For reaction A → P, rate constant $k = 1.5 \times 10^3 \ \mathrm{s}^{-1}$ at $27^{\circ}\mathrm{C}$

If activation energy for the above reaction is $60\ \mathrm{kJ}\ \mathrm{mol}^{-1}$, then the temperature (in $^{\circ}\mathrm{C}$) at which rate constant, $k = 4.5 \times 10^3\ \mathrm{s}^{-1}$ is ______. (Nearest integer)

Given : $\log 2 = 0.30$, $\log 3 = 0.48$, $R = 8.3\ \mathrm{J}\ \mathrm{K}^{-1}\ \mathrm{mol}^{-1}$, $\ln 10 = 2.3$

A → B (first reaction)

C → D (second reaction)

Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 hour. The activation energy of the second reaction is half of that of first reaction. If the rate constant at 500 K of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at 300 K is _______ × 10^-1 hour^-1 (nearest integer).

The half-life of ${ }^{65} \mathrm{Zn}$ is 245 days. After $x$ days, $75 \%$ of original activity remained. The value of $x$ in days is $\_\_\_\_$ . (Nearest integer)

(Given: $\log 3=0.4771$ and $\log 2=0.3010$ )

For the thermal decomposition of reactant $\mathrm{AB}(\mathrm{g})$, the following plot is constructed.

The half life of the reaction is ' $x^{\prime} \,\mathrm{min}$.

$x=$ $\_\_\_\_$ min. (Nearest integer)