For a reaction of order $(n - 1)$,what is the relationship between the half-life period $(t_{1/2})$ and the initial concentration of the reactant $([R]_0)$?

The bromination of acetone that occurs in acid solution is represented by this equation.
$CH_3COCH_{3(aq)} + Br_{2(aq)} \rightarrow CH_3COCH_2Br_{(aq)} + H^+_{(aq)} + Br^-_{(aq)}$
These kinetic data were obtained for given reaction concentrations.
Initial concentrations,$M$

$[CH_3COCH_3]$	$[Br_2]$	$[H^+]$
$0.30$	$0.05$	$0.05$
$0.30$	$0.10$	$0.05$
$0.30$	$0.10$	$0.10$
$0.40$	$0.05$	$0.20$

Initial rate,disappearance of $Br_2, M s^{-1}$
$5.7 \times 10^{-5}, 5.7 \times 10^{-5}, 1.14 \times 10^{-4}, 3.04 \times 10^{-4}$
Based on these data,the rate equation is

Write the differential rate expression for the following reaction and determine its order of reaction:
$5 Br^{-} + BrO_3^{-} + 6 H^{+} \rightarrow 3 Br_2 + 3 H_2 O$

Which one of the following statements regarding the order of a reaction is not correct?

The rate law equation for a reaction is $R = k[x][y]$. The rate of reaction doubles when:

For a certain chemical reaction $X \rightarrow Y$,the rate of formation of the product is plotted against time as shown in the figure. The number of correct statement$(s)$ from the following is $.......$.
$A$. Overall order of this reaction is one
$B$. Order of this reaction cannot be determined
$C$. In region-$I$ and $III$,the reaction is of first and zero order respectively
$D$. In region-$II$,the reaction is of first order
$E$. In region-$II$,the order of reaction is in the range of $0.1$ to $0.9$.