Calculate \(\Delta_r \mathrm{H}\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\) of the following reaction
\(\begin{array}{cc}\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(\mathrm{I})+7 / 2 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{I}) \\ \text { Molecule } & \Delta_{\mathrm{f}} \mathrm{H}^0\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right) \\ \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(\mathrm{I}) & -280 \\ \mathrm{CO}_2(\mathrm{~g}) & -400 \\ \mathrm{H}_2 \mathrm{O}(\mathrm{l}) & -290\end{array}\)

Which one of the following acts as autocatlyst during titration of \(\mathrm{KMnO}_4\) and oxalic acid in presence of dilute \(\mathrm{H}_2 \mathrm{SO}_4\) ?

Identify the correct pair from the following.

Which one of the following is not the correct characteristic property of physical adsorption?

In a first order reaction, the concentration of the reactant is reduced to \(1 / 8\) of the initial concentration in 75 minutes. The \(\mathrm{t}_{1 / 2}\) of the reaction (in minutes) is \((\log 2=0.30, \log 3=0.47, \log 4=0.60)\)

The sequence of reagents required to convert aniline to benzene nitrile are

The initial rates of decrease of \(\mathrm{I}_2\) in acetone - iodine reaction catalysed by \(\mathrm{H}^{+}\) are given in the table.
\(\begin{array}{|c|c|c|c|c|}
\hline \begin{array}{c}
\text { Experiment } \\
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{I}_2\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{H}^{+}\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial } \\
{\left[\mathrm{CH}_3 \mathrm{COCH}_3\right]} \\
\left(\mathrm{mol} \mathrm{L}^{-1}\right)
\end{array} & \begin{array}{c}
\text { Initial rate of decrease of } \mathrm{I}_2 \\
\left(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\right)
\end{array} \\
\hline 1 & 0.01 & 0.1 & 0.1 & 0.096 \\
2 & 0.01 & 0.2 & 0.1 & 0.192 \\
3 & 0.02 & 0.2 & 0.1 & 0.192 \\
4 & 0.01 & 0.2 & 0.2 & 0.384 \\
\hline
\end{array}\)
The order with respect to \(\mathrm{I}_2, \mathrm{H}^{+}\), acetone and total order of the reaction respectively are:

If four elements with atomic numbers \(Z-2\), \(Z-1, Z\) and \(Z+1\) are forming isoelectronic ions, the atomic number of the ion having largest size is

If the circles \(x^2+y^2+2 h x+2 k y=0\) and \(x^2+y^2+2 h^{\prime} x+2 k^{\prime} y=0\) touch each other, then \(\frac{h^{\prime} k}{h k^{\prime}}=\)

If \(\int \sqrt{\frac{x}{a^3-x^3}} d x=g(x)+c\), then \(g(x)\) is equal to :

Let \(\mathbf{u}\) and \(\mathbf{v}\) be two non-zero vectors. Then the magnitude of the cross product \(\mathbf{u} \times \mathbf{v}\) is always

If \(f(x)=\lim _{n \rightarrow \infty} n^2\left(x^{\frac{1}{n}}-x^{\frac{1}{n+1}}\right), x>0\), then \(\int x f(x) d x=\)

If the direction cosines of two lines are given by \(l+m+n=0\) and \(l^2-5 m^2+n^2=0\), then the angle between them is