A $$\to$$ B

The rate constants of the above reaction at 200 K and 300 K are 0.03 min$$^{-1}$$ and 0.05 min$$^{-1}$$ respectively. The activation energy for the reaction is ___________ J (Nearest integer)

(Given : $$\mathrm{ln10=2.3}$$

$$\mathrm{R=8.3~J~K^{-1}~mol^{-1}}$$

$$\mathrm{\log5=0.70}$$

$$\mathrm{\log3=0.48}$$

$$\mathrm{\log2=0.30}$$)

For reaction : $$\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{3}(\mathrm{~g})$$

$$\mathrm{K}_{\mathrm{p}}=2 \times 10^{12}$$ at $$27^{\circ} \mathrm{C}$$ and $$1 \mathrm{~atm}$$ pressure. The $$\mathrm{K}_{\mathrm{c}}$$ for the same reaction is ____________ $$\times 10^{13}$$. (Nearest integer)

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

The number of real roots of the equation $$\sqrt{x^{2}-4 x+3}+\sqrt{x^{2}-9}=\sqrt{4 x^{2}-14 x+6}$$, is :

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is :