What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half life time is $10 \ minute$?

$R \rightarrow P$ is a first order reaction. For this reaction,a graph of $\ln [R]$ (on $y$-axis) and time (on $x$-axis) gives a straight line with a negative slope. The intercept on the $y$-axis is equal to ($k =$ rate constant):

Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$(i) \ t_{1/2} \propto [R]_0^0$
$(ii) \ t_{1/2} = \frac{0.693}{k}$

The half-life values for two different first-order reactions $A$ and $B$ are $75 \ min$ and $2.5 \ h$ respectively. What is the ratio of their rate constants $\frac{k_A}{k_B}$?

In a first order reaction,$60 \%$ of the reactant converts into product in $45 \ minutes$. Calculate the rate constant of the reaction.

For which order reaction is a straight line parallel to the $x-$axis obtained by plotting a graph between half-life $(t_{1/2})$ and initial concentration '$a$'?