A mixture of 1 mole of $$\mathrm{H}_{2} \mathrm{O}$$ and 1 mole of $$\mathrm{CO}$$ is taken in a 10 litre container and heated to $$725 \mathrm{~K}$$. At equilibrium $$40 \%$$ of water by mass reacts with carbon monoxide according to the equation :

$$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})$$.

The equilibrium constant $$\mathrm{K}_{\mathrm{c}} \times 10^{2}$$ for the reaction is ____________. (Nearest integer)

Solid fuel used in rocket is a mixture of $$\mathrm{Fe}_{2} \mathrm{O}_{3}$$ and $$\mathrm{Al}$$ (in ratio 1 : 2). The heat evolved $$(\mathrm{kJ})$$ per gram of the mixture is ____________. (Nearest integer)

Given: $$\Delta \mathrm{H}_{\mathrm{f}}^{\theta}\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)=-1700 \mathrm{~kJ} \mathrm{~mol}^{-1}$$

$$\Delta \mathrm{H}_{\mathrm{f}}^{\theta}\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)=-840 \mathrm{~kJ} \mathrm{~mol}^{-1}$$

Molar mass of Fe, Al and O are 56, 27 and 16 g mol$$^{-1}$$ respectively.

In an electrochemical reaction of lead, at standard temperature, if $$\mathrm{E}^{0}\left(\mathrm{~Pb}^{2+} / \mathrm{Pb}\right)=\mathrm{m}$$ Volt and $$\mathrm{E}^{0}\left(\mathrm{~Pb}^{4+} / \mathrm{Pb}\right)=\mathrm{n}$$ Volt, then the value of $$\mathrm{E}^{0}\left(\mathrm{~Pb}^{2+} / \mathrm{Pb}^{4+}\right)$$ is given by $$\mathrm{m-x n}$$. The value of $$\mathrm{x}$$ is ___________. (Nearest integer)

Let R be a rectangle given by the lines $$x=0, x=2, y=0$$ and $$y=5$$. Let A$$(\alpha,0)$$ and B$$(0,\beta),\alpha\in[0,2]$$ and $$\beta\in[0,5]$$, be such that the line segment AB divides the area of the rectangle R in the ratio 4 : 1. Then, the mid-point of AB lies on a :