A sample of $$0.125 \mathrm{~g}$$ of an organic compound when analyzed by Duma's method yields $$22.78 \mathrm{~mL}$$ of nitrogen gas collected over $$\mathrm{KOH}$$ solution at $$280 \mathrm{~K}$$ and $$759 \mathrm{~mm}\, \mathrm{Hg}$$. The percentage of nitrogen in the given organic compound is __________. (Nearest integer)

Given :

(a) The vapour pressure of water of $$280 \mathrm{~K}$$ is $$14.2 \mathrm{~mm} \,\mathrm{Hg}$$.

(b) $$\mathrm{R}=0.082 \mathrm{~L}$$ atm $$\mathrm{K}^{-1} \mathrm{~mol}^{-1}$$

For a reaction, given below is the graph of $$\ln k$$ vs $${1 \over T}$$. The activation energy for the reaction is equal to ____________ $$\mathrm{cal} \,\mathrm{mol}^{-1}$$. (nearest integer)

(Given : $$\mathrm{R}=2 \,\mathrm{cal} \,\mathrm{K}^{-1} \,\mathrm{~mol}^{-1}$$ )

Among the following the number of state variables is ______________.

Internal energy (U)

Volume (V)

Heat (q)

Enthalpy (H)

$$ \text { Let } S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\} \text { and } $$

$$T=\left\{x \in \mathbb{Z}: x^{2}-7|x|+9 \leq 0\right\} \text {. } $$

Then the number of elements in $$\mathrm{S} \cap \mathrm{T}$$ is :