The standard free energy change \(\left(\Delta G^{\circ}\right)\) for the following reaction (in kJ ) at \(25^{\circ} \mathrm{C}\) is \(3 \mathrm{Ca}(\mathrm{s})+2 \mathrm{Au}^{3+}\) (aq. 1 M ) \(\rightarrow\) \(3 \mathrm{Ca}^{2+}(\mathrm{aq}, 1 \mathrm{M})+2 \mathrm{Au}(\mathrm{s})\)
(given : \(\mathrm{E}_{\mathrm{Au}^{3+} / \mathrm{Au}}^{\mathrm{o}}=+1.50 \mathrm{~V}, \mathrm{E}_{\mathrm{Ca}^{2+} / \mathrm{Ca}}^0=-2.87 \mathrm{~V}\), \(1 \mathrm{~F}=96500 \mathrm{C} \mathrm{mol}^{-1}\) )

The volume-temperature graphs of a given mass of an ideal gas at constant pressures are shown below. What is the correct order of pressures?

When bauxite powder is mixed with coke and reacted with nitrogen at \(2075 \mathrm{~K}\), carbon monoxide and \(X\) are formed. What is the gas formed when \(X\) is reacted with water?

The \% \(\left(\frac{W}{V}\right)\) of \(\mathrm{H}_2 \mathrm{O}_2\) in \(1.5 \mathrm{~N}\) solution is

The correct order of coagulating power of the following ions to coagulate the positive sol is
\(\underset{\mathrm{I}}{\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-},} \underset{\mathrm{II}}{\mathrm{Cl}^{-}}, \underset{\mathrm{III}}{\mathrm{SO}_4^{2-}}\)

The oxidation number of an element in a compound is evaluated on the basis of certain rules. Which of the following rules is not correct?
1. The oxidation number of hydrogen is always +1.
2. The algebraic sum of all the oxidation numbers of all elements in a compound is zero.
3. An element in the free or the uncombined state bears oxidation number zero.
4. In all its compounds, the oxidation number of fluorine is -1.

Which of the following is the correct order of increasing number of lone pair of electrons on the central atom?

Which of the following reactions are not feasible?
I. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CH}_2 \frac{\mathrm{HCl}}{\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2} \longrightarrow \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl}\)
II. \(\mathrm{C}_6 \mathrm{H}_6+\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl} \stackrel{\mathrm{AlCl}_3}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{CH}_3\right)_2\)
III. \(\mathrm{CH}_3 \mathrm{CHClCH}_2 \mathrm{Cl} \underset{\Delta}{\stackrel{\mathrm{KOH}}{\longrightarrow}} \mathrm{CH}_3 \mathrm{C} \equiv \stackrel{+}{\mathrm{CH}}\)
IV. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCH}_3 \stackrel{\mathrm{KMnO}_4 / \mathrm{H}^{+}}{\longrightarrow} \mathrm{CH}_3 \mathrm{COOH}\)

If \(\cos (\theta-\alpha), \cos \theta\) and \(\cos (\theta+\alpha)\) are in harmonic progressions, then \(2 \tan ^2 \theta=\)

Benzene and toluene form an ideal solution over the entire range of composition. The vapour pressure of pure benzene and toluene at \(T(\mathrm{~K})\) are \(50 \mathrm{~mm} \mathrm{Hg}\) and \(40 \mathrm{~mm} \mathrm{Hg}\) respectively. What is the mole fraction of toluene in vapour phase when \(117 \mathrm{~g}\) of benzene is mixed with \(46 \mathrm{~g}\) of toluene? (molar mass of benzene and toluene are 78 and \(92 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively)

From the following, identify the reactions which are responsible for depletion of ozone layer.
\(\begin{aligned}
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{NO}_2(g) \rightarrow \mathrm{ClONO}_2(g) \\
& \mathrm{CF}_2 \mathrm{Cl}_2(g) \xrightarrow{\text { uv }} \mathrm{Cl}(g)+\dot{\mathrm{CF}}_2 \mathrm{Cl}(g) \\
& \dot{\mathrm{Cl}}(g)+\mathrm{CH}_4(g) \rightarrow \mathrm{HCl}(g)+\dot{\mathrm{C}} \mathrm{H}_3(g) \\
& \dot{\mathrm{C}} \mathrm{l}(\mathrm{g})+\mathrm{O}_3(g) \rightarrow \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}_2(g) \\
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}(g) \rightarrow \dot{\mathrm{C}} \mathrm{l}(g)+\mathrm{O}_2(g)
\end{aligned}\)

The length of the subtangent at \((2,2)\) to the curve \(x^5=2 y^4\) is

$(\sin \theta -i\cos \theta {)}^3$ is equal to