Number of carbocations from the following that are not stabilized by hyperconjugation is _______.

Choose the correct statements from the following. \(A\). \(\mathrm{Mn}_2 \mathrm{O}_7\) is an oil at room temperature \(B\). \(\mathrm{V}_2 \mathrm{O}_4\) reacts with acid to give \(\mathrm{VO}_2^{2+}\) \(C\). \(\mathrm{CrO}\) is a basic oxide \(D\). \(\mathrm{V}_2 \mathrm{O}_5\) does not react with acid Choose the correct answer from the options given below :

Two solids dissociate as follows \(A\left( s \right) \rightleftharpoons B\left( g \right) + C\left( g \right);{K_{{p_1}}} = x\,at{m^2}\) \(D\left( s \right) \rightleftharpoons C\left( g \right) + E\left( g \right);{K_{{p_2}}} = y\,at{m^2}\)  The total pressure when both the solids dissociate simultaneously is

The standard entropy change for the reaction \(4 Fe ( s )+3 O _{2}( g ) \rightarrow 2 Fe _{2} O _{3}( s )\) is \(-550\, JK ^{-1}\) at \(298 \,K\). [Given : The standard enthalpy change for the reaction is \(-165\, kJ\, mol ^{-1}\). The temperature in \(K\) at which the reaction attains equilibrium is ... . (Nearest Integer)

The number of bent-shaped molecule/s from the following is \(.....\). \(N _3^{-}, NO _2^{-}, I _3^{-}, O _3, SO _2\)

The results given in the below table were obtained during kinetic studies of the following reaction: \(2 A + B \longrightarrow C + D\)

Experiment	\([ A ] / molL ^{-1}\)	\([ B ] / molL ^{-1}\)	Initial \(rate/molL\) \(^{-1}\) \(\min ^{-1}\)
\(I\)	\(0.1\)	\(0.1\)	\(6.00 \times 10^{-3}\)
\(II\)	\(0.1\)	\(0.2\)	\(2.40 \times 10^{-2}\)
\(III\)	\(0.2\)	\(0.1\)	\(1.20 \times 10^{-2}\)
\(IV\)	\(X\)	\(0.2\)	\(7.20 \times 10^{-2}\)
\(V\)	\(0.3\)	\(Y\)	\(2.88 \times 10^{-1}\)

\(X\) and \(Y\) in the given table are respectively :  

One mole of the octahedral complex compound \(\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}_3\) gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with excess of \(\mathrm{AgNO}_3\) solution to yield two moles of \(\mathrm{AgCl}_{(\mathrm{s})}\). The structure of the complex is which?

An optically active alkyl halide \(\mathrm{C}_4 \mathrm{H}_9 \mathrm{Br}\) [A] reacts with hot KOH dissolved in ethanol and forms alkene [B] as major product which reacts with bromine to give dibromide [C]. The compound [C] is converted into a gas [D] upon reacting with alcoholic \(\mathrm{NaNH}_2\). During hydration 18 gram of water is added to 1 mole of gas [D] on warming with mercuric sulphate and dilute acid at 333 K to form compound [E]. The IUPAC name of compound \([\mathrm{E}]\) is _______.

If \(S=\frac{7}{5}+\frac{9}{5^{2}}+\frac{13}{5^{3}}+\frac{19}{5^{4}}+\ldots .\), then \(160 \mathrm{~S}\) is equal to....... .

Let a variable line of slope \(m>0\) passing through the point \((4,-9)\) intersect the coordinate axes at the points \(A\) and \(B\). the minimum value of the sum of the distances of \(\mathrm{A}\) and \(\mathrm{B}\) from the origin is

In the above conversion the correct sequence of reagents to be added is

\(2.7 \mathrm{Kg}\) of each of water and acetic acid are mixed, The freezing point of the solution will be \(-\mathrm{x}^{\circ} \mathrm{C}\). Consider the acetic acid does not dimerise in water, nor dissociates in water \(\mathrm{x}=\) _______ (nearest integer) [Given : Molar mass of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\), acetic acid \(=60 \mathrm{~g} \mathrm{~mol}^{-1}\) ] \({ }^{\mathrm{K}_{\mathrm{f}}} \mathrm{H}_2 \mathrm{O}: 1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) \(\mathrm{K}_{\mathrm{r}}\) acetic acid : \(3.90 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) freezing point: \(\mathrm{H}_2 \mathrm{O}=273 \mathrm{~K}\), acetic acid \(=290 \mathrm{~K}\) ]

\(\begin{aligned}
& \mathrm{S}(\mathrm{~g})+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\mathrm{~g})+2 x \mathrm{kcal} \\
& \mathrm{SO}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{SO}_3(\mathrm{~g})+y \mathrm{kcal}
\end{aligned}\)

The heat of formation of \(\mathrm{SO}_2(\mathrm{~g})\) is given by :