In a first order reaction, the concentration of the reactant is reduced to $1 / 8$ of the initial concentration in 75 minutes. The $t_{1 / 2}$ of the reaction (in minutes) is $(\log 2=0.30, \log 3=0.47, \log 4=0.60)$

At $T(\mathrm{~K})$ the following equation is obtained for a first order reaction $\log \frac{k}{A}=-\frac{x}{T}$. The activation energy for this reaction is equal to ( $R=$ gas constant)

Consider the reaction given below

$$ A+2 B \longrightarrow 3 C+2 D $$

If rate of disappearance of $B$ is $x \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$, the ratio of rate of reaction and rate of appearance of $C$ is

Activation energy for the hydrolysis of sucrose by acid is $X \mathrm{~kJ} \mathrm{~mol}^{-1}$ whereas activation energy for the hydrolysis of sucrose by sucrase is $Y \mathrm{~kJ} \mathrm{~mol}^{-1} . X$ and $Y$ respectively are