The reaction $A + B \xrightarrow{k}$ product is first order with respect to $A$ and zero order with respect to $B$. If $a_0$ and $a_t$ are the concentrations of $A$ at $t = 0$ and after time $t \, sec$ respectively,then select the correct relationship -

For a first-order reaction,the time required for $93.75\%$ completion is $4$ times the half-life of the reaction. What is the relationship between the time required for $93.75\%$ completion and the half-life $(t_{0.5})$?

In a first order reaction,$60 \%$ of the reactant decomposes in $4.606 \ min$. What is the half-life of the reaction (in $min$)? (Given: $k = 0.1989 \ min^{-1}$)

The half-life of a first-order reaction is $10 \ min$. If the initial concentration is $0.08 \ mol \ L^{-1}$ and the concentration at some instant is $0.01 \ mol \ L^{-1}$,then $t =$ ........... $\min$.

At $300 \ K$,a gaseous reaction $A(g) \longrightarrow B(g) + C(g)$ follows first-order kinetics. Starting with pure $A$,the total pressure at the end of $20 \ min$ is $100 \ mm \ of \ Hg$. The total pressure after the completion of the reaction is $180 \ mm \ of \ Hg$. The partial pressure of $A$ at $20 \ min$ (in $mm \ of \ Hg$) is:

$A$ reactant undergoes $90\%$ decomposition in $366 \text{ minutes}$. What is the half-life of this first-order reaction?