For the reaction $2A + B \to \text{Product}$,the rate law is given as $\frac{-d[A]}{dt} = K[A]$. At a time when $t = \frac{1}{K}$,the concentration of the reactant $A$ is ($Co =$ initial concentration).

The time of half change of a first order reaction is ....... initial concentration.

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1/2} = 3 \text{ hours}$. The percentage of sucrose remaining after $6 \text{ hours}$ is . . . . . . . (Nearest integer) (Given: $\log 2 = 0.3010$ and $\log 3 = 0.4771$)

For a first-order reaction $A \rightarrow \text{product}$, the rate constant is $k = 2 \times 10^{-2} \text{ s}^{-1}$. If the initial concentration of $A$ is $[A]_0 = 1.0 \text{ mol dm}^{-3}$, find the value of $\log \frac{1}{[A]_t}$ after $t = 100 \text{ s}$.

Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.
Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$
Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$

For which of the following reactions is the half-life period independent of the initial concentration of the reactant?