The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

$$ \begin{array}{|c|c|} \hline \frac{1}{\mathrm{~T}}\left(\mathrm{~K}^{-1}\right) & \log _{10} \mathrm{~K}_{\mathrm{p}} \\ \hline 0.05 & 3.5 \\ \hline 0.06 & 2.5 \\ \hline 0.07 & 1.5 \\ \hline \end{array} $$

The magnitude of $\frac{\Delta \mathrm{H}^{\circ}}{\mathrm{R}}$ calculated from the above data is $\_\_\_\_$ . (Nearest integer)

If the half life of a first order reaction is 6.93 minutes then the time required for completion of $99 \%$ of the reaction will be $\_\_\_\_$ minutes.

(Given $: \log 2=0.3010$ )

Let $a, b \in \mathbb{C}$. Let $\alpha, \beta$ be the roots of the equation $x^2+a x+b=0$. If $\beta-\alpha=\sqrt{11}$ and $\beta^2-\alpha^2=3 i \sqrt{11}$, then $\left(\beta^3-\alpha^3\right)^2$ is equal to:

Let the sum of the first $n$ terms of an A.P. be $3 n^2+5 n$. Then the sum of squares of the first 10 terms of the A.P. is: