For the reaction $R \rightarrow P$,the half-life is independent of the initial concentration of the reactant,$R$. Which one of the following graphs is not correct for this reaction?

The half-life of a first order reaction is $30 \, min$. The time required for $75 \, \%$ completion of the same reaction will be $..... \, min$

Catalytic decomposition of hydrogen peroxide is a ........ order reaction.

Consider a certain reaction $A \rightarrow \text{Products}$ with $k = 2.0 \times 10^{-2} \ s^{-1}$. Calculate the concentration of $A$ remaining after $100 \ s$ if the initial concentration of $A$ is $1.0 \ mol \ L^{-1}$.

Two first order reactions have half-lives in the ratio $3 : 2$. Calculate the ratio of time intervals $t_1 : t_2$ if $t_1$ is the time period for $25\%$ completion of the first reaction and $t_2$ for $75\%$ completion of the second reaction. (in $: 1$)

Calculate the half-life of a first order reaction from the rate constants given below:
$(i) \ 200 \ s^{-1}$
$(ii) \ 2 \ min^{-1}$
$(iii) \ 4 \ years^{-1}$