What is the value of the slope when a graph is plotted of $\log \frac{[R]_0}{[R]}$ versus $t$ (time) for a first-order reaction?

Hydrolysis of sugar is a first order reaction. Write the reaction.

In a first order decomposition reaction,the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2 \ s$,respectively. The ratio $t_1 / t_2$ will be:

What is the rate constant of a first-order reaction if $0.08 \ mol$ of reactant reduces to $0.02 \ mol$ in $23.03 \ min$ (in $min^{-1}$)?

What is the time required for $75 \%$ completion of a first order reaction if the rate constant is $23.03 \text{ minute}^{-1}$ (in $\text{ s}$)?

$[A] \rightarrow [B]$. If the formation of compound $[B]$ follows first-order kinetics and after $70 \ min$ the concentration of $[A]$ was found to be half of its initial concentration,then the rate constant of the reaction is $x \times 10^{-6} \ s^{-1}$. The value of $x$ is $......$ (Nearest Integer).