A bacterial infection in an internal wound grows as ${\mathrm{N}}^{\mathrm{\text{'}}}\left(\mathrm{t}\right)={\mathrm{N}}_0\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{t}\right)$ , where the time $\mathrm{t}$ is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as $\frac{\mathrm{d}\mathrm{N}}{\mathrm{d}\mathrm{t}}=-5{\mathrm{N}}^2$ . What will be the plot of $\frac{{\mathrm{N}}_0}{\mathrm{N}}$ vs $\mathrm{t}$ after $1$ hour?

The rate constants for decomposition of acetaldehyde have been measured over the temperature range $700-1000 \mathrm{K}$. The data has been analysed by plotting $\mathrm{lnk}$ vs $\frac{{10}^3}{ \mathrm{T}}$ graph. The value of activation energy for the reaction is ${\mathrm{kJmol}}^{-1}$. (Nearest integer) (Given : $\mathrm{R}=8.31 \mathrm{J}{\mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$)

For a first order reaction, the time required for completion of $90\%$ reaction is '$\mathrm{x}$' times the half life of the reaction. The value of '$\mathrm{x}$' is

(Given: $\ln 10=2.303$ and $\log 2=0.3010$)