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 :

Let $$\alpha$$, $$\beta$$ be the roots of the equation $$x^{2}-\sqrt{2} x+\sqrt{6}=0$$ and $$\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1$$ be the roots of the equation $$x^{2}+a x+b=0$$. Then the roots of the equation $$x^{2}-(a+b-2) x+(a+b+2)=0$$ are :