For which of the following graphs of a first-order reaction will the value of the slope be $\frac{K}{2.303}$?

$A$ first order reaction has the rate constant $10^{-2} \ sec^{-1}$. If the initial concentration of reactant is $1 \ M$,then what will be the rate of reaction after $1 \ minute$?

The half-life of a first order reaction is $30 \, min$. The time required for $75 \, \%$ completion of the same reaction will be $..... \, min$

For a first-order reaction,it takes $40 \ min$ for $90\%$ completion. The half-life of the reaction is ..... (in $min$)

What is the half-life of a first-order reaction if the rate constant is $4.2 \times 10^{-2} \text{ day}^{-1}$ (in $\text{ days}$)?

The following is a first-order reaction:
$N_2O_5 \text{ (solution)} \rightarrow 2 NO_2 \text{ (solution)} + \frac{1}{2} O_2 \text{ (g)}$
In this reaction,$CCl_4$ is the solvent. The rate constant is $k = 5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$.
$(i)$ What will be the initial rate of reaction?
$(ii)$ Calculate the half-life $(t_{1/2})$.
$(iii)$ How much time is required to complete $75\%$ of the reaction?
$(iv)$ Calculate the concentration of $N_2O_5$ and $NO_2$ after $30 \ min$.