$2 \mathrm{mol}$ of $\mathrm{Hg}\left(\mathrm{g}\right)$ is combusted in a fixed volume bomb calorimeter with excess of ${\mathrm{O}}_2$ at $298 \mathrm{K}$ and $1 \mathrm{atm}$ into $\mathrm{HgO}\left(\mathrm{s}\right)$. During the reaction, temperature increases from $298.0 \mathrm{K}$ to $312.8 \mathrm{K}$. If heat capacity of the bomb calorimeter and enthalpy of formation of $\mathrm{Hg}\left(\mathrm{g}\right)$ are $20.00 \mathrm{kJ} {\mathrm{K}}^{-1}$ and $61.32 \mathrm{kJ} {\mathrm{mol}}^{-1}$ at $298 \mathrm{K}$, respectively, the calculated standard molar enthalpy of formation of $\mathrm{HgO}\left(\mathrm{s}\right)$ at $298 \mathrm{K}$ is $\mathrm{X} {\mathrm{kJmol}}^{-1}$. The value of $\left|\mathrm{X}\right|$ is___[Given: Gas constant $\mathrm{R}=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$]

The correct statement(s) about the following sugars \(X\) and \(Y\) is (are)

Under the same reaction conditions, initial concentration of \(1.386 \mathrm{~mol} \mathrm{dm}^{-3}\) of a substance becomes half in 40 s and 20 s through first-order and zero-order kinetics, respectively. Ratio \(\left(\frac{k_1}{k_0}\right)\) of the rate constants for first order \(\left(k_1\right)\) and zero \(\operatorname{order}\left(k_0\right)\) of the reaction is

Consider the following reaction.

On estimation of bromine in $1.00 \mathrm{g}$ of $\mathrm{R}$ using Carius method, the amount of $\mathrm{AgBr}$ formed (in $\mathrm{g}$) is____[Given: Atomic mass of \(\text H =1,\text C =12,\text O =16,\text P =31,\text {Br}\) \(=80,\text{Ag} =108]\)

Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the \(4 \times 4\) matrix given in the ORS.

When benzene sulphonic acid and \(p\)-nitrophenol are treated with \(\mathrm{NaHCO}_3\), the gases released respectively are

The cyanide process of gold extraction involves leaching out gold from its ore with ${\mathrm{C}\mathrm{N}}^{-}$ in the presence of $\mathrm{Q}$ in water to form $\mathrm{R}$ . Subsequently, $\mathrm{R}$ is treated with $\mathrm{T}$ to obtain $\mathrm{A}\mathrm{u}$ and $\mathrm{Z}$ . Choose the correct option(s).

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500 Hz$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length $50.7 cm and 83.9 cm$ . Which of the following statements is (are) true?

An organic compound \(\mathbf{P}\) having molecular formula \(\mathrm{C}_6 \mathrm{H}_6 \mathrm{O}_3\) gives ferric chloride test and does not have intramolecular hydrogen bond. The compound \(\mathbf{P}\) reacts with 3 equivalents of \(\mathrm{NH}_2 \mathrm{OH}\) to produce oxime \(\mathbf{Q}\). Treatment of \(\mathbf{P}\) with excess methyl iodide in the presence of \(\mathrm{KOH}\) produces compound \(\mathbf{R}\) as the major product. Reaction of \(\mathbf{R}\) with excess iso-butylmagnesium bromide followed by treatment with \(\mathrm{H}_3 \mathrm{O}^{+}\)gives compound \(\mathrm{S}\) as the major product.
The total number of methyl \(\left(-\mathrm{CH}_3\right)\) group(s) in compound \(\mathbf{S}\) is ________. (consider maximum value if there are two values)

The inductors of two $LR$ circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady-state values is_______$\mathrm{mJ}$.

Match each coordination compound in List-I with an appropriate pair of characteristics from List-II and select the correct answer using the code given below the lists
\(\left\{\right.\)en \(= H _2 NCH _2 CH _2 NH _2 ;\) atomic numbers \(\left.: T _{ i }=22, Cr =24 ; Co =27 ; Pt =78\right\}\)

	List – I		List – II
A.	$\left[\mathrm{C}\mathrm{r}{\left(\mathrm{N}{\mathrm{H}}_3\right)}_4\mathrm{C}{\mathrm{l}}_2\right]\mathrm{C}\mathrm{l}$	P.	Paramagnetic and exhibits ionization isomerism
B.	$\left[\mathrm{T}\mathrm{i}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5\mathrm{ }\mathrm{C}\mathrm{l}\right]{\left(\mathrm{N}{\mathrm{O}}_3\right)}_2$	Q.	Diamagnetic and exhibits cis - trans isomerism
C.	$\left[\mathrm{P}\mathrm{t}\left(\mathrm{e}\mathrm{n}\right)\left(\mathrm{N}{\mathrm{H}}_3\right)\mathrm{C}\mathrm{l}\right]\mathrm{N}{\mathrm{O}}_3$	R.	Paramagnetic and exhibits cis - trans isomerism
D.	$\left[\mathrm{C}\mathrm{o}{\left(\mathrm{N}{\mathrm{H}}_3\right)}_4{\left(\mathrm{N}{\mathrm{O}}_3\right)}_2\right]\mathrm{N}{\mathrm{O}}_3$	S.	Diamagnetic and exhibits ionization isomerism

The compound(s) formed upon combustion of sodium metal in excess air is (are)

Paragraph:
Read the following passage and answer the questions.
Question:
The value of \(|U|\) is