If the equilibrium constant for the reaction,
\(\mathrm{H}_2(g)+\mathrm{I}_2(g) \rightleftharpoons 2 \mathrm{HI}(g) \text { is } K\)
what is the equilibrium constant of
\(\mathrm{HI}(g) \rightleftharpoons \frac{1}{2} \mathrm{H}_2(g)+\frac{1}{2} \mathrm{I}_2(g) ?\)

Which one of the following is more readily hydrolysed by \(\mathrm{S}_{\mathrm{N}} 1\) mechanism?

A Lewis acid ' X ' reacts with \(\mathrm{LiAIH}_4\) in ether medium to give a highly toxic gas, ' Y '. ' Y ' when heated with \(\mathrm{NH}_3\) gives a compound known as inorganic benzene. 'Y' bums in oxygen and gives \(\mathrm{H}_2 \mathrm{O}\) and ' Z '. ' Z ' is

The pair of metals refined by "vapour phase refining" is

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

Identify the initiation step \(/ \mathrm{s}(\mathrm{X})\) and termination \(\mathrm{step} / \mathrm{s}(\mathrm{Y})\) of free radical chlorination of \(\mathrm{CH}_4\) from the following.
a) \(\dot{\mathrm{C}}_3+\dot{\mathrm{C}} \mathrm{l} \rightarrow \mathrm{CH}_3-\mathrm{Cl}\)
b) \(\dot{\mathrm{Cl}}+\dot{\mathrm{C}} l \rightarrow \mathrm{Cl}-\mathrm{Cl}\)
c) \(\dot{\mathrm{C}}_3+\mathrm{Cl}_2 \rightarrow \mathrm{CH}_3-\mathrm{Cl}+\dot{\mathrm{Cl}}\)
d) \(\mathrm{Cl}_2 \rightarrow 2 \dot{\mathrm{Cl}}\)
e) \(\mathrm{CH}_4+\dot{\mathrm{Cl}} \rightarrow \dot{\mathrm{C}} \mathrm{H}_3+\mathrm{HCl}\)
f) \(\mathrm{CH}_3+\dot{\mathrm{C}}_3 \rightarrow \mathrm{CH}_3-\mathrm{CH}_3\)

At \(298 \mathrm{~K}, 0.714\) moles of liquid A is dissolved in 5.555 moles of liquid B. The vapour pressure of the resultant solution is 475 torr. The vapour pressure of pure liquid A at the same temperature is 280.7 torr. What is the vapour pressure of pure liquid B in torr?

The locus of the variable point \(\mathrm{z}=\mathrm{x}+\mathrm{iy}\) whose amplitude is always equal to \(\theta\), is

Solve the following differential equation
\[
\left(x^2+1\right) \frac{d y}{d x}+4 x y=\frac{1}{x^2+1}
\]

If the eccentricity of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) is \(\sec \alpha\), then area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is

If \(f: R \rightarrow R\) defined by
\(f(x)=\left\{\begin{array}{cc}\frac{1+3 x^2-\cos 2 x}{x^2}, & \text { for } x \neq 0 \\k & , \text { for } x=0\end{array}\right.\)
is continuous at \(x=0\), then \(k\) is equal to

A steady current is flowing in a metallic conductor of non-uniform cross section. The physical quantity which remains constant is

Three flasks of equal volumes contain ${\mathrm{CH}}_4,{\mathrm{CO}}_2\&{\mathrm{Cl}}_2$ gases respectively. They will contain equal number of molecules if