Which among the following represents the expression for the $\left(\frac{3}{4}\right)^{\text{th}}$ life of a $1^{\text{st}}$ order reaction?

The half-life of a first order reaction having rate constant $K = 1.7 \times 10^{-5} \ s^{-1}$ is ........ $hr$.

$[A] \rightarrow [B]$. If the formation of compound $[B]$ follows first-order kinetics and after $70 \ min$ the concentration of $[A]$ was found to be half of its initial concentration,then the rate constant of the reaction is $x \times 10^{-6} \ s^{-1}$. The value of $x$ is $......$ (Nearest Integer).

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

The decomposition of $N_2O_5$ occurs as $2N_2O_5 \to 4NO_2 + O_2$ and follows first-order kinetics. Hence,

In a first order reaction,the concentration of the reactant is reduced to $25\%$ in one hour. The half-life period of the reaction is: (in $hr$)