For a first order reaction,the ratio of the time for $75 \% $ completion of a reaction to the time for $50 \% $ completion is $....$ . (Integer answer)

$A$ first order reaction which is $30\%$ complete in $30 \ min$ has a half-life period of .............. $min.$ (in $.2$)

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?

$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.

In the following first order reactions $A$ $\xrightarrow{K_1} B$ $\xrightarrow{K_2} \text{Product}$,find the ratio $K_1/K_2$ if $90\%$ of $A$ has been reacted in time $t$ while $99\%$ of $B$ has been reacted in time $2t$.

Find the rate constant of a first-order reaction in $sec^{-1}$ having a half-life of $2.5 \ hours$.