The alkaline hydrolysis of an ester is a ........ reaction.

$[A]_0 / \text{mol } L^{-1}$	$t_{1/2} / \text{min}$
$0.100$	$200$
$0.025$	$100$

For a given reaction $R \rightarrow P$,$t_{1/2}$ is related to $[A]_0$ as given in the table:
Given: $\log 2 = 0.30$
Which of the following is true?
$A.$ The order of the reaction is $1/2$.
$B.$ If $[A]_0$ is $1 \text{ M}$,then $t_{1/2}$ is $200 \sqrt{10} \text{ min}$.
$C.$ The order of the reaction changes to $1$ if the concentration of reactant changes from $0.100 \text{ M}$ to $0.500 \text{ M}$.
$D.$ $t_{1/2}$ is $800 \text{ min}$ for $[A]_0 = 1.6 \text{ M}$.
Choose the correct answer from the options given below:

For a chemical reaction,$A + 2B \to C + D$,the rate of reaction increases $3$ times when the concentration of $A$ only is increased $9$ times. While when the concentration of $B$ only is increased $2$ times,the rate of reaction also increases $2$ times. The order of this reaction is:

The rate constant for the reaction, $2 \,N_2O_{5(g)} \rightarrow 2 \,N_2O_{4(g)} + O_{2(g)}$ is $4.98 \times 10^{-4} \,s^{-1}$. What is the order of the reaction?

For a particular reaction,the variation of the rate constant with temperature is given by $\ln k_t = \ln k_0 + \left( \frac{\ln (2.5)}{10} \right) \times t$ $(t \geqslant 0 \, ^{\circ}C)$. Here,$k_0$ is the rate constant at $0 \, ^{\circ}C$ and $k_t$ is the rate constant at $t \, ^{\circ}C$. The temperature coefficient of the reaction,assuming that the rate constant increases by the same factor for every $10 \, ^{\circ}C$ rise in temperature,is:

During the kinetic study of the reaction $2A + B \rightarrow C + D$,the following results were obtained:

Experiment	$[A] \ (M), [B] \ (M)$ and Initial rate of formation of $D$
$i. \ [A]=0.1, [B]=0.1$	$6.0 \times 10^{-3} \ M \ s^{-1}$
$ii. \ [A]=0.3, [B]=0.2$	$7.2 \times 10^{-2} \ M \ s^{-1}$
$iii. \ [A]=0.3, [B]=0.4$	$2.88 \times 10^{-1} \ M \ s^{-1}$
$iv. \ [A]=0.4, [B]=0.1$	$2.40 \times 10^{-2} \ M \ s^{-1}$

Based on the above data,the overall order of the reaction is: