For the first order reaction with rate constant $k$,which expression gives the half-life period? (Initial concentration $= a$)

If $k$ is the rate constant and $t$ is the time,then the degree of dissociation for a substance undergoing decay with first-order kinetics is:

After how many seconds will the concentration of the reactant in a first order reaction be halved if the rate constant is $1.155 \times 10^{-3} \ s^{-1}$?

$A$ flask contains a mixture of compounds $AB$ and $XY$. Both decompose by first-order kinetics upon heating. If the half-life periods of $AB$ and $XY$ are $30 \ min$ and $10 \ min$ respectively,how many minutes will it take for the concentration of $AB$ to be four times the concentration of $XY$? (Assume initial concentrations of $AB$ and $XY$ are equal.)

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?

The rate constant $k = 2.303 \ min^{-1}$ for a particular reaction,and the initial concentration of the reactant is $1 \ mol/L$. What is the rate of reaction after $1 \ minute$?