For a reaction between substances $A$ and $B$,the rate law is given by: $\text{Rate} = K[A]^n[B]^m$. If the concentration of $A$ is doubled and the concentration of $B$ is halved,what will be the ratio of the new rate to the original rate?

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.

In the presence of $HCl$,sucrose gets hydrolysed into glucose and fructose. The concentration of sucrose was found to reduce from $0.4 \ M$ to $0.2 \ M$ in $1 \ hour$ and to $0.1 \ M$ in $2 \ hours$. The order of the reaction is:

Consider the following reactions:
$A$ $\rightarrow P_1; B$ $\rightarrow P_2; C$ $\rightarrow P_3; D$ $\rightarrow P_4$
The orders of the above reactions are $a, b, c,$ and $d,$ respectively. The following graph is obtained when $\log[\text{rate}]$ vs. $\log[\text{conc.}]$ are plotted:
Among the following,the correct sequence for the order of the reactions is:

For the reaction $A + B \to C + D$,if the concentration of $A$ is doubled without affecting the concentration of $B$,the rate doubles. If the concentration of $B$ is increased $9$ times without affecting the concentration of $A$,the rate becomes $3$ times. Determine the order of the reaction.

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: