The rate constant $(k)$ of a reaction is measured at different temperatures $(T),$ and the data are plotted in the given figure. The activation energy of the reaction in $kJ\, mol^{-1}$ is :
($R$ is gas constant)

$A$ reaction has an activation energy of $209 \, kJ \, mol^{-1}$. The rate increases $10$-fold when the temperature is increased from $27^{\circ} C$ to $X^{\circ} C$. The temperature $X$ is closest to
[Gas constant,$R = 8.314 \, J \, mol^{-1} \, K^{-1}$ ]

In a bimolecular reaction,the steric factor $P$ was experimentally determined to be $4.5$. The correct option$(s)$ among the following is(are)
$[A]$ The activation energy of the reaction is unaffected by the value of the steric factor
$[B]$ Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation
$[C]$ Since $P=4.5$,the reaction will not proceed unless an effective catalyst is used
$[D]$ The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally

Which of the following statements is correct?

Fill in the blanks:
$1.$ Common collision means ......... phenomenon in species.
$2.$ In collision theory,activation energy and proper orientation of the molecules together determine the ......... for an effective collision.

When the temperature changes from $20\,^oC$ to $50\,^oC$,the rate of reaction becomes three times. The activation energy $(E_a)$ for the reaction is $.... \, kJ \, mol^{-1}$ $(R = 8.314 \, J \, K^{-1} \, mol^{-1})$.