrm{Q}\right)$	The distance of the point $\left(0, 1, 2\right)$ from $H_0$ is	$\left(2\right)$	$\frac{1}{\sqrt{3}}$
$\left(\mathrm{R}\right)$	The distance of origin from $H_0$ is	$\left(3\right)$	$0$
$\left(\mathrm{S}\right)$	The distance of origin from the point of intersection of planes $y=z, x=1$ and $H_0$ is	$\left(4\right)$	$\sqrt{2}$
		$\left(5\right)$	$\frac{1}{\sqrt{2}}$

The correct option is

For the octahedral complexes of $\mathrm{F}{\mathrm{e}}^{3+}$ in $\mathrm{S}\mathrm{C}{\mathrm{N}}^{-}$ (thiocyanato-S) and in $\mathrm{C}{\mathrm{N}}^{-}$ ligand environments, the difference between the spin-only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is
[Atomic number of Fe = 26]