For a certain reaction $A \to P$,the half-life for different initial concentrations of $A$ is mentioned below:

$[A_0]$	$0.1 \ M$	$0.025 \ M$
$t_{1/2} \ (s)$	$100 \ s$	$50 \ s$

Which of the following option$(s)$ is/are correct?

Total order of reaction $X + Y \rightarrow XY$ is $3$. The order of reaction with respect to $X$ is $2$. State the differential rate equation for the reaction.

Consider the reaction:
$Cl_{2(aq)} + H_2S_{(aq)} \rightarrow S_{(s)} + 2H^{+}_{(aq)} + 2Cl^{-}_{(aq)}$
The rate equation for this reaction is:
$\text{rate} = k[Cl_2][H_2S]$
Which of these mechanisms is/are consistent with this rate equation?
$A.$ $Cl_2 + H_2S \rightarrow H^{+} + Cl^{-} + Cl^{+} + HS^{-}$ (slow)
$Cl^{+} + HS^{-} \rightarrow H^{+} + Cl^{-} + S$ (fast)
$B.$ $H_2S \rightleftharpoons H^{+} + HS^{-}$ (fast equilibrium)
$Cl_2 + HS^{-} \rightarrow 2Cl^{-} + H^{+} + S$ (slow)

For the reaction $A + B \rightarrow C$,select the appropriate rate law based on the following data:
$1$. $[A] = 0.012, [B] = 0.035 \rightarrow \text{Initial Rate} = 0.10$
$2$. $[A] = 0.024, [B] = 0.070 \rightarrow \text{Initial Rate} = 1.6$
$3$. $[A] = 0.024, [B] = 0.035 \rightarrow \text{Initial Rate} = 0.20$
$4$. $[A] = 0.012, [B] = 0.070 \rightarrow \text{Initial Rate} = 0.80$

In a chemical reaction $A$ is converted into $B$. The rates of reaction,starting with initial concentrations of $A$ as $2 \times 10^{-3} \ M$ and $1 \times 10^{-3} \ M$,are equal to $2.40 \times 10^{-4} \ M s^{-1}$ and $0.60 \times 10^{-4} \ M s^{-1}$ respectively. The order of reaction with respect to reactant $A$ will be

The rate law for a reaction between reactants $A$,$B$,and $C$ is $r = K[A][B][C]^2$. If the concentration of $A$ is halved,then the rate of reaction: