Consider the following reaction at \(298 \mathrm{~K}\). \(\frac{3}{2} \mathrm{O}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{O}_{3(\mathrm{~g})} \cdot \mathrm{K}_{\mathrm{P}}=2.47 \times 10^{-29} \text {. }\) \(\Delta_{\mathrm{r}} \mathrm{G}^{\ominus}\) for the reaction is_______ \(kJ\). (Given R \(\left.=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)\)

The correct decreasing order for acidic strength is

White precipitate of \(AgCl\) dissolves in aqueous ammonia solution due to formation of ..... .

Given below are two statements:
Statement I: In Lassaigne's test, the covalent organic molecules are transformed into ionic compounds.
Statement II: The sodium fusion extract of an organic compound having N and S gives prussian blue colour with \(\mathrm{FeSO}_4\) and \(\mathrm{Na}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]\)
In the light of the above statements, choose the correct answer from the options given below.

For the given compounds, the correct order of increasing \(\mathrm{pK}_{\mathrm{a}}\) value:

The resistance of conductivity cell containing \(0.01\, M\, KCl\) solution at \(298\, K\) is \(1750 \,\Omega\). If the conductively of \(0.01\, M \,KCl\) solution at \(298\, K\) is \(0.152 \times 10^{-3} \,S \,cm ^{-1}\), then the cell constant of the conductivity cell is \(..........\,\times 10^{-3} \,cm ^{-1}\).

The compound A, \(C_{8}H_{8}O_{2}\) reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol as

All five letter words are made using all the letters \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}\) and arranged as in an English dictionary with serial numbers. Let the word at serial number \(n\) be denoted by \(W_n\). Let the probability \(\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)\) of choosing the word \(\mathrm{W}_{\mathrm{n}}\) satisfy \(\mathrm{P}\left(\mathrm{W}_{\mathrm{n}}\right)=2 \mathrm{P}\left(\mathrm{W}_{\mathrm{n}-1}\right), \mathrm{n} \gt 1\).
If \(\mathrm{P}(\mathrm{CDBEA})=\frac{2^\alpha}{2^\beta-1}, \alpha, \beta \in \mathbb{N}\), then \(\alpha+\beta\) is equal to : _______

The  the circle passing through the foci of the \(\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1\) and having centre at \((0,3) \) is

A student has been given a compound "x" of molecular formula - \(C _6 H _7 N\). 'x' is sparingly soluble in water. However, on addition of dilute mineral acid , 'x' becomes soluble in water. 'x' when treated with \(CHCl _3\) and KOH (alc.) 'y' is produced. 'y' has a specific unpleasant smell. On treatment with benzenesulphonyl chloride, '\(x\)' gives a compound '\(z\)' which is soluble in alkali. The number of different "H" atoms present in '\(z\)' is:-

Element not showing variable oxidation state is :

Figure shows a part of an electric circuit. The potentials at points \(a , b\) and \(c\) are \(30\,V , 12\,V\) and \(2\,V\) respectively. The current through the \(20 \Omega\) resistor will be \(........\,A\)

\(SO _{2} Cl _{2}\) on reaction with excess of water results into acidic mixture \(SO _{2} Cl _{2}+2 H _{2} O \rightarrow H _{2} SO _{4}+2 HCl\) \(16\,moles\) of \(NaOH\) is required for the complete neutralisation of the resultant acidic mixture. The number of moles of \(SO _{2} Cl _{2}\) used is.