The rate constant of the reaction $2H_2O_{2(aq)} \to 2H_2O_{(l)} + O_{2(g)}$ is $3 \times 10^{-3} \ min^{-1}$. At what concentration of $H_2O_2$,the rate of reaction will be $2 \times 10^{-4} \ M \ s^{-1}$? ............ $M$

Calculate the amount of reactant in percent that remains after $60 \ min$ in a first-order reaction. $(k = 0.02303 \ min^{-1})$ (in $\%$)

Which one of the following plots is correct for a first order reaction?

An organic compound undergoes first-order decomposition. The time taken for its decomposition to $1/8$ and $1/10$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$? (Given: $\log_{10} 2 = 0.3$)

$A$ reaction has a rate constant $k = 2.4 \times 10^{-4} \ s^{-1}$. Find the ratio of $t_{99.9}$ to $t_{50}$.

Given below are two statements:
Statement $I$: The graph of $t_{1/2}$ versus initial concentration $[R]_0$ for a first-order reaction is a horizontal line.
Statement $II$: The graph of $\log \frac{[R]_0}{[R]}$ versus time $t$ for a first-order reaction is a straight line passing through the origin with a slope equal to $\frac{k}{2.303}$.
In the light of the above statements,choose the correct answer from the options given below: