At 290 K , a vessel (I) contains equal moles of three liquids (A, B, C). The boiling points of A, B and C are 350,373 and 308 K respectively. Vessel (I) is heated to 300 K and vapours were collected into vessel (II). Identify the correct statements. (Assume vessel (I) contains liquids and vapours and vessel (II) contains only vapours)
I. Vessel - I is rich in liquid \(B\)
II. Vessel - II is rich in vapour of C
III. The vapour pressures of A, B, C in Vessel (I) at 290 K follows the order \(\mathrm{C}\gt\mathrm{A}\gt\mathrm{B}\).

From the following data
\[
\begin{aligned}
& \mathrm{CH}_3 \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \\
& \Delta_r H^{\circ}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(l) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-393 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
&
\end{aligned}
\]
The standard enthalpy of formation of \(\mathrm{CH}_3 \mathrm{OH}(l)\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is

A gas obeys Charles law in the temperature range \(0-500\) \(\mathrm{K}\) at a given pressure. Its volume changes to zero at temperature of

Identify the Swarts reaction from the following:

In neutral medium potassium permanganate oxidises \(F\) to X. Identify the X

Using the data provided, find the value of equilibrium constant for the following reaction at $298 \mathrm{K}$ and $1$ atm pressure. ${\mathrm{NO}}_{\left(\mathrm{g}\right)}+\frac{1}{2}{\mathrm{O}}_2( \mathrm{g})\rightleftharpoons {\mathrm{NO}}_2( \mathrm{g})$
${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_{\left(\mathrm{g}\right)}\right)=90.4\mathrm{kJ}.{\mathrm{mol}}^{-1}$ ${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{H}}^0\left({\mathrm{NO}}_2\left(\mathrm{g}\right)\right)=32.48\mathrm{kJ}\cdot {\mathrm{mol}}^{-1}$ ${\mathrm{\Delta S}}^{\circ }@298\mathrm{K}=-70.8\mathrm{J}\cdot {\mathrm{K}}^{-1}\cdot {\mathrm{mol}}^{-1}$ $\mathrm{antilog}(0.50)=3162$

\(x\) grams of calcium carbonate was completely burnt in air. The weight of the solid residue formed is \(28 \mathrm{~g}\). What is the value of \(x\) (in grams)?

The value of \(x\) in \(\left(0, \frac{\pi}{2}\right)\) satisfying the equation \((\sin x)(\cos x)=\frac{1}{4}\) is

A pair of lines drawn through the origin forms a right angled isosceles triangle with right angle at the origin with the line \(2 x+3 y=6\). The area (in sq. units) of the triangle thus formed is

A uniform chain of length \(l\) and mass \(m\) lies on the surface of a smooth hemisphere of radius \(R(R>l)\) with one end tied to the top the hemisphere as shown in the figure.
Gravitational potential energy of the chain with respect to the base of the hemisphere is

If the differential equation obtained by eliminating A,B from \(y=\left(\sin ^{-1} x\right)^2+A \cos ^{-1} x+B\) is \(\left(a-x^2\right) y^{\prime \prime}-x y^{\prime}=b\), then \(\frac{b+a}{b-a}=\)

The rate constant, \(\mathrm{k}\) for a first order reaction, \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}(\mathrm{g}) \rightarrow \mathrm{C}_2 \mathrm{H}_4(\mathrm{~g})+\mathrm{HI}(\mathrm{g})\) is \(\mathrm{xs}^{-1}\) at \(600 \mathrm{~K}\) and \(4 \mathrm{x} \mathrm{s}^{-1}\) at \(700 \mathrm{~K}\).
The energy of activation of the reaction (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) is

If \((1, a),(b, 2)\) are conjugate points with respect to the circle \(x^2+y^2=25\), then \(4 a+2 b\) is equal to